The Whole Universe - Frame Dragging

[IM Egdall]

Here's what I think I undertstand:

 

Newton's bucket: a bucket of water is made to spin. The water rises up at the edge of the bucket. Looking at it per general relativity (GR) from two frames of reference:

 

(1) Ground reference frame - Bucket spins and makes water form concave surfrace.

 

(2) Bucket reference frame - From bucket's point-of-view, it is stationary and rest of universe is spinning. But if bucket at rest, what makes the water surface concave?

 

General relativity says: the rotation of the rest of the universe causes the water to become concave in case 2. This is due to frame dragging.

 

Imagine a massive rotating object, a huge hollow sphere (a shell) with the water bucket at its center. Since the particles which make up the sphere are moving, and moving particles have momentum, which are a source of gravity per GR -- spacetime inside (and outside) the hollow sphere is dragged by this rotational motion. So the space inside the sphere starts spinning in the same direction. This in turn causes the water surface in the "stationary" bucket to form a concave shape.

 

And calculations show that for a shell mass/energy on par with that contained in the universe, the frame dragging produces the same concave water surface as when the universe is stationary and the bucket is rotating.

 

Here's what I don't understand:

 

If there were no other mass/energy in the universe, per GR the water would still become concave. But In the bucket reference frame, it is at rest. With no mass/energy in the rest of the universe, there would be no frame-dragging effect. Right? So what makes the water become concave? What am I missing?

Edited October 2, 2011 by IM Egdall

[md65536]

General relativity says: the rotation of the rest of the universe causes the water to become concave in case 2. This is due to frame dragging.

This doesn't sound right to me. Do you have a reference?

The water becoming concave was explainable before GR and certainly doesn't need frame dragging (a very small effect that requires sensitive instruments to detect) to explain it.

 

See http://en.wikipedia.org/wiki/Fictitious_force

 

 

Perhaps with the right conditions, having the universe spin around a bucket of water would produce an effect (due to frame dragging) similar to spinning the bucket (either coincidentally or by choosing an appropriate bucket size or spin rate or whatever... I don't really know enough to say), but that doesn't mean that the 2 effects are equivalent.

 

 

[Iggy]

This doesn't sound right to me. Do you have a reference?

The water becoming concave was explainable before GR and certainly doesn't need frame dragging (a very small effect that requires sensitive instruments to detect) to explain it.

 

See http://en.wikipedia.org/wiki/Fictitious_force

 

 

Perhaps with the right conditions, having the universe spin around a bucket of water would produce an effect (due to frame dragging) similar to spinning the bucket (either coincidentally or by choosing an appropriate bucket size or spin rate or whatever... I don't really know enough to say), but that doesn't mean that the 2 effects are equivalent.

Before GR, the concave shape of the water was explainable by a fixed background. Newton said that it proved as much.

 

Einstein hoped that relativity would do away with a fixed background making all motion relative, an idea he coined Mach's principle (that is a good wiki article on the issue -- section 2 and 3 especially).

 

There is debate, though, as to whether GR fully realizes Mach's principle.

 

This paper would, I believe, support the specific idea that rotating a universe around a resting bucket of water causes the water to act as we expect... using GR I should say.

 

Here's what I don't understand:

 

If there were no other mass/energy in the universe, per GR the water would still become concave.

Why do you say this?

[Mystery111]

There is evidence suggesting the early universe possessed a spin

 

http://www.stardrive.org/index.php?option=com_content&view=article&id=4596:the-universe-may-have-been-born-spinning-according-to-new-findings-on-the-symmetry-of-the-cosmos&catid=43:science&Itemid=82

[IM Egdall]

Why do you say this?

 

I got the idea that a spinning universe with no other mass/energy besides the water bucket would still cause the water to become concave from Brian Greene, The Fabric of the Cosmos, p .417:

 

" whereas standard Machian reasoning would claim that the water would stay flat in the bucket spun in an infinite, empty universe, general relativity diagrees. What Pfister and Braun results show is that a sufficiently massive rotating sphere is able to completely block the usual influence of the space that lies beyond the sphere itself."

 

Again, I do not get this last part. A sufficiently massive rotating sphere implies a universe WITH mass/energy, doesn't it?

 

This doesn't sound right to me. Do you have a reference?

The water becoming concave was explainable before GR and certainly doesn't need frame dragging (a very small effect that requires sensitive instruments to detect) to explain it.

