Terra revolving round Sol question

[ben m]

Ynot, let's step back to the beginning. Can I walk you through something?

a) We're on ordinary Earth---no weird shells or GR or anything. You're sitting on a top, spinning at 1000 rpm. You feel a crazy centrifugal force. You're obviously spinning. No laws of physics broken there.

b) Imagine a line stretching straight out in front of you. A completely imaginary straight line, which (because you're spinning) is now whipping through space at 1000 rpm. It's just a figment of geometry---nothing wrong with that. But of course the end of the line is imagined to be zipping past the Sun, etc., at speeds much greater than c. Nothing wrong with that, there's no law of physics stopping an imaginary line from moving however you want it to.

c) Look at the Sun. Look at your line. Can you state the distance between them? Call this distance X---the distance between the Sun and your line-whipping-through-space. You can do this repeatedly, write down a bunch of X'es in your notebook at various times. Nothing wrong with that. The imaginary line is somewhere, the Sun is somewhere, of course you can just write down the distance.

d) Now that you have this notebook full of X-values, you might consider making predictions. If you watch the Sun's past X values, and draw some reasonable inferences, can you predict what X will be one second from now? Of course you can. The Sun is behaving regularly, so the distance X isn't leaping unexpectedly between values.

e) Does it bother you that this quantity X changes very fast? That dX/dt is (thought of as a velocity) much faster than light? It shouldn't. Of course the distance to an imaginary line that's moving faster than light can move faster than light.

f) Does it bother you that there are other tops nearby, other than the one you're riding on and that your imaginary-line emanates from? Of course not. The other tops don't stop you from drawing your imaginary line; your imaginary line doesn't stop the Earth from having other tops on it.

Well, you know what just happened? You just described a physical phenomenon in a rotating coordinate system. Your weird distance-measurement "X" is a coordinate measured on a rotating axis. Your ability to predict future values of X---that is a law-of-physics expressed in the rotating system. That's what "laws of physics" are.

OK? That's what we mean by it's OK to write ALL of the laws of physics in rotating coordinates. Coordinates are just distances-to-imaginary-axes. It's fine if those axes are rotating. There's no way to mess up the Universe by an imaginary-line-drawing exercise like the one above.

Sorry, Ynot, that's the last explanation I have in me. If you don't get that, or at least part of it, then I doubt anything else I write will help.

The subtle thing (and the thing you'll be forgiven for not getting) is when you add GR. As it turns out, gravitomagnetism in GR will take ordinary, non-spinning observers and make them feel like they're spinning. The "feel like" is accurate in every possible detail, from "my centrifugoscope arms are up" to "my X-axis seems to have whipped past the Sun at high speed" and so on. For GR-related reasons, physicists like to take this obscure "observer thinks he's moving" effect, and lump it in with more-familiar "observer thinks he's moving" effects caused by other aspects of gravity. And the right way to describe that is to say that all frames are equally valid. It's a good thing to say; the mathematics, physics, experiments, and thought-experiments behind it are sound. It is a somewhat complicated statement, since most people aren't used to the idea of "coordinates" as used in physics.

[Perpetual Student]

Originally Posted by ben m

Ynot, let's step back to the beginning. Can I walk you through something?

a) We're on ordinary Earth---no weird shells or GR or anything. You're sitting on a top, spinning at 1000 rpm. You feel a crazy centrifugal force. You're obviously spinning. No laws of physics broken there.

b) Imagine a line stretching straight out in front of you. A completely imaginary straight line, which (because you're spinning) is now whipping through space at 1000 rpm. It's just a figment of geometry---nothing wrong with that. But of course the end of the line is imagined to be zipping past the Sun, etc., at speeds much greater than c. Nothing wrong with that, there's no law of physics stopping an imaginary line from moving however you want it to.

c) Look at the Sun. Look at your line. Can you state the distance between them? Call this distance X---the distance between the Sun and your line-whipping-through-space. You can do this repeatedly, write down a bunch of X'es in your notebook at various times. Nothing wrong with that. The imaginary line is somewhere, the Sun is somewhere, of course you can just write down the distance.

d) Now that you have this notebook full of X-values, you might consider making predictions. If you watch the Sun's past X values, and draw some reasonable inferences, can you predict what X will be one second from now? Of course you can. The Sun is behaving regularly, so the distance X isn't leaping unexpectedly between values.

e) Does it bother you that this quantity X changes very fast? That dX/dt is (thought of as a velocity) much faster than light? It shouldn't. Of course the distance to an imaginary line that's moving faster than light can move faster than light.

f) Does it bother you that there are other tops nearby, other than the one you're riding on and that your imaginary-line emanates from? Of course not. The other tops don't stop you from drawing your imaginary line; your imaginary line doesn't stop the Earth from having other tops on it.

Well, you know what just happened? You just described a physical phenomenon in a rotating coordinate system. Your weird distance-measurement "X" is a coordinate measured on a rotating axis. Your ability to predict future values of X---that is a law-of-physics expressed in the rotating system. That's what "laws of physics" are.

OK? That's what we mean by it's OK to write ALL of the laws of physics in rotating coordinates. Coordinates are just distances-to-imaginary-axes. It's fine if those axes are rotating. There's no way to mess up the Universe by an imaginary-line-drawing exercise like the one above.

