General Relativity

[Perpetual Student]

Several months ago on a thread about relativity, there was a discussion concerning the concept that all frames of reference are equally valid under general relativity. The physicists who participated asserted that (as an extreme example) it would be equally valid to view the whole universe as revolving around Phobos (one of the moons of Mars) compared to any other perspective (the CMBR, for example). The mathematics, of course would be vastly more complicated, but that would not invalidate that particular consequence of GR.
At that time, I argued that we all really know that the whole universe is not really revolving around Phobos, even though GR allows that perspective for anyone who might be inclined to use it. The professionals told me I was dead wrong! -- All frames of reference are equally valid! To my dissatisfaction, that’s where the discussion ended.
After several months of further reflection, it still seems to me that if that is the case, if we cannot use Occam’s razor (or some similar concept), to conclude that the universe is not really revolving around Phobos, it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner. Any comments?

[drkitten]

Several months ago on a thread about relativity, there was a discussion concerning the concept that all frames of reference are equally valid under general relativity. The physicists who participated asserted that (as an extreme example) it would be equally valid to view the whole universe as revolving around Phobos (one of the moons of Mars) compared to any other perspective (the CMBR, for example).

Did they really say this?

This seems odd, as if this were true, we would experience centripetal acceleration towards Phobos, and acceleration is detectable (if only as pseudo-gravity).

[Kwalish Kid]

Yes, rotation is still absolute in GR, at least in the sense that we can actually identify rotating solutions with and without matter in our model universe. Godel was able to demonstrate that rotating universe had closed time-like loops at a certain radius out from the centre of rotation.

But it is true that we can construct a reference frame in which Phobos is at rest and not-rotating. However, to do so we also have to introduce certain strange distortions to all descriptions of physical forces that will, in effect, compensate for this special nature of Phobos.

[drkitten]

Yes, rotation is still absolute in GR, at least in the sense that we can actually identify rotating solutions with and without matter in our model universe. Godel was able to demonstrate that rotating universe had closed time-like loops at a certain radius out from the centre of rotation.

But it is true that we can construct a reference frame in which Phobos is at rest and not-rotating. However, to do so we also have to introduce certain strange distortions to all descriptions of physical forces that will, in effect, compensate for this special nature of Phobos.

... which, in turn, means that Occam's razor still applies (pace the OP); we reject because of the distortions that would need to be introduced. Yes?

[sol invictus]

After several months of further reflection, it still seems to me that if that is the case, if we cannot use Occam’s razor (or some similar concept), to conclude that the universe is not really revolving around Phobos, it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner. Any comments?

Do you regard it as a fundamental flaw in SR that we cannot conclude that the solar system is at rest? Isn't it absurd that it's just as valid to regard the sun and all the planets as moving at .999999999999c as it is to take them to be at rest?

Did they really say this?

This seems odd, as if this were true, we would experience centripetal acceleration towards Phobos, and acceleration is detectable (if only as pseudo-gravity).

But we do experience an acceleration towards Phobos, that's why we (along with the rest of the universe) keep orbiting it. Can we measure it? Of course not - can you measure your acceleration towards the sun? Acceleration is not detectable when you are freely falling.

[sol invictus]

... which, in turn, means that Occam's razor still applies (pace the OP); we reject because of the distortions that would need to be introduced. Yes?

Simplicity, and hence Occam, is entirely in the eye of the beholder.

If you were describing a Phobian road race, you would almost certainly want to use the frame PS finds so distasteful. After all, how often do you hear commentators at NASCAR events reporting the speeds of the cars in, say, the frame in which the Milky Way isn't rotating? How often do weather forecasters describe the motion of hurricanes in an inertial frame, rather than one in which the earth is at rest and they have to introduce Coriolis forces?

[Perpetual Student]

Simplicity, and hence Occam, is entirely in the eye of the beholder.

If you were describing a Phobian road race, you would almost certainly want to use the frame PS finds so distasteful. After all, how often do you hear commentators at NASCAR events reporting the speeds of the cars in, say, the frame in which the Milky Way isn't rotating? How often do weather forecasters describe the motion of hurricanes in an inertial frame, rather than one in which the earth is at rest and they have to introduce Coriolis forces?

I would say that a non-rotating observer in intergalactic space, looking through his telescope at this Phobian road race, would have a more accurate perspective of the motions of the universe.

Do you regard it as a fundamental flaw in SR that we cannot conclude that the solar system is at rest? Isn't it absurd that it's just as valid to regard the sun and all the planets as moving at .999999999999c as it is to take them to be at rest?

No, we know that all inertial frames provide the same physics. That is not true of accelerating frames.

[drkitten]

Simplicity, and hence Occam, is entirely in the eye of the beholder.

But implicit in the discussion is the idea that the "beholder" is a cosmologist, not a race commentator. (We're discussing the question of whether "the universe is rotating," after all, which is a cosmological issue.)

[sol invictus]

I would say that a non-rotating observer in intergalactic space, looking through his telescope at this Phobian road race, would have a more accurate perspective of the motions of the universe.

That's the point. Depending on what one wishes to describe, different frames will allow more or less complex descriptions. There isn't a single one that's simple for everything - quite the contrary.


No.

Why not? The extension - from the equivalence of inertial frames to the equivalence of non-inertial frames - is extremely natural (in fact necessary).

But implicit in the discussion is the idea that the "beholder" is a cosmologist, not a race commentator. (We're discussing the question of whether "the universe is rotating," after all, which is a cosmological issue.)

We are? That's not how I read the OP.

In the case of the universe, there is a class of frames in which the part of it we can see has a simple description on large scales.

Are the frames in that class rotating? I don't know how to answer that question, actually. Rotating frames in flat spacetime can be distinguished from non-rotating frames (via the presence or absence of fictitious forces). I don't know how to make such a distinction in curved spacetime - there are forces in all frames, and there is no distinction between "gravitational" forces and "fictitious" forces.

[Perpetual Student]

Why not? The extension - from the equivalence of inertial frames to the equivalence of non-inertial frames - is extremely natural (in fact necessary).



You did not see the edit to my comment. All inertial frames provide the same physics. That is not true of accelerating frames.

[Manopolus]

(edit) Never mind, I'm off on my own little planet here, and my frame of reference on this subject is not particularly notable.

[sol invictus]

You did not see the edit to my comment. All inertial frames provide the same physics. That is not true of accelerating frames.

Sure it is. They predict exactly the same physics, just like inertial frames. Anything else would be nonsense.

There's a very useful analogy (which in fact is so precise it's hardly an analogy). Consider a flat map of the surface of the earth. Since the earth's surface is curved, the map must be distorted. That means that when you use it to determine the distance between two locations, say Tokyo and Capetown, you can't just measure the distance on the map using a straightedge and multiply by some scale. Instead, the distance will be a more complicated function that depends on the locations of the two cities and the map projection. But given that function, you can use the map to compute the actual distance.

If you had a whole set of maps, each equipped with its corresponding function, you could compute the distance between Tokyo and Capetown (or any other two locations) using each map and you'd always get the same, correct answer. If one map+function didn't give you the correct answer, you'd know that either the map or the function is wrong, or the map is correct be isn't describing the same planet.

It's exactly the same in GR. If two frames predict different physics, either you made a mistake or they're describing two physically different spacetimes. But given one spacetime, we can use any frame we want and we will always get consistent and correct answers, just as we can make any projection we want and we will always get a useable map. It's just that some frames/projections are more simple than others for certain purposes.

[Perpetual Student]

OK, the galaxies within the observable universe are receding from one another due to cosmic expansion, local galaxies have some random motions influenced by local gravity, the galaxy rotates on an axis, the sun revolves around that axis, the earth revolves around the sun, etc., etc. I am certain that that is what is really happening. GR may provide the facility (through monumental mathematical gymnastics) to view the whole of the universe in some other way. That is fine and a good tool of GR when it might provide some facility in analyzing some aspect of the universe, but that does not change the reality of the nature of the universe. I would conclude that GR is an incomplete theory in that it cannot provide a preference for the real universe. On the other hand, perhaps that is really not the case since Occam's razor along with GR does lead us to the correct viewpoint.

[Perpetual Student]

Simplicity, and hence Occam, is entirely in the eye of the beholder.

If you were describing a Phobian road race, you would almost certainly want to use the frame PS finds so distasteful. After all, how often do you hear commentators at NASCAR events reporting the speeds of the cars in, say, the frame in which the Milky Way isn't rotating? How often do weather forecasters describe the motion of hurricanes in an inertial frame, rather than one in which the earth is at rest and they have to introduce Coriolis forces?

Anyone describing a Phobian road race is doing only just that, he is not describing the universe.

[Perpetual Student]

Originally Posted by Perpetual Student
You did not see the edit to my comment. All inertial frames provide the same physics. That is not true of accelerating frames.
Sure it is. They predict exactly the same physics, just like inertial frames. Anything else would be nonsense.

Is it not true that all experiments conducted in all inertial frames will produce identical results while that is not the case for rotating vs. non-rotating frames?

[Skwinty]

Is it not true that all experiments conducted in all inertial frames will produce identical results while that is not the case for rotating vs. non-rotating frames?


If the universe is rotating then there cannot be non rotating frames ?:confused:

[Giggywig]

OK, the galaxies within the observable universe are receding from one another due to cosmic expansion, local galaxies have some random motions influenced by local gravity, the galaxy rotates on an axis, the sun revolves around that axis, the earth revolves around the sun, etc., etc. I am certain that that is what is really happening. GR may provide the facility (through monumental mathematical gymnastics) to view the whole of the universe in some other way. That is fine and a good tool of GR when it might provide some facility in analyzing some aspect of the universe, but that does not change the reality of the nature of the universe. I would conclude that GR is an incomplete theory in that it cannot provide a preference for the real universe. On the other hand, perhaps that is really not the case since Occam's razor along with GR does lead us to the correct viewpoint.
I believe what GR tells you is that the Universe does not have a preference. You are choosing the "correct viewpoint" based on YOUR viewpoint.

[sol invictus]

OK, the galaxies within the observable universe are receding from one another due to cosmic expansion, local galaxies have some random motions influenced by local gravity, the galaxy rotates on an axis, the sun revolves around that axis, the earth revolves around the sun, etc., etc. I am certain that that is what is really happening. GR may provide the facility (through monumental mathematical gymnastics) to view the whole of the universe in some other way. That is fine and a good tool of GR when it might provide some facility in analyzing some aspect of the universe, but that does not change the reality of the nature of the universe. I would conclude that GR is an incomplete theory in that it cannot provide a preference for the real universe. On the other hand, perhaps that is really not the case since Occam's razor along with GR does lead us to the correct viewpoint.

Nonsense. What you are saying here is precisely analogous to someone claiming that the earth is "really" at rest, and it's a deficiency in SR that the earth's rest frame isn't privileged, or that a map that doesn't distort the US much is more "real" than one that doesn't distort Antarctica much.

Anyone describing a Phobian road race is doing only just that, he is not describing the universe.

We don't know how to describe the universe, because we can't see most of it. We see one patch, and that patch has a simple description (or at least its gross, large-scale features do). If all we knew of was a small area around our village, a description in which the earth is round rather than flat would look needlessly complex.

Again - you can use any frame you like, just as you can use any map projection you care to. A description which does not allow that is simply incomplete. Is there a "best" or "simplest" description? That depends entirely on what you're trying to describe. If what you want to describe is the universe as a whole, we don't know the answer. If it's just our observable patch, then yes, we do know the answer, just as we know the answer for a road race on Phobos.

[sol invictus]

Is it not true that all experiments conducted in all inertial frames will produce identical results while that is not the case for rotating vs. non-rotating frames?

How do you conduct an experiment "in" a frame?

Frames are just human labeling conventions . They have no more connection to reality or intrinsic meaning than the sequence of symbols C-A-T does to the animal it describes in English.

If anything, an experiment is conducted "in" every possible frame simultaneously, and the laws of physics - used correctly in any one of those frames - will always correctly predict the results.

[Perpetual Student]

If the universe is rotating then there cannot be non rotating frames ?:confused:

I have never heard of a theory involving a rotating universe. Is there such a theory?

[Skwinty]

I have never heard of a theory involving a rotating universe. Is there such a theory?

Every thing we observe in the universe is surely rotating, or has angular momentum/velocity?
Is it incorrect to say the universe is rotating?

[Perpetual Student]

How do you conduct an experiment "in" a frame?

Frames are just human labeling conventions . They have no more connection to reality or intrinsic meaning than the sequence of symbols C-A-T does to the animal it describes in English.

If anything, an experiment is conducted "in" every possible frame simultaneously, and the laws of physics - used correctly in any one of those frames - will always correctly predict the results.

Here:

Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.

and

The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.

FROM: LINK (http://en.wikipedia.org/wiki/Inertial_frame_of_reference)

[sol invictus]

Every thing we observe in the universe is surely rotating, or has angular momentum/velocity?
Is it incorrect to say the universe is rotating?

Rotation picks out an axis. If you said "the universe is rotating", most people would take that to mean that there is a special axis in the universe, and that at least some physical phenomena depend on distance from that axis. But there isn't any evidence for such an axis in the part of the universe we can see.

Of course as we've been discussing you're free to choose a frame in which there is such an axis of rotation - but you'd find that when you compute anything physical (i.e. measurable in an experiment), the distance from the axis always miraculously cancels out.

[Perpetual Student]

Every thing we observe in the universe is surely rotating, or has angular momentum/velocity?
Is it incorrect to say the universe is rotating?

If the universe wee rotating as a whole we would detect it in the CBMR.

[sol invictus]

Here:



and



FROM: LINK (http://en.wikipedia.org/wiki/Inertial_frame_of_reference)

I don't see anything in there I disagree with (although I would word some things differently), or anything that disagrees with what I've said here, or that explains how to perform an experiment "in" a frame.

By the way nothing in that article applies to the universe, because it's all for the special case of flat spacetime. The universe cannot be described by an inertial frame - no such frame exists.

[Skwinty]

If the universe wee rotating as a whole we would detect it in the CBMR.

Surely to assert that, then In 5000 years time,you would need to send another space craft to the exact last location and perform a recording.

A comparison could then made.

[DSo]

If the universe wee rotating as a whole we would detect it in the CBMR.

Could we? How?

[Perpetual Student]

Surely to assert that, then In 5000 years time,you would need to send another space craft to the exact last location and perform a recording.

A comparison could then made.

LINK (http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961217a.html)

[Perpetual Student]

I don't see anything in there I disagree with (although I would word some things differently), or anything that disagrees with what I've said here, or that explains how to perform an experiment "in" a frame.

By the way nothing in that article applies to the universe, because it's all for the special case of flat spacetime. The universe cannot be described by an inertial frame - no such frame exists.

I don't understand your objection to the word "in." I am moving along "in" my spaceship relative to local stuff around me. I throw a ball up and it comes straight down. That is my experiment "in" my inertial frame. If I were "in" an accelerating frame it would not come straight down.

[drkitten]

Rotation picks out an axis. If you said "the universe is rotating", most people would take that to mean that there is a special axis in the universe, and that at least some physical phenomena depend on distance from that axis. But there isn't any evidence for such an axis in the part of the universe we can see.

Of course as we've been discussing you're free to choose a frame in which there is such an axis of rotation - but you'd find that when you compute anything physical (i.e. measurable in an experiment), the distance from the axis always miraculously cancels out.

.... which is basically what I said earlier (and that you disagreed with then).

If the universe is rotating "around Phobos," then there's an axis that goes through Phobos, and some physical phenomena depend on distance from Phobos. Since the opening post talked about "the whole universe as revolving around Phobos," I feel comfortable restricting our attention to large-scale phenomena (i.e. we're not talking about a Phobon basketball game where the purely local gravity well dominates our measurements or something like that.)

By your own admission, if we set up such a system (formally), we find that the distance cancels out. This is exactly what Occam said could be ignored -- entities (in this case, "the distance to the axis through Phobos) that are not necessary for understanding should not be multiplied.

I would also point out that the hypothesis that the universe is revolving around Phobos involves at least three free parameters that have no effect on any of our calculations -- two in the orientation of the axis, and one in the rotational speed. Again, Occam suggests that free parameters with no effect should be discarded.

Occam's razor therefore tells us that the hypothesis that the universe is revolving around Phobos is not parsimonious and can be rejected.

[Raze]

Here:

Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.
and


The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.


and

FROM: LINK (http://en.wikipedia.org/wiki/Inertial_frame_of_reference)


Wasn't this the exact problem GR was designed to solve?

[dasmiller]

Surely to assert that, then In 5000 years time,you would need to send another space craft to the exact last location and perform a recording.

But as I understand it, it's pretty much meaningless to speak of the "exact last location" together with "in 5000 years time" since there's no preferred coordinate system in which to have a fixed location. You could certainly specify a coordinate system and revisit the point that, 5000 years later, had the same coordinates. But there are an infinite number of equally-valid coordinate systems, and in general they'll diverge pretty quickly.

[Perpetual Student]

I don't see anything in there I disagree with (although I would word some things differently), or anything that disagrees with what I've said here, or that explains how to perform an experiment "in" a frame.

By the way nothing in that article applies to the universe, because it's all for the special case of flat spacetime. The universe cannot be described by an inertial frame - no such frame exists.

Why couldn't the CBMR be the basis of such a frame?

[sol invictus]

I don't understand your objection to the word "in." I am moving along "in" my spaceship relative to local stuff around me. I throw a ball up and it comes straight down. That is my experiment "in" my inertial frame. If I were "in" an accelerating frame it would not come straight down.

That makes no sense at all. If by "in" a frame you mean "at rest in", then the ball would not come back down, it would bounce off the inside of your ship.

If I show you two maps of the earth that use different projections, which one are you "in"?

.... which is basically what I said earlier (and that you disagreed with then).

If the universe is rotating "around Phobos," then there's an axis that goes through Phobos, and some physical phenomena depend on distance from Phobos.

Nope. Not one physical phenomenon depends on that distance - not if we're talking about the universe we actually live in, at least (which is rotating around Phobos in some set of frames).

By your own admission, if we set up such a system (formally), we find that the distance cancels out. This is exactly what Occam said could be ignored -- entities (in this case, "the distance to the axis through Phobos) that are not necessary for understanding should not be multiplied.

It's impossible to set up a coordinate system in which there are no distances that cancel out. But anyway, I never claimed the Phobocentric coordinates are the simplest ones to describe the large scale structure of the observable part of our universe.

I would also point out that the hypothesis that the universe is revolving around Phobos involves at least three free parameters that have no effect on any of our calculations -- two in the orientation of the axis, and one in the rotational speed. Again, Occam suggests that free parameters with no effect should be discarded.

All frames contain free parameters - an infinite number of them, actually.

Occam's razor therefore tells us that the hypothesis that the universe is revolving around Phobos is not parsimonious and can be rejected.

No, it tells us absolutely nothing of the kind. It's completely useless for deciding this question, actually - because what you refer to as a "hypothesis" is no such thing, since it's completely equivalent to the "hypothesis" that the universe is not revolving around Phobos. (Again, let me make clear that I am talking about different choices of frame in the same universe.)

[sol invictus]

Why couldn't the CBMR be the basis of such a frame?

It's not time-independent.

[Raze]

I don't understand the fuss. Aren't we just talking about arbitrary frames of reference?


How fast am I currently moving? :eye-poppi


ETA- If Phobos is not as valid as any other place to call rest, are you all saying that people standing on Phobos will feel as if they are moving and accelerating in some strange fashion that you wouldn't feel anywhere else in the universe on a body of equal size and mass?

[drkitten]

I don't understand the fuss. Aren't we just talking about arbitrary frames of reference?

That's kind of the point of Occam. If you have two apparently arbitrary ways to describe the same data, pick the one with the fewest entities.

[Hellbound]

I don't understand your objection to the word "in." I am moving along "in" my spaceship relative to local stuff around me. I throw a ball up and it comes straight down. That is my experiment "in" my inertial frame. If I were "in" an accelerating frame it would not come straight down.

Just to add to what sol invictus posted, this is a perfect example.

Both your examples are inertial reference frames (as he pointed out). There's no way to distinguish if one, both, or neither are at rest or in motion (without outside references). With the ball coming stright down, you coul dbe at rest within a gravity field, or at a constant acceleration straight up. The second, you could be accelerating across a gravity field, or at rest at an angle to a gravity field, or just accelerating.

[Ziggurat]

That's the point. Depending on what one wishes to describe, different frames will allow more or less complex descriptions. There isn't a single one that's simple for everything - quite the contrary.

Sure, but that doesn't make everything equivalent. You can call a road race of Phobos equivalent to a road race on earth. But once you introduce cosmology, well, you really do have something unique and special. There may be an absurd number of possible road races in the universe, each with its simplest reference frame, but there's only one cosmos. And there's only one co-moving reference frame for that one cosmos. On a certain level, yes, it's not any more valid than any other reference frame. And Occam's razor is ultimately about convenience, not truth. But nonetheless, there still remains one reference frame which is unique for everyone, everywhere. I don't think you can construct any other reference frame which is similarly unique for everyone.

[Ziggurat]

It's not time-independent.

Perhaps you can't form an interial reference frame using the CMB, but you can form a unique reference frame using it.

[Raze]

That's kind of the point of Occam. If you have two apparently arbitrary ways to describe the same data, pick the one with the fewest entities.

But how do you know which of the infinite possible reference frames is the simplest?

[Perpetual Student]

Sure, but that doesn't make everything equivalent. You can call a road race of Phobos equivalent to a road race on earth. But once you introduce cosmology, well, you really do have something unique and special. There may be an absurd number of possible road races in the universe, each with its simplest reference frame, but there's only one cosmos. And there's only one co-moving reference frame for that one cosmos. On a certain level, yes, it's not any more valid than any other reference frame. And Occam's razor is ultimately about convenience, not truth. But nonetheless, there still remains one reference frame which is unique for everyone, everywhere. I don't think you can construct any other reference frame which is similarly unique for everyone.

Isn't that the point here? For millennia mankind used the surface of earth as a special reference frame for describing the universe (turtles all the way down and all). Over the years we learned that there is nothing special about the surface of the earth as a reference.
The CMB rest frame is perhaps the only currently available universal frame of reference for best describing the universe, at least that part of it that we can observe. I don't know how we can escape the conclusion that that unique frame of reference tells us what the universe is actually doing. GR is simply incomplete in that respect.

[Raze]

Isn't that the point here? For millennia mankind used the surface of earth as a special reference frame for describing the universe (turtles all the way down and all). Over the years we learned that there is nothing special about the surface of the earth as a reference.
The CMB rest frame is perhaps the only currently available universal frame of reference for best describing the universe, at least that part of it that we can observe. I don't know how we can escape the conclusion that that unique frame of reference tells us what the universe is actually doing. GR is simply incomplete in that respect.

Why? Is this an argument that the CMB rest frame would result in a simpler mathematical description (the Occam's Razor argument).

Another question: does GR already include the possibility of using the CMB as a rest frame? If so how is GR incomplete?

[sol invictus]

That's kind of the point of Occam. If you have two apparently arbitrary ways to describe the same data, pick the one with the fewest entities.

What's an "entity"?

Sure, but that doesn't make everything equivalent. You can call a road race of Phobos equivalent to a road race on earth. But once you introduce cosmology, well, you really do have something unique and special. There may be an absurd number of possible road races in the universe, each with its simplest reference frame, but there's only one cosmos.

How do you know? All we can see is a part of it, a part which we can be nearly certain is a very small part.

And there's only one co-moving reference frame for that one cosmos. On a certain level, yes, it's not any more valid than any other reference frame. And Occam's razor is ultimately about convenience, not truth. But nonetheless, there still remains one reference frame which is unique for everyone, everywhere. I don't think you can construct any other reference frame which is similarly unique for everyone.

There's one set of reference frames - it's certainly not unique (for example if the universe is spatially flat, rotations and translations preserve all the properties you're talking about, as do time reparametrizations).

That set is in any case defined only up to perturbations, which - while present - are admittedly small on the scales we can observe. There's absolutely no reason to think they remain small on larger scales, however.

Another thing to note that this frame is obviously not inertial, because it defines a rest frame. Frames in constant motion with respect to that rest frame will see something different (in particular, they will see a dipole temperature anisotropy in the CMB).

But again, I'm not arguing with the assertion that that class of frames are the most convenient to describe cosmology on large scales. They are - but there is nothing fundamental about that, any more than there is about the statement that the road race on Phobos is most conveniently described using Phobocentric coordinates.

[sol invictus]

I don't know how we can escape the conclusion that that unique frame of reference tells us what the universe is actually doing.

Very, very easily.

First, it's not unique even if we ignore the fact that there are perturbations (see my reply to Zig above).

Second, there are perturbations which destroy the whole concept of a precise unique frame. The universe is not homogeneous and isotropic, it's just approximately so, and even that only on a particular range of scales.

Third, we can only see part of the universe, and have no evidence at all that the perturbations remain small on larger scales (i.e. no reason to think it remains approximately homogeneous and isotropic on larger than horizon scales).

Fourth, even if we ignore all of the above, your objection would only make sense if there was only one possibility - if the universe must always have that unique frame. But we know for certain that isn't true (because there are perturbations, and because everything we know about physics says it isn't).

Fifth, even if we ignore all of the above, the ability of GR to describe more than one frame is a feature without which it would simply be incomplete. Asking that it only be able to describe physics in one special frame is like asking for a theory of linguistics that only works on one language, or requiring that map-making theory only admit one projection, or that arithmetic only work in Roman numerals... it's utter nonsense.

The whole point of GR - the stroke of genius that led to it - was Einstein's realization that physics cannot possibly depend on the coordinates we humans choose to describe it with, and that following that fact through actually carries profound and mathematically powerful consequences.

[sol invictus]

Let me give another example. Suppose you're presented with an arrangement of two concentric metal pipes, one inside the other with the space in between filled with an insulator. The pipes are fairly long and straight, and you're asked to calculate their capacitance. What do you do?

Well, if you've taken any physics you know exactly how to start. You measure the radii of the pipes, then write down the equations for capacitance - and you use cylindrical coordinates, because that's the approximate symmetry of the problem (approximate because no real pipe is perfectly round, and on microscopic scales they're not even remotely close to it). Then you do a simple integral and get the capacitance - approximately. I certainly don't dispute that that is the quickest and easiest way to go.

Now, suppose someone comes along and insists on doing the calculation using spherical coordinates. If she does everything correctly, of course she will get the same, correct answer. She'll have to work harder, but the physics is exactly the same - obviously! She's simply labelled points differently, and how could that possibly matter?

Is there anything more correct about the first method than the second? Are the pipes "in" cylindrical coordinates, but not "in" spherical? (That's a question for you, PS.) Is it a deficiency of the theory that it cannot tell us which coordinates "really" describe those pipes? Can we conclude anything about the world from the fact that the section of pipe we can see is roughly cylindrically symmetric?

[Ziggurat]

How do you know? All we can see is a part of it, a part which we can be nearly certain is a very small part.

In a sense, yes, we don't know. We assume large-scale homogeneity. With that assumption, the conclusion becomes inevitable. Without that assumption, we can't conclude much of anything about cosmology. So I'll stick with it for now.