 

 

The idea of this thought-experiment is to show one effect of Einstein's Principle of General Covariance. Per general relativity, any reference frame will do. Newton says the only legitimate reference frame is absolute space itself. The bucket is spinning with respect to absolute space.

 

Einstein says there is no absolute space. The bucket itself is a legitimate reference frame, per the Principle of General Covariance. But in this frame, the bucket is at rest. So what makes the water go concave" From this point-of-view, the rest of the universe is rotating in the opposite direction. And through frame-dragging, this causes the water to go concave!

 

I learned this from Brian Greene's The Fabric of the Cosmos, beginning of Chapter 14. He also gives references in the endnotes: D. Brill and J. Cohen, Phys. Rev. vol 143, no. 4, 1011 (1966) and H. Pfister and K. Braun, Class. Quantum Grav. 2, 909 (1985).

Edited October 3, 2011 by IM Egdall

[md65536]

The idea of this thought-experiment is to show one effect of Einstein's Principle of General Covariance. Per general relativity, any reference frame will do. Newton says the only legitimate reference frame is absolute space itself. The bucket is spinning with respect to absolute space.

 

Einstein says there is no absolute space. The bucket itself is a legitimate reference frame, per the Principle of General Covariance. But in this frame, the bucket is at rest. So what makes the water go concave" From this point-of-view, the rest of the universe is rotating in the opposite direction. And through frame-dragging, this causes the water to go concave!

 

I learned this from Brian Greene's The Fabric of the Cosmos, beginning of Chapter 14. He also gives references in the endnotes: D. Brill and J. Cohen, Phys. Rev. vol 143, no. 4, 1011 (1966) and H. Pfister and K. Braun, Class. Quantum Grav. 2, 909 (1985).

I don't really know about any of this but I still have doubts and questions:

 

I don't think GR says that any reference frame will do (according to http://en.wikipedia....eral_covariance, general covariance applies to "arbitrary differentiable coordinate transformations", while GR involves "local Lorentz covariance (which applies to all frames)".

 

The link to Lorentz covariance says "In standard physics, Lorentz symmetry is 'the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space'. Lorentz covariance is a related concept, covariance being a measure of how much two variables change together."

 

So about the bold parts: The second implies what I thought, that the equivalence principle in GR doesn't apply directly to the fictitious forces in rotating systems????

 

Yet, the first bold part seems to imply that the "frame" of a rotating bucket would count.

 

The quotes at the bottom of http://en.wikipedia....reference_frame seem to help:

 

 

Treat the fictitious forces like real forces, and pretend you are in an inertial frame.

— Louis N. Hand, Janet D. Finch Analytical Mechanics, p. 267

 

This equation has exactly the form of Newton's second law, except that in addition to F, the sum of all forces identified in the inertial frame, there is an extra term on the right...This means we can continue to use Newton's second law in the noninertial frame provided we agree that in the noninertial frame we must add an extra force-like term, often called the inertial force.

— John R. Taylor: Classical Mechanics; p. 328

 

 

What this means to me is that rotating a bucket vs. rotating the universe around a bucket are not equivalent, because there is nothing (to my knowledge) that would make the fictitious forces equal. The suggestion that a massive vs. massless universe would produce different fictitious forces (due to frame dragging I guess) makes me more confident that there is nothing that would ensure that the fictitious forces are always equal. The only way I can see the fictitious forces equaling each other (when spinning a bucket vs. spinning the universe around the bucket, where the universe has an arbitrary mass) is if the mass of the bucket is dependent on the mass of the rest of the universe... which could be the case but again I know of nothing that suggests it is so.

Edited October 4, 2011 by md65536

[Iggy]

I got the idea that a spinning universe with no other mass/energy besides the water bucket would still cause the water to become concave from Brian Greene, The Fabric of the Cosmos, p .417:

 

" whereas standard Machian reasoning would claim that the water would stay flat in the bucket spun in an infinite, empty universe, general relativity diagrees. What Pfister and Braun results show is that a sufficiently massive rotating sphere is able to completely block the usual influence of the space that lies beyond the sphere itself."

 

Again, I do not get this last part.

I read the quote in context and I honestly don't quite get it either. I'm not familiar with Pfister and Braun's work, but I would have assumed that their solution proved Mach's principle positive in the case of a rotating universe (where the universe is approximated by a rotating shell) but that the solution did not disprove the principle in terms of an empty universe. But, I really don't know.

 

What this means to me is that rotating a bucket vs. rotating the universe around a bucket are not equivalent, because there is nothing (to my knowledge) that would make the fictitious forces equal.