I can't speak for others, but the above is quite clear.

Quote:

The subtle thing (and the thing you'll be forgiven for not getting) is when you add GR. As it turns out, gravitomagnetism in GR will take ordinary, non-spinning observers and make them feel like they're spinning. The "feel like" is accurate in every possible detail, from "my centrifugoscope arms are up" to "my X-axis seems to have whipped past the Sun at high speed" and so on. For GR-related reasons, physicists like to take this obscure "observer thinks he's moving" effect, and lump it in with more-familiar "observer thinks he's moving" effects caused by other aspects of gravity. And the right way to describe that is to say that all frames are equally valid. It's a good thing to say; the mathematics, physics, experiments, and thought-experiments behind it are sound. It is a somewhat complicated statement, since most people aren't used to the idea of "coordinates" as used in physics.

Unless I am misreading the material I have looked at, the effects of gravitomagnetism you describe above have not been experimentally confirmed.

[ben m]

Originally Posted by Perpetual Student

Unless I am misreading the material I have looked at, the effects of gravitomagnetism you describe above have not been experimentally confirmed.

Gravity Probe B was basically a free-falling gyroscope. A free-falling gyroscope in flat space should point its axis to a fixed location on the sky (taking the celestial sphere to be an inertial reference system). Nonetheless, GPB's gyroscope axis was seen to rotate across the sky as though it were in a rotating system.

[ynot]

Thanks I do appreciate your time and effort. I think some of the problem is the different way our minds work and communicate. You guys seem to think abstract mathmatically and I think more practical mechanically. Before I can even start trying to understand what you've said I need to clarify a few points. I will comment within your post on colour.

Originally Posted by ben m

Ynot, let's step back to the beginning. Can I walk you through something?
Yes

a) We're on ordinary Earth---no weird shells or GR or anything. You're sitting on a top, spinning at 1000 rpm. You feel a crazy centrifugal force. You're obviously spinning. No laws of physics broken there.
Okay

b) Imagine a line stretching straight out in front of you. A completely imaginary straight line, which (because you're spinning) is now whipping through space at 1000 rpm. It's just a figment of geometry---nothing wrong with that. But of course the end of the line is imagined to be zipping past the Sun, etc., at speeds much greater than c. Nothing wrong with that, there's no law of physics stopping an imaginary line from moving however you want it to.
Okay

c) Look at the Sun. Look at your line. Can you state the distance between them? Call this distance X---the distance between the Sun and your line-whipping-through-space. You can do this repeatedly, write down a bunch of X'es in your notebook at various times. Nothing wrong with that. The imaginary line is somewhere, the Sun is somewhere, of course you can just write down the distance.

Problem! The line is continually travelling past the Sun and the distance between them is constantly changing. Do you mean the the distance from the end of the line to the sun when the line is closest to the Sun (as if it wasn't spinning and pointing directly at the sun)? Don't know why I need to write down a bunch of X'es. I'm assuming the Top and Sun are always the same distance apart and X is always the same. Can't go any further until these questions are answered.

I'm going move on and assume you mean to measure the distance between the end of the Line and the Sun many times at many points as it moves toward and away from the Sun as the line spins. Don't know why you would define all these different distances with a common symbol X though. I would have thought X, X1, X2, etc.

d) Now that you have this notebook full of X-values, you might consider making predictions. If you watch the Sun's past X values, and draw some reasonable inferences, can you predict what X will be one second from now? Of course you can. The Sun is behaving regularly, so the distance X isn't leaping unexpectedly between values.
Problem! What do you mean by “the Sun's past X values”? I thought X related to both the Sun and Line to represent the distance or distances between them. The Sun isn't behaving at all, it's just sitting there.

e) Does it bother you that this quantity X changes very fast? That dX/dt is (thought of as a velocity) much faster than light? It shouldn't. Of course the distance to an imaginary line that's moving faster than light can move faster than light.

f) Does it bother you that there are other tops nearby, other than the one you're riding on and that your imaginary-line emanates from? Of course not. The other tops don't stop you from drawing your imaginary line; your imaginary line doesn't stop the Earth from having other tops on it.

Well, you know what just happened? You just described a physical phenomenon in a rotating coordinate system. Your weird distance-measurement "X" is a coordinate measured on a rotating axis. Your ability to predict future values of X---that is a law-of-physics expressed in the rotating system. That's what "laws of physics" are.

OK? That's what we mean by it's OK to write ALL of the laws of physics in rotating coordinates. Coordinates are just distances-to-imaginary-axes. It's fine if those axes are rotating. There's no way to mess up the Universe by an imaginary-line-drawing exercise like the one above.

Sorry, Ynot, that's the last explanation I have in me. If you don't get that, or at least part of it, then I doubt anything else I write will help.

The subtle thing (and the thing you'll be forgiven for not getting) is when you add GR. As it turns out, gravitomagnetism in GR will take ordinary, non-spinning observers and make them feel like they're spinning. The "feel like" is accurate in every possible detail, from "my centrifugoscope arms are up" to "my X-axis seems to have whipped past the Sun at high speed" and so on. For GR-related reasons, physicists like to take this obscure "observer thinks he's moving" effect, and lump it in with more-familiar "observer thinks he's moving" effects caused by other aspects of gravity. And the right way to describe that is to say that all frames are equally valid. It's a good thing to say; the mathematics, physics, experiments, and thought-experiments behind it are sound. It is a somewhat complicated statement, since most people aren't used to the idea of "coordinates" as used in physics.