There's one set of reference frames - it's certainly not unique (for example if the universe is spatially flat, rotations and translations preserve all the properties you're talking about, as do time reparametrizations).

Close enough for the current discussion.

Another thing to note that this frame is obviously not inertial

I never said it was. I said it was unique.

But again, I'm not arguing with the assertion that that class of frames are the most convenient to describe cosmology on large scales. They are - but there is nothing fundamental about that, any more than there is about the statement that the road race on Phobos is most conveniently described using Phobocentric coordinates.

I didn't use the term "fundamental", but rather "unique". The Phobos frame is not unique. The co-moving cosmological frame (or if you insist, set of frames) is unique. And as far as I am aware, it is the only reference frame which is unique. Whether you choose to consider that to be indicative of something "fundamental" seems to be a semantic issue of what you consider "fundamental", and that question holds little interest to me.

[sol invictus]

In a sense, yes, we don't know. We assume large-scale homogeneity. With that assumption, the conclusion becomes inevitable. Without that assumption, we can't conclude much of anything about cosmology. So I'll stick with it for now.


Actually we don't need that assumption for much of anything - most of cosmology doesn't depend on what's outside our current horizon (even the asymptotic future in most realistic scenarios).


Close enough for the current discussion.


I don't agree at all. For one thing the existence of perturbations destroys the entire argument (such as it was), because it means that there isn't even a unique class of frames. How can there be something fundamentally important about an approximation?


I never said it was. I said it was unique.


But it isn't unique even if we ignore perturbations.


I didn't use the term "fundamental", but rather "unique". The Phobos frame is not unique.


We were originally discussing the frame in which Phobos isn't rotating. That's not unique, but it's not much less unique (in any sense I can think of) than the cosmic "rest frame".

The co-moving cosmological frame (or if you insist, set of frames) is unique. And as far as I am aware, it is the only reference frame which is unique.

But again, it's not.

The part of the CMB we can see is approximately rotationally invariant, and (probably) approximately translation invariant. To the extent those are good approximations, we can use those symmetries to define a special class of reference frames. Those are convenient because the approximate symmetries are manifest in them, and hence they are relatively simple to use.

But that's as far as it goes - there is no sense in which those reference frames tell us what the universe is "really" doing (the idea is absurd). Please see my example above with the pipes, it might help.

[Perpetual Student]

Let me give another example. Suppose you're presented with an arrangement of two concentric metal pipes, one inside the other with the space in between filled with an insulator. The pipes are fairly long and straight, and you're asked to calculate their capacitance. What do you do?

Well, if you've taken any physics you know exactly how to start. You measure the radii of the pipes, then write down the equations for capacitance - and you use cylindrical coordinates, because that's the approximate symmetry of the problem (approximate because no real pipe is perfectly round, and on microscopic scales they're not even remotely close to it). Then you do a simple integral and get the capacitance - approximately. I certainly don't dispute that that is the quickest and easiest way to go.

Now, suppose someone comes along and insists on doing the calculation using spherical coordinates. If she does everything correctly, of course she will get the same, correct answer. She'll have to work harder, but the physics is exactly the same - obviously! She's simply labelled points differently, and how could that possibly matter?

Is there anything more correct about the first method than the second? Are the pipes "in" cylindrical coordinates, but not "in" spherical? (That's a question for you, PS.) Is it a deficiency of the theory that it cannot tell us which coordinates "really" describe those pipes? Can we conclude anything about the world from the fact that the section of pipe we can see is roughly cylindrically symmetric?

Thanks for taking the time to indulge me in this question. First, I will admit that my resolve in this matter has been weakened by your arguments, but my intuition will not yield.
I do see the point you are making above. There is nothing more "correct" about the two approaches. Both will yield the same capacitance. Neither method is really describing the capacitance of the pipes in a more "real" way.
But this example is only dealing with an electrical property of that particular geometry for a capacitor. It is not designed to tell us anything about the actual geometry of the configuration. Because the spherical coordinates lead to the same answer, can we conclude that the capacitor consists of two concentric spheres? Are two concentric spheres the same as two concentric cylinders? We know that is not the case from simple geometry and you defined the problem as consisting of two concentric cylinders, in the first place.
So, even though neither approach better describes the device, one of them does use the "real" geometry and is consequently simpler, as you said. Could we not say the same about GR, as we use it to describe the whole universe. A spot on the surface of Phobos will not yield a better answer than the rest frame of the CMB, but the latter is simpler and perhaps more accurately describes the real universe.
I also understand that Einstein's great realization was "that physics cannot possibly depend on the coordinates we humans choose to describe it with, and that following that fact through actually carries profound and mathematically powerful consequences." But GR is after all only a model. Do you not agree it is incomplete if we cannot use it to conclude that the whole universe is not revolving around a spot on the surface of Phobos?

[Ziggurat]

I don't agree at all. For one thing the existence of perturbations destroys the entire argument (such as it was), because it means that there isn't even a unique class of frames. How can there be something fundamentally important about an approximation?

The "close enough" was in reference to the fact that the co-moving frame is really a set of frames, not a single frame. They are related to each other in rather trivial ways, unlike the set of all reference frames available, or even the various Phobos-like frames for racing in.


We were originally discussing the frame in which Phobos isn't rotating. That's not unique, but it's not much less unique (in any sense I can think of) than the cosmic "rest frame".

Sure it is. You know it is. You're arguing otherwise because you want to point out that mathematically all these frames get handled the same way, which is true. Which is true, but doesn't change my point.

But that's as far as it goes - there is no sense in which those reference frames tell us what the universe is "really" doing (the idea is absurd). Please see my example above with the pipes, it might help.

I saw your pipes example already. And the thing about your pipe example is that the simplicity of solving the problem in cylindrical coordinates does in fact indicate something about the pipe: namely, the pipe has cylindrical symmetry. The pipe is really being cylindrical. The co-moving reference frame likewise does indeed indicate something real about the universe: the average motion of mass in the universe. It really is doing that. The validity of alternative reference frames or coordinates doesn't change that.

[sol invictus]

Because the spherical coordinates lead to the same answer, can we conclude that the capacitor consists of two concentric spheres?

No, of course not. Any coordinate choice would give the same answer.

Are two concentric spheres the same as two concentric cylinders?

No, they aren't. There is a real physical difference that real, measurable quantities depend on. And indeed, it is the case that the part of the CMB we can see is approximately symmetric under a certain group of symmetry transformations, and we know that because we measured it.


Could we not say the same about GR, as we use it to describe the whole universe. A spot on the surface of Phobos will not yield a better answer than the rest frame of the CMB, but the latter is simpler and perhaps more accurately describes the real universe.

If you want to describe the part of the CMB we can observe, it's simplest to use coordinates in which its approximate symmetries are manifest, yes. That's all that can be said.


I also understand that Einstein's great realization was "that physics cannot possibly depend on the coordinates we humans choose to describe it with, and that following that fact through actually carries profound and mathematically powerful consequences." But GR is after all only a model. Do you not agree it is incomplete if we cannot use it to conclude that the whole universe is not revolving around a spot on the surface of Phobos?

Do you not agree that Maxwell's equations are incomplete if they cannot tell us that we must use cylindrical coordinates to describe those pipes?

We can use Maxwell's equations plus measurements of the capacitance to determine that the pipes are roughly cylindrically symmetric. Similarly, we can use GR plus cosmological measurements to determine that the part of the CMB we can see is roughly homogeneous and isotropic.

And we can say is that no physical quantities of relevance to cosmology depend in any particularly simple way on the distance from the axis of rotation of Phobos. But that's it, that's all we can say.

What's this obsession with the CMB, anyway? Sure, it's the largest scale thing we can observe right now. But 50 years ago we hadn't observed it, and 50 years from now we might be observing something even larger. And even the CMB is only approximately homogeneous and isotropic.

[sol invictus]

Sure it is. You know it is.

Actually I'm honestly not sure it is in any well-defined sense. But if you think so, go ahead and try to argue for it. (You could try to define your frame at every point by requiring that the CMB have zero dipole, but then the large scale structure distribution won't have zero dipole due to perturbations and peculiar motions. On the other side I can choose my Phobocentric coordinates so Phobos has zero rotation, and then try to extend those coordinates in the simplest analogue to a rigidly rotating frame there is in an FRW cosmology, which I think is unique if we ignore those perturbations.)


I saw your pipes example already. And the thing about your pipe example is that the simplicity of solving the problem in cylindrical coordinates does in fact indicate something about the pipe: namely, the pipe has cylindrical symmetry. The pipe is really being cylindrical. The co-moving reference frame likewise does indeed indicate something real about the universe: the average motion of mass in the universe. It really is doing that. The validity of alternative reference frames or coordinates doesn't change that.

I'm not saying there isn't a real fact about the universe that accounts for the simplicity of certain classes of frames for describing certain observables. I'm saying three other things:

1) The fact some physical situation may have a certain set of symmetries does not force us to use a set of coordinates in which those symmetries are manifest, nor is that lack of being forced a deficiency in our theories. Quite the contrary, it's a requirement of any complete theory that it make sense in any coordinates.

2) The part of the CMB we can see is only approximately symmetric, and we know we're only seeing a small part of the whole thing.

3) The CMB is just one set of observations. Other sets of observations have different approximate symmetries, and the CMB isn't particularly unique or special except in that now, in 2010, it's the biggest thing we can observe.

[Raze]

Because the spherical coordinates lead to the same answer, can we conclude that the capacitor consists of two concentric spheres?

How do you get this conclusion? Spherical coordinates just means you define the location of a point based upon the radial distance from the origin, an inclination angle from a location directly above the point (ETA-from a fixed zenith direction), and an azimuth angle from a reference plane perpendicular to the inclination angle that passes through the origin.

It's just a way to define the location of the point.

With cylindrical coordinates you have a radius, an angle and a height. That's the difference.

[Perpetual Student]

Do you not agree that Maxwell's equations are incomplete if they cannot tell us that we must use cylindrical coordinates to describe those pipes?

We can use Maxwell's equations plus measurements of the capacitance to determine that the pipes are roughly cylindrically symmetric. Similarly, we can use GR plus cosmological measurements to determine that the part of the CMB we can see is roughly homogeneous and isotropic.

Well, I would venture to say that Maxwell's equations were never intended for that purpose and it would be unfair to characterize them as incomplete. So, perhaps the same thing should be said about GR in the context of this discussion. Are not all models limited to a particular context and purpose?
That leads me to the position that we should not expect GR to decide whether a spot on Phobos or the CMB is an more accurate description of the workings of the universe. GR doesn't care and was not constructed to care.
Consequently, we should use something like common sense, Occam's razor or the simplicity of the mathematics to tell us what is really happening.
I will go to my grave (or ashes) absolutely firm in the belief that the universe does not revolve around a spot on Phobos and I have not spent my life on the back of a turtle.

[Perpetual Student]

How do you get this conclusion? Spherical coordinates just means you define the location of a point based upon the radial distance from the origin, an inclination angle from a location directly above the point (ETA-from a fixed zenith direction), and an azimuth angle from a reference plane perpendicular to the inclination angle that passes through the origin.

It's just a way to define the location of the point.

With cylindrical coordinates you have a radius, an angle and a height. That's the difference.

Exactly! So?

[Tim Thompson]

I have never heard of a theory involving a rotating universe. Is there such a theory?
Yes. See the Gödel metric (http://en.wikipedia.org/wiki/Gödel_metric) & Gödel, 1949 (http://adsabs.harvard.edu/abs/1949RvMP...21..447G). Gödel's original paper is not freely available, but many of the 436 citations are.

... but that does not change the reality of the nature of the universe.
I don't think it is possible under any circumstances to know what is the reality of the universe. I think the best we can do is know the relationship of consistency between our model of the universe and our observations of the universe. When we find the two in high accord we tend to treat the model as if it is reality, but we must keep in mind that is it always only a model.

[schrodingasdawg]

Several months ago on a thread about relativity, there was a discussion concerning the concept that all frames of reference are equally valid under general relativity. The physicists who participated asserted that (as an extreme example) it would be equally valid to view the whole universe as revolving around Phobos (one of the moons of Mars) compared to any other perspective (the CMBR, for example). The mathematics, of course would be vastly more complicated, but that would not invalidate that particular consequence of GR.

This is correct. One can devise a coordinate system in which Phobos is at rest, and in which everything else (Mars, the planets, starts, galaxies, etc.) is revolving around it. A complicated metric will be needed to describe the universe using such a coordinate system, and this metric will describe a rather contrived looking spacetime with all the right gravitational forces needed to keep the universe in motion.

At that time, I argued that we all really know that the whole universe is not really revolving around Phobos, even though GR allows that perspective for anyone who might be inclined to use it. The professionals told me I was dead wrong! -- All frames of reference are equally valid!

The professionals are right. To say that any particular frame of reference (or any class of reference frames) describes 'reality' is a metaphysical statement.

I like sol's post on the matter:
Frames are just human labeling conventions . They have no more connection to reality or intrinsic meaning than the sequence of symbols C-A-T does to the animal it describes in English.

I think this sums up GR's attitude towards coordinates quite concisely.

[Raze]

Because the spherical coordinates lead to the same answer, can we conclude that the capacitor consists of two concentric spheres?

How do you get this conclusion? Spherical coordinates just means you define the location of a point based upon the radial distance from the origin, an inclination angle from a location directly above the point (ETA-from a fixed zenith direction), and an azimuth angle from a reference plane perpendicular to the inclination angle that passes through the origin.

It's just a way to define the location of the point.

With cylindrical coordinates you have a radius, an angle and a height. That's the difference.

Exactly! So?


Well, I failed to realize that your question was rhetorical. My apologies.

[Perpetual Student]

Is it really essential to accept that reality is so utterly relative because GR makes it possible to see it that way? Is it really just as valid to see all the resulting complex and convoluted motions and the required fictitious forces to explain all the motions of the universe from the perspective of a spot on the surface of Phobos as it is to view the universe from, say, a non-rotating point in intergalactic space?
Doesn't this tell us that we need something more than GR to understand the universe?

[Vorpal]

Is it really essential to accept that reality is so utterly relative because GR makes it possible to see it that way?
Of course it is. Or rather, it's as essential as your earlier appeal to Occam's razor. A theory that treats all frames equally is simpler than one that manufactures special classes of (say) "fundamental frame" and "fictitious frame". If "entities" cuts across anything meaningful, it's that, because we're ascribing objective reality to some frames but not others. The presence of so-called fictitious forces is not at all comparable, because they are just a coordinate effect, and coordinates are neither objectively real nor claimed to be.

Is it really just as valid to see all the resulting complex and convoluted motions and the required fictitious forces to explain all the motions of the universe from the perspective of a spot on the surface of Phobos as it is to view the universe from, say, a non-rotating point in intergalactic space?
Yes. There is no observational reason to treat either as "more real".

Doesn't this tell us that we need something more than GR to understand the universe?
If you insist on this, I think you better abandon Occam in the interests of self-consistency, because what you actually want is a theory which makes a metaphysical, unempirical distinction.

[Farsight]

Is it really essential to accept that reality is so utterly relative because GR makes it possible to see it that way?No, not at all. IMHO the people who advocate this don't actually understand general relativity. When you read the original at The Foundation of the General Theory of Relativity (3.6Mbytes) (http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf) Einstein is talking about the equations of motion. Yes, motion is relative, your motion does affect your measurements, and motion through space is affected by a concentration of energy tied up in the mass of a planet. But at the same time the CMBR really is a de-facto absolute reference frame.

Is it really just as valid to see all the resulting complex and convoluted motions and the required fictitious forces to explain all the motions of the universe from the perspective of a spot on the surface of Phobos as it is to view the universe from, say, a non-rotating point in intergalactic space?No. It's mathematical science fiction.

Doesn't this tell us that we need something more than GR to understand the universe?General relativity doesn't cover everything, so yes. But you shouldn't think it ought to be scrapped. The real problem you're experiencing is that people say they understand it when actually, they don't.

[Vorpal]

No, not at all. IMHO the people who advocate this don't actually understand general relativity. When you read the original at The Foundation of the General Theory of Relativity (3.6Mbytes) (http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf) Einstein is talking about the equations of motion.
You don't understand what "equations of motions" means in physics. But that's a minor issue. I have read Einstein's work, and directing attention to §13 of your source, Einstein states it very explicitly that he considers the connection coefficients to be the components of the gravitational field. But this is manifestly coordinate-dependent; e.g., in flat spacetime, take cylindrical coordinates (r,θ,z). Then the only nonzero coefficients are:
[1] Γrθθ = -r, Γθrθ = Γθθr = 1/r,
and so under this interpretation, in cylindrical coordinates there is a nonvanishing gravitational field. But the corresponding geodesic equations are:
[2] r" - r(θ')² = 0, θ" + (2/r)r'θ' = 0, z" = 0.
This is very obviously what Newtonian mechanics calls the centrifugal force, or explicitly if we make θ rotate with a constant angular velocity. If you wanted Einstein's authority to support PS's programme of cutting out fictitious forces, then you did not succeed, since it does the exact opposite: the fictitious forces that PS dislikes, are, according to Einstein, the very components of the gravitational field!

Yes, motion is relative, your motion does affect your measurements, and motion through space is affected by a concentration of energy tied up in the mass of a planet. But at the same time the CMBR really is a de-facto absolute reference frame.
You don't understand what "absolute reference frame" means in physics either, and that's a much more important deficiency. The maximal-isotropy frame is special in some senses, but not in terms of the laws of physics, so it is not "absolute" in the sense actually meant when discussing relativity.

The real problem you're experiencing is that people say they understand it when actually, they don't.
There is certainly a lot of that going on, but here it's mostly in the singular.

[Farsight]

You don't understand what "equations of motions" means in physics. But that's a minor issue.Oh yes I do. Einstein talked about curvilinear motion through space, and about clocks clocking up motion. And he repeats "equations of motion" throughout The Foundation of the General Theory of Relativity.

I have read Einstein's work, and directing attention to §13 of your source, Einstein states it very explicitly that he considers the connection coefficients to be the components of the gravitational field.And at the foot of page 178 he says "the law of motion" which he repeats at the top of page 179.

But this is manifestly coordinate-dependent; e.g., in flat spacetime, take cylindrical coordinates (r,θ,z). Then the only nonzero coefficients are: [1] Γrθθ = -r, Γθrθ = Γθθr = 1/r,
and so under this interpretation, in cylindrical coordinates there is a nonvanishing gravitational field. But the corresponding geodesic equations are:
[2] r" - r(θ')² = 0, θ" + (2/r)r'θ' = 0, z" = 0. This is very obviously what Newtonian mechanics calls the centrifugal force, or explicitly if we make θ rotate with a constant angular velocity. If you wanted Einstein's authority to support PS's programme of cutting out fictitious forces, then you did not succeed, since it does the exact opposite: the fictitious forces that PS dislikes, are, according to Einstein, the very components of the gravitational field!I didn't want that. But your example is not in line with §13. The geodetic straight line is defined independently of a system of reference. Your cylindrical system of coordinates is an aspect of your motion that shapes your measurement and creates those fictitious forces. A real gravitational field is different. It's there because gμv varies. All observers will agree on this, it isn't relative, it isn't the result of your selected coordinates and your motion, it is in no way fictitious.

You don't understand what "absolute reference frame" means in physics either, and that's a much more important deficiency.I said de-facto. And I do understand about laws of physics being "special" in that absolute reference frame. But I also understand that the laws of physics do not in reality exist. They are man-made rules drawn up from observations and measurements, all of which are affected by our motion and by the space we move through. I also understand that a reference frame does not actually exist. You cannot look up to the sky and point one out. It is an artefact of measurement. You can use the CMBR to absolutely determine your motion through the universe. GR is all about motion, and you can't get any more absolute than that.

The maximal-isotropy frame is special in some senses, but not in terms of the laws of physics, so it is not "absolute" in the sense actually meant when discussing relativity.It's the rest frame of the universe. Physics is about the universe, and we can be 100% confident that it isn't rotating round Phobos. Absolutely.

[sol invictus]

I didn't want that. But your example is not in line with §13. The geodetic straight line is defined independently of a system of reference.


That could be interpreted in a way that makes it correct, but I doubt it's what you meant. A geodesic in flat space will be "straight" written in Cartesian coordinates - i.e. its trajectory will be linear in the coordinates - but that same geodesic will not look straight in curvilinear coordinates on the same space.

Your cylindrical system of coordinates is an aspect of your motion

Nonsense. Coordinate choices need have nothing whatsoever to do with the motion of any particular observer.

A real gravitational field is different.

Not according to Einstein - and not according to me, for that matter. There is no true distinction (or if there is, I don't know what it is).

It's there because gμv varies.

gμv varies in cylindrical coordinates on flat Minkowski space. Fail.

All observers will agree on this, it isn't relative

All observers will agree on the results of every physical experiment - which of course does not include the constancy of the metric.

Farsight, it's clear to everyone that you don't have any idea what you're talking about. Please stick to your own crank threads. This is an educational forum.

[schrodingasdawg]

Is it really essential to accept that reality is so utterly relative because GR makes it possible to see it that way?

Yes. Look at special relativity for an analogue. In SR, all inertial frames of reference are equally valid. It's possible to, say, suggest that there is one special reference frame that is at absolute rest, i.e. the frame at which the ether is at rest, and to suppose that the ether (and thus the EM fields and all) transform in such a way that the ether rest frame and all other inertial frames cannot be distinguished experimentally. I believe this is the gist of the Lorentz Ether Theory: SR + some special, but metaphysical, rest frame. Obviously SR is the better theory because it has fewer entities (no ether, no absolute rest frame) and makes the same predictions.

Now imagine we had some analogue of LET for GR: we have some theory that makes all the exact same predictions of GR, but in addition suggests there is some undetectable entity that is at rest, and is non-rotating, in some particular coordinate system: therefore, this coordinate system is 'special' and describes a universe at rest. GR is the better theory (by Occam's razor), since it suggests the existence of fewer entities and makes the same predictions.

[Perpetual Student]

Yes. Look at special relativity for an analogue. In SR, all inertial frames of reference are equally valid. It's possible to, say, suggest that there is one special reference frame that is at absolute rest, i.e. the frame at which the ether is at rest, and to suppose that the ether (and thus the EM fields and all) transform in such a way that the ether rest frame and all other inertial frames cannot be distinguished experimentally. I believe this is the gist of the Lorentz Ether Theory: SR + some special, but metaphysical, rest frame. Obviously SR is the better theory because it has fewer entities (no ether, no absolute rest frame) and makes the same predictions.

Now imagine we had some analogue of LET for GR: we have some theory that makes all the exact same predictions of GR, but in addition suggests there is some undetectable entity that is at rest, and is non-rotating, in some particular coordinate system: therefore, this coordinate system is 'special' and describes a universe at rest. GR is the better theory (by Occam's razor), since it suggests the existence of fewer entities and makes the same predictions.

Isn't that analogy a bit off, since there is no experiment one can conduct in an inertial frame to distinguish it in any way as special, but one can conduct an experiment to distinguish rotation from non-rotation?

[sol invictus]

Isn't that analogy a bit off, since there is no experiment one can conduct in an inertial frame to distinguish it in any way as special, but one can conduct an experiment to distinguish rotation from non-rotation?

No! Again, using rotating coordinates cannot possibly change physical results, any more than using spherical coordinates for the pipes will give a different capacitance.

Note that one can from the inside distinguish a rotating lab in empty (flat) space from a non-rotating lab in empty (flat) space, but that's not what we're talking about. Those are two different physical situations. We're talking about using two different coordinate systems to describe the same physical situation.

You made a very similar statement earlier:


No, we know that all inertial frames provide the same physics. That is not true of accelerating frames.

Sure it is. They predict exactly the same physics, just like inertial frames. Anything else would be nonsense.

There's a very useful analogy (which in fact is so precise it's hardly an analogy). Consider a flat map of the surface of the earth. Since the earth's surface is curved, the map must be distorted. That means that when you use it to determine the distance between two locations, say Tokyo and Capetown, you can't just measure the distance on the map using a straightedge and multiply by some scale. Instead, the distance will be a more complicated function that depends on the locations of the two cities and the map projection. But given that function, you can use the map to compute the actual distance.

If you had a whole set of maps, each equipped with its corresponding function, you could compute the distance between Tokyo and Capetown (or any other two locations) using each map and you'd always get the same, correct answer. If one map+function didn't give you the correct answer, you'd know that either the map or the function is wrong, or the map is correct be isn't describing the same planet.

It's exactly the same in GR. If two frames predict different physics, either you made a mistake or they're describing two physically different spacetimes. But given one spacetime, we can use any frame we want and we will always get consistent and correct answers, just as we can make any projection we want and we will always get a useable map. It's just that some frames/projections are more simple than others for certain purposes.

[Vorpal]

And at the foot of page 178 he says "the law of motion" which he repeats at the top of page 179.
As usual you're paying more attention to the word choice rather than

I didn't want that. But your example is not in line with §13.
It is perfectly in line with it, what I've said in other threads on this topic, and also very explictly confirms what sol has been saying longer than anyone else.

A real gravitational field is different.
Maybe you should pay attention to the last sentence of §13. The connection coefficients Γαμν are explicitly dependent on the coordinate components of gμv and fail to form a tensor. That's about as coordinate-dependent as it can possibly get.

The deep irony is that just about the only thing you've been right about (in another thread) is that Einstein's view that Γαμν are the components of the gravitational field has been historically rejected by many physicists precisely because it is coordinate-dependent. This is actually a pretty minor intepretational issue, since it's possible to do all the observervational aspects of GTR without ever mentioning a "gravitational field", but it shows that you can't even be bothered to be self-consistent.

It's there because gμv varies. All observers will agree on this, it isn't relative, it isn't the result of your selected coordinates and your motion, it is in no way fictitious.
... that's actually quite remarkable. It was always obvious that you don't understand what you're trying to talk about, but it is now clear that you haven't even tried expressing gμv in any curvilinear coordinates, ever. And since the procedure in this case can be carried out by any decent high-school calculus student, involving nothing more complicated than differentiation and substitution, that's very strange.

Cartesian: gμv = diag(-1,1,1,1)
Cylindrical: gμv = diag(-1,1,r²,1)

This is a bit like talking about Newtonian physics without having any idea what "slope" is, much less "derivative" or "differential equation."

It's the rest frame of the universe. Physics is about the universe, and we can be 100% confident that it isn't rotating round Phobos. Absolutely.
Probably, yes. I think we might test for this in the approximation of the galaxies as a fluid (which is pretty standard in cosmological models) by seeing if the vorticity vanishes. If it does, then this statement is coordinate-independent and should ensure that, on the large-scale, there is no rotation about anything, Phobos or otherwise. But note that has nothing to do with picking out an extra-special frame of reference.

[Perpetual Student]

No! Again, using rotating coordinates cannot possibly change physical results, any more than using spherical coordinates for the pipes will give a different capacitance.
OK, I understand that.