While they are not equal (they are, after all, different frames) I believe it has been pretty well shown that the same thing happens in each coordinate system. The solution of each gives the same future.

 

The thing that makes the fictitious forces equal is the mass itself. In the frame where the bucket is at rest there is a tremendous amount of mass rotating around the bucket. In GR, if you move mass you get a gravitational force analogous to the way moving a charge classically gives you an electromagnetic force. So, rotating a lot of mass around something should create a gravitational field that seems to have the exact same effect as the classical pseudo-forces.

 

Einstein gave a sort of philosophical outlook on this in something he wrote... that I'm having a hard time finding... ah!... http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity

 

I don't have time to re-read it at the moment so I can't quote a salient part, but I suspect that the paragraph starting "There are several reasons that compel us to willingly accept" would hit the nail more or less on the head.

[IM Egdall]

I agree with Iggy. Well said.

[md65536]

The thing that makes the fictitious forces equal is the mass itself. In the frame where the bucket is at rest there is a tremendous amount of mass rotating around the bucket. In GR, if you move mass you get a gravitational force analogous to the way moving a charge classically gives you an electromagnetic force. So, rotating a lot of mass around something should create a gravitational field that seems to have the exact same effect as the classical pseudo-forces.

 

I'm confused.

 

Reason 1: Suppose you're rotating a tremendous amount of mass around the bucket, which causes gravitational forces that have the exact same effect as the classical pseudo-forces present when rotating just the bucket. Now suppose that you remove some of this tremendous mass (half, or nearly all, or whatever). The gravitational force effect should decrease. With a negligible enough mass rotating around the bucket, the force on the bucket will be negligible. Then, if the forces involved in rotating the bucket are equal to forces when rotating the universe around the bucket, then it must be the case that rotating a bucket of water in a mostly empty universe will not cause the water's surface to curve. -- This is an intriguing idea, because it means that the mass of the water in the bucket depends on the amount of mass in the universe. But I've never heard of that before. It would imply that the gravitational pull on the mass in the bucket by all the rest of the mass in the universe is what gives the water its inertia.

 

Reason 2: Suppose you're rotating a tremendous amount of mass around the bucket, which causes gravitational forces that have the exact same effect as the classical pseudo-forces present when rotating just the bucket. Now suppose that you also rotate the bucket to match the rotation of the tremendous mass. What happens in this coordinate system should be the same as in another coordinate system, such as a frame that is also rotating with the universe and bucket. In the latter frame, nothing is rotating, and so there should be no curvature of the water's surface. This means that in the former frame (in which everything is rotating) there should be no surface curvature. Does this mean that the fictitious forces evident when rotating a bucket cancel out the forces that would be caused by rotating the universe around the bucket?

[IM Egdall]

I'm confused.

 

Reason 1: Suppose you're rotating a tremendous amount of mass around the bucket, which causes gravitational forces that have the exact same effect as the classical pseudo-forces present when rotating just the bucket. Now suppose that you remove some of this tremendous mass (half, or nearly all, or whatever). The gravitational force effect should decrease. With a negligible enough mass rotating around the bucket, the force on the bucket will be negligible. Then, if the forces involved in rotating the bucket are equal to forces when rotating the universe around the bucket, then it must be the case that rotating a bucket of water in a mostly empty universe will not cause the water's surface to curve. -- This is an intriguing idea, because it means that the mass of the water in the bucket depends on the amount of mass in the universe. But I've never heard of that before. It would imply that the gravitational pull on the mass in the bucket by all the rest of the mass in the universe is what gives the water its inertia.

 

Reason 2: Suppose you're rotating a tremendous amount of mass around the bucket, which causes gravitational forces that have the exact same effect as the classical pseudo-forces present when rotating just the bucket. Now suppose that you also rotate the bucket to match the rotation of the tremendous mass. What happens in this coordinate system should be the same as in another coordinate system, such as a frame that is also rotating with the universe and bucket. In the latter frame, nothing is rotating, and so there should be no curvature of the water's surface. This means that in the former frame (in which everything is rotating) there should be no surface curvature. Does this mean that the fictitious forces evident when rotating a bucket cancel out the forces that would be caused by rotating the universe around the bucket?