[Farsight]

Originally Posted by Ben m

...OK? That's what we mean by it's OK to write ALL of the laws of physics in rotating coordinates. Coordinates are just distances-to-imaginary-axes. It's fine if those axes are rotating. There's no way to mess up the Universe by an imaginary-line-drawing exercise like the one above...

You don't mess up the universe, you mess up your understanding. See this NASA article on gravity probe B. Note the mention of "vortex" and "twist". The gyroscope's motion is due to local effects. It's in twisted space, not rotating space, and it precesses because it's rotating.

[Kwalish Kid]

Originally Posted by Farsight

You don't mess up the universe, you mess up your understanding. See this NASA article on gravity probe B. Note the mention of "vortex" and "twist". The gyroscope's motion is due to local effects. It's in twisted space, not rotating space, and it precesses because it's rotating.

It would be better to actually look at the physics rather than ignore what was written and confuse things with a pop science article.

It's clear that Ben m is discussing a set of rotating coordinates. You cannot stop people from considering a set of rotating coordinates because you happened to find an article about a topic slightly related. That is the height of a non sequitor.

[jadey]

Originally Posted by ynot

So can I finally conclude that the “huge (thick) shell of matter” is actually the “extraterrestrial Universe“ (from the Earth's frame)?

If so why do you say “shells” rather than “shell”? I don‘t think you‘re talking about multi-verses. As I’ve asked before, does each frame create it’s own reality and the Universe spins on one axis for one frame and a different axis for another concurrently? When two tops are spinning in opposite directions is the Universe concurrently spinning in opposing directions? When a million things are spinning about a million axis is the Universe also spinning about a million axis concurrently?

Isn’t a frame essentially merely a position of observation?

I hate to stick my nose in where it doesn't belong, but I'm trying to understand all this as well. The following is how I'm understanding it ...

I think that you may be confusing matters by trying to comingle multiple concurrent frames of reference. I believe the experts have stated that you need to perform a physics translation (don't know the term) when switching between reference frames.

Consider a scenario where Top A and B are separated by 1 meter, with Top A spinning clockwise at 1000 RPM and Top B spinning counter-clockwise at 1000 RPM.

Reference Frame A - Top A stationary (non rotating): All objects in the universe (including top B) complete 1000 counter-clockwise revolutions around Top A every minute. Top B also appears to be rotating on its axis at 1000 RPM.

Reference Frame B - Top B stationary (non rotating): All objects in the universe (including top A) complete 1000 clockwise revolutions around Top B every minute. Top A also appears to be rotating on its axis at 1000 RPM.

Note that Reference Frame A includes (and acurately predicts the behavior of) Top B. Likewise, reference Frame B includes (and acurately predicts the behavior of) Top A. Frames A and B seem to predict conflicting motions, but do so in different languages. Once you translate them to a common language (reference frame), they won't contradict eachother. You can't just add/combine Frames A & B and state that the universe is now revolving two opposing directions concurrently, because there is no reference frame that made that prediction. There is no single frame of reference that is making conlicting/inconsistent predictions.

Don't know if that helps or not.

[H'ethetheth]

Originally Posted by sol invictus

From a NASA page on Gravity Probe B:

Originally Posted by NASA

...imagine that the earth were standing still and that the rest of the universe were rotating around it: would its equator still bulge? Newton would have said "No". According to standard textbook physics the equatorial bulge is due to the rotation of the earth with respect to absolute space...

Any questions, Farsight?

I have a question about this, though. If Newton were to answer this, wouldn't he have to posit some virtual forces to get the universe consistently rotating around the earth, which should, in effect, come down to describing it in a rotating frame of reference, and would thus cause the earth to bulge at the equator?

[sol invictus]

Originally Posted by H'ethetheth

I have a question about this, though. If Newton were to answer this, wouldn't he have to posit some virtual forces to get the universe consistently rotating around the earth, which should, in effect, come down to describing it in a rotating frame of reference, and would thus cause the earth to bulge at the equator?

No, not necessarily. For instance, there could be a very large point mass at the center of the earth. That would allow the rest of the universe to rotate around it (although not as a cylinder), but it wouldn't make the equator bulge. Or there could be a super-strong pole piercing the axis of the earth and continuing on both sides, to which the rest of the objects of the universe are attached by super-strong cables.

What's different in GR is that the distant rotating masses drag the space with them, effectively making it rotate. That just doesn't happen in Newtonian gravity. It's the equivalent of a magnetic effect, in the sense that it goes away if you send the speed of light to infinity - and Newton is the low-speed (and low-field) limit of GR.

[H'ethetheth]

Originally Posted by sol invictus

No, not necessarily. For instance, there could be a very large point mass at the center of the earth. That would allow the rest of the universe to rotate around it (although not as a cylinder), but it wouldn't make the equator bulge. Or there could be a super-strong pole piercing the axis of the earth and continuing on both sides, to which the rest of the objects of the universe are attached by super-strong cables.

