General Relativity

[Perpetual Student]

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

 

[drkitten]

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

Did they really say this?

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

 

[Kwalish Kid]

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

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

 

[drkitten]

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

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

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

 

[sol invictus]

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

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

Did they really say this?

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

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

 

[sol invictus]

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

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

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

 

[Perpetual Student]

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

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

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

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

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

 

[drkitten]

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

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

 

[sol invictus]

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

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

No.

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

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

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

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

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

 

[Perpetual Student]

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

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

 

[Manopolus]

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

 

[sol invictus]

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

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

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

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

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

 

[Perpetual Student]

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

 

[Perpetual Student]

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

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

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

 

[Perpetual Student]

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

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

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

 

[Skwinty]

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

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

 

[Giggywig]

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

I believe what GR tells you is that the Universe does not have a preference. You are choosing the "correct viewpoint" based on YOUR viewpoint.

 

[sol invictus]

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

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

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

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

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

 

[sol invictus]

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

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

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

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

 

[Perpetual Student]

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

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