 

Good arguments. Let me try to answer them:

 

As to reason 1 -- I think you are rediscovering the equivalence of gravity and inertia. See link: http://philsci-archive.pitt.edu/1287/1/A1085285

 

As to reason 2 -- I believe if the bucket rotates to match the rotation of the universe, then there is no relative rotation between the two. This is equivalent to a reference frame where the bucket and universe are at rest. I think you have to consider only relative rotation. There is no absolute rotation in Einstein's construct.

[md65536]

Good arguments. Let me try to answer them:

 

As to reason 1 -- I think you are rediscovering the equivalence of gravity and inertia. See link: http://philsci-archi...1287/1/A1085285

 

As to reason 2 -- I believe if the bucket rotates to match the rotation of the universe, then there is no relative rotation between the two. This is equivalent to a reference frame where the bucket and universe are at rest. I think you have to consider only relative rotation. There is no absolute rotation in Einstein's construct.

The reference you give doesn't seem reputable.

 

I can't think of any way to disprove what you're saying, and the more I think about it, the more it seems reasonable.

 

 

The equivalence principle in GR implies that if you were in an enclosed space, you wouldn't be able to detect any distinguishing difference between say a rocket accelerating through space, vs. a box sitting stationary in a gravitational field of the right characteristics.

 

You're saying that you would also not be able to distinguish between having the box shook, vs. having everything else in the universe except the box shook.

 

 

But since acceleration is equivalent to being in a gravitational field, then if accelerating the box is equivalent to accelerating the rest of the universe, then being stationary in a gravitational field is equivalent to accelerating the entire universe. So frame dragging is equivalent to gravity. I could buy that... I can imagine gravity as a sort of "standing wave" of dragged (or simply curved) space that provides a constant dragging-like effect. I think this is similar to what your link talks about.

 

Is this speculative, or is it accepted science?

 

 

 

 

Einstein says there is no absolute space. The bucket itself is a legitimate reference frame, per the Principle of General Covariance. But in this frame, the bucket is at rest. So what makes the water go concave" From this point-of-view, the rest of the universe is rotating in the opposite direction. And through frame-dragging, this causes the water to go concave!

 

Another way to look at this though is to consider the case where the different parts of the bucket are not part of the same frame, but are instead moving independently in different directions. Then if you have the material of the bucket keep the bucket together (through tension, which acts as a force that would be proportional to the inertia of the moving parts of the bucket that must be overcome), you have the force of tension accelerating the different parts also in different directions, and the end result is that the parts of the bucket remain essentially fixed relative to each other.

 

In this case you're claiming that the inertia of different parts of the bucket aimed in different directions, is equivalent to the frame-dragging force of a rotating universe pulling on different parts of the bucket in different directions.

 

Again I can't prove you wrong and it sounds reasonable. But I'm not yet convinced and I think that the rotating frames you're describing better corresponds to multiple frames that are being accelerated in different directions.

 

It could also be "both", if there is also an equivalence principle that says that any (or some specifically configured) sets of different frames are equivalent to some single frames.

 

 

 

 

Addendum: After posting that I got to thinking about how you could distinguish between a rotating system that is made up of multiple frames, vs a single rotating frame of reference. http://en.wikipedia.org/wiki/Inertial_frame_of_reference may have an answer: "The presence of fictitious forces indicates the physical laws are not the simplest laws available". The quote applies to distinguishing inertial frames from non-inertial... so I don't know if it fully answers the question for this thread. But I think that in the case of spinning the whole universe and the bucket vs spinning only the observer's frame of reference, the former is not an inertial frame of reference but the latter is.

 

If you are in a frame where "the physical laws are not the simplest laws available", then a physical law that has a generally covariant formulation would not be the simplest formulation of that law in another frame in which simpler laws are available.

 

However!, since frame-dragging forces would also be fictitious forces (http://en.wikipedia.org/wiki/Gravitomagnetism), they could still be equivalent to inertial fictitious forces.

 

In conclusion I may not have any clue about what I'm talking about here.

Edited October 6, 2011 by md65536

[Iggy]

The reference you give doesn't seem reputable.

 

h2g2 not reputable!?!?

 

Well... I guess that may be, but I've heard it is "more popular than the Celestial Home Care Omnibus, better selling than Fifty More Things to do in Zero Gravity, and more controversial than Oolon Colluphid's trilogy of philosophical blockbusters Where God Went Wrong, Some More of God's Greatest Mistakes and Who is this God Person Anyway?"

 

In conclusion I may not have any clue about what I'm talking about here.

 

I'm certain I don't. I did, however, find a good read on the role of Mach's principle in GR.