What's different in GR is that the distant rotating masses drag the space with them, effectively making it rotate. That just doesn't happen in Newtonian gravity. It's the equivalent of a magnetic effect, in the sense that it goes away if you send the speed of light to infinity - and Newton is the low-speed (and low-field) limit of GR.

Okay, thanks. I think I understand that somewhat.

[ben m]

Originally Posted by ynot

I will comment within your post on colour.

Quote:

c) Look at the Sun. Look at your line. Can you state the distance between them? Call this distance X---the distance between the Sun and your line-whipping-through-space. You can do this repeatedly, write down a bunch of X'es in your notebook at various times. Nothing wrong with that. The imaginary line is somewhere, the Sun is somewhere, of course you can just write down the distance.

Problem! The line is continually travelling past the Sun and the distance between them is constantly changing. Do you mean the the distance from the end of the line to the sun when the line is closest to the Sun (as if it wasn't spinning and pointing directly at the sun)?

Take a freeze-frame snapshot. In this snapshot, the line is somewhere, the Sun is where it usually is. Measure the distance between them. (I was thinking of the perpendicular distance, but that's not important.) No, I emphatically do NOT mean "wait until the line is close to the sun, then measure something". Think about how you measure distances normally. If you want to measure "the distance between Mario Andretti and the finish line", you just ... take a snapshot, and measure the distance. If you want to measure "the distance between Dale Earnhart and Mario Andretti", same idea, even if they're both moving.

Quote:

Don't know why I need to write down a bunch of X'es.

Because you're in the middle of an exercise in understanding coordinate systems.

Quote:

I'm assuming the Top and Sun are always the same distance apart and X is always the same. Can't go any further until these questions are answered.

The top and the Sun are always the same distance apart. However, X is not the distance between the top and the Sun, X is the distance between a sweeping-imaginary-line and the Sun. At one moment the line is pointed right at the Sun, and going right through it, so X=0. At another moment, the line might be missing the Sun by 100,000,000 miles to the side, so X=100,000,000.

Quote:

Don't know why you would define all these different distances with a common symbol X though. I would have thought X, X1, X2, etc.

Think about how you'd write, say, "the position of an accelerating car". You usually write a formula like "x = 1/2 a t^2", in which x is the car's position, and it depends on time. Another way to say it is that you're writing down x(t).

Quote:

Quote:

d) Now that you have this notebook full of X-values, you might consider making predictions. If you watch the Sun's past X values, and draw some reasonable inferences, can you predict what X will be one second from now? Of course you can. The Sun is behaving regularly, so the distance X isn't leaping unexpectedly between values.

Problem! What do you mean by “the Sun's past X values”? I thought X related to both the Sun and Line to represent the distance or distances between them. The Sun isn't behaving at all, it's just sitting there.

[/quote]

When I say "the Sun's past X-values" I mean "the collection of X-values you've written down." (Note that, once you've defined this sweeping line, I presume you can measure its distance to anything you like. You can measure the distance X between the line and the Sun, or the distance X between the line and Mario Andretti, or the distance X between the line and your own nose. "The Sun's X-value" specifies the distance between the line and the Sun.) Yes, the value of X changes over time---you're right that these changes are mostly due to the line's motion, not the Sun's.

[ynot]

Originally Posted by ben m

Take a freeze-frame snapshot. In this snapshot, the line is somewhere, the Sun is where it usually is. Measure the distance between them. (I was thinking of the perpendicular distance, but that's not important.) No, I emphatically do NOT mean "wait until the line is close to the sun, then measure something". Think about how you measure distances normally. If you want to measure "the distance between Mario Andretti and the finish line", you just ... take a snapshot, and measure the distance. If you want to measure "the distance between Dale Earnhart and Mario Andretti", same idea, even if they're both moving.

Or you could have just said my assumption was correct.

Originally Posted by ben m

Because you're in the middle of an exercise in understanding coordinate systems.

I can’t understand the whole if I don’t understand the parts.

Originally Posted by ben m

The top and the Sun are always the same distance apart. However, X is not the distance between the top and the Sun, X is the distance between a sweeping-imaginary-line and the Sun. At one moment the line is pointed right at the Sun, and going right through it, so X=0. At another moment, the line might be missing the Sun by 100,000,000 miles to the side, so X=100,000,000.

We have to measure from a constant point on the sweeping line so lets say it has a length from the centre of the Top to the centre of the Sun and we always measure from the outer end if the Line to the centre of the Sun.

Originally Posted by ben m

Think about how you'd write, say, "the position of an accelerating car". You usually write a formula like "x = 1/2 a t^2", in which x is the car's position, and it depends on time. Another way to say it is that you're writing down x(t).
When I say "the Sun's past X-values" I mean "the collection of X-values you've written down." (Note that, once you've defined this sweeping line, I presume you can measure its distance to anything you like. You can measure the distance X between the line and the Sun, or the distance X between the line and Mario Andretti, or the distance X between the line and your own nose. "The Sun's X-value" specifies the distance between the line and the Sun.) Yes, the value of X changes over time---

Okay so let’s say I have taken 10 measurements from the end of the Line to the centre of the Sun from various “snapshot” positions and those measurements have unit values of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Now what?

