General Relativity

[Thabiguy]

Originally Posted by Perpetual Student

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]

Originally Posted by Hellbound

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...37fd6cb097.jpg

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]

Originally Posted by Perpetual Student

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]

Originally Posted by Perpetual Student

Can I conclude that the rocks are really rotating because the meter and string shows it or not?

Originally Posted by Tim Thompson

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]

Originally Posted by Tim Thompson

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.

Quote:

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).

Quote:

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]

Quote:

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]

Originally Posted by UncaYimmy

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]

Originally Posted by Perpetual Student

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.

Quote:

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.

Quote:

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]

Originally Posted by UncaYimmy

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.

Originally Posted by Perpetual Student

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]

Originally Posted by sol invictus

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.

Quote:

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?

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.

Quote:

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.

Quote:

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]

Originally Posted by Perpetual Student

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]

Originally Posted by schrodingasdawg

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]

Originally Posted by ynot

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]

Originally Posted by ynot

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

[Perpetual Student]

Originally Posted by 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)?

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.

Quote:

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.

Quote:

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

Based on my latter comment, I would guess there is no way to make such a determination.

[schrodingasdawg]

Originally Posted by DeiRenDopa

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.

Originally Posted by DeiRenDopa

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...rved_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]

Originally Posted by Perpetual Student

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]

Originally Posted by 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.

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]

Originally Posted by Perpetual Student

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]

Originally Posted by sol invictus

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]

Originally Posted by Vorpal

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

Why?

[Roboramma]

Originally Posted by Perpetual Student

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]

Originally Posted by Perpetual Student

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]

Originally Posted by Perpetual Student

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.

Originally Posted by Perpetual Student

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 and mathematics of black hole denialism 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 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]

Originally Posted by Perpetual Student

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"?

Originally Posted by Perpetual Student

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.

Originally Posted by 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?

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]

Quote:

... 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]

Originally Posted by Perpetual Student

That is, perhaps, the most persuasive point of all.

But you remain unpersuaded, right?

Quote:

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.

Quote:

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?

Quote:

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.

Quote:

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]

Originally Posted by Perpetual Student

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]

Originally Posted by Perpetual Student

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]

Originally Posted by drgsrinivas

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]

Originally Posted by drgsrinivas

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.

Edited by kmortis:

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]

Originally Posted by Perpetual Student

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.