[IM Egdall]

Frame dragging is accepted science -- a recognized prediction of general relativity. Testing it, however, has been a challenge because iti s a very small effect for the rotating Earth.

 

NASA launched Gravity Probe B in 2004 to measure frame dragging. After lots of problems, the team says they have confirmed Einstein's prediction to 15%. (NASA Science Report - Dec. 2008).

Edited October 6, 2011 by IM Egdall

[md65536]

I'm not going to get this for some time. I can imagine some thought experiments but can't yet make sense of them.

If there were no other mass/energy in the universe, per GR the water would still become concave.

Why do you say that? Perhaps this is not true.

Edit: Okay I just realized that this question was already asked verbatim and answered.

 

 

http://en.wikipedia....ravitomagnetism says "The main consequence of the gravitomagnetic force, or acceleration, is that a free-falling object near a massive rotating object will itself rotate." Clearly this requires a rotating mass.

 

I think that the Pfister and Braun results suggest is that the same effects happen with a nearby mass, and don't require an entire universe filled with mass to produce the effect???

 

 

h2g2 not reputable!?!?

There's a "strenuous" objection at the bottom of the entry that I'd like to check out but I guess I'll have to wait while Sub-Etha is down.

 

 

 

 

On a bit of a tangent, http://en.wikipedia..../Frame-dragging mentions "static mass increase".

It implies that yes, if you remove mass from the universe, other masses will decrease (may be negligible except for nearby masses).

I'm not sure what the effect of removing nearly all of the mass in the universe would be.

If the effect is big, then...

 

Given that "we live in an accelerating Universe, one in which the objects which are not gravitationally bound to us right now (i.e., not in the local group) will eventually speed away from us and accelerate out of the Universe we can observe" (http://scienceblogs....f_the_unive.php), as mass disappears from our observable universe, the mass that remains in the observable universe will also decrease. If it's significant enough (eg. enough to completely change how a bucket of water behaves), it could be that gravitationally bound objects could cease to be gravitationally bound.

 

However, given the Pfister and Braun reference, large nearby masses should completely overwhelm the effects of the rest of the universe, so we shouldn't float away from planets or have planets break free from suns or anything, I guess. ?

 

Now I'm feelin too dum for this thread.

Edited October 7, 2011 by md65536

[IM Egdall]

Now I'm feelin too dum for this thread.

 

Welcome to the club.

[md65536]

Okay wait... you're saying that a rotating frame of reference (say where a bucket is at rest and the universe is spinning around it) is equally valid as a frame of reference where only the bucket is spinning?

 

If I go outside and twist my head around, and consider my head's frame of reference, then the sun is moving around me at many times the speed of light. How can that be valid?

 

(Though its distance to me doesn't change. Is it only the rate of change of distance between something moving and something at rest that cannot exceed c? In polar coordinates with my head at the origin, the sun's movement when I twist my head seems minor.)

[IM Egdall]

Okay wait... you're saying that a rotating frame of reference (say where a bucket is at rest and the universe is spinning around it) is equally valid as a frame of reference where only the bucket is spinning?

 

If I go outside and twist my head around, and consider my head's frame of reference, then the sun is moving around me at many times the speed of light. How can that be valid?

 

(Though its distance to me doesn't change. Is it only the rate of change of distance between something moving and something at rest that cannot exceed c? In polar coordinates with my head at the origin, the sun's movement when I twist my head seems minor.)

 

Yes in your reference frame, that dizzy feeling you get when you spin around is caused by the frame dragging produced by the rotation of the rest of the universe.

 

And yes, when you spin around, from your point-of-view, stars that are far enough away are moving faster than the speed of light. But you can not use this effect to send a signal faster than the speed of light -- so relativity rules are not violated.

[md65536]

And yes, when you spin around, from your point-of-view, stars that are far enough away are moving faster than the speed of light. But you can not use this effect to send a signal faster than the speed of light -- so relativity rules are not violated.

What's important is that the stars are not moving through space, but rather that space itself is moving (rotating around you), and there's no speed limit on that.

That's the real reason that SR's rules are not violated.

 

 

The energy required to rotate all of space (corresponding to rotating a frame of reference with no mass at rest in it) would necessarily be zero.

That's fine, because you don't actually have to move anything through space to do this, and that's where energy expenditure happens.

 

 

But here's where I'm getting confused:

My limited understanding of space/spacetime is that its properties are defined by mass.