Originally Posted by ben m

"The Sun's X-value" specifies the distance between the line and the Sun.)

Which is exactly the same as the distance between the Sun and the Line. I don't know why it needs to be called either the Sun's or Line's value. It's the distance value between the Line and Sun at a particular time during the sweep of the Line. We could call it the Sun/Line value.

Originally Posted by ben m

you're right that these changes are mostly due to the line's motion, not the Sun's.

The changes are due entirely to the Line’s motion. In this scenario the Sun doesn’t move at all. Perhaps we should just call it a Ball. The Ball and the Top don’t move relative to each other but the Top is spinning about it’s axis and the imaginary Line sweeps around from that axis with the spin of the Top. Okay?

[Farsight]

Originally Posted by H'ethetheth

I have a question about this, though. If Newton were to answer this, wouldn't he have to posit some virtual forces to get the universe consistently rotating around the earth, which should, in effect, come down to describing it in a rotating frame of reference, and would thus cause the earth to bulge at the equator?

I don't think so. I think he'd give the rotating universe short shrift. Newton said this in a letter to Dr Richard Bentley on 25 February 1692:

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it”.

He's saying that gravity is not some magical mysterious action-at-a-distance thing. He also said this in Opticks queries 20 and 21:

"Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?"

He's saying that light curves because the space it moves through is inhomogeneous. That's a very local phenomenon, even though the locally-inhomogeneous space is caused by a massive body like a star some distance away. I think he'd say the same about gravitomagnetism, and would be happy with the NASA article and the way the rotating gyroscope precesses because its local space is twisted.

[Kwalish Kid]

Originally Posted by Farsight

I don't think so. I think he'd give the rotating universe short shrift. Newton said this in a letter to Dr Richard Bentley on 25 February 1692:

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it”.

A great example of cherry-picking in ignorance of the actual science! Newton set aside these reservations because of the evidence he was able to produce for gravity being innate, inherent, and essential to matter without the need for a special medium. He went so far as to castigate those who would argue against scientific results on the basis of imagining things on the basis of such speculation (it's called the fourth rule of reasoning).

Quote:

He's saying that gravity is not some magical mysterious action-at-a-distance thing. He also said this in Opticks queries 20 and 21:

"Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?"

Another great example of cherry-picking: here are some purely speculative parts of the Optiks, looking at results disconnected from the work on gravity and not used in the reasoning of the Principia. Anyone who reads the actual books, rather than picking out those quotations that seem to support their own vision uninformed by the science, will see how foolish it is to stress these quotations in this context.

Quote:

He's saying that light curves because the space it moves through is inhomogeneous.

Even if he were, it has nothing whatsoever to do with his theory of universal gravity. It is one of the worst examples of argument from authority that one can do: attempting to use the authority of a figure to support a position that they specifically abandon and repudiate.

[Farsight]

Originally Posted by jadey

...Note that Reference Frame A includes (and acurately predicts the behavior of) Top B. Likewise, reference Frame B includes (and acurately predicts the behavior of) Top A. Frames A and B seem to predict conflicting motions, but do so in different languages. Once you translate them to a common language (reference frame), they won't contradict eachother. You can't just add/combine Frames A & B and state that the universe is now revolving two opposing directions concurrently, because there is no reference frame that made that prediction. There is no single frame of reference that is making conlicting/inconsistent predictions.
Don't know if that helps or not.

I think it helps a bit, jadey. But I think it helps more if you think of each spinning top as a planet, replace the universe with the sun, and forget about the year. On one planet scientist A says "in my reference frame the sun goes round my earth every day, and it's a perfectly valid reference frame". On the other planet scientist B says "in my reference frame the sun goes round my earth every day, and it's a perfectly valid reference frame". But then on each planet somebody invents the telecope and the radio, and they start talking. Then they see the bigger simpler picture of how things really are. They realise that their respective reference frames do not have any tangible existence. They realise that there is no reference frame as such, and that this thing they call a reference frame is just a cipher for how they see things due to their state of motion. Then they develop a frame-independent way of describing the world, and they call it general relativity.

[ben m]

Originally Posted by ynot

The changes are due entirely to the Line’s motion. In this scenario the Sun doesn’t move at all. Perhaps we should just call it a Ball. The Ball and the Top don’t move relative to each other but the Top is spinning about it’s axis and the imaginary Line sweeps around from that axis with the spin of the Top. Okay?

Yes, that's totally fine. Keep going!

[ynot]

Originally Posted by ben m

Yes, that's totally fine. Keep going!

But you're "walking" me. So what's the next step?

I think it needs to be a step from this - "Okay so let’s say I have taken 10 measurements from the end of the Line to the centre of the Sun from various “snapshot” positions and those measurements have unit values of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Now what?"

[ben m]

Originally Posted by ynot

But you're "walking" me. So what's the next step?

You should be in the middle of step d, and starting to think about step e.