Note that one can from the inside distinguish a rotating lab in empty (flat) space from a non-rotating lab in empty (flat) space, but that's not what we're talking about. Those are two different physical situations. We're talking about using two different coordinate systems to describe the same physical situation.
Isn't the fact that we can make that distinction of any significance? I understand that we can use any coordinate system (including a rotating one) to describe the same physical situation. If I were out in empty space in my lab and saw that I was rotating, would it not be unreasonable for me to reject the notion that I was rotating, but that the whole universe is revolving around me? I understand that the mathematics of GR allow me to see it either way, but would you not say that, in reality, the universe is not revolving around me? My rotation can easily be achieved by a simple application of energy. Getting the whole universe to revolve around me would be inconceivable. Is that not of any significance in deciding what is really happening?

You made a very similar statement earlier:

I am well aware of that. I get it that GR allows one to look at it either way, but I find it difficult to simply accept that is as far as our knowledge can take us because of GR and that we have no other tools to use to make these kind of distinctions.
Here I am in intergalactic space observing the universe around me. So, I press a button and activate some rockets to get my ship to rotate. I understand that by creating fictitious forces and convoluted physics I can also conclude my little rockets set the whole universe in motion. Do we really want to leave it at that and not find a way to determine that the former perspective is a superior reflection of reality, and not merely more convenient mathematically?

Originally Posted by sol invictus
Sure it is. They predict exactly the same physics, just like inertial frames. Anything else would be nonsense.

There's a very useful analogy (which in fact is so precise it's hardly an analogy). Consider a flat map of the surface of the earth. Since the earth's surface is curved, the map must be distorted. That means that when you use it to determine the distance between two locations, say Tokyo and Capetown, you can't just measure the distance on the map using a straightedge and multiply by some scale. Instead, the distance will be a more complicated function that depends on the locations of the two cities and the map projection. But given that function, you can use the map to compute the actual distance.

If you had a whole set of maps, each equipped with its corresponding function, you could compute the distance between Tokyo and Capetown (or any other two locations) using each map and you'd always get the same, correct answer. If one map+function didn't give you the correct answer, you'd know that either the map or the function is wrong, or the map is correct be isn't describing the same planet.

It's exactly the same in GR. If two frames predict different physics, either you made a mistake or they're describing two physically different spacetimes. But given one spacetime, we can use any frame we want and we will always get consistent and correct answers, just as we can make any projection we want and we will always get a useable map. It's just that some frames/projections are more simple than others for certain purposes.

OK, using the above analogy, each map and correct function gives us the same correct answer. That's great, but now let's ask which map is the correct one? You would say they are all equally valid, and that my question makes no sense.
Not true! The earth actually has one actual shape and size. These other models have value and are great tools but they do not tell us what the earth actually is. To understand what the earth really is we must look at the actual earth. So, GR gives us an infinite number of ways to examine the universe. But just like the earth itself is the only "real" map of itself, there is only one real universe, and it does not revolve around my little pathetic ship!

[Vorpal]

Isn't the fact that we can make that distinction of any significance? I understand that we can use any coordinate system (including a rotating one) to describe the same physical situation. If I were out in empty space in my lab and saw that I was rotating, would it not be unreasonable for me to reject the notion that I was rotating, but that the whole universe is revolving around me?
Yes, but not for reasons of any particular frame being special. Besides the stress on your ship walls (which is by itself sufficient to distinguish the two cases), the case where the universe rotates about an axis that happens to go through you has a nonvanishing vorticity tensor, whereas the case of you rotating does not. You keep replacing the argument about the same physical situation in different coordinate systems with different physical situation in different coordinate systems.

OK, using the above analogy, each map and correct function gives us the same correct answer. That's great, but now let's ask which map is the correct one? You would say they are all equally valid, and that my question makes no sense.
Not true! The earth actually has one actual shape and size. These other models have value and are great tools but they do not tell us what the earth actually is.
They are, and they do. They're all diffeomorphic to the Earth (at least almost everywhere), so they all have the same geometry as any other map and the Earth.

___
Side question: is the von Stockum dust a provably unique solution under the conditions of axisymmetry and rigid rotation of a fluid?

[schrodingasdawg]

If I were out in empty space in my lab and saw that I was rotating, would it not be unreasonable for me to reject the notion that I was rotating, but that the whole universe is revolving around me? I understand that the mathematics of GR allow me to see it either way, but would you not say that, in reality, the universe is not revolving around me? My rotation can easily be achieved by a simple application of energy. Getting the whole universe to revolve around me would be inconceivable. Is that not of any significance in deciding what is really happening?

Just as getting the whole universe to revolve around you would be inconceivable, so would getting the whole universe to stop if it already were revolving around you. You can apply energy to yourself so that you begin rotating, or stop rotating, in some particular coordinate system. For instance, suppose you are stationary with respect to one of the comoving frames: you can apply energy and rotate, so that you feel your arms being pulled to your sides (of course, this is just their inertia in this CS). Suppose you were describing the same phenomenon in a CS which describes the entire universe as revolving around you with the same angular velocity that you were spinning with respect to the comoving frame (but in the opposite direction): then you would have begun spinning, and applied energy to yourself so that you were no longer spinning; and when you ceased spinning, the feeling of your arms being pulled outwards would be due to the gravitational field of the revolving universe.

Okay, that was wordy, and perhaps poorly stated. The point is that the measurable effects of you spinning v. you not spinning (with respect to either coordinate system), such as the feeling of your arms being tugged at, is an issue of something physically going on. The issue of which coordinate system to use is just a labeling issue. Where as in the coming frame you went from not spinning to spinning, in the revolving frame you went from spinning to not spinning. The question "was I really spinning" can only be answered with "in these particular coordinates . . . "

. . . I can also conclude my little rockets set the whole universe in motion.

I think this may be a point of confusion for you. To go from describing some portion of the universe as 'stationary' with respect to some comoving frame to describing it as revolving around a point is a change of coordinates. Using your rockets to change the angular velocity of your spacecraft doesn't set the universe into motion any more than turning around rotates the universe. Regardless of whether you use a comoving or revolving frame, the angular velocity of your ship is changed by the rockets: it's your ship that was set into motion, not the universe.

(Of course, to be fair, one can always construct a reference frame that has changing angular velocity [with respect to a comoving frame], such as one that starts off stationary and accelerates up to some angular velocity. The reference frame could even be constructed so that your ship is not rotating at any point, prior to, during, or after being boosted. But the rockets were still having a physical effect on your ship, not the universe: in that coordinate system, the universe's motion would've changed as it did regardless of whether your ship was accounted for; the rockets merely counteracted the gravitational forces [which exist in this angularly accelerating CS] that would've spun the ship had they not been counteracted.)

[Uncayimmy]

Note that one can from the inside distinguish a rotating lab in empty (flat) space from a non-rotating lab in empty (flat) space, but that's not what we're talking about. Those are two different physical situations. We're talking about using two different coordinate systems to describe the same physical situation.

I think this one paragraph encapsulates the problem in communication. I hold no expertise on the physics end of things, but I think I might have an angle on the perception thing. I keep reading threads like this and wondering if I'm not thinking hard enough or if I actually get what's going on.

While I have not done the math, it is my understanding that relativity allows me to pick any set of coordinates as a frame of reference (not using the official term reference frame in an attempt to keep it in layman's terms) and describe the universe. In other words, no matter how you look at it, the "rules" (equations) are going to allow you make predictions that will be born out by experiment.

Where Newton's laws "fail" is that they are inadequate for describing the universe under some frames of reference or at least some conditions (may not be using the correct terminology). While those "laws" of motion are perfectly suitable for everyday life, they are not useful for all conditions. For my own lack of a better term, Newton's laws "prefer" that you hang out here on earth for the most part and look at things without getting into badass speeds.

Where I think the confusion lies is trying to reconcile relativity with what we mere mortals understand based on our perceptions and knowledge. For example, I'm cool with believing that the earth rotates on its axis while orbiting the sun along with the other planets. Relativity says (I think) that you can describe all of this with the earth being "motionless" in a frame of reference, and all the laws of physics will still apply.

This leads to the inevitable, "Yeh, but the earth is really orbiting the sun, right?" The response seems to be, "It doesn't make any difference. The laws of physics are the same."

"Yeh, but the earth is really orbiting the sun, right? It's not really stationary with everything else flying about in paths that just don't seem realistic."

"But it doesn't matter. When you pull your car into your garage, are you really going 3MPH? It's convenient to look at it that way, but from the vantage point of another galaxy, the earth is rotating while orbiting the sun and the whole solar system is orbiting the galaxy. Is that any less real than your 3MPH?"

That exchange seems to be the gist of what I'm reading here. If I'm wrong, please correct me. Assuming I've got that part right, here's the question I'd like the experts to address. If reasonable, please address it from your expert level as well as that of the Average Joe.

When I pull my car into my garage, is there any possible way for me to know that I pulled in at 3MPH rather (say) than the entire frigging planet moved towards my stationary car? If there is, that makes me "comfortable" that there exists a "reality" of some sorts. If there is, however, that doesn't mean there's a preferred reference frame because relativity, I believe, could explain the actions from any reference frame you could imagine and do it accurately.

For me personally, this is simply curiosity. I'm not trying to overturn the world of physics or solve some metaphysical conundrum.

Thanks for any time devoted to this. It is appreciated.

[dasmiller]

This leads to the inevitable, "Yeh, but the earth is really orbiting the sun, right?" The response seems to be, "It doesn't make any difference. The laws of physics are the same."

"Yeh, but the earth is really orbiting the sun, right? It's not really stationary with everything else flying about in paths that just don't seem realistic."

"But it doesn't matter.

And I suspect that the word "really" is a big part of the problem, because it implies that there's some underlying "real" reference frame and we just haven't figured out what it is (but in our hearts, we think we know).

If we go back to Sol's map analogy -yes, there are a number of ways to make 2D maps of a 3D globe, but which one is the "real" one? Why, none of them, of course. It's not that we haven't figured out the "real" one yet - there isn't one. Mercator projections have their advantages, as do Behrman, Miller, etc. But none will give accurate results for all cases if you're simply doing 2D measurements on them. And if you're doing the math required to get accurate results, then you can get accurate results from any of them, and then they're all "real."

[schrodingasdawg]

When I pull my car into my garage, is there any possible way for me to know that I pulled in at 3MPH rather (say) than the entire frigging planet moved towards my stationary car?

When you pull your car into the garage at 3 mph, there's no way to know that it was your car moving rather than the Earth moving, so both descriptions are equally valid. One is just more convenient for our everyday purposes.

When you drive a car at 80 mph on the freeway, it's equally valid to describe both the car as moving with respect to the stationary freeway and the freeway as moving with respect to the stationary car. We can model either case using a coordinate system, which is just a way of assigning four real numbers to every event in space and time. The case is described by some coordinate system where the spatial parts are Cartesian and the origin is some point on the asphalt, not moving with respect to the street; the latter case is also a simple coordinate system, but one where the car can be described as stationary.

Both coordinate systems are valid, but something to keep in mind is that in the coordinate system where your car is stationary, you need to keep your foot on the accelerator to remain stationary: for the same reason that someone on a treadmill needs to keep running to stay in place.

When you accelerate a car from 0 mph to 80 mph at a rate of 20 mph/s on a northbound lane, the speed of your car is changing in either of the above described coordinate systems. In the CS where the road is stationary, your car is accelerating from 0 to 80 mph and is traveling north; in the CS that an 80 mph car would be stationary in, your car is de-accelerating from going 80 mph southbound to a complete stop. Either description is valid.

A third coordinate system can be constructed, in which the accelerating car is stationary. In this system, the road begins stationary, but begins to move to the south and accelerates to moving at 80 mph. As the road starts moving, you and your car experience a constant force pushing you to the south with a magnitude of 20 mph/s times your mass; and you need to apply your foot to the gas pedal to counteract this constant force.

The thing to keep in mind when using this third coordinate system is that you used the gas pedal to keep your car stationary against the southward constant force: using the gas pedal didn't cause the force.

(Another thing to keep in mind is that while Newton's mechanics usually describes the southward force as 'fictitious'---the mathematical artifact of a non-inertial frame of reference---general relativity describes this as a very real [at least in this coordinate system] gravitational field. But I suppose the relativist philosophy can be extended to Newton's mechanics anyway.)

So, none of that seems like an immediate answer to your question, and even seems to go off-topic. But I think the examples can be instructive. I basically want to say that while motion is relative---and thus, whether you pulled into your garage or the garage moved around your car isn't knowable---the fact of the matter is that you're controlling the motion of your car, not the motion of the planet, when you drive; and this is true regardless of what coordinate system you're using. (Of course, to be pedantic, there's always that bit about Newton's third law and you're actually applying a negligible force to the Earth with your car... but whatever.)

[Uncayimmy]

When you pull your car into the garage at 3 mph, there's no way to know that it was your car moving rather than the Earth moving, so both descriptions are equally valid. One is just more convenient for our everyday purposes.

<snipped excellent explanation>

So, none of that seems like an immediate answer to your question, and even seems to go off-topic. But I think the examples can be instructive. I basically want to say that while motion is relative---and thus, whether you pulled into your garage or the garage moved around your car isn't knowable---the fact of the matter is that you're controlling the motion of your car, not the motion of the planet, when you drive; and this is true regardless of what coordinate system you're using. (Of course, to be pedantic, there's always that bit about Newton's third law and you're actually applying a negligible force to the Earth with your car... but whatever.)

I suppose that if I took a physics course in college I would have late night gabfests about this stuff, so it's probably old hat for many of you. You're definitely addressing what I think is the core issue. Here's where I begin to stumble.

Suppose in your highway example I look at the car next to me. It would seem that your descriptions would have to apply to both of us. It would seem that it can't be the earth moving relative to my stationary car and the other car moving on a stationary earth at the same time. It would seem it's one or the other. So the natural inclination in my puny mind is to think that one of them is "real" while the other is merely a description. It would also seem that given enough blood flow to the brain I could figure out a way to determine which one of many is "real."

If you could take that ball and run with it, I would be appreciative. I'm not disputing anything you've said. I'm just trying to wrap my head around it.

[sol invictus]

Isn't the fact that we can make that distinction of any significance?

Sure. It says two different physical situations are "really" different, and two different metric describing the same physical space (i.e. related by a coordinate transformation) are "really" the same.

The infinity of metrics that describe our universe includes a set in which it rotates around Phobos.

If I were out in empty space in my lab and saw that I was rotating, would it not be unreasonable for me to reject the notion that I was rotating, but that the whole universe is revolving around me?

That depends on what you mean precisely. By "saw that I was rotating" I will assume you mean you're in a sealed lab, and you measured forces consistent with the lab rotating around its axis in a locally flat space.

In that situation it would not be reasonable to reject the idea that the universe is rigidly rotating under the influence of "fictitious forces" (or an axi-symmetric gravity field, take your pick) around your (stationary) lab's axis at exactly the rate corresponding to the forces you measure, because that's a completely equivalent description to the one you prefer.

I understand that the mathematics of GR allow me to see it either way, but would you not say that, in reality, the universe is not revolving around me? My rotation can easily be achieved by a simple application of energy. Getting the whole universe to revolve around me would be inconceivable.

Changing your velocity can easily be achieved by walking. Getting the entire earth to move would be inconceivable.


Is that not of any significance in deciding what is really happening?


Well, is the earth "really" at rest?


OK, using the above analogy, each map and correct function gives us the same correct answer. That's great, but now let's ask which map is the correct one? You would say they are all equally valid, and that my question makes no sense.
Not true! The earth actually has one actual shape and size. These other models have value and are great tools but they do not tell us what the earth actually is. To understand what the earth really is we must look at the actual earth. So, GR gives us an infinite number of ways to examine the universe. But just like the earth itself is the only "real" map of itself, there is only one real universe, and it does not revolve around my little pathetic ship!

I don't understand what you're saying. The earth itself is not a map at all, so how can it be the only "real" map?

Is that city "really" Genoa or "really" Genova?

"The universe is rotating around Phobos under the influence of a certain set of fictitious forces" is a sentence that stands for a set of physically observable predictions. If those predictions are verified, it's just as good a description as any other.

[sol invictus]

Suppose in your highway example I look at the car next to me. It would seem that your descriptions would have to apply to both of us. It would seem that it can't be the earth moving relative to my stationary car and the other car moving on a stationary earth at the same time. It would seem it's one or the other. So the natural inclination in my puny mind is to think that one of them is "real" while the other is merely a description. It would also seem that given enough blood flow to the brain I could figure out a way to determine which one of many is "real."

You seem to have jumped from saying "both descriptions can't be valid at the same time" to saying "therefore one or the other is real".

Try that on the map analogy. Two maps, two projections (the function that tells you how "stretched" the map is, and therefore how to convert map distances into real distances). The projections are different, so they can't both be valid for both maps. You should pick one map and one projection and use that for everything, or carefully switch from one to the other. But obviously neither is more real than the other.

[Perpetual Student]

I don't understand what you're saying. The earth itself is not a map at all, so how can it be the only "real" map?

Sorry for the poor choice of words. The point I attempted to make is that even though we know that all of our maps and accompanying functions give the same correct results, we do know these results only have meaning (or purpose) because they tell us something about the "real" earth. The real earth has the simplest of all accompanying functions. Similarly, even though GR gives us an infinite set of maps and functions, are they not all describing some real universe, which also has some simplest of all accompanying functions? Would this not tell us that Occam's razor guides us to a best description of the real universe?

[Perpetual Student]

I think this may be a point of confusion for you. To go from describing some portion of the universe as 'stationary' with respect to some comoving frame to describing it as revolving around a point is a change of coordinates. Using your rockets to change the angular velocity of your spacecraft doesn't set the universe into motion any more than turning around rotates the universe. Regardless of whether you use a comoving or revolving frame, the angular velocity of your ship is changed by the rockets: it's your ship that was set into motion, not the universe.

(Of course, to be fair, one can always construct a reference frame that has changing angular velocity [with respect to a comoving frame], such as one that starts off stationary and accelerates up to some angular velocity. The reference frame could even be constructed so that your ship is not rotating at any point, prior to, during, or after being boosted. But the rockets were still having a physical effect on your ship, not the universe: in that coordinate system, the universe's motion would've changed as it did regardless of whether your ship was accounted for; the rockets merely counteracted the gravitational forces [which exist in this angularly accelerating CS] that would've spun the ship had they not been counteracted.)

I don't have any problem with the above, but it seems to me to contradict sol's position.

[sol invictus]

Sorry for the poor choice of words. The point I attempted to make is that even though we know that all of our maps and accompanying functions give the same correct results, we do know these results only have meaning (or purpose) because they tell us something about the "real" earth. The real earth has the simplest of all accompanying functions.

That doesn't make any more sense than what you said before. What's the "function" you claim the "real earth" "has"?

The minute you write down any such function, you're no longer talking about the "real earth", you're talking about a map (or metric) of it. But then we're back where we started.

Similarly, even though GR gives us an infinite set of maps and functions, are they not all describing some real universe, which also has some simplest of all accompanying functions? Would this not tell us that Occam's razor guides us to a best description of the real universe?

That doesn't make sense for the same reason as above.

I don't have any problem with the above, but it seems to me to contradict sol's position.

How?

[Uncayimmy]

You seem to have jumped from saying "both descriptions can't be valid at the same time" to saying "therefore one or the other is real".
There's no "seem" about it. That's exactly what I did. It's a perfectly natural reaction for which I feel no shame.

Try that on the map analogy. Two maps, two projections (the function that tells you how "stretched" the map is, and therefore how to convert map distances into real distances). The projections are different, so they can't both be valid for both maps. You should pick one map and one projection and use that for everything, or carefully switch from one to the other. But obviously neither is more real than the other.

On a personal note, Sol, I've noticed lately that your patience seems to be growing thin and your attention to detail lacking. That's understandable. Dealing with cranks can wear on you, and dealing with people like myself, perfect examples of "a little knowledge is a dangerous thing," is no picnic.

I said already that I am not seeking a preferred frame of reference. I said that I would use whatever reference was most expedient for solving my problem. What seems to be the issue here is how these frames of reference correlate to reality, which is loosely defined as the physical world.

If I win a free space shuttle trip and take a look at the earth from space, I'm gonna say that the reality is that it's a big ball. So while various map projections are excellent for particular tasks, a globe probably represents most closely what I see. Of course, the globe itself is not reality - it's a representation of reality. Then again, on my drive from Phoenix to Cape Canaveral, I'm going to think that a flat map most closely represents that so-called reality. None of this bothers me in the least.

But let's instead go to a race track and watch two dragsters go at it. As I understand it I could describe the race as the earth moving under the vehicles, both of which use their engines to stay in place. If I plug in all the numbers, I'll get the same results as if the ground was stationary and the vehicles moved. I've no problems with that. I can accept that I really can't perform a test to know which way it happened in the physical world.

Where I think the confusion exists is this human desire to relate the description to our experiences. Why would pressing the accelerator cause the earth to move under the vehicle? Since both vehicles follow essentially the same route in the physical world, I would think that it not possible for the earth to be stationary and moving at the same time. So physically I think there must be one thing that "actually" happened, which has no bearing on the validity of my descriptions.

Intuitively I think that if I make enough observations I can arrive at understanding what "really" happened. I have not done this, so I don't know. I'm not particularly bothered by this, but I think it irritates the hell out of Perpetual Student, assuming I am describing things properly from his perspective.

[Perpetual Student]

Intuitively I think that if I make enough observations I can arrive at understanding what "really" happened. I have not done this, so I don't know. I'm not particularly bothered by this, but I think it irritates the hell out of Perpetual Student, assuming I am describing things properly from his perspective.

Yes, but I would substitute the word "perplexes" for "irritates."

[schrodingasdawg]

Suppose in your highway example I look at the car next to me. It would seem that your descriptions would have to apply to both of us. It would seem that it can't be the earth moving relative to my stationary car and the other car moving on a stationary earth at the same time. It would seem it's one or the other. So the natural inclination in my puny mind is to think that one of them is "real" while the other is merely a description. It would also seem that given enough blood flow to the brain I could figure out a way to determine which one of many is "real."

Right. When you're describing the two cars on the highway, say one going at 80 mph and the other at 120 mph, you have to choose a particular set of coordinates to describe the situation. You can choose one where the road is stationary, and the cars do have those speeds; you can choose one where you are stationary, so that the road is going at 80 mph southwards (assuming you're both heading north in the road-stationary frame) and the other driver is going at 40 mph north; you can choose one where the other car is stationary, the road is going 120 mph south, and you're going 40 mph south; or you can choose any other reference frame where perhaps none of these three things is stationary.

Now, you can describe each of the cars separately using different frames of reference if you want. i.e. you can use the frame where you're stationary to describe your car and the frame where the speed-demon is stationary to describe his car. If you want to make any direct comparison between both you and the speeder, you need to keep in mind that you've described both in different coordinate systems and you need to apply a change of coordinates to make the comparison.

Or, more simply, you can use the same coordinate system to describe both cars at the same time. You're right that multiple different coordinate systems cannot be applicable at the same time, but all are equally valid: the you-stationary, speeder-stationary, or road-stationary frames of reference can all be used to describe the three objects.

If you could take that ball and run with it, I would be appreciative. I'm not disputing anything you've said. I'm just trying to wrap my head around it.

Nah, it's fine. The difference between a crackpot and someone curious about a subject is usually pretty obvious, and I think it's clear that you fall into the latter group.

[Perpetual Student]

That doesn't make any more sense than what you said before. What's the "function" you claim the "real earth" "has"?

The minute you write down any such function, you're no longer talking about the "real earth", you're talking about a map (or metric) of it. But then we're back where we started.
I see that and it is quite troublesome as I attempt to get to a "real" perspective of the universe. After all, our models do only model!

That doesn't make sense for the same reason as above.
As UncaYimmy pointed out a globe would be the best representation: it would have the simplest function, one dealing with non-varying scale.
Isn't that fact (the simpler function) at the root of the reason why the globe as a closer representation to the actual earth? If the globe were as close as we could make it to the actual size of the earth, it would be even better since no scale factor would be needed. Similarly, I believe that the simplest functions should give us the closest representation of the actual universe.

How?

Well, OK, then you do argee that (schrodingasdawg) "Using your rockets to change the angular velocity of your spacecraft doesn't set the universe into motion any more than turning around rotates the universe. Regardless of whether you use a comoving or revolving frame, the angular velocity of your ship is changed by the rockets: it's your ship that was set into motion, not the universe."
Sorry, I'm confused.

[Uncayimmy]

Yes, but I would substitute the word "perplexes" for "irritates."

No offense was intended by my choice of words. When I'm perplexed enough to pursue a solution and don't find one readily, I get irritated. I guess I was projecting.

[Kwalish Kid]

I see that and it is quite troublesome as I attempt to get to a "real" perspective of the universe. After all, our models do only model!
But what else could you ask for?
Similarly, I believe that the simplest functions should give us the closest representation of the actual universe.
Given the incredible complexity of the universe, why should this be the case?
Well, OK, then you do argee that (schrodingasdawg) "Using your rockets to change the angular velocity of your spacecraft doesn't set the universe into motion any more than turning around rotates the universe. Regardless of whether you use a comoving or revolving frame, the angular velocity of your ship is changed by the rockets: it's your ship that was set into motion, not the universe."
But here's the question: are you moving relative to some universal standard or is the universe rotating and you accidentally happened to match that rotation with your rockets?

[sol invictus]

As UncaYimmy pointed out a globe would be the best representation: it would have the simplest function, one dealing with non-varying scale.

No - that completely misses the point. Spacetime is curved (and in a very complex way). That's why I picked a curved space - the 2D surface of the earth - as an example. Replacing it with a globe destroys the analogy.


Well, OK, then you do argee that (schrodingasdawg) "Using your rockets to change the angular velocity of your spacecraft doesn't set the universe into motion any more than turning around rotates the universe. Regardless of whether you use a comoving or revolving frame, the angular velocity of your ship is changed by the rockets: it's your ship that was set into motion, not the universe."

The rockets only affect your ship, not the rest of the universe, yes. Whether its your ship or the universe that ends up in motion depends on frame, though - your rockets might just rotate the ship, or they might resist the force that would otherwise rotate it and stop it from rotating, while the rest of the universe ends up rotating.

[Perpetual Student]

No - that completely misses the point. Spacetime is curved (and in a very complex way). That's why I picked a curved space - the 2D surface of the earth - as an example. Replacing it with a globe destroys the analogy.
Yes, that does miss the point! OK, I've got it.


The rockets only affect your ship, not the rest of the universe, yes. Whether its your ship or the universe that ends up in motion depends on frame, though - your rockets might just rotate the ship, or they might resist the force that would otherwise rotate it and stop it from rotating, while the rest of the universe ends up rotating.
OK, I've also got that. Both explanations are equally valid. I see that this is a profound concept and I would imagine it leads to important consequences that this layman can only imagine.
However, we know that I decided to rotate my ship at a particular moment in time and that it is not possible that I just happened to choose the moment that the universe started to rotate in the opposite direction and, consequently, that I prevented my ship from rotating with the universe. How can we ignore the decision that I made and not conclude that there is a preferred frame, at least in this narrow context? GR cannot stand alone with no further context, excluding common sense.
Sol, do you really believe that we cannot make any distinction between these two possible frames in order to conclude that only one of them actually reflects reality?