My limited understanding of frame-dragging is something like... when you move mass through spacetime, spacetime gets dragged along with the mass (but since spacetime is defined both by the moving mass and other mass that it's moving relative to, the mass both pulls space along with it AND moves through the space (leaving it behind)... depending on how much mass is moving).

 

So according to the basic ideas of this thread:

If you were to say accelerate a certain amount of mass in the +x direction by a certain amount, it would require some amount of energy.

If you increased the amount of mass you were applying this acceleration to, it would require more energy.

However, due to frame dragging, any accelerated mass would pull on other mass, making it slightly easier for a second unit of mass to be accelerated than the first.

The total energy required relative to the amount of mass accelerated would look maybe like one half-cycle of a sine wave, increasing slower and slower until it leveled out... at "half the mass of the universe (assuming the half that gets accelerated and the half that doesn't are symmetrically distributed)". The most energy you would expend would be in taking half the universe and moving it relative to the other half (you could tweak it higher by optimizing the choice of mass, but if you've already chosen a symmetric half, you shouldn't be able to use more energy in accelerating it, just by choosing additional mass to accelerate).

 

At the halfway point, the inertial effect of all the "rest" mass equals the frame-dragging effect of all the accelerated mass. After that point, the frame-dragging effect outweighs inertia and it actually becomes easier to accelerate more mass. Or perhaps what I'm trying to say is that by accelerating that much mass, you're moving spacetime along with the mass more than you're leaving spacetime behind... ??? sorry for my confused words. The more that spacetime moves with your mass, the less you're having to move the mass through spacetime. Beyond the half-way point, your "rest frame" is no longer the best rest frame... the frame of the accelerated mass is a better rest frame, and it's equivalent to having all of the remaining mass that you haven't touched accelerate in the opposite direction. If you keep adding mass, eventually you've accelerated all the mass in the universe, and dragged all of spacetime effortlessly along with it, and have used 0 energy, and it's equivalent to accelerating an imaginary massless frame of reference in the opposite direction.

 

If what I wrote makes sense and is true or at least "kinda true" then I think I understand now.

 

 

So the point would be that rotating a bucket through space is not technically equivalent to moving the rest of the universe through space around the bucket, BUT because moving that much of the universe would bring space along with it, either way the only thing that is moving through space is the bucket.

Edited October 9, 2011 by md65536

[IM Egdall]

So the point would be that rotating a bucket through space is not technically equivalent to moving the rest of the universe through space around the bucket, BUT because moving that much of the universe would bring space along with it, either way the only thing that is moving through space is the bucket.

 

boy, this is getting tough to sort out. I think rotating the bucket is technicallly equivalent to rotating the rest of the universe. This is Einstein's Principle of General Covariance -- there is no "preferred" frame of reference. Any reference frame is as valid as any other one. So the bucket spins in the universe frame, and the universe spins in the bucket frame. And both ways of looking at it produce identical physical results.

 

I also think your talk of moving through space for the bucket but not moving through space for the universe is not quite right. There is no absolute space in relativity -- so space doesn't move along with the universe. Both the bucket and universe are moving though space and through time or spacetime.

Edited October 9, 2011 by IM Egdall

[Mystery111]

I believe the universe spins. If we find enough evidence suggesting that the universe spins, then there is a new problem.

 

 

 

What is it spinning relative to? The only way to answer that is by saying there must be something outside the universe, which goes directly against what relativity has to say about space and time in general.

[md65536]

boy, this is getting tough to sort out. I think rotating the bucket is technicallly equivalent to rotating the rest of the universe. This is Einstein's Principle of General Covariance -- there is no "preferred" frame of reference. Any reference frame is as valid as any other one. So the bucket spins in the universe frame, and the universe spins in the bucket frame. And both ways of looking at it produce identical physical results.

 

I also think your talk of moving through space for the bucket but not moving through space for the universe is not quite right. There is no absolute space in relativity -- so space doesn't move along with the universe. Both the bucket and universe are moving though space and through time or spacetime.

 

Yeah, I agree. I've been mixing up inertial motion and acceleration.

 

 

I think you're saying that if you accelerated all the mass in the universe around a bucket, it would be equivalent to accelerating just the bucket into a spin.

I'm saying that if you were to try to do that, frame dragging would make it so that you're not actually accelerating anything anymore, except the bucket.

Whether you try to spin the bucket, or the universe, it is the bucket that will accelerate. In either case, the bucket is not an inertial frame.