ETA: responding to your edited post. If we're really talking about the Sun, a 0.15-Tm (tera-meter) long line, and a 1000 rpm top, the measurements would look something like this:

t = 0 seconds, x = 0 Tm
t = 0.001 s, x = 0.001 Tm
t = 0.002 s, x = 0.003 Tm
t = 0.003 s, x = 0.004 Tm
t = 0.004 s, x = 0.006 Tm
t = 0.005 s, x = 0.007 Tm


First, does it bother you that dx/dt---the *relative* velocity between your line and the Sun---is faster than 3x10^8 meters per second, the inertial-frame speed of light?

Second, do you think that a physicist could write down an equation for x(t), and dx/dt, etc., that could predict what x(0.006 s) will be?

Third, what's the difference between the equations written above, and a law of motion, written in a rotating coordinate system.

[ynot]

Originally Posted by ben m

You should be in the middle of step d, and starting to think about step e.

Okay . . .

Originally Posted by ben m

d) Now that you have this notebook full of X-values, you might consider making predictions. If you watch the Sun's past X values, and draw some reasonable inferences, can you predict what X will be one second from now? Of course you can. The Sun is behaving regularly, so the distance X isn't leaping unexpectedly between values.

I have recorded ten different distances between the Line and Ball and (as long as the speed of sweep of the line is constant) I can use those measurements to predict where the Line and Ball will be relative to each other and the distance between them at any particular time. I don't have an X value. Unless X means distance values then I have 10 distance values.

Originally Posted by ben m

e) Does it bother you that this quantity X changes very fast? That dX/dt is (thought of as a velocity) much faster than light? It shouldn't. Of course the distance to an imaginary line that's moving faster than light can move faster than light.

Not sure what thinking about my emotional state has to do with anything. But no I’m not bothered by any of this. Other than your use of "X".

Have we completed steps d) and e)?

ETA - I'm also "happy" with f)

[Farsight]

Originally Posted by sol invictus

What's different in GR is that the distant rotating masses drag the space with them, effectively making it rotate.

This isn't true. The earth doesn't drag space along with it as it moves through space. Yes, the earth's rotation causes frame-dragging, but the space is rotated a little rather than rotating. It's twisted, like the NASA article said. And it's got nothing to do with hypothetical distant masses. If the universe contained very few distant masses, we'd still be able to detect the frame-dragging caused by the earth's rotation.

Originally Posted by sol invictus

It's the equivalent of a magnetic effect...

This is true. That magnetic effect is the result of frame-dragging too. Take a look at a vector field, and remember the electron magnetic dipole moment and electron spin. The peculiar motion of an electron in a magnetic field isn't all that different to the gyroscope in the gravitomagnetic field.

[ben m]

Originally Posted by ynot

Okay . . .

I have recorded ten different distances between the Line and Ball and (as long as the speed of sweep of the line is constant) I can use those measurements to predict where the Line and Ball will be relative to each other and the distance between them at any particular time ...

But no I’m not bothered by any of this.

Have we completed steps d) and e)?

ETA - I'm also "happy" with f)

Good. Then, modulo your dislike of my notation, you're ready for the end of the post.

This exercise is precisely what it means to live in a rotating coordinate system. "Ordinary" familiar coordinates (Cartesian coordinates are the ones you plug into Newton's Laws of Motion) are nothing more or less than than measurements of distances between (a) objects and (b) imaginary-reference-lines, conventionally labeled x, y, and z.

In the exercise above, you stated that you can construct coordinates other than "distances to inertial x,y,z lines". In particular, you constructed weird coordinates with respect to a non-inertial, rotating line. And you claimed, at least, that it's possible to write down the laws of physics in a way that handles (explains, predicts, etc.) the values of weird coordinates.

That's it. That's what I wanted to say.

[ynot]

Originally Posted by ben m

Good. Then, modulo your dislike of my notation, you're ready for the end of the post.

This exercise is precisely what it means to live in a rotating coordinate system. "Ordinary" familiar coordinates (Cartesian coordinates are the ones you plug into Newton's Laws of Motion) are nothing more or less than than measurements of distances between (a) objects and (b) imaginary-reference-lines, conventionally labeled x, y, and z.

In the exercise above, you stated that you can construct coordinates other than "distances to inertial x,y,z lines". In particular, you constructed weird coordinates with respect to a non-inertial, rotating line. And you claimed, at least, that it's possible to write down the laws of physics in a way that handles (explains, predicts, etc.) the values of weird coordinates.

That's it. That's what I wanted to say.

I'm busy at the moment so will have to came back to it later.

I added this between posts - "I don't have an X value. Unless X means distance values then I have 10 distance values".

[Perpetual Student]

Originally Posted by ben m

Gravity Probe B was basically a free-falling gyroscope. A free-falling gyroscope in flat space should point its axis to a fixed location on the sky (taking the celestial sphere to be an inertial reference system). Nonetheless, GPB's gyroscope axis was seen to rotate across the sky as though it were in a rotating system.

Maybe I'm really misunderstanding something here. My apologies if I am!
So, I put a top in motion on my table so that it is spinning and consequently standing upright. To be clear, are you saying that we can alternatively regard this (the uprightness of my top) as a consequence of the gravitomagnetism of the "shell of matter" of the universe rotating around my top?