[Mashuna]

However, we know that I decided to rotate my ship at a particular moment in time and that it is not possible that I just happened to choose the moment that the universe started to rotate in the opposite direction and, consequently, that I prevented my ship from rotating with the universe. How can we ignore the decision that I made and not conclude that there is a preferred frame, at least in this narrow context? GR cannot stand alone with no further context, excluding common sense.
Sol, do you really believe that we cannot make any distinction between these two possible frames in order to conclude that only one of them actually reflects reality?

From my (entirely layman's) understanding, in the example above in can be argued that your ship was previously rotating with the universe, then you applied a counter force to stop that rotation. It's not the case that the universe suddenly started rotating in the opposite direction when you applied thrust.

[Uncayimmy]

However, we know that I decided to rotate my ship at a particular moment in time and that it is not possible that I just happened to choose the moment that the universe started to rotate in the opposite direction and, consequently, that I prevented my ship from rotating with the universe.
What Mashuna said. It seems to me you started with a preferred reference frame, which was a stationary universe and rocket. How do you know it wasn't already moving and you just slowed down?

[Roboramma]

Personally I look at it all like this: there are certain invariant properties that don't depend on which set of coordinates you happen to be using. Before Einstien, for instance, the distance between two points was thought to be one such invariant. The time between two events taking place was another. It makes sense to us to see the world that way: that no matter how you look at it, these two things are the same distance from each other.
But when we measure that distance, we can choose any arbitrary coordinate system to make our measurement. I could say, for instance, Jim is five feet to the left of Sally. Making Sally, I suppose, the origin of my coordinate system.
Then again, I could say, "Sally is five feet in front of the door, Jim is five feet further still." Which puts the door at the origin and the line which crosses through Sally and the door the x-axis. 10-5 still equals 5. And if I tilted the axis 45 degrees, I'd still get the same answer.
On the other hand, I could figure out their exact latitude and longitude, and then measure the distance that way. Here, too, the distance works out to be the same.

You might ask the question, "Yes, but which of these is the real coordinate system, which is of these describes the universe that we live in?" Well, they all do. "How far is Sally from the real origin" doesn't have a valid answer.

We can also pick a coordinate system which is moving relative to Jim and Sally. One in which, say, the train that's passing by outside would measure as stationary. What's interesting is that according to Galilean relativity, the distance between Jim and Sally remains the same. In fact, everything is the same in this system, except that the velocities of objects measure differently. That's not an invariant, but the velocity of this object relative to that one is.

Now when Einstein came along we found that with a moving frame, the distance and time actually do vary, and thinking about it so too do relative velocities. But there are still invariant properties. I think the spacetime intervals between events is one such thing. So to ask questions like, "Yes, but how far apart are Jim and Sally, really?" No longer has a valid answer. The answer is different in different coordinate systems, and there is no way to distinguish the 'right' one from the 'wrong' one. But the invariant properties don't differ.

Just like you can't say how far Sally is from the "real" origin, you can't say if she's "really" moving or not. And, based on Sol's posts, it seems to me that the same argument applies to rotation as well. But it doesn't matter, what's "real" are those invariant properties. At least, that's my layman's view.

Happy to have the experts correct my misunderstandings. :)

[sol invictus]

However, we know that I decided to rotate my ship at a particular moment in time and that it is not possible that I just happened to choose the moment that the universe started to rotate in the opposite direction

It's "not possible"? Why?

The frame in which your ship never moves is an extremely special one, but it's certainly "possible". As Mashuna and UncaYimmy point out, another possibility is to choose a frame where your ship is initially rotating and later comes to rest. Of course there are an infinite number of other possibilities in between and not in between.

consequently, that I prevented my ship from rotating with the universe. How can we ignore the decision that I made and not conclude that there is a preferred frame, at least in this narrow context?


We're back to where we started - in that case there's a simple model for the specific set of phenomena we're discussing (that your ship was at rest in a locally flat space and then started to rotate under the influence of its rockets) and a whole bunch of less convenient models. Generally in science we prefer the simplest model, I'll grant you that. But that's all we can say (and I'll refer you back to the capacitance example and let you decide whether spherical or cylindrical or some other coordinates are "real").


Sol, do you really believe that we cannot make any distinction between these two possible frames in order to conclude that only one of them actually reflects reality?

If "only one of them reflects reality" then GR isn't just incomplete - it's wrong. GR's predictions for the results of physical experiments are identical in those two frames, so you could never under any circumstances falsify one and not the other (any more than you could decide between two frames in relative motion in SR).

And to be honest I have trouble imagining how it could be otherwise, how you could have a correct and complete theory that doesn't allow you to use whatever coordinates you choose.

[sol invictus]

But it doesn't matter, what's "real" are those invariant properties.

That's correct - the results of experiments cannot possibly depend on what coordinates you use; therefore, all physical results depend only on coordinate invariants.

Just like you can't say how far Sally is from the "real" origin, you can't say if she's "really" moving or not. And, based on Sol's posts, it seems to me that the same argument applies to rotation as well.

Well... it's a little more subtle than that. If you're in flat empty space there is a special set of frames - the inertial frames of SR. Those can be characterized mathematically in various ways (they're coordinate systems in which the metric takes Minkowski form, the Christoffel connection is zero, etc.).

What we can say - to be very precise - is that you will never be able to do an experiment that distinguishes an inertial frame in which your apparatus is at the origin from one in which it's not. Similarly you cannot distinguish between inertial frames in which it's at constant velocity with respect to the origin. But you can distinguish inertial frames in which it's accelerating (including rotating around, say, the origin) from those in which it's not (Newton's bucket is a famous example). So in that sense, acceleration and rotation are absolute in flat spacetime.

However everything gets far more complex if the spacetime is curved. There are no longer any inertial frames - but the existence of inertial frames was essential for the statements I just made. If the spacetime is "asymptotically flat" (i.e. gets closer and closer to flat the farther you go from some finite collection of localized sources of energy) you can use that to make some definite statements (including about rotation). But in general, in curved space it's very hard to say anything like the above paragraph that applies outside a small region. And of course in either flat or curved spacetime you can always use either of two coordinate systems that are rotating with respect to each other, and get predictions from each that are perfectly consistent.

[Perpetual Student]

From my (entirely layman's) understanding, in the example above in can be argued that your ship was previously rotating with the universe, then you applied a counter force to stop that rotation. It's not the case that the universe suddenly started rotating in the opposite direction when you applied thrust.

Why would the universe be rotating around me?

[Thabiguy]

Why would the universe be rotating around me?

Perhaps the problem is that you consider rotation to be a physical phenomenon, something that happens "for real". But rotation is really only a description, a tag that we put on the underlying physical phenomena when we want to explain them. Whether something is rotating or not depends entirely on your choice of coordinate system. Your house, most people would say, is not rotating, because in the reference system they use it really is not. In another coordinate system, it is rotating, once every 23 hours and 56 minutes. Both statements are true in the respective systems.

"Rotation" is just a name for a particular way that certain numbers change in your system of describing things. If you are concerned with what's real, then look at things that can be measured. For example, when you're standing in a ship that you would call rotating, there will be a measurable force between your feet and the floor, you will see that the path of a thrown ball is curved. Those are real phenomena that can be actually measured.

And the point is that everyone will agree on those. They may just have different explanations for the same effects, but surely there's no problem with there being multiple ways to explain something. For example, one observer will explain the effects with the rotation of your ship and inertia, in another observer's coordinate system the observed effects are due to centrifugal and Coriolis forces - but those are just words, saying the same thing differently. Both will agree what weight the scales will show when you step on them, both will agree what number on the target you hit with your ball. And they will all agree that when you fire the rockets, you will feel and observe the effects, and the rest of the universe won't feel anything. Isn't that the reality and certainty you want?

When you accept that 'rotation' is just a short word for some particular way that numbers dance in your way of explaining stuff (which is fine to use if it's clear what you mean), you may see that the question "is it really rotating or not?" makes about as much sense as the question "is your rounded height really even or odd?"

Did that help?

[Perpetual Student]

Perhaps the problem is that you consider rotation to be a physical phenomenon, something that happens "for real". But rotation is really only a description, a tag that we put on the underlying physical phenomena when we want to explain them. Whether something is rotating or not depends entirely on your choice of coordinate system. Your house, most people would say, is not rotating, because in the reference system they use it really is not. In another coordinate system, it is rotating, once every 23 hours and 56 minutes. Both statements are true in the respective systems.

"Rotation" is just a name for a particular way that certain numbers change in your system of describing things. If you are concerned with what's real, then look at things that can be measured. For example, when you're standing in a ship that you would call rotating, there will be a measurable force between your feet and the floor, you will see that the path of a thrown ball is curved. Those are real phenomena that can be actually measured.

And the point is that everyone will agree on those. They may just have different explanations for the same effects, but surely there's no problem with there being multiple ways to explain something. For example, one observer will explain the effects with the rotation of your ship and inertia, in another observer's coordinate system the observed effects are due to centrifugal and Coriolis forces - but those are just words, saying the same thing differently. Both will agree what weight the scales will show when you step on them, both will agree what number on the target you hit with your ball. And they will all agree that when you fire the rockets, you will feel and observe the effects, and the rest of the universe won't feel anything. Isn't that the reality and certainty you want?

When you accept that 'rotation' is just a short word for some particular way that numbers dance in your way of explaining stuff (which is fine to use if it's clear what you mean), you may see that the question "is it really rotating or not?" makes about as much sense as the question "is your rounded height really even or odd?"

Did that help?

Nonsense! Rotation is accompanied by forces that can be measured. For example, the earth's rotation causes a decrease in the weight of objects at the equator compared to their weight at the poles. I understand that an alternative view that the whole universe is rotating around the earth can also work under GR with the application of fictitious forces, etc. Which do you think is really happening?

[Perpetual Student]

It's "not possible"? Why?

The frame in which your ship never moves is an extremely special one, but it's certainly "possible". As Mashuna and UncaYimmy point out, another possibility is to choose a frame where your ship is initially rotating and later comes to rest. Of course there are an infinite number of other possibilities in between and not in between.

My point was that the two events would have to occur precisely at the same time. It has the same probability of randomly choosing a given point on the real line. What would you say that is?

... Generally in science we prefer the simplest model, I'll grant you that. But that's all we can say (and I'll refer you back to the capacitance example and let you decide whether spherical or cylindrical or some other coordinates are "real").

Why do we "prefer" the simplest model? Might it be closer to the underlying reality?

If "only one of them reflects reality" then GR isn't just incomplete - it's wrong. GR's predictions for the results of physical experiments are identical in those two frames, so you could never under any circumstances falsify one and not the other (any more than you could decide between two frames in relative motion in SR).

I don't get that. Why can't GR be correct but incomplete? Can't you just see it as a powerful tool, an excellent model, but other input is needed to complete our grasp of reality?

Consider an electrical device that is simply a black box with two wires coming out of it. We have instruments with which we can measure the capacitance, the resistance, the inductance, etc. Our instruments are "correct" in that we can measure all the properties mentioned above. But, those instruments are limited in that the actual internal geometry and materials of the device remain a mystery to us. That does not make the instruments and our understanding of those properties incorrect; it simply makes them incomplete. We would need something else, like an x-ray machine to learn more.

[schrodingasdawg]

My point was that the two events would have to occur precisely at the same time. It has the same probability of randomly choosing a given point on the real line. What would you say that is?

The coordinate system would be chosen so that the two events occur simultaneously.

Why do we "prefer" the simplest model?

Because it's simpler.

I don't get that. Why can't GR be correct but incomplete? Can't you just see it as a powerful tool, an excellent model, but other input is needed to complete our grasp of reality?

The issue here is that GR is inherently coordinate-independent. Physics interprets the statement "some coordinate systems are special" as "the laws of physics take a special form in these coordinate systems," which is in direct contradiction with GR. If by "some coordinate systems are special," you mean "some coordinate systems are special in some metaphysical way, but the (empirically detectable) laws of physics are the same in all possible coordinate systems," that's in violation of Occam's razor.

If "some coordinate systems are special" means that "the laws of physics aren't any different in these coordinate systems, but the math is easier to work out," there isn't any disagreement there, except with what's meant by "special."

'Course, you're not actually using the word "special": you're using "correct" and "real," so I'm assuming you mean that in the sense of "metaphysically special," which is a statement in violation of Occam's razor since the laws of physics are the same in the "correct" coordinate system as they are in all other coordinate systems.

[Michael C]

My point was that the two events would have to occur precisely at the same time. It has the same probability of randomly choosing a given point on the real line. What would you say that is?

Let's imagine that your spaceship is floating free in space, with no rocket engine working. At a specific moment, you start up the rockets that make the ship rotate. From an infinity of possible frames of reference, here are a few that might be used to look at this event:

- One where your spaceship is initially at rest and then starts rotating.
- One where your spaceship is initially rotating and then stops rotating.
- One where you spaceship is always at rest.

In the third frame, the universe will initially be at rest but will start rotating at the moment you turn the rocket engines on. In this frame, new forces will also appear at the moment the universe starts rotating. All this happens because you defined the frame in the way you did. This doesn't mean that some huge change in the universe has actually occurred just the moment you decided to start rotating your spaceship: it simply means that you are using a complicated frame of reference.

Why do we "prefer" the simplest model? Might it be closer to the underlying reality?

The "simplest model" will change depending on what part of the universe we want to observe. For instance, for most events that occur on Earth we are probably best served by a frame of reference where the Earth is stationary. In order to analyse the motion of the Solar system, we'll probably choose a frame of reference where the Sun is always at the centre of the frame. If we're studying Saturn's rings, we'll centre our frame on Saturn. In each case, we are best served by a frame of reference where the mathematics come out simplest: then we can most easily calculate things in order to analyse what is happening and make predictions. What the principle of relativity tells us is that in each situation we are at liberty to choose whichever frame makes our sums easier, since all frames are equally valid.

I don't get that. Why can't GR be correct but incomplete? Can't you just see it as a powerful tool, an excellent model, but other input is needed to complete our grasp of reality?

I'm sure that GR is both correct and incomplete. However, if it were to be found out that there was a "real" coordinate system for the universe that was inherently different to all other systems, GR wouldn't be correct at all: it would be totally negated. The very basis of GR is that all frames of reference are equally valid.

[Thabiguy]

Nonsense! Rotation is accompanied by forces that can be measured. For example, the earth's rotation causes a decrease in the weight of objects at the equator compared to their weight at the poles. I understand that an alternative view that the whole universe is rotating around the earth can also work under GR with the application of fictitious forces, etc. Which do you think is really happening?

I actually tried to address that in the very post you've replied to.

What really is happening are the forces that can be measured. Whether something is rotating or not depends on the coordinate system.

Maybe the problem lies in the inconsistent interpretation of the word "rotating".

You seem to prefer to use "rotating" to refer to a planet like the Earth, where objects at the equator weigh less than objects at the poles. But all observers agree that objects at the Earth's equator weigh less than objects at the poles (because after all the scales can only show a single reading), so if you insist on this interpretation of "rotating", then the Earth is "rotating" in all coordinate systems. Your objections against coordinate systems in which the Earth is not "rotating" are then moot, because under this interpretation of "rotating", there are no such systems.

On the other hand, when one says that in one coordinate system the Earth is rotating and in another one it is stationary, then the word "rotating" refers to a circular motion (in this case of the surface of the Earth), i.e. that coordinates change in certain regular patterns. Whether this happens, of course depends on the choice of your coordinate system. And the forces felt by objects at the equator and the poles don't depend on whether the Earth is rotating or not.

You can use any coordinate system to predict that objects will weigh less at the equator; in some the Earth will be rotating, in some it won't. That's what I meant when I said that "rotation" is a short for a piece of math in your model and not much more.

In fact, your apparent tendency to equate "rotation" with "bulging at the equator" already comes from presuming a certain kind of coordinate system (inertial frame in flat spacetime). It is in this kind of system that the two are related; but in others, they may not be.

Did that make it clearer or muddier?

[dasmiller]

Why do we "prefer" the simplest model? Might it be closer to the underlying reality?

I'm not sure that there's an "underlying reality" to get closer to.

If we go back to the globe (but not the maps) - we express locations in latitude/longitude, with 0 latitude at the equator and 0 long at some British streetcorner. But we could construct arbitrarily complex systems for doing the same function - suppose the coordinate axes weren't at right angles? Or that we defined 0-0 as the subsolar point, so it wasn't stationary with respect to the Earth's crust? The math might be harder, but would that mean that our coordinate system is "farther" from the underlying reality? I'd argue "no" because there's no underlying reality. The spatial relationships between cities are what they are; the coordinate system (lat/long in this case) is just part of a technique to help us understand the spatial relationships, so the coordinate system itself is entirely made-up.

And so, I suspect, is the universe. These reference frames are completely made-up things; we make them up because when we do certain mathematical operations with them, they let us accurately predict relationships among objects in our universe. But the reference frames themselves are no closer to an underlying reality than the lat/long system.

[Tim Thompson]

It might be worth reviewing Newton's "spinning bucket problem". It is relevant here, and is one of the key features in history that leads, indirectly perhaps, to general relativity ...

http://www.gap-system.org/~history/HistTopics/Newton_bucket.html
http://en.wikipedia.org/wiki/Bucket_argument

[Perpetual Student]

Thanks for all the responses above and thanks, Tim Thompson, for those links. Perhaps they will help clarify things
OK, let's look at Newton's two rocks in empty space attached by a rope. If the system rotates the rope is taut if the system does not rotate the rope is slack.
Suppose the rope is slack. Can we make the rope taut by choosing a coordinate system that rotates around the center of gravity of the two rocks?
Or, alternatively, if the rope is taut can we make it slacken by choosing a coordinate system that does not rotate with respect to the rocks?
I don't think we can change reality by the act of choosing a coordinate system. Either the rope/rock system is rotating or not, because either the rope is slack or not.
How do we escape the fact that regardless of coordinate system there is a reality here. Either the system is rotating or not, the reality of which can be readily determined.

[schrodingasdawg]

Suppose the rope is slack. Can we make the rope taut by choosing a coordinate system that rotates around the center of gravity of the two rocks? Or, alternatively, if the rope is taut can we make it slacken by choosing a coordinate system that does not rotate with respect to the rocks?

No. Whether the rope is taut or slack is a physical invariant. All coordinate systems will agree on this.

I don't think we can change reality by the act of choosing a coordinate system.

Neither do I. I would suppose that sol et al will also agree with this.

Either the rope/rock system is rotating or not, because either the rope is slack or not.

This is where the disagreement is occurring. If the rope/rock system is slack, a coordinate system can be chosen where the rope is rotating and the centripetal force keeping the rocks in circular motion is due to gravitational forces instead of tension. So while the tautness/slackness of the system is a physical invariant that will be reproduced by all coordinate systems, whether or not the system is rotating is not a physical invariant.

How do we escape the fact that regardless of coordinate system there is a reality here. Either the system is rotating or not, the reality of which can be readily determined.

We don't escape the fact that there is a reality. However, whether the system is rotating is not part of that reality.

[Uncayimmy]

No. Whether the rope is taut or slack is a physical invariant. All coordinate systems will agree on this.
Will they agree it is straight and not curved? If it's curved and it's a rope, then it's not slack in "reality." Is that where you're heading, PS?

[Reality Check]

Thanks for all the responses above and thanks, Tim Thompson, for those links. Perhaps they will help clarify things
OK, let's look at Newton's two rocks in empty space attached by a rope. If the system rotates the rope is taut if the system does not rotate the rope is slack.
...
In Newton's two rocks in empty space attached by a rope (http://www.gap-system.org/~history/HistTopics/Newton_bucket.html), the rope is stated to be taut since the rock have been set to be rotating. Thus it is never slack. He used this in an empty universe to argue for absolute space.
If the rope is slack then we have a different physical system . A coordinate change does change one physical system into another physical system. It is a way of describing the same physical system differently.

[sol invictus]

Suppose the rope is slack. Can we make the rope taut by choosing a coordinate system that rotates around the center of gravity of the two rocks?
Or, alternatively, if the rope is taut can we make it slacken by choosing a coordinate system that does not rotate with respect to the rocks?

Of course not. A force meter in the middle of the rope reads something. That's a physical experiment, so it must be a coordinate invariant.

I don't think we can change reality by the act of choosing a coordinate system.

As I've said I don't know how many times so far, we cannot affect the results of physical experiments by our choice of coordinates. So if "the results of physical experiments" are what you mean by "reality", then yes.

And if that's the case, you'd better think pretty hard about your questions regarding whether rotation is "real".

Either the rope/rock system is rotating or not, because either the rope is slack or not.

You've just contradicted yourself.

The rope is either slack or not. In both cases we can choose coordinates in which the rocks are rotating, or not.


How do we escape the fact that regardless of coordinate system there is a reality here. Either the system is rotating or not, the reality of which can be readily determined.

What - have you now decided that "tense rope" = "rotation" or something? What will you do when there's no rope, or when some ropes are slack and some aren't?

Did you read my response to Roboramma?

[Thabiguy]

ETA: I posted this before I noticed sol's reply, so apologies if parts of it kinda repeat what he's already written.

Thanks for all the responses above and thanks, Tim Thompson, for those links. Perhaps they will help clarify things
OK, let's look at Newton's two rocks in empty space attached by a rope. If the system rotates the rope is taut if the system does not rotate the rope is slack.

You mean, if it rotates in an inertial frame.

Suppose the rope is slack. Can we make the rope taut by choosing a coordinate system that rotates around the center of gravity of the two rocks?
Or, alternatively, if the rope is taut can we make it slacken by choosing a coordinate system that does not rotate with respect to the rocks?

Of course not.

I don't think we can change reality by the act of choosing a coordinate system.

If by reality you mean measurable quantities, then you're of course right.

Either the rope/rock system is rotating or not, because either the rope is slack or not.

The correct conclusion should have been: Either the rope is slack or not, and whether the rope/rock system is rotating or not is a different issue.

Again, rotation simply means moving in circles. When the rope is taut and you choose a rope-centered, rope-fixed coordinate system, then no part of your system is moving in circles; it's trivial to verify. The rocks are provably stationary in that coordinate system, so any insistence that they are going in circles in that coordinate system, because the rope is taut, does not make sense.

Perhaps you want to say that - say, when the rope is slack - that any system in which the rocks are rotating is "inferior" to the one in which they aren't. Well, this is another way of saying that there is a special class of frames - the inertial frames - in which the laws of physics are particularly convenient for some purposes. That's what special relativity tells us.

But look what you've done: you've chosen a scenario in flat spacetime and without gravity. Yes, it could be argued that when you restrict yourself to that, general relativity is an overkill, because special relativity handles those cases just as well and is simpler.

But general relativity is not restricted to flat spacetime, it's a theory of gravity and it's meant to deal with much more complicated setups than the one you propose. In more general situations, your equivalence rotation=taut just breaks down. For example, when the two rocks orbit each other, then the rope will be slack, and yet the rocks will rotate with respect to distant stars. Or, if the rocks are falling towards a massive body, the rope may be taut (due to tidal forces), even if the rocks don't rotate with respect to distant stars.

These were just simple examples; the point is that when you've got sufficiently curved spacetime, inertial frames go out the window, so one way or another, any coordinate system you may choose will be "inferior" according to your standard. Thus the choice of coordinate system ultimately becomes a matter of convenience.

[schrodingasdawg]

Will they agree it is straight and not curved? If it's curved and it's a rope, then it's not slack in "reality." Is that where you're heading, PS?

I don't know what you mean. Can you elaborate?

[Perpetual Student]

Thanks, again to everyone. I would very much like to get a grasp on this.
Here goes: So, out in empty space, I have a system of two rocks tied to a rope and the system is rotating so that a force meter in the middle of the rope confirms the forces associated with that rotation. I can choose a reference frame under GR that has the universe rotating around the rock/rope system, but we would know that the system is really rotating because of the meter. So, (choice 1) there is a real description of events here, the choice of frame is irrelevant.
Now, I thought I understood that we could conjure up a reference frame that has the system not rotating, using fictitious gravity (whatever that means) to account for the force seen on the meter and a rotating universe to explain the same situation (choice two).
So, which is it?

[sol invictus]

Thanks, again to everyone. I would very much like to get a grasp on this.
Here goes: So, out in empty space, I have a system of two rocks tied to a rope and the system is rotating so that a force meter in the middle of the rope confirms the forces associated with that rotation. I can choose a reference frame under GR that has the universe rotating around the rock/rope system, but we would know that the system is really rotating because of the meter. So, (choice 1) there is a real description of events here, the choice of frame is irrelevant.
Now, I thought I understood that we could conjure up a reference frame that has the system not rotating, using fictitious gravity (whatever that means) to account for the force seen on the meter and a rotating universe to explain the same situation (choice two).
So, which is it?

I don't understand your question - it's not either/or. The statements labeled "choice 1" and "choice 2" are both true according to GR (apart from a few minor semantic quibbles that I don't think are essential, like "fictitious gravity" and precisely what you mean by "irrelevant").

[Uncayimmy]

I don't know what you mean. Can you elaborate?

I was thinking about moving trains and dropping balls. If I'm on a moving train and drop a ball, it follows a straight path to the floor of the train car. For an observer on the ground it follows a curve on the way down. If I attach a string to the ball before I drop it and let it stretch out behind the ball, is that string straight? According to me, yes. What about the ground based observer?

I could be to totally blowing this, so think simple mistake rather than profound inference.

[Hellbound]

I was thinking about moving trains and dropping balls. If I'm on a moving train and drop a ball, it follows a straight path to the floor of the train car. For an observer on the ground it follows a curve on the way down. If I attach a string to the ball before I drop it and let it stretch out behind the ball, is that string straight? According to me, yes. What about the ground based observer?

I could be to totally blowing this, so think simple mistake rather than profound inference.

The ground observer would see it as straight, too...it just moves sideways at the same rate as the ball.

[Uncayimmy]

The ground observer would see it as straight, too...it just moves sideways at the same rate as the ball.

I disagree.

http://www.phys.unsw.edu.au/einsteinlight/jw/module1_Galileo_and_Newton.htm

[Perpetual Student]

I don't understand your question - it's not either/or. The statements labeled "choice 1" and "choice 2" are both true according to GR (apart from a few minor semantic quibbles that I don't think are essential, like "fictitious gravity" and precisely what you mean by "irrelevant").

OK, so you did understand my poorly worded question and the answer is both. I am not the one here who first used the term "fictitious forces" and "fictitious gravity." I'm merely trying to understand what is meant by those terms.
So, both?
Let me try this: I'm cruising along in intergalactic space and I come across two rocks, string and meter as previously described, which is a system, that from my perspective is rotating. So, I want to know what is really happening. I put myself in synchronous rotation with the rocks for further analysis, so I now have the universe revolving around me. Can I conclude that the rocks are really rotating because the meter and string shows it or not?

[Hellbound]

I disagree.

http://www.phys.unsw.edu.au/einsteinlight/jw/module1_Galileo_and_Newton.htm

Nothing there contradicts me, that I can see.