This implies that you cannot accelerate (uniformly?) the entire universe. If you could somehow try, then frame-dragging would undo your work and the universe would remain an inertial frame.

 

Rotating an empty frame of reference and rotating some mass (like a bucket) are not equivalent.

However, rotating an empty frame of reference, and rotating all the mass in the universe, are equivalent.

 

 

 

Also, choosing a frame of reference where a mass is moving relative to you is equivalent to choosing a frame of reference where it's at rest relative to you, but they're not identical, due to length contraction and time dilation. Yes, there is no absolute space in relativity, but if you choose a different frame of reference you change distances and times. I don't think it's possible to choose a valid frame where normal matter is moving faster than c relative to space in the frame.

[Iggy]

...I'll have to wait while Sub-Etha is down.

 

I think you're saying that if you accelerated all the mass in the universe around a bucket, it would be equivalent to accelerating just the bucket into a spin.

Probably Einstein or Mach would be happiest with us saying that the "bucket rotates relative to the rest of the universe". In a coordinate system where the bucket is at rest the background stars rotate and in a coordinate system where the background stars are at rest the bucket rotates... that they are two ways of describing the same thing.

 

It is the same thing to say "the bucket rotates relative to the background stars" and "the background stars rotate relative to the bucket".

 

EDIT...

 

IM, you said it much better:

Any reference frame is as valid as any other one. So the bucket spins in the universe frame, and the universe spins in the bucket frame. And both ways of looking at it produce identical physical results.

 

...EDIT

 

I'm saying that if you were to try to do that, frame dragging would make it so that you're not actually accelerating anything anymore, except the bucket.

It might be better to think in terms of an accelerating rocket. If a rocket is accelerating in a straight line in deep space, Mach would have us say "the rocket accelerates relative to the background stars".

 

In a coordinate system where the background stars are at rest it must be a logical fact that the rocket accelerates. It changes velocity in that coordinate system.

 

In a coordinate system where the rocket is at rest it must logically follow that the background stars accelerate. They change velocity.

 

What accelerates would then be a matter of choice. It depends on frame.

 

...In either case, the bucket is not an inertial frame.

Right. The rocket is likewise not an inertial frame. Inertial pseudo forces exist in the frame.

 

In a coordinate system where the rocket accelerates (the background mass is at rest) the inertial forces are expected in the rocket.

 

In a coordinate system where the background mass accelerates (the rocket is at rest) the force that the people on the rocket feel is gravitational. The accelerating background mass creates a uniform gravitational field throughout the universe pointing in the rocket's aft direction. So, the rocket is fixed in this coordinate system... 'held' in place. Everything else in the universe is falling, and accelerating as it falls toward the rear direction of the rocket. The background stars don't feel as if they are accelerating because they are falling weightless in a uniform gravitational field. The rocket feels as if it is accelerating because even though it is at rest in this frame, it is at rest in a gravitational field... like a person standing on a planet's surface.

 

The general principle of relativity therefore implies that acceleration is not absolute even though it can be said in an absolute sense that some frames are inertial and some are not.

 

Also, choosing a frame of reference where a mass is moving relative to you is equivalent to choosing a frame of reference where it's at rest relative to you, but they're not identical, due to length contraction and time dilation.

One reason why the above argument (with the linearly accelerating rocket) is compelling is for the twin paradox. Using general relativity you can let the 'traveling' twin be at rest for the whole thought experiment. Even though the earth twin is moving in that frame and the rocket twin is at rest, the rocket twin is still younger at the end because of the time dilation produced by the uniform gravitational field.

 

With GR you can choose a coordinate system where the earth twin is at rest or choose a frame where the rocket twin is at rest and either way the earth twin is older at the conclusion.

 

I don't think it's possible to choose a valid frame where normal matter is moving faster than c relative to space in the frame.

The ergosphere of a rotating black hole is a good example of how non-local velocity (if that concept can even have meaning in GR) is greater than c.

Edited October 12, 2011 by Iggy

[md65536]

In a coordinate system where the background mass accelerates (the rocket is at rest) the force that the people on the rocket feel is gravitational. The accelerating background mass creates a uniform gravitational field throughout the universe pointing in the rocket's aft direction. So, the rocket is fixed in this coordinate system... 'held' in place. Everything else in the universe is falling, and accelerating as it falls toward the rear direction of the rocket. The background stars don't feel as if they are accelerating because they are falling weightless in a uniform gravitational field. The rocket feels as if it is accelerating because even though it is at rest in this frame, it is at rest in a gravitational field... like a person standing on a planet's surface.