[Kwalish Kid]

Originally Posted by Farsight

This isn't true. The earth doesn't drag space along with it as it moves through space. Yes, the earth's rotation causes frame-dragging, but the space is rotated a little rather than rotating. It's twisted, like the NASA article said. And it's got nothing to do with hypothetical distant masses. If the universe contained very few distant masses, we'd still be able to detect the frame-dragging caused by the earth's rotation.

Please demonstrate the difference as it appears in the equations.

[ben m]

Originally Posted by ynot

I'm busy at the moment so will have to came back to it later.

I added this between posts - "I don't have an X value. Unless X means distance values then I have 10 distance values".

Yes, you have 10 distance values. I used the variable X to label these distance values. This is what physicists do, Ynot. Crack open an intro physics textbook and you'll find 1000 pages of "we define x to be the height ... we solve for y ... we take the derivative of dz(t)/dt to find the velocity v_z" and so on.

[ynot]

Originally Posted by Perpetual Student

Maybe I'm really misunderstanding something here. My apologies if I am!
So, I put a top in motion on my table so that it is spinning and consequently standing upright. To be clear, are you saying that we can alternatively regard this (the uprightness of my top) as a consequence of the gravitomagnetism of the "shell of matter" of the universe rotating around my top?

And apparently this happens for every top and every spinning thing on Earth and in the Entire Universe. The rotation of the Earth relative to the rest of the Universe doesn’t seem to interfere with this force. Or even when a gyroscope is spinning about it‘s axis as well as precessing on a different axis. Apparently the Universe acts as this shell for all spins on all axis concurrently, but force applied to a particular spinning thing doesn’t seem to effect any other. How can a force that’s strong enough to defeat gravity be focused so accurately on absolutely every single spinning thing concurrently?

[ben m]

Originally Posted by Perpetual Student

Maybe I'm really misunderstanding something here. My apologies if I am!
So, I put a top in motion on my table so that it is spinning and consequently standing upright. To be clear, are you saying that we can alternatively regard this (the uprightness of my top) as a consequence of the gravitomagnetism of the "shell of matter" of the universe rotating around my top?

To be honest, I'm getting tired of talking about it.

There are two separate issues.

(a) Are we allowed to label the coordinates of everything in the Universe in just such a way that your top's coordinates are constants, like an object sitting still, rather than rotating? Yes we are. If we do so, do the relabeled-laws-of-physics still predict that the top stays upright, gyroscope-style? Yes they do; the relabeled laws of physics include centripetal and Coriolis forces which indeed account for the stable angle between your top and the Earth.

(b) "Well," you say, "I don't wanna deal with centripetal and Coriolis forces. I want to just look at the distant stars, pick a coordinate system in which those stars are at rest, and declare myself finished with wacky coordinates, can't I do that?" No you can't. In the presence of gravitomagnetic effects, centripetal and Coriolis forces are still there in the coordinate system in which distant stars are at rest. In the presence of gravitomagnetic effects, to find a centripetal-force-free coordinate system, you have to pick one where the distant stars are rotating.

(c) Suppose you are locked in a room with your spinning top. You've waved your arms around and determined that the room is feeling no centripetal forces. But you can't look at the mass distribution around you. Can you predict, based on this information, whether the stars are sweeping past your window (as though you were rotating) or not (as though you were still)? No you can't---a nearby spinning mass, shell-like or otherwise, would make you make the wrong prediction.

(d) You're not in a windowless room. Look into space. Is there actually a huge shell of matter out there, spinning? No. (Well, there could be one beyond the observable horizon.) Therefore there is no gravitomagnetic source-current that would make you spin. So don't worry about it.

[ynot]

Originally Posted by ben m

Yes, you have 10 distance values. I used the variable X to label these distance values. This is what physicists do, Ynot. Crack open an intro physics textbook and you'll find 1000 pages of "we define x to be the height ... we solve for y ... we take the derivative of dz(t)/dt to find the velocity v_z" and so on.

Do you use X to somehow represent all the values at once or in a manner that any single value could be used and it doesn‘t matter which it is?

[ben m]

Originally Posted by ynot

Do you use X to somehow represent all the values at once or in a manner that any single value could be used and it doesn‘t matter which it is?

The standard notation is x(t). x is a function of time. For a more familiar example, when you're learning how to compute the path of a cannonball, you might write "x = v*t." The position x is found by multiplying v time the time t. If you measure x at t=0, you get x=0. If you measure x at t=3, you get x=3v. And so on.

[ynot]

Is the top spinning at 1000 rpm or is the Sun orbiting the non spinning top at 1000 rpm?

If the top was on Earth and Sun was travelling at the speed of light it would take more than 50 minutes for the Sun to orbit the top once. Along way from achieving 1 rpm let alone 1000 rpm. Obviously under “normal” conditions therefore when a top is spinning at 1000 rpm it isn’t a viable alternative option to claim that the Sun could be orbiting the top at 1000 rpm.

So what’s the “special” relativity effect that makes it possible. Put simply and without explanation is it time dilation?

[ben m]

Originally Posted by ynot

If the top was on Earth and Sun was travelling at the speed of light it would take more than 50 minutes for the Sun to orbit the top once. Along way from achieving 1 rpm let alone 1000 rpm. Obviously under “normal” conditions therefore when a top is spinning at 1000 rpm it isn’t a viable alternative option to claim that the Sun could be orbiting the top at 1000 rpm.