The ball would follow an arc, but as the person holding the string is moving at the same rate as the ball, the string would be straight and moving sideways. I've attached a photo that should explain it (please don't criticize the lack of artistic talent ;) ).
http://forums.randi.org/imagehosting/thum_6874bc37fd6cb097.jpg (http://forums.randi.org/vbimghost.php?do=displayimg&imgid=19691)

The blue represents the path the ball fills over the time, the straight black lines the string. The black circles are the positions of the ball at the various time intervals.

Just to make clear, it's the appearance of the string my earlier post was concerned with, not the ball path. Hope this clears up any confusion.

[sol invictus]

OK, so you did understand my poorly worded question and the answer is both. I am not the one here who first used the term "fictitious forces" and "fictitious gravity." I'm merely trying to understand what is meant by those terms.
So, both?
Let me try this: I'm cruising along in intergalactic space and I come across two rocks, string and meter as previously described, which is a system, that from my perspective is rotating. So, I want to know what is really happening. I put myself in synchronous rotation with the rocks for further analysis, so I now have the universe revolving around me. Can I conclude that the rocks are really rotating because the meter and string shows it or not?

You've lost me again.

What does "really rotating" mean? How do you know that "I now have the universe revolving around me"? What does "the string shows it" mean? If it means the string is under tension, what was the point of going into synchronous rotation with it? You could have just looked at the string to see if it was tense or not, and you can obviously do that even if you're rotating relative to it.

Anyway whatever the answers to my questions are, the answer to yours (to the extent I can guess what you're asking) is no.

For example (to steal from Thabiguy) the rocks might be falling into the gravitational field of something so that the string is taut because of tidal forces (that have nothing obvious to do with rotation). Or perhaps there's a combination of both tidal forces and rotation at work. How can you distinguish? I don't know any way that works in general - which is why I advocate the position that there is no true distinction.

[Perpetual Student]

You've lost me again.
Sorry, I am really trying.

What does "really rotating" mean? How do you know that "I now have the universe revolving around me"? What does "the string shows it" mean? If it means the string is under tension, what was the point of going into synchronous rotation with it? You could have just looked at the string to see if it was tense or not, and you can obviously do that even if you're rotating relative to it.

OK, I my rotation is irrelevant. Scratch that part.

Anyway whatever the answers to my questions are, the answer to yours (to the extent I can guess what you're asking) is no.
OK, no.


For example (to steal from Thabiguy) the rocks might be falling into the gravitational field of something so that the string is taut because of tidal forces (that have nothing obvious to do with rotation). Or perhaps there's a combination of both tidal forces and rotation at work. How can you distinguish? I don't know any way that works in general - which is why I advocate the position that there is no true distinction.

Well, let me modify the experiment by putting it in intergalactic space, so there are no gravitational, electric, thermodynamic, etc. forces that can have any measurable influence. But we do see distant galaxies. Now what? Can we conclude that the system is really rotating or not?

[sol invictus]

Well, let me modify the experiment by putting it in intergalactic space, so there are no gravitational, electric, thermodynamic, etc. forces that can have any measurable influence. But we do see distant galaxies. Now what? Can we conclude that the system is really rotating or not.

Why do you need the distant galaxies? If they can't have any effect, they could be either "really rotating" or "really not rotating", so how can they help?

Regardless, if there are no other forces or any sources of energy or mass, the spacetime is flat. In that case, I refer you to my previous post. Since you still refuse to explain what you mean by "really rotating", that will have to do.

Well... it's a little more subtle than that. If you're in flat empty space there is a special set of frames - the inertial frames of SR. Those can be characterized mathematically in various ways (they're coordinate systems in which the metric takes Minkowski form, the Christoffel connection is zero, etc.).

What we can say - to be very precise - is that you will never be able to do an experiment that distinguishes an inertial frame in which your apparatus is at the origin from one in which it's not. Similarly you cannot distinguish between inertial frames in which it's at constant velocity with respect to the origin. But you can distinguish inertial frames in which it's accelerating (including rotating around, say, the origin) from those in which it's not (Newton's bucket is a famous example). So in that sense, acceleration and rotation are absolute in flat spacetime.

However everything gets far more complex if the spacetime is curved. There are no longer any inertial frames - but the existence of inertial frames was essential for the statements I just made. If the spacetime is "asymptotically flat" (i.e. gets closer and closer to flat the farther you go from some finite collection of localized sources of energy) you can use that to make some definite statements (including about rotation). But in general, in curved space it's very hard to say anything like the above paragraph that applies outside a small region. And of course in either flat or curved spacetime you can always use either of two coordinate systems that are rotating with respect to each other, and get predictions from each that are perfectly consistent.

[Perpetual Student]

Why do you need the distant galaxies? If they can't have any effect, they could be either "really rotating" or "really not rotating", so how can they help?
Well, I thought we might need some refererence to determine whether I am rotating relative to the rest of the universe. But maybe we don't need it.

Regardless, if there are no other forces or any sources of energy or mass, the spacetime is flat. In that case, I refer you to my previous post. Since you still refuse to explain what you mean by "really rotating", that will have to do.
From your previous post, you said, "But you can distinguish inertial frames in which it's accelerating (including rotating around, say, the origin) from those in which it's not (Newton's bucket is a famous example)."
So, that tells me that if the meter shows the forces associated with rotation, it is unambiguous that the rock/rope system is rotating and the universe is not revolving around the system. OK?

[Thabiguy]

So, that tells me that if the meter shows the forces associated with rotation, it is unambiguous that the rock/rope system is rotating and the universe is not revolving around the system. OK?

In flat spacetime.

[Uncayimmy]

Nothing there contradicts me, that I can see.

The ball would follow an arc, but as the person holding the string is moving at the same rate as the ball, the string would be straight and moving sideways. I've attached a photo that should explain it (please don't criticize the lack of artistic talent ;) ).
http://forums.randi.org/imagehosting/thum_6874bc37fd6cb097.jpg (http://forums.randi.org/vbimghost.php?do=displayimg&imgid=19691)

The blue represents the path the ball fills over the time, the straight black lines the string. The black circles are the positions of the ball at the various time intervals.

Just to make clear, it's the appearance of the string my earlier post was concerned with, not the ball path. Hope this clears up any confusion.

Big thanks for taking the time to make the drawing. It's greatly appreciated. I did think you were referring to the path the ball followed rather than the string - a simple misunderstanding. Is there no reference frame where we could see the string as being curved? Part of my brain is nagging me that there is, but I haven't been able to envision it. When it comes to things like this, I am not confident enough in my knowledge to say that there isn't simply because I cannot figure it out.

[sol invictus]

From your previous post, you said, "But you can distinguish inertial frames in which it's accelerating (including rotating around, say, the origin) from those in which it's not (Newton's bucket is a famous example)."
So, that tells me that if the meter shows the forces associated with rotation, it is unambiguous that the rock/rope system is rotating and the universe is not revolving around the system. OK?

I don't know, because you still haven't told us what it means to you to say that something is "really rotating".

If you mean "at rest in some inertial frame" then yes - but only in flat spacetime, because in curved spacetimes (such as the one we inhabit) there are no inertial frames.

[Tim Thompson]

Can I conclude that the rocks are really rotating because the meter and string shows it or not?
I don't think it is possible under any circumstances to know what is the reality of the universe. I think the best we can do is know the relationship of consistency between our model of the universe and our observations of the universe. When we find the two in high accord we tend to treat the model as if it is reality, but we must keep in mind that is it always only a model.

I think I see two things at issue here. One of them is what "really" really means, and the other is the difference between coordinate systems and reference frames (the wikipedia pages tend to make the same mistake, in my view, of equating to two improperly).

I would say that "coordinate system" refers to your particular choice of orthogonal coordinates for identifying points and/or loci of points (e.g., Cartesian, spherical polar, ellipsoidal-hyperbolic, & etc.), whereas a "reference frame" refers to the fundamental properties of spacetime. So, an "inertial" reference frame is Euclidean (a geometric description) or non-accelerated (a kinematic description), and a non-inertial reference frame is either curved (a geometric description) or accelerated (a kinematic description). The geometric or kinematic descriptions are just different ways of treating the same physics.

On the surface of Earth we can assume we are in an inertial reference frame, subject to non-linear Coriolis forces, or we can assume we are in a non-inertial reference frame feeling the effect of rotation. A sufficiently local experiment will not distinguish between the two.

Then there is the philosophical vs the practical problem of defining real (if you want real headaches over reality, just look into quantum mechanics). You keep coming back to the concept of what is "really" happening, but I don't think there is any general agreement here over what "really" really means. I think that while you & Sol might use the same word, you are likely not saying the same thing with it.

I hold to a strictly limited concept of "real". As in the quote above, I don't think you are asking a meaningful question, because I don't think it is possible to ever know what is "really" happening, or even that anything at all is "really" happening, in the philosophical sense. Only practical reality means anything to me, and practical reality is what we observe when we do an experiment. Take Newton's rocks. If those two rocks and the rope between them are alone in the universe (in which case we cannot be there to observe them), then it is of no observational consequence whether they are rotating in an inertial (non-rotating) universe, or at rest in a non-inertial (rotating) universe. The system behaves exactly the same in every sense in either case. So we pick one for convenience sake. Pick "rocks are rotating" because it makes things easier to understand, but it is not correct to say that it is "really happening" and the alternative is "really not happening", because no experiment exists that can distinguish one from the other.

Therein lies the secret: You cannot pick the "real" alternative unless you can perform an experiment that will distinguish by its outcome between the two. You can pick one because it makes more sense to you, but if you call it "real", it is a subjective judgement, not a difference between objective realities.

[sol invictus]

the difference between coordinate systems and reference frames (the wikipedia pages tend to make the same mistake, in my view, of equating to two improperly).

I equate them. I don't think there's any distinction.

I would say that "coordinate system" refers to your particular choice of orthogonal coordinates for identifying points and/or loci of points (e.g., Cartesian, spherical polar, ellipsoidal-hyperbolic, & etc.), whereas a "reference frame" refers to the fundamental properties of spacetime.


That's non-standard. For example it's very common to refer to "different" inertial reference frames in special relativity (e.g. two that are in motion with respect to each other) - but the spacetime in SR is always the same (Minkowski space).


Therein lies the secret: You cannot pick the "real" alternative unless you can perform an experiment that will distinguish by its outcome between the two. You can pick one because it makes more sense to you, but if you call it "real", it is a subjective judgement, not a difference between objective realities.

That's my view, which is why I argue that one cannot decide whether the universe is "really" rotating - because I can always find frames in which it is and frames in which it isn't, without changing my predictions for any experiment.

[Perpetual Student]

That's my view, which is why I argue that one cannot decide whether the universe is "really" rotating - because I can always find frames in which it is and frames in which it isn't, without changing my predictions for any experiment.

Is it possible that you 'cannot decide whether the universe is "really" rotating' because of a deficiency of your state of knowledge and models, not a characteristic of the universe, which must be either unambiguously rotating or not? I am aware that physicists do believe that the universe is actually ambiguous (relative) in this way, but it seems to me this may be more hubris than science. There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong!

[Hellbound]

Big thanks for taking the time to make the drawing. It's greatly appreciated. I did think you were referring to the path the ball followed rather than the string - a simple misunderstanding. Is there no reference frame where we could see the string as being curved? Part of my brain is nagging me that there is, but I haven't been able to envision it. When it comes to things like this, I am not confident enough in my knowledge to say that there isn't simply because I cannot figure it out.

No, I don't think there is, but I reserve the right to be corrected by those more knowledgeable :)

I could see a situation where, say, a black hole (or some equally dense gravitational anomoly) bent light to make it appear curved, or refraction effects, but that's a bit beyond reference frame ;)

[sol invictus]

Is it possible that you 'cannot decide whether the universe is "really" rotating' because of a deficiency of your state of knowledge and models, not a characteristic of the universe, which must be either unambiguously rotating or not?


Of course - anything is possible (particularly since you still haven't said what "really rotating" is, so the statement is so vague as to be entirely meaningless).

But as I told you, if one cannot choose coordinates in which an initially non-rotating universe rotates, then GR is not just incomplete - it's entirely and completely wrong, and in a way that I frankly cannot even imagine.

I am aware that physicists do believe that the universe is actually ambiguous (relative) in this way, but it seems to me this may be more hubris than science.

You don't think assertions like "it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner" illustrate a certain degree of hubris?

It may well be the case that there exists a good definition of angular momentum for cosmological spacetimes (as there is for asymptotically flat spacetimes), and one could then choose to call spacetimes with zero angular momentum "non-rotating", and those with it non-zero "rotating". But as I've been trying to explain, one can always choose coordinates on a non-rotating object so it rotates.... and the physics in the new coordinates will be (and must be) identical.

There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong!

If you want to draw some lessons from the history of physics, I suggest the following:

1) "common sense" doesn't apply at all in regimes outside the human scale and the human environment, and not even always there

2) Established theories very rarely - if ever - prove to be entirely wrong. Instead they turn out to be approximations that are valid and useful in certain regimes, but must be replaced by something more general and complete in others.

[schrodingasdawg]

Is there no reference frame where we could see the string as being curved?

No. The curvature of something is an invariant that doesn't depend on reference frame.

There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong!

It's attributed to William Thomson (Lord Kelvin), but that's actually disputed.

[Perpetual Student]

Of course - anything is possible (particularly since you still haven't said what "really rotating" is, so the statement is so vague as to be entirely meaningless).
But as I told you, if one cannot choose coordinates in which an initially non-rotating universe rotates, then GR is not just incomplete - it's entirely and completely wrong, and in a way that I frankly cannot even imagine.
It appears that it is my ignorance of GR that is the problem. Because GR replaces Newton's theory of gravity, I have not regarded Newton's theory as wrong, but simply limited. I have seen GR as extending not replacing Newton's gravity. There are many physical laws that break down at extreme sizes, pressure, etc. But, I have never regarded that as making those laws wrong, but only limited.

You don't think assertions like "it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner" illustrate a certain degree of hubris?
:busted OK, fair enough. I was trying to be provocative. I have a deep respect for physicists and their area of expertise. Unfortunately, there is much of modern physics that is not readily intuitive for a layman. If I thought my assertions here were actually correct, I would not bother people on this forum; instead, I would write a book like Terence Witt or establish a website and launch an ant-GR campaign like a certain Mr. Mozina does with his EU stuff.

It may well be the case that there exists a good definition of angular momentum for cosmological spacetimes (as there is for asymptotically flat spacetimes), and one could then choose to call spacetimes with zero angular momentum "non-rotating", and those with it non-zero "rotating". But as I've been trying to explain, one can always choose coordinates on a non-rotating object so it rotates.... and the physics in the new coordinates will be (and must be) identical.
Actually, I do think I am beginning to understand this. The point appears to be that the nature of GR under discussion here is so fundamental, that if there were some "outside" way of establishing some single thing as absolutely rotating, it would invalidate the whole theory.



If you want to draw some lessons from the history of physics, I suggest the following:

1) "common sense" doesn't apply at all in regimes outside the human scale and the human environment, and not even always there

2) Established theories very rarely - if ever - prove to be entirely wrong. Instead they turn out to be approximations that are valid and useful in certain regimes, but must be replaced by something more general and complete in others.
Two excellent and relevant points. I really hope this exchange has not been too tedious for you. If it has, perhaps you can gain some small satisfaction in knowing that it has been very helpful for me.

BUT: I still do hate it that I can't view the earth as really rotating.

[ynot]

BUT: I still do hate it that I can't view the earth as really rotating.
Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern?

I have as much if not more trouble accepting Relativity as you do by the way.

[Uncayimmy]

No. The curvature of something is an invariant that doesn't depend on reference frame.
Groovy. Then I shall trouble myself no more with it.

[Sideroxylon]

Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern?

I have as much if not more trouble accepting Relativity as you do by the way.

That the coriolis effect acts on water going down drains is apparently bunk:
http://www.snopes.com/science/coriolis.asp

[sol invictus]

Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern?


It doesn't (and yes, I've actually checked myself). Coriolis force is too weak to matter much on the scale of a bathtub or sink. A better question is why large storms curl opposite ways in the two hemispheres.

If you want to explain Corliois force without rotation, it's simple - you must simply introduce a force field that acts on all mass uniformly with a force exactly proportional to the mass.

Kind of like gravity, huh?

[DeiRenDopa]

Maybe tangential, or even OT, but perhaps not tooo much ...

How does the core of the discussion in this (excellent, many thanks PS! :) ) thread relate to equivalence principle(s)?

IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase?

Lastly, if it's any help PS, the relationship between a well-established theory in contemporary physics and 'reality' is a topic not for the faint of heart. Among other things, IM(NSH)O, those who tackle this from a philosophical background all too often make serious mistakes (albeit rather subtle ones; these folk tend to be, after all, really really smart), and those from a strong physics background all too often show they have not bothered to absorb some painfully learned core lessons in philosophy. In any case, here's something you might like to start with: how can you, PS, determine what's real (part of reality), and what's not? In principle, of course :p

[Perpetual Student]

Maybe tangential, or even OT, but perhaps not tooo much ...

How does the core of the discussion in this (excellent, many thanks PS! :) ) thread relate to equivalence principle(s)?
Do you mean, for example, the equivalence of gravitational and inertial mass?
I guess the relationship is fundamental, since, as I understand things, under GR, going from one reference frame to another inevitably involves the interchangeability of these two aspects of mass.

IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase?
As a layman, I have come to the (provisional) conclusion that the term "laws of physics" is a bit of a stretch. All we really have are models, that tell us (approximately) how nature behaves. If there are any real fundamental descriptions of reality, that we could label as absolute laws, these remain to be discovered.

Lastly, if it's any help PS, the relationship between a well-established theory in contemporary physics and 'reality' is a topic not for the faint of heart. Among other things, IM(NSH)O, those who tackle this from a philosophical background all too often make serious mistakes (albeit rather subtle ones; these folk tend to be, after all, really really smart), and those from a strong physics background all too often show they have not bothered to absorb some painfully learned core lessons in philosophy. In any case, here's something you might like to start with: how can you, PS, determine what's real (part of reality), and what's not? In principle, of course :p
Based on my latter comment, I would guess there is no way to make such a determination.

[schrodingasdawg]

How does the core of the discussion in this (excellent, many thanks PS! :) ) thread relate to equivalence principle(s)?

The equivalence principle states that a being held at a constant position in a uniform gravitational field is indistinguishable from being at a constant position in a uniformly accelerated (relative to an inertial frame) reference frame. A change-of-coordinates to an inertial frame would get rid of the gravitational field, i.e. a frame of reference where an object in freefall is at rest is indistinguishable from an inertial frame of reference.

If we're really naive, we can assume this suggests that gravitational forces are fictitious. But real gravitational fields aren't uniform, so they can't be completely gotten rid of by a change-of-coordinates. The equivalence principle still suggests an equivalence between 'fictitious' and gravitational forces, however, so the other conclusion---that what we call 'fictitious' forces in Newton's formulation of mechanics should be described as gravitational forces in the coordinate systems in which they appear---is taken. After all, there's no fundamental reason that any particular perceived gravitational force should be taken as either real or fictitious, as all of them are indistinguishable from a fictitious force, and it's impossible to get rid of all of them at once: and there's no way to determine the coordinate system that correctly determines which are real and which aren't.

Of course, that's fairly sloppy reasoning, but it's the best way I can think to relate the equivalence principle to the discussion. (I'm open to corrections to my sloppy reasoning. I'm here to learn as much as anything.) The better reason for taking the coordinate system dependent forces as being legitimate gravitational forces in the coordinate system in which they appear, as opposed to some mathematical artifact as in Newton's mechanics, is that we can formulate the laws of physics so that they're the same in all coordinate systems, suggesting that none of the coordinate systems is in any way special and we cannot determine a special coordinate system which tells us which forces are real and which are fictitious.

IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase?

The laws of physics are fairly generalized formulas from which the motion and behavior of matter can be derived. The Einstein Field Equations, for instance, are a law of physics: they, together with a few initial conditions (they are differential equations), can be used to figure out the behavior of the gravitational field. The geodesic equation, when given a spacetime geometry and some initial conditions, can be used to calculate the path that it will take. Both of these are formulated in a way that's the same in all coordinate systems.

Maxwell's equations, in their common form, only apply to inertial frames of reference. They have been reformulated so that they are true in all coordinate systems (and all spacetime geometries, including curved ones).

http://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime
(If I'm not mistaken, even in a flat Minkowski spacetime, a change to curvilinear coordinates will still require that covariant differentiation be done, so the Maxwell laws need their form changed a bit even though the curvature tensors will be zero.)

[Perpetual Student]

Some comments made recently on another thread have stimulated some further thoughts about this subject. We have many situations in solving mathematical equations for some real physical system where we get negative or imaginary numbers that we toss aside because they are clearly not viable solutions for our specific analysis. For example: If we had some quadratic equation involving money, (√-1)$100.00 would make no sense and we would reject it and consider only real solutions to the quadratic as our real answer.
(Note that this has nothing to do with situations and systems where imaginary numbers are meaningful and even essential.)
So, my question is, could it not be that even though GR renders all coordinate systems valid, the one where everything revolves around Princeton NJ, for example, would be rejected as a real description of the entire universe even though it might have some specific utility? It would be rejected as not real just as we would reject i$100 as a mathematical solution for a financial problem.
I seems that there should be a place for common sense and judgement here, just as there would be judgement used in rejecting a negative or imaginary number where it would make no sense.
I am anticipating the response that there can be no preferred frame under GR -- end of discussion.
OK, similarly, from the perspective of pure mathematics, there can be no preferred solution to a quadratic -- all solutions are equally valid. Consider that all solutions may not be meaningful for some real situation that is being modeled but by choosing a preferred solution to a quadratic we are not rejecting quadratic equations. Can we not treat GR in the same way?

[Vorpal]

We discard (√-1)$100 and keep, say, $44 because they have different implications for our financial situation and one of them does not match how money works. Other times, we discard solutions if they don't satisfy constraints/boundary conditions on our problem.

If different coordinate systems had different implications for our physical situation, that's indeed a lot of incentive to keep one and discard another. But they don't. And given that they don't, making a criteria to sort them in the first place is more than a little ad hoc and of no practical value.

And that, by the way, doesn't inherently have to do with GTR per se. It is just one example of physical theory that doesn't care about coordinates. A universe that comes with its own coordinates seems to me to be quite bizarre, but YMMV.

[Mehdimentio]

It simply contradicts common sense, intuition and rationality to view things otherwise.?
Since when does science have to be in accordance with all of the above?

[Roboramma]

It seems to me that the solutions to quadratic equations are simply ways in which the equation can work out to equality. If you are looking for a solution to a specific equation because the equation models some particular system that you're looking at, you know that at least one of those ways must match your actual system. In that case, it makes sense to look at the other properties of the system, that are not modeled by the equation, to see if they are consistent or not with each of the possible solutions. If they aren't consistent with a particular solution, then that solution can be discarded.

I don't see how this applies to coordinate transforms in GR.

[Perpetual Student]

It seems to me that the solutions to quadratic equations are simply ways in which the equation can work out to equality. If you are looking for a solution to a specific equation because the equation models some particular system that you're looking at, you know that at least one of those ways must match your actual system. In that case, it makes sense to look at the other properties of the system, that are not modeled by the equation, to see if they are consistent or not with each of the possible solutions. If they aren't consistent with a particular solution, then that solution can be discarded.

I don't see how this applies to coordinate transforms in GR.

It was intended as an analogy. Because quadratics can give us useless answers, we do not abandon quadratics and we do not accept all the useless answers.

[sol invictus]

It was intended as an analogy. Because quadratics can give us useless answers, we do not abandon quadratics and we do not accept all the useless answers.

But the coordinate system you mention is far from useless, especially if you happen to be in Princeton, NJ. When was the last time you took the velocity of the solar system in its orbit around the center of the Milky Way into account in calculating the time it will take you to drive to the grocery store?

[corbin]

I think the short answer to your conundrum, PS, is that you've run into a place where science ends and philosophy begins. There really IS no scientific reason to believe that one explanation for motion is better than any other.

I've recently become very interested in this subject myself... still need to digest the Wiki articles on it.

[Perpetual Student]

But the coordinate system you mention is far from useless, especially if you happen to be in Princeton, NJ. When was the last time you took the velocity of the solar system in its orbit around the center of the Milky Way into account in calculating the time it will take you to drive to the grocery store?

Consider this:
Just as √-1 is very meaningful in many contexts but useless in others, the Princeton, NJ coordinate system is useful in the context you mention but meaningless when doing cosmology. It's when we do cosmology and ask questions about the nature of the universe that we reject Princeton, NJ as being a meaningful basis for a coordinate system.
So, does it not seem that the Princeton, NJ system in the context of the whole universe is analogous to an "imaginary" answer -- as √-1 would be when we get $i100.00 as an answer for a financial question?

[Perpetual Student]

...
A universe that comes with its own coordinates seems to me to be quite bizarre, but YMMV.

Why?

[Roboramma]

Consider this:
Just as √-1 is very meaningful in many contexts but useless in others, the Princeton, NJ coordinate system is useful in the context you mention but meaningless when doing cosmology. It's when we do cosmology and ask questions about the nature of the universe that we reject Princeton, NJ as being a meaningful basis for a coordinate system.
So, does it not seem that the Princeton, NJ system in the context of the whole universe is analogous to an "imaginary" answer -- as √-1 would be when we get $i100.00 as an answer for a financial question?

The issue that I have with your analogy is that when we discard √-1 as an answer to a financial question there are valid reasons to do so. What reason do you have to discard a coordinate system in which Princeton, NJ is put at rest?

[theprestige]

It's when we do cosmology and ask questions about the nature of the universe that we reject Princeton, NJ as being a meaningful basis for a coordinate system.

Isn't it rather the whole point that all coordinate systems are equally meaningful? I think the real reason cosmologists don't use PNJ Coordinates is that they're not particularly convenient. But "convenient" and "meaningful" are two entirely different things.

[W.D.Clinger]

So, my question is, could it not be that even though GR renders all coordinate systems valid, the one where everything revolves around Princeton NJ, for example, would be rejected as a real description of the entire universe even though it might have some specific utility?


Yes, but you may not have expected me to highlight the critical word in your question. See below.


I am anticipating the response that there can be no preferred frame under GR -- end of discussion.


Although that response is correct, it should be the beginning of discussion.

In this context, "coordinate system" is synonymous with a coordinate patch or chart in the sense of differential geometry. Any such chart is just one of many possible homeomorphisms between an open subset of the spacetime manifold (or manifold with boundary) and an open subset of 4-dimensional Euclidean space (or space with boundary), regarded as Minkowski space.

The entire spacetime manifold is covered by a full atlas, which is a collection of such charts subject to a condition that says they play nicely together. (Their compositions of the form f(g-1(x)) are diffeomorphisms, and the higher order derivatives exist also.) In general, it takes more than one chart to cover a manifold. The 2-sphere, for example, cannot be covered by a single chart.

So far as we know, a chart that's approximately at rest with respect to the cosmic microwave background radiation covers as much of the known universe as any other chart can cover.

For all I know, a chart that says the residents of Princeton are being accelerated directly upward at 9.8 m/s2 may not be able to cover so much of the universe.

Locally preferred charts may run into coordinate singularities or other pathologies when you try to extend them to cover large sections of the universe. That's why, for all I know, a chart "where everything revolves around Princeton NJ" might have to "be rejected as a real description of the entire universe".

We've seen an example of that in both the Black holes (http://forums.randi.org/showthread.php?t=230895) and mathematics of black hole denialism (http://forums.randi.org/showthread.php?postid=8092280#post8092280) threads. Schwarzschild coordinates work just fine as a static description of spacetime around an isolated star or black hole, but they run into a coordinate singularity at the event horizon of a black hole. To obtain a chart that includes the event horizon, you have to give up the illusion of staticity and use different coordinates, such as Painlevé-Gullstrand (http://forums.randi.org/showpost.php?p=8096061&postcount=12) or Lemaître or Eddington-Finkelstein or Kruskal-Szekeres coordinates. Of the coordinate systems just mentioned, it is my understanding that Kruskal-Szekeres coordinates are the only ones that can describe the largest possible spacetime manifold that contains an isolated black hole and satisfies Einstein's field equations.

That gives you an example of why some coordinate systems must be "rejected as a real description of the entire universe", even though those coordinate systems make perfect sense (and may even be preferred!) when describing some small piece of the universe.

[Perpetual Student]

Thanks for all the thoughtful responses. Here's another angle:

Earlier in this thread there was a lot of discussion about using the rest frame of the CMB as a basis for establishing the "real" reference frame of the universe. That idea was roundly rejected because it would violate GR. Now that's an interesting expression: "violating" GR.
Would we say that because we reject $i100 as an answer to a financial question that we are "violating" quadratic equations? Why is the one example a "violation" and the other simply an obvious and practical decision? The CMB is the largest and most pervasive thing we know of in the universe. The CMB has a crucial historical significance for the universe. Why would we be "violating" some equation if we make the practical and obvious decision that the CMB tells us what the actual frame of reference of the whole universe really is, while Princeton, NJ has some value only in some very local and very specific analysis?

[sol invictus]

Consider this:
Just as √-1 is very meaningful in many contexts but useless in others, the Princeton, NJ coordinate system is useful in the context you mention but meaningless when doing cosmology. It's when we do cosmology and ask questions about the nature of the universe that we reject Princeton, NJ as being a meaningful basis for a coordinate system.
So, does it not seem that the Princeton, NJ system in the context of the whole universe is analogous to an "imaginary" answer -- as √-1 would be when we get $i100.00 as an answer for a financial question?

There are many problems with that. The biggest one is that an imaginary or complex amount of money may simply not make sense at all. But the coordinate system based on Princeton does make sense cosmologically - it's just extremely inconvenient. There's no bright line you can draw with coordinate systems - they are related to each other by continuous transformations, so how do you decide where to put the boundary between "meaningful for cosmology" and "not meaningful for cosmology"?

Why?

My answer is that coordinates are a human convention. A universe endowed with its own special coordinates would have to one with some sort of underlying "grid" built into its fundamental structure, a grid with a particular shape (Cartesian versus polar, for example, or square versus hexagonal versus...).

Such a thing is possible, but it's very bizarre. It stinks of the worst kind of "looking under the lamp-post" logic - it's like believing that English is the language of the universe.

Thanks for all the thoughtful responses. Here's another angle:

Earlier in this thread there was a lot of discussion about using the rest frame of the CMB as a basis for establishing the "real" reference frame of the universe. That idea was roundly rejected because it would violate GR. Now that's an interesting expression: "violating" GR.
Would we say that because we reject $i100 as an answer to a financial question that we are "violating" quadratic equations? Why is the one example a "violation" and the other simply an obvious and practical decision? The CMB is the largest and most pervasive thing we know of in the universe. The CMB has a crucial historical significance for the universe. Why would we be "violating" some equation if we make the practical and obvious decision that the CMB tells us what the actual frame of reference of the whole universe really is, while Princeton, NJ has some value only in some very local and very specific analysis?

It's because coordinate invariance is the single most basic and fundamental ingredient of general relativity. By itself it defines the theory almost uniquely. Understanding the constraints coordinate invariance imposes is what allowed Einstein to formulate the theory in the first place. It's analogous to what is sometimes called "gauge invariance", if that means anything to you - the freedom to change coordinate reflects a redundancy in our preferred description of the system, not a fact about physics or reality. Choosing to call that round red object "apple" versus "pomme" doesn't change anything about the object.

To abandon that is an absolutely radical change in the basic structure. Such a change to a very successful theory would require compelling justification.

[Perpetual Student]

... coordinate systems ... are related to each other by continuous transformations...

That is, perhaps, the most persuasive point of all.
However, for this layman, just as we have a grounding for time (with the universe some 13.75 years old), I would like to think of space as also having some grounding. So looking at the infinity of coordinate systems that are related by continuous transformations, I can argue that the one with the simplest description of the universe is the preferred one. It is likely that it would be one, or close to one, with the CMB at rest. It may not currently have much of a scientific basis, but it makes good common sense.
Here's another consideration: I'm not sure what this means, but I have seen the universe described as either infinite and bounded or finite. In either case, there should be no difficulty in concluding it has a center, unless some geometric rationale prohibits it -- like being on the surface of the analog of a sphere in four dimensions. Does GR necessarily give us such a geometry?

[theprestige]

That is, perhaps, the most persuasive point of all.
But you remain unpersuaded, right?

However, for this layman, just as we have a grounding for time (with the universe some 13.75 years old), I would like to think of space as also having some grounding.
As a layman looking for spatial grounding, you could do a lot worse than a coordinate system centered on your town square (i.e., a localized version of your PNJ coordinates).

For this layman, I'm having a hard time understanding why cosmic space needs "some grounding", or why it would matter to me from a layman's perspective if it didn't have it.

So looking at the infinity of coordinate systems that are related by continuous transformations, I can argue that the one with the simplest description of the universe is the preferred one.

And if there isn't a single coordinate system that gives a complete "description of the universe" (whatever that means)?

What if the idea of "simplest description" depends on what part of the universe you're looking at, and which questions you're trying to answer?

If the whole point is that cosmologists can freely switch from one coordinate system to another, whenever it is convenient to do so, why would they bother trying to define one as "preferred"? Wouldn't it make more sense to simply develop an appreciation for the capabilities of each one, and simply prefer whichever one is most convenient for the question at hand?

It is likely that it would be one, or close to one, with the CMB at rest.

Even if a coordinate system at rest with regard to the CMB were somehow "preferred", what would that actually mean to cosmologists? We already know that GR provides a description of the universe that is independent of any particular coordinate system. So "preferring" CMB coordinates wouldn't really be helpful. Indeed, such a preference would end up being an unnecessary entity that would have to promptly be discarded as soon as it was acknowledged.

And cosmologists would be discarding it anyway, whenever some other system was more convenient to their inquiries.

So from the perspective of GR it can't truly be "preferred", and from the perspective of practical applications it pretty much won't be preferred.

It may not currently have much of a scientific basis, but it makes good common sense.
It's been this layman's experience that appeals to "good common sense" is counter-productive to establishing a good scientific basis for anything. Besides, to the extent that "common sense" is relevant, it suggests that cosmologists have no need of a preferred coordinate system, and would ignore one half the time anyway.

[drgsrinivas]

At that time, I argued that we all really know that the whole universe is not really revolving around Phobos, even though GR allows that perspective for anyone who might be inclined to use it. The professionals told me I was dead wrong! -- All frames of reference are equally valid! To my dissatisfaction, that’s where the discussion ended.
After several months of further reflection, it still seems to me that if that is the case, if we cannot use Occam’s razor (or some similar concept), to conclude that the universe is not really revolving around Phobos, it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner. Any comments?

If you believe in commonsense and logic, you will immediately throw away your Relativity.

If you believe in Relativity, then don't bother about logic and rationality.

When you don't have to bother about logic, then you don't have to bother about the experimental evidence also- You can (mis)interpret any data/ observation as strongly supportive of your belief system because you don't have to be logical while interpreting.

For example, if someone believes that ants are the biggest enemies to mankind, then every movement of every ant may be interpreted as part of an organised coup against the humans.

What is important is your belief- Do you believe in Logic or Relativity? Identify your belief and stick to the same. Two opposite religions can't go together.

You can't expect things to be logical at one time and ignore the same logic at another time as per your convenience.

www.debunkingrelativity.wordpress.com

[sol invictus]

Here's another consideration: I'm not sure what this means, but I have seen the universe described as either infinite and bounded or finite. In either case, there should be no difficulty in concluding it has a center, unless some geometric rationale prohibits it -- like being on the surface of the analog of a sphere in four dimensions. Does GR necessarily give us such a geometry?

All the evidence we have is consistent with the universe not having a center. None of the standard cosmologies have either a boundary or a center; instead, they are homogeneous (every point is identical to every other point, which precludes both centers and boundaries) and isotropic (all directions are equivalent).

[Perpetual Student]

If you believe in commonsense and logic, you will immediately throw away your Relativity.

If you believe in Relativity, then don't bother about logic and rationality.

When you don't have to bother about logic, then you don't have to bother about the experimental evidence also- You can (mis)interpret any data/ observation as strongly supportive of your belief system because you don't have to be logical while interpreting.

For example, if someone believes that ants are the biggest enemies to mankind, then every movement of every ant may be interpreted as part of an organised coup against the humans.

What is important is your belief- Do you believe in Logic or Relativity? Identify your belief and stick to the same. Two opposite religions can't go together.

You can't expect things to be logical at one time and ignore the same logic at another time as per your convenience.

www.debunkingrelativity.wordpress.com

Nonsense! All science is based on logic and logic is what resulted in the discovery of relativity and continues to drive its development. Many aspects of relativity and quantum theory are counter-intuitive but that does not mean that they defy logic.

[Ziggurat]

If you believe in commonsense and logic, you will immediately throw away your Relativity.

If you believe in Relativity, then don't bother about logic and rationality.

removed personal comment

[edd]

http://abstrusegoose.com/449

[Perpetual Student]

So, it seems, based on the physicists who have respond here (thanks to all), that I've traveled on a road leading to another dead end. We spend all our lives (at least, I have) with an encompassing feeling that we are in some "place." This "place" leads me to think in terms of my day-to-day coordinate system. I am here and stationary; my wife is in the office; my grandchildren are 120 miles to the west, etc. But I know that is a narrow and unrealistic perspective. I am also rotating, revolving and spiraling in some complex dance, when compared to the CMB.
Nevertheless, my "intellectual" big picture perspective would like the universe to be a well defined "place" in the same way. The vast structures we see shaping the observable universe give me a sense of place in the universe, but GR and the impossibility of a preferred coordinate system seems to take some of that away -- and I find that disturbing. If I did not have such a strong dedication to science and the scientific method, it would be tempting for me to give in to the dark side and take up some crackpot anti-relativity belief system.

[Ziggurat]

Nevertheless, my "intellectual" big picture perspective would like the universe to be a well defined "place" in the same way. The vast structures we see shaping the observable universe give me a sense of place in the universe, but GR and the impossibility of a preferred coordinate system seems to take some of that away -- and I find that disturbing. If I did not have such a strong dedication to science and the scientific method, it would be tempting for me to give in to the dark side and take up some crackpot anti-relativity belief system.

If you relax what you mean by "preferred", then GR actually does provide something that may suit your purposes, and you actually alluded to it. And that's the co-moving reference frame of the universe, which we can observe by watching the CMB. This reference frame isn't preferred in the sense that the laws of physics are any different in this frame from any other frame. But it is still a unique reference frame in terms of a number of observable details of the universe, such as the CMB being essentially isotropic. In more tangible terms than the CMB, the co-moving reference frame is the reference frame in which mater is (on average) stationary within the universe. Local measurements can't distinguish this reference frame from any other reference frame (so again, the laws of physics are no different), but we're not confined to local measurements, and large-scale measurements (like the CMB) are sensitive to it. So if you want a reference frame on which you can hang a sense of place without everything becoming seemingly completely arbitrary, well, the co-moving reference frame can serve that purpose perfectly well.

[Farsight]

Perpetual Student: don't think that general relativity is the problem here. Instead the problem is what some people say about general relativity. They're often mathematicians rather than physicists and cosmologists, and broadly speaking, they take the phrase "all coordinate systems are equally valid" and put a spin on it that delivers a different meaning altogether.

To appreciate this, take a very very simple case where we have no gravity at all, where we have 20 static objects in our universe, and we are not concerned about time, merely distance. You can adopt a coordinate system with an origin of your choice, with X Y and Z directions of your choice, and with units of your choice. I can make totally different choices, and our coordinate systems are equally valid.

Let's now change the scenario such that one object is the Earth, and along with another 8 objects called the planets, it orbits a tenth object called the Sun. The other 10 objects are very distant stars. You are free to use any coordinate system of your choice, and it's just as valid as mine. But just because it's a valid coordinate system, it doesn't mean the the Sun goes round the Earth. In similar vein you are free to use a local map of your town as the basis of a coordinate system, but that doesn't mean the Earth doesn't spin.

I agree with Zig's sentiment re the CMB rest frame (http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation#CMBR_dipole_ anisotropy). This allows you to gauge your motion through the universe. It doesn't provide an "absolute reference frame" because when you're in a black box you can't see it, and so you still can't tell whether you're moving. But we study the universe, we look outside that black box, and that CMB rest frame tells us important information about motion within our universe. And we note that Einstein did not assert that the universe revolves around Phobos just because "all coordinate systems are equally valid".

[DazzaD]

Minor point but possibly important..

Generally speaking cosmologists ARE mathematicians.

In most universities the cosmology "department" is normally located within the mathematics department.

There is a very sensible reason for this.

We need to distinguish between "the laws of physics appear to be the same in all frames of reference" from "what I am calculating here doesnt tally with my everyday sense of appreciation of the world around me".

There is no requirement for the second statement to happen.

[alexi_drago]

This is very likely a really stupid question but if the earth was the centre and everything is rotating around it then does that mean that everything (roughly) at neptune and beyond is travelling faster than c?

[sol invictus]

This is very likely a really stupid question but if the earth was the centre and everything is rotating around it then does that mean that everything (roughly) at neptune and beyond is travelling faster than c?

The coordinate speed of objects at large enough distance will certainly exceed c. But that doesn't pose any problem - you can transform to that frame, and it makes correct predictions. Rotating frames are not inertial, and it's only in inertial frames that c is the speed limit.

[Perpetual Student]

The coordinate speed of objects at large enough distance will certainly exceed c. But that doesn't pose any problem - you can transform to that frame, and it makes correct predictions. Rotating frames are not inertial, and it's only in inertial frames that c is the speed limit.

So, with Princeton NJ as my stationary place, how would I calculate the kinetic energy of some very distant object traveling in a huge circle around me at many times c? If I use:

E = \dfrac{mc^2}{\sqrt{1-\dfrac{v^2}{c^2}}}

I seem to be in a lot of trouble, with an imaginary number in the denominator.

[Farsight]

Don't bother. It's pseudoscience garbage. And there's a lot of it about.

[Almo]

If you believe in commonsense and logic, you will immediately throw away your Relativity.

Incorrect. General Relativity has been shown to explain things we can't explain otherwise.

[Mashuna]

http://t0.gstatic.com/images?q=tbn:ANd9GcQRkSoOrCyjOUbVaRk6ofcld1ooqA6Uf H_75ymkVl2efge0JavUjVHuSyJ5sQ

This thread (http://forums.randi.org/showthread.php?postid=8157752#post8157752) should answer your question.

[sol invictus]

So, with Princeton NJ as my stationary place, how would I calculate the kinetic energy of some very distant object traveling in a huge circle around me at many times c? If I use:

E = \dfrac{mc^2}{\sqrt{1-\dfrac{v^2}{c^2}}}

I seem to be in a lot of trouble, with an imaginary number in the denominator.

You have to use the correct expression for the coordinate. Here's a simpler example of your "trouble" - spherical coordinates. An object near the origin can have an angular coordinate theta that changes arbitrarily rapidly with time. If you tried to use the time derivative of theta for "v", you'd get in just as much trouble (more actually, since it has the wrong units).

[Perpetual Student]

You have to use the correct expression for the coordinate.
/.../


Yes...? And that is...?

[Perpetual Student]

If you relax what you mean by "preferred", then GR actually does provide something that may suit your purposes, and you actually alluded to it. And that's the co-moving reference frame of the universe, which we can observe by watching the CMB. This reference frame isn't preferred in the sense that the laws of physics are any different in this frame from any other frame. But it is still a unique reference frame in terms of a number of observable details of the universe, such as the CMB being essentially isotropic. In more tangible terms than the CMB, the co-moving reference frame is the reference frame in which mater is (on average) stationary within the universe. Local measurements can't distinguish this reference frame from any other reference frame (so again, the laws of physics are no different), but we're not confined to local measurements, and large-scale measurements (like the CMB) are sensitive to it. So if you want a reference frame on which you can hang a sense of place without everything becoming seemingly completely arbitrary, well, the co-moving reference frame can serve that purpose perfectly well.
I don't think I have been saying anything very different from the above. However, going one small step further to say that I would like to view the universe as it actually is -- with the CMB stationary -- seems to provoke accusations of GR anathema.
I have accepted that GR allows us to view and examine the universe or any part of it using any frame of reference -- and all these analyses would be perfectly accurate and valid.
However, when I ask myself, "what is the universe?" describing it as some vast complexity gyrating around Princeton, NJ does not seem to be a very good answer. The universe is not that! It is the immense structure that we all know and love with the CMB stationary! With that thought, I can sleep better.

[sol invictus]

Yes...? And that is...?

It depends on the coordinates. For spherical coordinates it would be something like $v=\partial x/\partial t \rightarrow r \partial \theta/\partial t$. Even though $ \partial \theta/\partial t$ can be arbitrarily large near the origin r=0, in all physical solutions the factor of r renders the velocity finite (and less than c).

Similarly, in any other coordinate system there will be some expression for the energy that depends on the analog of v. The equations of motion in those coordinates will guarantee that the energy can never become infinite or imaginary, just as they guarantee that the derivative of the Cartesian coordinate position of a particle with respect to time never exceeds c.

All of that holds true precisely because the laws of physics are invariant (or covariant, really) under coordinate transformations. If you get shot with an infinite energy bullet, it hurts a lot. Getting hurt a lot is a physical outcome. If infinite energy bullets (and the corresponding outcome) are forbidden in Cartesian coordinates, then they are forbidden in all other coordinates as well.

[Perpetual Student]

It depends on the coordinates. For spherical coordinates it would be something like $v=\partial x/\partial t \rightarrow r \partial \theta/\partial t$. Even though $ \partial \theta/\partial t$ can be arbitrarily large near the origin r=0, in all physical solutions the factor of r renders the velocity finite (and less than c).

Similarly, in any other coordinate system there will be some expression for the energy that depends on the analog of v. The equations of motion in those coordinates will guarantee that the energy can never become infinite or imaginary, just as they guarantee that the derivative of the Cartesian coordinate position of a particle with respect to time never exceeds c.

All of that holds true precisely because the laws of physics are invariant (or covariant, really) under coordinate transformations. If you get shot with an infinite energy bullet, it hurts a lot. Getting hurt a lot is a physical outcome. If infinite energy bullets (and the corresponding outcome) are forbidden in Cartesian coordinates, then they are forbidden in all other coordinates as well.
I guess I'm missing something again. If r is something like a billion light years, how can we avoid
r\partial \theta/\partial t$ \rightarrow \partial x/\partial t = v
from exceeding c? What does using spherical coordinates have to do with anything, since v = rω and a sufficiently large r will result in v exceeding c for any ω?

[Astrodude]

So, with Princeton NJ as my stationary place, how would I calculate the kinetic energy of some very distant object traveling in a huge circle around me at many times c? If I use:

E = \dfrac{mc^2}{\sqrt{1-\dfrac{v^2}{c^2}}}

I seem to be in a lot of trouble, with an imaginary number in the denominator.

You'd have to calculate the velocity relative to a truly inertial reference frame, which doesn't exist in general relativity, if you were to use that formula. That formula is an approximation for real space as it only applies to Euclidian metrics. Princeton, NJ is inert relative to the Earth(hopefully), but it is not inert relative to an observer somewhere on another planet like Mars. General relativity avoids this by dealing with all frames of reference with a tensor to describe all motion in terms of curved spacetime. Accurate calculation of the kinetic energy would require calculating the geodesic deviation of your frame with respect to the object which should eventually give:

E_k = mc^2({\sqrt{\dfrac{g_t_t}{g_t_t+g_s_sv^2}}-1})

With g being the metric tensor.

[sol invictus]

I guess I'm missing something again. If r is something like a billion light years, how can we avoid
r\partial \theta/\partial t$ \rightarrow \partial x/\partial t = v
from exceeding c?

The same thing that forbids it from happening in Cartesian coordinates - the equations of motion in those coordinates that follow from the underlying laws of physics.

What does using spherical coordinates have to do with anything, since v = rω and a sufficiently large r will result in v exceeding c for any ω?

It's just an example that shows why the question is naive. "v" has to be defined with the coordinates you're using, and the expression for the energy may also take a different form in different coordinates.

The point is, if the laws of physics forbid physical quantities from being infinite or imaginary in Cartesian coordinates, they forbid them from being infinite or imaginary in every other coordinate system too. So there can't possibly be anything to worry about.

[Astrodude]

OK, similarly, from the perspective of pure mathematics, there can be no preferred solution to a quadratic -- all solutions are equally valid. Consider that all solutions may not be meaningful for some real situation that is being modeled but by choosing a preferred solution to a quadratic we are not rejecting quadratic equations. Can we not treat GR in the same way?

General relativity usually does this. The invariant differential metric of the space time is usually given in quadratic form as:
ds^2={g^{\mu \nu}dx_{\mu}dx_\nu=ds'^2

However, the metric is ds and not ds^2 and for calculation purposes only the positive square root is used, a line of thinking similar to your own on quadratics. So physicists have definitely heard your argument about general relativity.

Personally, I agree with Mendel Sachs and George Raetz and suspect that this disregard is scientifically incorrect and consider the quaternion reformulation of general relativity to be the most accurate description of gravitation and spacetime. I think the main reasons people reject it are because 'sol_invictus' line of thinking about imaginary quantities leads to a false interpretation of the formalism, and that the Mach principle is required to give a quaternion formalism any meaning.

[Ziggurat]

I don't think I have been saying anything very different from the above. However, going one small step further to say that I would like to view the universe as it actually is -- with the CMB stationary -- seems to provoke accusations of GR anathema.

That's because "as it actually is" doesn't mean anything in this context. The co-moving reference frame is very convenient, and it suits our intuition, but the universe isn't any less real in any other coordinate system. And as long as you handle the math correctly, all these different coordinate systems will make exactly the same predictions. So how can one reference frame be any less real than any other reference frame if they all describe reality equally well? We can prefer one over another for a whole host of reasons (a particular calculation becomes easier, the equations of motion look simpler, it matches our intuition better, or whatever), but these are our own human preferences. The universe cares not one bit about any of them.

[Perpetual Student]

That's because "as it actually is" doesn't mean anything in this context. The co-moving reference frame is very convenient, and it suits our intuition, but the universe isn't any less real in any other coordinate system. And as long as you handle the math correctly, all these different coordinate systems will make exactly the same predictions. So how can one reference frame be any less real than any other reference frame if they all describe reality equally well? We can prefer one over another for a whole host of reasons (a particular calculation becomes easier, the equations of motion look simpler, it matches our intuition better, or whatever), but these are our own human preferences. The universe cares not one bit about any of them.
We have been over this many times in this thread and some others, but I'll state the case on more time in an attempt to achieve some clarity.
Let's say the solar system is the whole universe to simplify the model a little. Now, GR will allow us to examine and describe this universe from the perspective of any frame we can imagine: Phobos, Titan, Princeton, or any molecule on or in any object we might choose. The universe does not care one iota; it is the same universe with the same physics every time. Some of these frames are very convenient for some particular purpose.
However, for me it is very compelling that the mathematics is dizzyingly complex for the whole universe when we choose any of these frames but simplifies strikingly when we have the sun in the "middle" with the planets orbiting with the moons orbiting around the planets, etc. That tells me that GR is not telling the whole story. The heliocentric essence of the solar system is "missed" by GR. There simply must be more to it all than GR is capable of telling us! That latter comment gets a rousing Bronx cheer from physicists because they see GR as a complete and final description of the universe. I remain skeptical -- and, yes. it is only a mere layman's skepticism and of little consequence.

[Perpetual Student]

You'd have to calculate the velocity relative to a truly inertial reference frame, which doesn't exist in general relativity, if you were to use that formula. That formula is an approximation for real space as it only applies to Euclidian metrics. Princeton, NJ is inert relative to the Earth(hopefully), but it is not inert relative to an observer somewhere on another planet like Mars. General relativity avoids this by dealing with all frames of reference with a tensor to describe all motion in terms of curved spacetime. Accurate calculation of the kinetic energy would require calculating the geodesic deviation of your frame with respect to the object which should eventually give:

E_k = mc^2({\sqrt{\dfrac{g_t_t}{g_t_t+g_s_sv^2}}-1})

With g being the metric tensor.

Thanks for trying. As sol invictus and others have said, it would be easier to discuss GR if I had a handle on tensor calculus. Sadly, my MS in mathematics (some 45 years ago -- yikes!) included only a cursory introduction to tensors -- not much beyond defining them -- so as much as I have tried with this 72 year old brain, I have not made much headway. If anyone can recommend a book like "tensor calculus for dummies" I might give it a try again.

[Vorpal]

However, for me it is very compelling that the mathematics is dizzyingly complex for the whole universe when we choose any of these frames but simplifies strikingly when we have the sun in the "middle" with the planets orbiting with the moons orbiting around the planets, etc. That tells me that GR is not telling the whole story.
Again, YMMV, but I have the completely opposite reactions to those situations.

Let's step back from the universe at large and do something way more basic: elementary geometry. Let's say you have a piece of paper with some geometric figures drawn on it. Lines, circles, maybe other conic sections... whatever. You're trying to figure out the answers to some questions about them. Knowing that analytic geometry is good for something, you lay down some Cartesian coordinates and go to town.

Have conic sections? Some Cartesian axes make them a bit complicated, while others very simple (depending on how they align on the major/minor axes). Have a circle? Maybe polar would work better. Etc.

And yet all these coordinates you can lay down are not the thing you're investigating. Coordinates are not geometry. They're just a book-keeping device. Those figures on that paper are not changed one bit by your choice of coordinates. None of their properties change. All the intrinsic questions you can ask about them have the same answers.

I really can't imagine the the universe to be different. So to add to how sol invictus answered your previous question of "why?", your view seem to me horrifyingly anthropocentric. It's really is like saying English is the universe's language because you personally are more conversant in it.

Or in the above analogy, are you going to tell me there the one true coordinate system for those figures on that paper?

[Astrodude]

Thanks for trying. As sol invictus and others have said, it would be easier to discuss GR if I had a handle on tensor calculus. Sadly, my MS in mathematics (some 45 years ago -- yikes!) included only a cursory introduction to tensors -- not much beyond defining them -- so as much as I have tried with this 72 year old brain, I have not made much headway. If anyone can recommend a book like "tensor calculus for dummies" I might give it a try again.