I will take a deep breath and say it again.

In a rotating coordinate system, the speed-of-light limit does not mean what you think it does.

Quote:

So what’s the “special” relativity effect that makes it possible. Put simply and without explanation is it time dilation?

No. The special effect is covariance.

[sol invictus]

Originally Posted by Farsight

This isn't true. The earth doesn't drag space along with it as it moves through space.

Yes it does, in a very similar way to how it drags space around with it when it rotates. If the earth is moving, it imparts a kick of momentum to anything it passes by. In the limit it's moving very close to c, it drags a thin shockwave of spacetime behind it, much like a wake, that kicks anything it passes through.

Quote:

If the universe contained very few distant masses, we'd still be able to detect the frame-dragging caused by the earth's rotation.

So?

[ynot]

Originally Posted by ben m

I will take a deep breath and say it again.

In a rotating coordinate system, the speed-of-light limit does not mean what you think it does.



No. The special effect is covariance.

Thanks

[H'ethetheth]

Originally Posted by Farsight

I don't think so. I think he'd give the rotating universe short shrift. Newton said this in a letter to Dr Richard Bentley on 25 February 1692:

... I think he'd say the same about gravitomagnetism, and would be happy with the NASA article and the way the rotating gyroscope precesses because its local space is twisted.

Well, he wouldn't, would he? He's been dead for quite a while.

Look, I wasn't literally talking about the person called Isaac Newton, necessarily; I just meant "using Newtonian mechanics". Sorry if that wasn't clear.

[Farsight]

You did say If Newton were to answer this. But OK, if you ask Newtonian mechanics instead, you quickly appreciate that it applies to the top. The inertia of the body is down to that body. Ditto for the moment of inertia, which used to be called "angular mass". It isn't down to some mystic distant shell of matter rotating at some mythical speed that somebody is trying to pass off as general relativity when it's nothing of the sort. In another thread Sol was trying to paint a picture of infalling space in a gravitational field, now he's trying to paint a picture of rotating space in a gravitomagnetic field, and general relativity just isn't like that. It's like the bowling ball and the "twisted dimple" on the NASA page. It's pushed down, but it isn't falling down. It's rotated, but it isn't rotating. Space emulates a rubbery solid rather than a flowing fluid.

[H'ethetheth]

Originally Posted by Farsight

You did say If Newton were to answer this. But OK, if you ask Newtonian mechanics instead, you quickly appreciate that it applies to the top. The inertia of the body is down to that body. Ditto for the moment of inertia, which used to be called "angular mass". It isn't down to some mystic distant shell of matter rotating at some mythical speed that somebody is trying to pass off as general relativity when it's nothing of the sort.

Er...
I don't understand how this addresses my question about using Newtonian mechanics to explain the bulging equator of a stationary earth in a rotating universe.

ETA: I said Newton in stead of Newtonian mechanics because the NASA article also seems to use his name in that way.

[anglolawyer]

Forgive me for barging in with a question probably of no relevance to the current state of this thread but, going back to the OP, if the universe contained only terra but no sol (or vice versa) would it be possible to assign a mass to terra? I mean could it have the mass either of a humongous gas giant like Jupiter or of a grain of sand but there would be no way to tell unless you stuck something else in the universe with it?

And supposing the answer is no, would terra acquire mass, or measurable mass, if you inserted a microscopic piece of dust into the same universe at some outlandish distance away (or at any distance but it's more graphic to imagine a large one)?

[Farsight]

Yes. The earth has a gravitational field, the magnitude of which depends on its "active gravitational mass" which is the same as its inertial mass. You can tell it's got a mass because you fall down.

[Farsight]

Originally Posted by H'ethetheth

Er... I don't understand how this addresses my question about using Newtonian mechanics to explain the bulging equator of a stationary earth in a rotating universe.

See what I said above. You don't use Newtonian mechanics for that, you use Newtonian mechanics to explain the bulging equator of a rotating earth. At the pole some rock is just sitting there with respect to the earth, at the equator another rock is doing 1070 miles an hour with respect to the first rock, and the velocity of a body remains constant unless the body is acted upon by an external force.

[H'ethetheth]

Originally Posted by Farsight

See what I said above. You don't use Newtonian mechanics for that, you use Newtonian mechanics to explain the bulging equator of a rotating earth. At the pole some rock is just sitting there with respect to the earth, at the equator another rock is doing 1070 miles an hour with respect to the first rock, and the velocity of a body remains constant unless the body is acted upon by an external force.

Sorry, but that still does not address anything about the question.

Let me explain:
NASA asked the question what Newton(-ian mechanics) would say about a stationary earth in a rotating universe, and assumed Newton(-ian mechanics) would say that such an earth would not bulge.
However, I don't think he/it would say that, because (barring something like sol invictus' super-strong cables solution) Newton(-ian mechanics) would have to posit some way for the universe to freely rotate around the earth that is itself consistent with Newtonian mechanics. This would result in some set of fictitious forces that would necessarily behave exactly like the fictitious forces that arise in a rotating reference frame. This would then necessarily subject the mass of the earth to internal stresses that would cause it to bulge.