There are some great, quick sites to learn basic tensor calculus. MIT open course ware, Khan academy, lots of Youtube videos, and others can do the trick. Try Edmund Bertschinger's textbook "Introduction to Tensor Calculus for General Relativity"
http://web.mit.edu/edbert/GR/gr1.pdf

[sol invictus]

Thanks for trying. As sol invictus and others have said, it would be easier to discuss GR if I had a handle on tensor calculus. Sadly, my MS in mathematics (some 45 years ago -- yikes!) included only a cursory introduction to tensors -- not much beyond defining them -- so as much as I have tried with this 72 year old brain, I have not made much headway. If anyone can recommend a book like "tensor calculus for dummies" I might give it a try again.

Math is just a tool, and it sounds to me from your posts that you're interested in physics. If so, I recommend Hartle's book on general relativity - it's intended for physics undergrads, so it probably doesn't require a high level of math.

[Perpetual Student]

OK, thanks Astrodude and sol invictus. I'm going to give those a try. Starting with Introduction to Tensor Calculus for General Relativity (MIT) by Edmund Bertschinger. (I already downloaded it and printed it for easier reading.) Hartle's book on general relativity is a bit expensive, so I'll see how I do with the MIT paper first.
Beware: If these books give me the knowledge I need, I may overturn GR with a new theory. What should I call it? PerpetualStudentivity?:D
Vorpal, your argument makes perfect sense and seems to defy any good response -- other than -- the universe is not a bunch of lines and conics on a sheet of paper.
But -- seriously, don't you think the earth really rotates on its axis, rather than the rest of the universe revolving around the earth?
Isn't the latter an ugly picture of the universe?:eye-poppi

[theprestige]

the universe as it actually is -- with the CMB stationary
The CMB is actually stationary relative to what, exactly?

We have been over this many times in this thread and some others, but I'll state the case on more time in an attempt to achieve some clarity.
Let's say the solar system is the whole universe to simplify the model a little. Now, GR will allow us to examine and describe this universe from the perspective of any frame we can imagine: Phobos, Titan, Princeton, or any molecule on or in any object we might choose. The universe does not care one iota; it is the same universe with the same physics every time. Some of these frames are very convenient for some particular purpose.
However, for me it is very compelling that the mathematics is dizzyingly complex for the whole universe when we choose any of these frames but simplifies strikingly when we have the sun in the "middle" with the planets orbiting with the moons orbiting around the planets, etc.
Actually, it's already been pointed out that you're flatly wrong about how the math simplifies in this scenario. Don't believe me? Try plotting your next trip to the bathroom in a heliocentric reference frame, and then tell us how strikingly simple the math is.

That tells me that GR is not telling the whole story. The heliocentric essence of the solar system is "missed" by GR. There simply must be more to it all than GR is capable of telling us!
Since GR tells us a) that the simplicity of a reference frame depends on your point of view, b) that there's more than one point of view, and c) that all points of view are equally valid, I'm not at all sure what you think is actually being missed by GR. Certainly GR easily accommodates the heliocentric "essence" of the solar system, just as it easily accommodates the geocentric "essence" of the Earth-Moon system, the Princeton-centric "essence" of Princeton, NJ, and the CMB-centric "essence" of the universe at large. Of course, GR accommodates all of these "essences" by not considering any of them actually "essential". Most physicists seem to consider this a feature. You for some, reason, insist on thinking of it as a bug.

[Perpetual Student]

So, I'm sitting here having a cup of coffee and decide to set my grandchild's spinning top in motion. Have I set the whole universe in motion revolving around the top? GR will allow me to describe the universe that way, but we all know the historical fact that it was the flick of my hand that did the job and I am not strong enough to move all the galaxies, CMB, and stuff of the whole universe.
A collapsing cloud of gas and dust gave rise to the sun and the planets. The angular momentum and other forces of the original cloud resulted in the motions of the planets and the rotating sun. This cloud of gas and dust did not set the whole universe in motion.
So, what's my point? We actually know the history and causality of things so we know how things happened -- how planets, stars and galaxies and the CMB came about. GR does not! The planets actually do go around the sun! We know how that happened. GR does not know history and seems to be oblivious to causality. GR is not the whole story!
OK, now back to my reading of Introduction to Tensor Calculus for General Relativity.

[Vorpal]

Vorpal, your argument makes perfect sense and seems to defy any good response -- other than -- the universe is not a bunch of lines and conics on a sheet of paper.
Not so different in any sense relevant here. Coordinates are book-keeping device for whatever you're measuring. Be that the trajectory of electrons or lines or conic sections or other geometric figures is not important.

Actually, it's even more appropriate for the subsequent discussion: in relativity events are causally connected if and only one is within the other's light cone. So you're pretty much literally picking different coordinates to describe those cones. And just as the geometric figures don't care about which coordinates you pick, neither do those light cones--causal relationships.

But -- seriously, don't you think the earth really rotates on its axis, rather than the rest of the universe revolving around the earth?
No. I think those kinds of questions of "really" are just metaphysical fluff at best. Physical reality is whatever can be measured.

Isn't the latter an ugly picture of the universe?:eye-poppi
No. I think it's much more beautiful. Or to be more precise, the generality of laws that don't care about which book-keeping devices humans use is to me a much more beautiful picture of the universe.

So, I'm sitting here having a cup of coffee and decide to set my grandchild's spinning top in motion. Have I set the whole universe in motion revolving around the top? GR will allow me to describe the universe that way, but we all know the historical fact that it was the flick of my hand that did the job and I am not strong enough to move all the galaxies, CMB, and stuff of the whole universe.
Of course you aren't. The events that cause what you see on the distant galaxies around you are causally disconnected from you. Absolutely nothing you do can affect them. (Though in principle you have some ability to affect sufficiently later events in those galaxies.) Causal relations are real things. If event A caused event B, then this relationship holds regardless what coordinates you pick to keep track of things.

It seems to me that you're begging the question. Your argument starts with the supposition that picking a rotating frame actually does something physical, and then you correctly conclude that this leads to completely nonsensical conclusions. But then we diverge on what to draw from this:
1) You keep the supposition and find GTR at fault for not respecting it.
2) Others simply throw the supposition out.
Or at least, that's my impression--you seem to be treating picking a rotating frame as the same thing as physically spinning around. But it isn't at all! I can predict what I would see if I spin around without picking a rotating frame. Or I can pick a rotating frame and predict what I would see while staying inertial.

All those coordinate choices affect is the system I use to write down the observations I make. It's no different than deciding to graph data on a log-log graph or a Cartesian graph, or write my notes in English or German. It does not change reality in anyway; it's just a representation.


P.S. There are very good reasons to believe that GTR is not the whole story, but they 't have little to do with the issues raised here.

[sol invictus]

So, I'm sitting here having a cup of coffee and decide to set my grandchild's spinning top in motion. Have I set the whole universe in motion revolving around the top? GR will allow me to describe the universe that way

Complete nonsense. Changing coordinates does not in any way change anything physical, imply causality, imply any motive force of any kind, and it doesn't happen at a particular time (because nothing "happens" at all, and anyway the coordinates include time).

If you click your mouse to zoom in on a digital map, you've suddenly forced everything to expand to ten times its previous size! How could your mouse possibly be so powerful?

[Farsight]

Again, I'd like to reiterate that the problem here is with what people say general relativity says, rather than with what general relativity actually says. Here's an example:

....Since GR tells us a) that the simplicity of a reference frame depends on your point of view, b) that there's more than one point of view, and c) that all points of view are equally valid...

However all points of view aren't equally valid. To understand this, take out a CD and put it on a table. Look down at it, and note that from this point of view it looks circular. Now take a couple of steps back and look at it again. It now looks ovoid rather than circular. But it isn't. When you see an unfamiliar object, think about what you do. You look at it, then you move your head and look at it again from another angle. To make out what it is, you combine different points of view to understand what it is you're looking at. You don't just say "all points of view are equally valid". You try to see the big picture, which is what GR tries to do.

[Perpetual Student]

Vorpal and sol invictus:
Your responses are weak. I think I have made a convincing argument that history and causality can give us information so we have preferred frames of reference at various levels.
Looking at the solar system, the heliocentric one is preferred since we know how the solar system formed and how its parts went into motion. Yes, the earth and the planets are really going around the sun.
Looking at the galaxy, we know that certain forces gave the galaxy its shape and its motions, so its preferred frame gives us a information as to what the galaxy really is.
We may not have precise knowledge about how galaxy clusters were formed, but we are familiar with the forces involved, dark matter, etc. so we can hypothesize historical accounts for clusters and super clusters. The more we understand the genesis of these structures -- the great voids and walls, the clearer the preferred frame becomes.
The motion of the spinning top on my table has a known genesis so we know it's spinning and the universe has not been set in motion revolving around the top.
Finally, we know about the big bang and the CMB, so we have knowledge of its genesis and the ultimate preferred frame of the known universe is unambiguously revealed to us.
So, it is our knowledge of history and causality that supplies the information lacking in GR to discover preferred frames -- including the ultimate one, so thankfully GR is not the only tool in our bag.

[Vorpal]

PS, your argument is nothing more than bare assertion.

We do know the history and causality of many of those things... and coordinates and in no way enter in those relationships. If solar flare erupts and takes out a satellite, then this a completely frame-independent relationship and no frame whatsoever will make it false. Not Earth-centric, not Princeton-centric, not anything. And so forth for every causal relationship whatsoever.

You simply state that questions like "what goes around what" is a frame-independent relationship of that sort. It's just begging the question.

[corbin]

I agree that GR gives no preferred reference frame, but I don't think causality is what does.

To me, it seems like the only place where you are going to get an answer as to why one particular arrangement of physical reality really is the case (or why none are preferred) is the place where nobody in this thread wants to go - metaphysics.

Note: A "metaphysical" answer to the question of "why isn't there a preferred reference frame?" would be something along the lines of "because raw sense data is itself subjective" or "because all referents are in the same category." Any answer uses elements outside the realm of science in its explanation, like the idea of a referent or the idea of raw sense data as qualia, and is therefore in a branch of philosophy called metaphysics, rather than part of science.

[Ziggurat]

Vorpal and sol invictus:
Your responses are weak. I think I have made a convincing argument that history and causality can give us information so we have preferred frames of reference at various levels.

Causality has nothing to do with this. All reference frames preserve causality.

Looking at the solar system, the heliocentric one is preferred since we know how the solar system formed and how its parts went into motion.

No, you are wrong. The development of the solar system can be tracked in any reference frame. If it couldn't, then different reference frames wouldn't be equivalent. But the entire point of GR is making them all equivalent, and it accomplishes that.

Perhaps you really mean is that solar dynamics are easier to track in a heliocentric coordinate system. And that's true. But my walk to the bathroom becomes harder than a geocentric reference frame. And the motion of other stars within our galaxy is also harder in a heliocentric coordinate system than in a coordinate system based on the galaxy's center of mass. And so on, and so on. There are, for practical reasons, very good reasons to prefer one reference frame over another for a particular problem. But which frame works best will change from problem to problem, and if you don't have any problem in mind, then there truly is no reason to prefer one reference frame over another.

Yes, the earth and the planets are really going around the sun.
Looking at the galaxy, we know that certain forces gave the galaxy its shape and its motions, so its preferred frame gives us a information as to what the galaxy really is.

No, it doesn't. Every reference frame will provide the exact same predictions.

We may not have precise knowledge about how galaxy clusters were formed, but we are familiar with the forces involved, dark matter, etc. so we can hypothesize historical accounts for clusters and super clusters. The more we understand the genesis of these structures -- the great voids and walls, the clearer the preferred frame becomes.

Necessarily false, since (again) all reference frames will produce identical predictions.

The motion of the spinning top on my table has a known genesis so we know it's spinning and the universe has not been set in motion revolving around the top.

That is in fact no more valid than a reference frame which was always spinning with respect to the earth. You simply momentarily placed a top at rest in that frame, but your actions did nothing more than change the motion of that top.

Finally, we know about the big bang and the CMB, so we have knowledge of its genesis and the ultimate preferred frame of the known universe is unambiguously revealed to us.

Define "preferred". Because as far as I can tell, the universe has no preferences at all.

[dasmiller]

Looking at the solar system, the heliocentric one is preferred since we know how the solar system formed and how its parts went into motion. Yes, the earth and the planets are really going around the sun.

No, they really are not.

The simplest possible system would consist of 2 rigid point-masses revolving around their common center of mass, so even a hugely-simplified solar system wouldn't have particularly simple math in a true heliocentric coordinate system. Since there are more than 2 bodies in the solar system, and since none of 'em are perfectly rigid or perfectly spherical, things are quite a bit more complicated than that, none of which makes a simple heliocentric system any more elegant for accurate orbit predictions.

[Perpetual Student]

Causality has nothing to do with this. All reference frames preserve causality.
It is your decision to ignore causality. It's another source of information to assist in deciding questions about what body is revolving and/or rotating with respect to another. Choosing to ignore information is an option but It can only impoverish our understanding.

No, you are wrong. The development of the solar system can be tracked in any reference frame. If it couldn't, then different reference frames wouldn't be equivalent. But the entire point of GR is making them all equivalent, and it accomplishes that.
Yes that's true and I did not say anything to contradict that. Using causality to decide questions of reality is a logical and scientifically valid procedure.

Perhaps you really mean is that solar dynamics are easier to track in a heliocentric coordinate system. And that's true. But my walk to the bathroom becomes harder than a geocentric reference frame. And the motion of other stars within our galaxy is also harder in a heliocentric coordinate system than in a coordinate system based on the galaxy's center of mass. And so on, and so on. There are, for practical reasons, very good reasons to prefer one reference frame over another for a particular problem. But which frame works best will change from problem to problem, and if you don't have any problem in mind, then there truly is no reason to prefer one reference frame over another.
I am not discussing which frame might be best for some particular purpose. I am using all available tools to decide which frame best describes reality.


No, it doesn't. Every reference frame will provide the exact same predictions.
Yes they do. All frames provide the same predictions but some describe reality better than others and I am proposing that there is a best one.

Necessarily false, since (again) all reference frames will produce identical predictions.
Wrong! See my response above.

That is in fact no more valid than a reference frame which was always spinning with respect to the earth. You simply momentarily placed a top at rest in that frame, but your actions did nothing more than change the motion of that top.
That's the point. My actions changed the top, not he universe; therefore we know the universe has not been changed by my actions and the top is really moving.

Define "preferred". Because as far as I can tell, the universe has no preferences at all.

The universe does not have thoughts. I am describing the reality of the universe.

dasmiller
No, they really are not.

The simplest possible system would consist of 2 rigid point-masses revolving around their common center of mass, so even a hugely-simplified solar system wouldn't have particularly simple math in a true heliocentric coordinate system. Since there are more than 2 bodies in the solar system, and since none of 'em are perfectly rigid or perfectly spherical, things are quite a bit more complicated than that, none of which makes a simple heliocentric system any more elegant for accurate orbit predictions.
That has nothing to do with my point.

[W.D.Clinger]

Causality has nothing to do with this. All reference frames preserve causality.
It is your decision to ignore causality. It's another source of information to assist in deciding questions about what body is revolving and/or rotating with respect to another. Choosing to ignore information is an option but It can only impoverish our understanding.
Ziggurat isn't ignoring causality. Please pay attention to what he wrote, especially the part I highlighted.


No, it doesn't. Every reference frame will provide the exact same predictions.
Yes they do. All frames provide the same predictions but some describe reality better than others and I am proposing that there is a best one.
Please define what you mean by "better".


Necessarily false, since (again) all reference frames will produce identical predictions.
Wrong! See my response above.
Your disagreement with Ziggurat's correct statement suggests that your argument is based upon some misunderstanding of general relativity.


Define "preferred". Because as far as I can tell, the universe has no preferences at all.

The universe does not have thoughts. I am describing the reality of the universe.
As do all admissible frames.

So far as I can tell, your argument is based upon ascribing your own preferences to the universe, or to your own arbitrary use of the word "reality" to describe some frames while decrying others' use of that same word to describe other frames that use different numbers to describe exactly the same physical reality.

[Perpetual Student]

There are some great, quick sites to learn basic tensor calculus. MIT open course ware, Khan academy, lots of Youtube videos, and others can do the trick. Try Edmund Bertschinger's textbook "Introduction to Tensor Calculus for General Relativity"
http://web.mit.edu/edbert/GR/gr1.pdf

Edmund Bertschinger's textbook "Introduction to Tensor Calculus for General Relativity" is fantastic. Thanks! I also found a YouTube video of a 70 minute lecture by the same author about general relativity. He is an excellent lecturer.
I am making some progress.

[Perpetual Student]

W.D.Clinger
Originally Posted by Ziggurat
Causality has nothing to do with this. All reference frames preserve causality. It is your decision to ignore causality. It's another source of information to assist in deciding questions about what body is revolving and/or rotating with respect to another. Choosing to ignore information is an option but It can only impoverish our understanding. Ziggurat isn't ignoring causality. Please pay attention to what he wrote, especially the part I highlighted.
I am not contesting that all reference frames preserve causality. I am suggesting that causality can guide us to a better understanding of reality -- as in, "I caused the top on my table to spin so it is spinning and the universe is not rotating around my top."

Please define what you mean by "better".
bet·ter adj. Comparative of good.
. Greater in excellence or higher in quality.
. More useful, suitable, or desirable: found a better way to go; a suit with a better fit than that one.
. More advantageous or favorable; improved: a better chance of success.

Your disagreement with Ziggurat's correct statement suggests that your argument is based upon some misunderstanding of general relativity.
My understanding of GR is not at issue and you have no basis for that statement since I am basing my arguments on information outside of GR.

So far as I can tell, your argument is based upon ascribing your own preferences to the universe, or to your own arbitrary use of the word "reality" to describe some frames while decrying others' use of that same word to describe other frames that use different numbers to describe exactly the same physical reality.
Then clearly you have not understood my argument.

[W.D.Clinger]

Your disagreement with Ziggurat's correct statement suggests that your argument is based upon some misunderstanding of general relativity.
My understanding of GR is not at issue and you have no basis for that statement since I am basing my arguments on information outside of GR.
Why, then, did you say Ziggurat's correct statement was "wrong"?


Then clearly you have not understood my argument.
Although I have read your argument, I do not understand it.

As in your response to Ziggurat, your argument has included several statements that are flat-out incorrect. If those incorrect statements are irrelevant to your argument, then omitting them from your argument might make your argument easier to understand.

[Perpetual Student]

Why, then, did you say Ziggurat's correct statement was "wrong"?
If you trace the progress of the dialog, you will see that I intended to say that he was "wrong" in his insistence that causality cannot be used to decide which frame(s) describe reality, not that he is wrong that all reference frames preserve causality. Sorry for my lack of clarity.

Although I have read your argument, I do not understand it.

As in your response to Ziggurat, your argument has included several statements that are flat-out incorrect. If those incorrect statements are irrelevant to your argument, then omitting them from your argument might make your argument easier to understand.

Obviously, I don't believe anything I said is incorrect. I cannot and do not intend to contest GR; it would be absurd for me to do so. In any case, sweeping generalities like the above statement are useless in a discussion like this.

[W.D.Clinger]

If you trace the progress of the dialog, you will see that I intended to say that he was "wrong" in his insistence that causality cannot be used to decide which frame(s) describe reality, not that he is wrong that all reference frames preserve causality. Sorry for my lack of clarity.
I understood that the first time.

Please explain how it is possible to interpret your "wrong" response as anything other than flat-out incorrect. As Ziggurat had noted:

Causality has nothing to do with this. All reference frames preserve causality.

....Every reference frame will provide the exact same predictions.

....(again) all reference frames will produce identical predictions.


According to general relativity, all admissible reference frames are in complete, 100% mathematically precise agreement about all matters of causality.

Why, then, are you arguing that causality can be used to decide which frames describe reality better than others?

How can that aspect of your argument be regarded as anything other than flat-out incorrect?

(Unless, of course, you are rejecting the relevant parts of general relativity, but I don't think rejection of general relativity is part of your argument.)

[Perpetual Student]

Complete nonsense. Changing coordinates does not in any way change anything physical, imply causality, imply any motive force of any kind, and it doesn't happen at a particular time (because nothing "happens" at all, and anyway the coordinates include time).

If you click your mouse to zoom in on a digital map, you've suddenly forced everything to expand to ten times its previous size! How could your mouse possibly be so powerful?

"Complete nonsense" right back at you! I said nothing about changing coordinates. I said, if I put top in motion, it is actually rotating (it has angular momentum) and the universe is actually not revolving around my top. We can tell because we can trace the chain of causality that resulted in the top's motion.

[sol invictus]

"Complete nonsense" right back at you! I said nothing about changing coordinates. I said, if I put top in motion, it is actually rotating (it has angular momentum) and the universe is actually not revolving around my top. We can tell because we can trace the chain of causality that resulted in the top's motion.

And that reasoning is complete nonsense. The chain of causality is identical in all coordinate systems.

[Roboramma]

"Complete nonsense" right back at you! I said nothing about changing coordinates. I said, if I put top in motion, it is actually rotating (it has angular momentum) and the universe is actually not revolving around my top. We can tell because we can trace the chain of causality that resulted in the top's motion.

How do you know that the top wasn't rotating the other way before you spun it, and your actions didn't simply stop it?

Or maybe it was already rotating in the direction in which you spun it, and now you've sped it up even more? Or something else?

No one is saying that you changed the rest of the universe by spinning the top, PS. They are saying that you can describe the universe in a frame in which the top was already rotating the other way (and is now at rest), and for everything that you can measure, it will be exactly the same as if you'd described it in a frame in which it was originally at rest and is now rotating.

So what's real? Perhaps none of the frames themselves are the reality, but rather the things that are true no matter what frame you choose: the relationships between things: the things that can actually be measured.

[Ziggurat]

It is your decision to ignore causality.

Unless you mean something completely different by the word "causality" from what everyone in physics means by the word, then this statement is completely wrong.

It's another source of information

Causality isn't a source of information. It's statements like this that make me think you must mean something completely different from what everyone else here means, but you haven't defined what you mean by causality. I suggest you do so in order to avoid further confusion.

Yes that's true and I did not say anything to contradict that. Using causality to decide questions of reality is a logical and scientifically valid procedure.

But you haven't decided questions of reality, you've only decided questions of preference, namely your own.

In Newtonian mechanics, the position you are advocating makes some sense. There are inertial reference frames, and non-inertial reference frames, and you can tell which is which by the existence of position-dependent forces which are always proportional to mass (such as centrifugal forces). We call these fictitious forces, and they disappear when we adopt an inertial reference frame. But even here, all you can do is select a class of reference frames which are special, you cannot pick a single reference frame which represents "reality".

But this position doesn't actually make sense in general relativity, because there literally is no difference between gravity and fictitious forces. So there is no way to remove all position-dependent forces which are proportional to mass. But there's also no need to. Everything works regardless of which frame you pick, as long as you handle it correctly.

I am not discussing which frame might be best for some particular purpose. I am using all available tools to decide which frame best describes reality.

But all frames describe reality equally well. And the proof is that all frames provide the exact same description, because all frames will make the exact same predictions.

Yes they do. All frames provide the same predictions but some describe reality better than others and I am proposing that there is a best one.

You must have a strange definition of "better". Because from where I'm sitting, the ONLY criteria for how well any theory describes reality is the accuracy of its predictions. But if all reference frames provide the exact same answer, their accuracy is all identical. So there is no meaningful sense in which any description is better than any other description. What counts as "better" for you, then, is nothing objective. Because again, the only objective better or worse is accuracy. Anything beyond that is merely your personal preferences, which the universe doesn't care about.

That's the point. My actions changed the top, not he universe; therefore we know the universe has not been changed by my actions and the top is really moving.

No. You missed my point completely. Your actions only changed the top. But that does not, and never did, preclude us from adopting a reference frame that rotates with respect to our table. Hell, we can choose such a reference frame even without a top. But it is the physics of the reference frame, NOT your hand, that makes the universe spin. If you thought otherwise, you completely failed to understand what reference frames are about.

The universe does not have thoughts. I am describing the reality of the universe.

No you aren't. You kept using the term "preferred". But the universe cannot prefer anything if it doesn't think.

[Michael C]

All frames provide the same predictions but some describe reality better than others and I am proposing that there is a best one.

In order to describe a particular part of the universe there are certainly frames that are more convenient than others, but there is no single "best" frame to be used for every phenomenon in the universe.

What is the best frame for describing the motion of your grandchild's top? I'd choose a frame in which the floor on which it is spinning is at rest. If you were to use a frame based on the CMB, would that give a better description of what the top is "really" doing?

[ben m]

I suspect the thing you're missing, PS, is this. Let's talk about the table underneath your toy top.

1) I can write down a coordinate frame in which the table is rotating. In this coordinate system, distant objects (e.g., the stars) are moving under something you'd probably call a Coriolis force. This force obeys all of the laws of physics. By the way, you might happen to choose this coordinate system such that all coordinates on the top are stationary.

2) I can write down another coordinate frame, in which all coordinates on the table are stationary. In this frame, the coordinates of distant objects (e.g., the stars) are moving under something you'd probably call Newton's Laws. But the coordinates that describe a *point on the surface of the top* are now going in little circles.

3) Heck, I can write down a coordinate system that is of type (1) for all t < 0, then of type (2) for all t > 0. In this coordinate system, the actual laws of physics would have to be written with a "discontinuity" at t=0, which explains (in a way that passes all experimental tests) why a distant-star's coordinates would suddenly "brake", so that at t=-1 the star is orbiting the top and at t=+1 the star is at rest. That's a weird system, but those physical laws, expressed in those coordinates, are in fact correct. Why would you choose such a wacky coordinate system? Well, perhaps because they would label a point on the surface of the top as "stationary", even though a child reached over at t=0 and applied a force that stopped the top from spinning.

Does that make it clear how the "causality" works? "the stars grind to a halt at t=0" is the expected physical behavior of the stars according to an observer who has re-labeled their coordinate system at t=0.

[Perpetual Student]

... <rude comment snipped>... The chain of causality is identical in all coordinate systems.

Yes, but you continue to miss the point. See below.

[Perpetual Student]

I suspect the thing you're missing, PS, is this. Let's talk about the table underneath your toy top.

1) I can write down a coordinate frame in which the table is rotating. In this coordinate system, distant objects (e.g., the stars) are moving under something you'd probably call a Coriolis force. This force obeys all of the laws of physics. By the way, you might happen to choose this coordinate system such that all coordinates on the top are stationary.

2) I can write down another coordinate frame, in which all coordinates on the table are stationary. In this frame, the coordinates of distant objects (e.g., the stars) are moving under something you'd probably call Newton's Laws. But the coordinates that describe a *point on the surface of the top* are now going in little circles.

3) Heck, I can write down a coordinate system that is of type (1) for all t < 0, then of type (2) for all t > 0. In this coordinate system, the actual laws of physics would have to be written with a "discontinuity" at t=0, which explains (in a way that passes all experimental tests) why a distant-star's coordinates would suddenly "brake", so that at t=-1 the star is orbiting the top and at t=+1 the star is at rest. That's a weird system, but those physical laws, expressed in those coordinates, are in fact correct. Why would you choose such a wacky coordinate system? Well, perhaps because they would label a point on the surface of the top as "stationary", even though a child reached over at t=0 and applied a force that stopped the top from spinning.

Does that make it clear how the "causality" works? "the stars grind to a halt at t=0" is the expected physical behavior of the stars according to an observer who has re-labeled their coordinate system at t=0.

You use the phrase "I can...(choose such and such) a coordinate system." I have no basis to disagree with that. I am not a physicist; as a layman I accept what physicists say; specifically, GR makes all coordinate systems equally valid. That is one of the key features of GR, along with providing a theory of gravity that is consistent with experiments, consistent with SR and reduces to Newton's gravity at slow speeds and weak gravity. OK, it's a powerful mathematical description of the universe, of reality -- a mathematical model of reality.
But it is not the only tool we have when we ponder what reality is, what the universe is. Consider this:
You said, "I can write down a coordinate frame in which the table is rotating. In this coordinate system, distant objects (e.g., the stars) are moving under something you'd probably call a Coriolis force. This force obeys all of the laws of physics. By the way, you might happen to choose this coordinate system such that all coordinates on the top are stationary."
My contention is that even though the above comment is true (as far as I know -- I am a layman), it does not tell the whole story. We can still decide what is "really happening." Based on all I have heard and read, GR will not do this -- all coordinate systems tell us what is "really happening" according to GR. Do we stop thinking at this point? Do we just say, oh well, GR is king; there is no such thing as what is "really happening"? I don't accept that! We know the history and we know the causation of the spinning top. I did it! It is really spinning! GR is only a mathematical model; it is not real. It is limited.
Should that surprise anyone? -- that our best models of reality are limited?
There is every reason to believe that the universe is a real place with an ultimate reality that we will probably never fully comprehend. As a real object, the universe has a real time and a real place. The CMB tells us something about that real time and place. The theory of general relativity allows us to examine it from any frame of reference we choose for our own convenience; the physics will be the same regardless. But we have that CMB giving us information regarding which of these frames is the real thing.

[Perpetual Student]

Thanks for all the above comments. I don't have the time or stamina to respond to all, so I have chosen one to best make my point.

[Ziggurat]

You use the phrase "I can...(choose such and such) a coordinate system." I have no basis to disagree with that. I am not a physicist; as a layman I accept what physicists say; specifically, GR makes all coordinate systems equally valid. That is one of the key features of GR, along with providing a theory of gravity that is consistent with experiments, consistent with SR and reduces to Newton's gravity at slow speeds and weak gravity. OK, it's a powerful mathematical description of the universe, of reality -- a mathematical model of reality.
But it is not the only tool we have when we ponder what reality is, what the universe is.

Sure. If you want to ponder what reality is, we have philosophy too. But if you want to describe reality in a quantifiable manner, well, science is in fact the only thing we've got. And GR is our best large-scale theory for doing so.

My contention is that even though the above comment is true (as far as I know -- I am a layman), it does not tell the whole story. We can still decide what is "really happening."

How can we decide what's happening? Unless you're a solipsist, then nothing we decide has any effect on what reality actually is. It's not a choice we can make. We can choose how to represent reality, we can even choose what we believe reality to be, but we cannot actually choose what reality itself is.

Perhaps you mean we can determine what is "really happening". If so, well, you picked the wrong word. And the difference matters. Furthermore, how are we to determine what is "really happening" when all these different possibilities are identical? There is no one "really happening". There cannot be one "really happening". And that is true for the very simple reason that there is no difference between the different reference frames.

Based on what all I have heard and read, GR will not do this -- all coordinate systems tell us what is "really happening" according to GR. Do we stop thinking at this point?

No. We do one of three things.

1) We try to find out if GR is wrong, which we do by experimental tests. This is ongoing.
2) We look for alternative models which can describe observations equally well. Theorists have been doing this for decades, and so far we have nothing as good as GR.
3) We stop doing science and start doing philosophy.

You are, at best, engaged in option 3, but don't understand that you've stopped doing science.

There is every reason to believe that the universe is a real place with an ultimate reality that we will probably never fully comprehend. As a real object, the universe has a real time and a real place.

A real time and a real place? How do you know? Why must time and place be absolute in order to be real? Why is GR's picture any less real? Again, the only answers you will be able to provide would be philosophical, but at that point you've stopped doing science. We have another forum for philosophy.

[theprestige]

My contention is that even though the above comment is true (as far as I know -- I am a layman), it does not tell the whole story. We can still decide what is "really happening." Based on all I have heard and read, GR will not do this -- all coordinate systems tell us what is "really happening" according to GR. Do we stop thinking at this point? Do we just say, oh well, GR is king; there is no such thing as what is "really happening"? I don't accept that! We know the history and we know the causation of the spinning top. I did it! It is really spinning! GR is only a mathematical model; it is not real. It is limited.
Earlier you claimed that a heliocentric coordinate system is the best one for describing the solar system, because we know from causality that what is "really happening" in the solar system is that the planets are orbiting the sun.

But this is a false claim--or rather, it is only relatively true: What is "really happening" in the solar system depends on your point of view. From the point of view of the galactic center, for example, your bedtime story about heliocentric causality is totally wrong. From the point of view of the galactic center, the Earth isn't orbiting the sun at all. It's orbiting the galactic center, and its orbit is variously perturbed by its nearer neighbors.

From the point of view of the galactic center, your "causality" dictates that the solar system didn't form around the sun at all, but around the galactic center. There is probably no physically true property of your causally-heliocentric coordinate system, that is not equally true, equally valid, and equally preferable in a causally-galactocentric coordinate system.

You might prefer the heliocentric coordinates for philosophical reasons, or reasons of taste, or reasons of convenience. But there's no physical reason or scientific reason to prefer them (and 99% of the time you don't even prefer the heliocentric coordinates, since they're wildly inconvenient and counter-intuitive for daily life on the surface of the third rock from the sun).

[Michael C]

The CMB tells us something about that real time and place. The theory of general relativity allows us to examine it from any frame of reference we choose for our own convenience; the physics will be the same regardless. But we have that CMB giving us information regarding which of these frames is the real thing.

So once more: if you describe the motion of your grandchild's top using a frame based on the CMB, does it tell us what is "really happening"? When we use this frame, does it give a better description of the reality of the top's motion than when we use a frame where the floor of the room is at rest?

[ynot]

How do you know that the top wasn't rotating the other way before you spun it, and your actions didn't simply stop it?

Or maybe it was already rotating in the direction in which you spun it, and now you've sped it up even more? Or something else?

No one is saying that you changed the rest of the universe by spinning the top, PS. They are saying that you can describe the universe in a frame in which the top was already rotating the other way (and is now at rest), and for everything that you can measure, it will be exactly the same as if you'd described it in a frame in which it was originally at rest and is now rotating.

So what's real? Perhaps none of the frames themselves are the reality, but rather the things that are true no matter what frame you choose: the relationships between things: the things that can actually be measured.

You obviously have no idea of the observable properties of whether a top is spinning or not (or perhaps you have temporarily forgotten).

[alexi_drago]

Probably another stupid question and not about a rotating frame, but I'm curious about this.
Say you have a spaceship travelling along and on one side of it there's a laser firing a beam across the width of the ship to a detector on the other side, does the point that the laser hits the detector vary as the ship speeds up or slows down?

[Perpetual Student]

Sure. If you want to ponder what reality is, we have philosophy too. But if you want to describe reality in a quantifiable manner, well, science is in fact the only thing we've got. And GR is our best large-scale theory for doing so.
The fact that GR is the best we have does not mean it is the only thing we have and, of course, some day we may have something better.

How can we decide what's happening? Unless you're a solipsist, then nothing we decide has any effect on what reality actually is. It's not a choice we can make. We can choose how to represent reality, we can even choose what we believe reality to be, but we cannot actually choose what reality itself is.
Rotating and revolving bodies have measurable forces associated with those motions. Conjuring up all the ficticious forces necessary to imagine such bodies are at rest is possible under GR, but should give us some clue about what is really happening.

Perhaps you mean we can determine what is "really happening". If so, well, you picked the wrong word. And the difference matters. Furthermore, how are we to determine what is "really happening" when all these different possibilities are identical? There is no one "really happening". There cannot be one "really happening". And that is true for the very simple reason that there is no difference between the different reference frames.
See my comment above.

No. We do one of three things.

1) We try to find out if GR is wrong, which we do by experimental tests. This is ongoing.
2) We look for alternative models which can describe observations equally well. Theorists have been doing this for decades, and so far we have nothing as good as GR.
3) We stop doing science and start doing philosophy.
You are, at best, engaged in option 3, but don't understand that you've stopped doing science.
4) We stay with science and we use our brains and any and all other available information to discover what model(s) best reflect reality.



A real time and a real place? How do you know? Why must time and place be absolute in order to be real? Why is GR's picture any less real? Again, the only answers you will be able to provide would be philosophical, but at that point you've stopped doing science. We have another forum for philosophy.

This post made by someone some time ago is interesting:
Sure, but that doesn't make everything equivalent. You can call a road race of Phobos equivalent to a road race on earth. But once you introduce cosmology, well, you really do have something unique and special. There may be an absurd number of possible road races in the universe, each with its simplest reference frame, but there's only one cosmos. And there's only one co-moving reference frame for that one cosmos. On a certain level, yes, it's not any more valid than any other reference frame. And Occam's razor is ultimately about convenience, not truth. But nonetheless, there still remains one reference frame which is unique for everyone, everywhere. I don't think you can construct any other reference frame which is similarly unique for everyone.

[Perpetual Student]

So once more: if you describe the motion of your grandchild's top using a frame based on the CMB, does it tell us what is "really happening"? When we use this frame, does it give a better description of the reality of the top's motion than when we use a frame where the floor of the room is at rest?

There are measurable forces associated with rotation. That's a big clue.

[Ziggurat]

4) We stay with science and we use our brains and any and all other available information to discover what model(s) best reflect reality.

What does that even mean?

The only answer science will provide in regards to how well a model reflects reality is how accurate its predictions are. ANYTHING beyond that is no longer science. This is what you refuse to come to terms with. You aren't doing science anymore.

[Ziggurat]

There are measurable forces associated with rotation. That's a big clue.

Correction: there are measurable forces associated with your choice of coordinates. But that is true for any and all coordinate choices. Rotation is not special in this regard.

ETA: we can even take it a step further with a concrete example. Let's say we take a big patch of empty, flat space-time. In the middle of it, we stick a really massive spherical shell. Around the shell, spacetime becomes curved, and "fictitious forces" appear. Inside the shell, though, spacetime remains flat. Very far away from the shell, spacetime also remains close to flat.

Now let's spin our spherical shell. What happens inside? Well, inside, if we use coordinates which are not rotating with respect to distant objects, then we actually get forces. And those forces look like the forces one introduces in Newtonian mechanics when one adopts a rotating reference frame. Except we're not rotating. But to remove these forces from our equations of motion, we would actually need to adopt a reference frame which rotated. But if we do that, then we re-introduce those fictitious forces for distant objects. So it turns out that it isn't even possible to remove all these fictitious forces from any reference frame.

[Perpetual Student]

Earlier you claimed that a heliocentric coordinate system is the best one for describing the solar system, because we know from causality that what is "really happening" in the solar system is that the planets are orbiting the sun.

But this is a false claim--or rather, it is only relatively true: What is "really happening" in the solar system depends on your point of view. From the point of view of the galactic center, for example, your bedtime story about heliocentric causality is totally wrong. From the point of view of the galactic center, the Earth isn't orbiting the sun at all. It's orbiting the galactic center, and its orbit is variously perturbed by its nearer neighbors.

From the point of view of the galactic center, your "causality" dictates that the solar system didn't form around the sun at all, but around the galactic center. There is probably no physically true property of your causally-heliocentric coordinate system, that is not equally true, equally valid, and equally preferable in a causally-galactocentric coordinate system.

You might prefer the heliocentric coordinates for philosophical reasons, or reasons of taste, or reasons of convenience. But there's no physical reason or scientific reason to prefer them (and 99% of the time you don't even prefer the heliocentric coordinates, since they're wildly inconvenient and counter-intuitive for daily life on the surface of the third rock from the sun).

I can look at the universe quite well at various levels. The biggest is the universal CMB with the great walls, super clusters and voids of galaxies all moving about in random elliptical motions about local centers of gravity. Within that, then I can visualize our local cluster with galaxies doing a similar dance on a smaller scale. Within that I can visualize our galaxy, a great pinwheel with our sun out on one of the arms rotating about the central black hole every 200 million years or so, while the planets revolve around the sun in their various orbits, with moons revolving around them. It is one magnificent dance of countless huge structures, clusters, galaxies, stars, planets, moons, comets and asteroids. I can imagine quite well a single frame that takes it all in -- the one with the CMB stationary -- as a naturally occurring preferred frame of reference.

Having said all that, the earth has a bulge at the equator telling us it is rotating.

[Perpetual Student]

Correction: there are measurable forces associated with your choice of coordinates. But that is true for any and all coordinate choices. Rotation is not special in this regard.

ETA: we can even take it a step further with a concrete example. Let's say we take a big patch of empty, flat space-time. In the middle of it, we stick a really massive spherical shell. Around the shell, spacetime becomes curved, and "fictitious forces" appear. Inside the shell, though, spacetime remains flat. Very far away from the shell, spacetime also remains close to flat.

Now let's spin our spherical shell. What happens inside? Well, inside, if we use coordinates which are not rotating with respect to distant objects, then we actually get forces. And those forces look like the forces one introduces in Newtonian mechanics when one adopts a rotating reference frame. Except we're not rotating. But to remove these forces from our equations of motion, we would actually need to adopt a reference frame which rotated. But if we do that, then we re-introduce those fictitious forces for distant objects. So it turns out that it isn't even possible to remove all these fictitious forces from any reference frame.

As I mentioned above, the earth has a central bulge revealing its rotation. Saturn, which rotates much faster has an even more marked central bulge, which I believe is a ratio of about 11 to 10 when compared to the distance from pole to pole.

[theprestige]

Having said all that, the earth has a bulge at the equator telling us it is rotating.

Does GR have a problem predicting or explaining that bulge, in any reference frame?

[Reality Check]

I can look at the universe quite well at various levels.
...
I can imagine quite well a single frame that takes it all in -- the one with the CMB stationary -- as a naturally occurring preferred frame of reference.

The problem is that all of the other reference frames that you mentioned are also "naturally occurring preferred frame of references"!
Your preference for that frame is personal and subjective.
In GR there is no preferred frame of reference. All frames of reference are equivalent.

I personally prefer the naturally occurring preferred frame of reference where I am the center of the universe and everything rotates around me (:)). That does not make this a useful or convenient frame of reference.

[Ziggurat]

As I mentioned above, the earth has a central bulge revealing its rotation. Saturn, which rotates much faster has an even more marked central bulge, which I believe is a ratio of about 11 to 10 when compared to the distance from pole to pole.

That doesn't address a single thing I said.

[Perpetual Student]

Does GR have a problem predicting or explaining that bulge, in any reference frame?

I hope not. Does GR tells us that the bulge is there because the earth is clearly and unambiguously rotating on its axis as opposed to the universe revolving around the earth?

[Perpetual Student]

In GR there is no preferred frame of reference. All frames of reference are equivalent.


Yes, in GR.

[Perpetual Student]

That doesn't address a single thing I said.

I believe it addresses everything you said.

[theprestige]

I hope not. Does GR tells us that the bulge is there because the earth is clearly and unambiguously rotating on its axis as opposed to the universe revolving around the earth?

As I understand it, GR tells us that the real thing that the earth is really doing happens--in reality--independently of what coordinates we use to keep track of when and where it does it.

And as I understand it, when we compare GR with other explanations that do depend on a specific coordinate system to explain what's really going on, we find that such systems without exception fall short of the success we enjoy when we explain things with GR.

[Reality Check]

Yes, in GR.
And also in general physics there is no "naturally occurring preferred frame of reference".
There are frames of reference that make calculations easier or harder. There are not "naturally occurring". They are just the ones a person would prefer to make their calculations easier. A different person with a different set of skills might prefer a different frame.

[Perpetual Student]

And also in general physics there is no "naturally occurring preferred frame of reference".
There are frames of reference that make calculations easier or harder. There are not "naturally occurring". They are just the ones a person would prefer to make their calculations easier. A different person with a different set of skills might prefer a different frame.

Is the earth really rotating or not?

[Ziggurat]

I believe it addresses everything you said.

You are wrong about that. What's more, the only way you could think it did is if you badly misunderstood what I said. But you've done so in a way that I can't even figure out how to address whatever your misconceptions are. I''ve run out of ways to try to explain this. What I've said has not sunk it, and I don't know what else will. So I think I'll call it quits, I don't see any more purpose here.

[Perpetual Student]

As I understand it, GR tells us that the real thing that the earth is really doing happens--in reality--independently of what coordinates we use to keep track of when and where it does it.

...



I don't think you will get agreement on that from the GR crowd here.
So, is the earth really rotating? Can GR tell us that?

[Michael C]

There are measurable forces associated with rotation. That's a big clue.

That's no answer to my question. I asked you this:

if you describe the motion of your grandchild's top using a frame based on the CMB, does it tell us what is "really happening"? When we use this frame, does it give a better description of the reality of the top's motion than when we use a frame where the floor of the room is at rest?

[W.D.Clinger]

As I understand it, GR tells us that the real thing that the earth is really doing happens--in reality--independently of what coordinates we use to keep track of when and where it does it.

...



I don't think you will get agreement on that from the GR crowd here.
:confused:

Why not? Why do you think theprestige's remarks should be controversial?


So, is the earth really rotating? Can GR tell us that?


If Perpetual Student can figure out what he means by "really rotating", then GR will probably be able to tell us whether the earth is really rotating. Einstein suggested that such definitions should be covariant, which means a satisfactory definition of "really rotating" should be independent of coordinates, as theprestige wrote.

Einstein's development of GR was inspired in part by what Einstein called Mach's principle. Ziggurat mentioned a highly relevant thought experiment related to GR's Lense-Thirring effect (http://en.wikipedia.org/wiki/Frame-dragging), which has been observed in experiments, but Perpetual Student ignored that (along with most everything else Ziggurat had to say).

[Farsight]

Say you have a spaceship travelling along and on one side of it there's a laser firing a beam across the width of the ship to a detector on the other side, does the point that the laser hits the detector vary as the ship speeds up or slows down?Yes and no. Yes, in that if the ship is accelerating, the light beam appears to curve downwards. That's the principle of equivalence. But if the ship isn't acclerating, you can't tell how fast it's going by looking at the laser beam. That's the principle of invariance, which was Einstein's original name for relativity. Your horizontals go a bit awry.

[Perpetual Student]

:confused:

Why not? Why do you think theprestige's remarks should be controversial?
My question is very simple. Is the earth really rotating or is the universe revolving around the earth? Does GR shed any light on that Question?

If Perpetual Student can figure out what he means by "really rotating", then GR will probably be able to tell us whether the earth is really rotating. Einstein suggested that such definitions should be covariant, which means a satisfactory definition of "really rotating" should be independent of coordinates, as theprestige wrote.
We know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Is it really that difficult for you to understand?

Einstein's development of GR was inspired in part by what Einstein called Mach's principle. Ziggurat mentioned a highly relevant thought experiment related to GR's Lense-Thirring effect (http://en.wikipedia.org/wiki/Frame-dragging), which has been observed in experiments, but Perpetual Student ignored that (along with most everything else Ziggurat had to say).
I am well aware of the history of Newton's bucket, Mach's thoughts and Einstein's inspiration and I don't think we need Ziggurat's Gedankenexperiment about frame dragging, when no one seems to be able to answer the question whether the earth is really rotating or is the universe revolving around the earth. Is it really that painful for you and Ziggurat to have me pass on his Gedankenexperiment? Well, tell me if the earth is really rotating and then perhaps I will relieve your pain.

[Perpetual Student]

That's no answer to my question. I asked you this:

if you describe the motion of your grandchild's top using a frame based on the CMB, does it tell us what is "really happening"? When we use this frame, does it give a better description of the reality of the top's motion than when we use a frame where the floor of the room is at rest?
All frames should describe the motion of the top equally well, based on my layman's understanding of GR. But, apparently, there is no information forthcoming from GR about what is "really happening."
Does that answer your question?

[sol invictus]

We know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Is it really that difficult for you to understand?


Is it really so difficult for you to understand that GR's predictions for all experiments are absolutely identical in all coordinate systems?

Forces that cause stresses inside an object can be measured, and the results of those measurements will be identical regardless of whether one uses coordinates in which the object is rotating or coordinates in which it isn't.

[Perpetual Student]

Is it really so difficult for you to understand that GR's predictions for all experiments are absolutely identical in all coordinate systems?

Forces that cause stresses inside an object can be measured, and the results of those measurements will be identical regardless of whether one uses coordinates in which the object is rotating or coordinates in which it isn't.

I have no basis to believe otherwise. What is your issue?
Do you agree that the earth is really rotating even though, under GR, we have a frame where it is not rotating?

[sol invictus]

I have no basis to believe otherwise. What is your issue?

You keep referring to bulges at the earth's equator and the stresses that rotating objects feel as though they had some relevance. They don't.

Do you agree that the earth is really rotating even though, under GR, we have a frame where it is not rotating?

I don't think the statement "the earth is really rotating" means anything until you define it more carefully.

[Michael C]

All frames should describe the motion of the top equally well, based on my layman's understanding of GR. But, apparently, there is no information forthcoming from GR about what is "really happening."
Does that answer your question?

Well, my question was asking you which frame you consider to best describe what is "really happening". I know that all frames are equally valid in GR, but you have been saying that there must be a "preferred" one that somehow describes reality better than the others. You have also said that:

I can imagine quite well a single frame that takes it all in -- the one with the CMB stationary -- as a naturally occurring preferred frame of reference.

Do you consider that a frame where the CMB is stationary is a naturally occurring preferred frame of reference for describing the motion of the top?

[W.D.Clinger]

My question is very simple. Is the earth really rotating or is the universe revolving around the earth? Does GR shed any light on that Question?
Yes. You've been objecting to the light.


We know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Is it really that difficult for you to understand?
Why do you speak of forces causing parts to fly off? Why don't you speak instead of the parts' inertia and of geodesics?


I am well aware of the history of Newton's bucket, Mach's thoughts and Einstein's inspiration and I don't think we need Ziggurat's Gedankenexperiment about frame dragging, when no one seems to be able to answer the question whether the earth is really rotating or is the universe revolving around the earth.
Why do you dismiss frame dragging as irrelevant?

You've been unwilling to consider what GR has to say about rotation. Now you're arguing that centrifugal forces have some kind of privileged reality.

In a certain coordinate system that's nearly at rest with respect to the cosmic microwave background, those centrifugal forces don't even exist. How do you reconcile that fact with your talk above of forces that cause parts to fly off?

[Perpetual Student]

You keep referring to bulges at the earth's equator and the stresses that rotating objects feel as though they had some relevance. They don't.

I don't think the statement "the earth is really rotating" means anything until you define it more carefully.

As I said above, we know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Even if it were the only thing in the universe, the parts would fly off telling us it is rotating. In contrast, if an object is not put into rotation (in a friction free situation), but an enclosure around it is set in rotation, those forces would not be felt by the object and parts will not fly off. Is it really that difficult to understand?

[Perpetual Student]

Well, my question was asking you which frame you consider to best describe what is "really happening". I know that all frames are equally valid in GR, but you have been saying that there must be a "preferred" one that somehow describes reality better than the others.
It is my understanding that under GR, all frames will do the job, but some may be more convenient than others. None tell us what is really happening.
Do you consider that a frame where the CMB is stationary is a naturally occurring preferred frame of reference for describing the motion of the top?

The CMB appears to be the best frame for understanding the real nature of the universe -- until a better one is revealed. The total motion of the top, moving along in some complex path with respect to the CMB tells the whole story. It will take into account its spinning on the table as well as all the other motions associated with the earth, solar system, galaxy, etc. The top is really spinning in all frames but the ones where we choose to look at it as stationary, which, I contend, may be convenient for some purpose, but is not a true representation of reality.

[edd]

The top is really spinning in all frames but the ones where we choose to look at it as stationary, which, I contend, may be convenient for some purpose, but is not a true representation of reality.

I'm not sure I understand your argument. How can it not be a true representation of reality when it represents the same reality with exactly the same observable results as the representation you think is true?

[Perpetual Student]

I'm not sure I understand your argument. How can it not be a true representation of reality when it represents the same reality with exactly the same observable results as the representation you think is true?
Isn't it obvious? Because the top is really rotating. We could detect that rotation with instruments on the top. Any frame where the top is stationary does not reveal that rotation. It may be a better frame for studying the molecular structure of the top, but it is quite poor for determining what is moving: the top or the universe?

[edd]

Isn't it obvious? Because the top is really rotating. We could detect that rotation with instruments on the top. Any frame where the top is stationary does not reveal that rotation.

But they do - the physics of the other frames make the same predictions for what the instruments on the top read.

[Perpetual Student]

But they do - the physics of the other frames make the same predictions for what the instruments on the top read.

Then you agree that we can say that the top is really rotating and we can say that the universe is not revolving around the top. We can say that is really what is happening! That is what I have been contending all along. Others have been saying that there is no distinction under GR between the top rotating and the universe revolving -- both perspectives are equally valid, even though we would need convoluted fictitious forces to have the universe revolving.

[edd]

Then you agree that we can say that the top is really rotating and we can say that the universe is not revolving around the top. We can say that is really what is happening! That is simply what I have been contending all along. Others have been saying that there is no distinction under GR between the top rotation and the universe revolving -- both perspectives are equally valid.

Maybe I should rephrase my earlier post. I'd have to give a bit more thought to how to better say it, but it's more likely one of the others here will clarify again.

[sol invictus]

As I said above, we know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Even if it were the only thing in the universe, the parts would fly off telling us it is rotating.

So if an object is surrounded by some masses that tend to cause it to stretch or fly apart, would you say it is therefore rotating?


In contrast, if an object is not put into rotation (in a friction free situation), but an enclosure around it is set in rotation, those forces would not be felt by the object and parts will not fly off. Is it really that difficult to understand?

It is hard to understand, mainly because it's false.

[Perpetual Student]

Yes. You've been objecting to the light.


Why do you speak of forces causing parts to fly off? Why don't you speak instead of the parts' inertia and of geodesics?


Why do you dismiss frame dragging as irrelevant?

You've been unwilling to consider what GR has to say about rotation. Now you're arguing that centrifugal forces have some kind of privileged reality.

In a certain coordinate system that's nearly at rest with respect to the cosmic microwave background, those centrifugal forces don't even exist. How do you reconcile that fact with your talk above of forces that cause parts to fly off?

I do not understand your point. Why can't we go with the simple question about the earth's rotation, which is evidenced by its equatorial bulge or a spinning top where instruments can reveal the forces associated with its rotation? These phenomena reveal true unambiguous rotation. If the universe consisted of only one single object, rotation could be detected by these forces. That is the point of Newton's "rotating spheres."