The only way that I could make sense of this thread is to understand that what any observer feels is the same independent of frame of reference.

"Feeling" acceleration means measuring it, and my (mis)understanding of acceleration was that the acceleration that is measured is acceleration.

 

Google schooled me (schoogled?): http://en.wikipedia....er_acceleration

"In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. This contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers."

 

 

If you rotate a bucket, the rest of the universe feels negligible acceleration from it. If you consider a frame where it is the rest of the universe rotating, the universe still feels negligible acceleration and the bucket (though at rest) is affected by proper acceleration. No matter how it is done, if you accelerate the entire universe in a way that is physically equivalent to rotating just a bucket, then the universe is only undergoing coordinate acceleration.

 

Since the two frames are equivalent, in neither will anyone experience any measurable difference to be able to distinguish the frames. When we say "we're rotating the bucket in the universe" vs "we're rotating the universe around the bucket", we can't say that we're doing only one but not the other. It is not just that the "physical forces are equivalent", but rather that both scenarios are actually occurring. Whatever can be said to be happening in any valid frame, is happening.

 

 

So I think you and IM Egdall are right, it's just taking me awhile to get it.

 

 

This all must mean that coordinate acceleration alone has no effect on the physical universe.

I think it means that all proper acceleration must be relative to some other mass, which still makes for some confusing thought experiments. But I think they all eventually end up with a conclusion of "Of course it must be so!"

 

 

For example, even in a universe that contains only the bucket of water, if you want to "set the bucket spinning" in some way that maximizes its proper acceleration, you still need something to make it spin. If some force pushes it, you need something to push against.

 

Say for example that the bucket has water jets and it can use some of its contents to set it spinning. It shoots water out into the otherwise empty universe. Here, it should still be able to experience some form of proper acceleration because it is accelerating relative to the water it sent out. I'm not sure, but my guess is that the proper acceleration the bucket experiences relative to this expelled water is significant enough that a classical treatment of this mostly empty universe would correspond to a relativistic treatment -- it wouldn't matter if there was a massive universe at some great distance all around it or not.

 

Edit: That is... it wouldn't matter if there was a universe originally at rest around it. If the bucket is spinning relative to the universe around it, it must have at some point in the past accelerated relative to the universe's mass... or something like that...

Edited October 12, 2011 by md65536

[between3and26characterslon]

And if you have two buckets spinning in opposite directions is the universe spinning the other way to boths buckets at the same time, or two buckets spinning in the same direction at different rates. What about if only one bucket is spinning (and the universe is therefore spinning in the opposite direction) would this not cause the other bucket to spin.

[md65536]

And if you have two buckets spinning in opposite directions is the universe spinning the other way to boths buckets at the same time

The rest frame of one bucket or of the other or the average of the two are all valid, as are an infinite other possible frames of references.

 

The buckets can "push off each other" like two dancers, and thus can have proper acceleration.

One bucket will always be able to "tell" that it is spinning relative to the other bucket AND vice versa.

 

If you start two identical buckets at rest with no proper acceleration, and then use one to push off the other symmetrically, the "equal and opposite" forces will ensure that they each experience equal and opposite proper acceleration.

 

If you use something else in the universe to "push off of", then they will always have a momentum I think, relative to that other mass (even if the momentum is eventually "absorbed" by the rest of the universe). In such cases you could have one bucket feeling "at rest" while the other feels like it is spinning, or both feeling like they're spinning in the same direction at different rates, or spinning in opposite directions at different or equal rates.

 

I'm not sure I know what I'm talking about!, but for now it feels like it makes sense. I no longer think there is anything in relativity that would deny correspondence with classical physics.

 

or two buckets spinning in the same direction at different rates. What about if only one bucket is spinning (and the universe is therefore spinning in the opposite direction) would this not cause the other bucket to spin.

 

If one bucket is at rest with the rest of the universe, and the universe is "spinning in the opposite direction", then the bucket is also similarly spinning. It would not experience frame dragging relative to the rest of the universe; it would not have proper acceleration; it should remain at rest relative to the universe (ignoring negligible frame-dragging of the other bucket).

 

Another question: If the universe only consisted of two buckets with a relative spin to them, would frame-dragging cause their spins to slow over time until they are relatively at rest?

 

And same with the linear case; would frame-dragging mean that any pair of masses with relative velocity will tend towards being at relative rest?

 

I can't think of how to set up such a thought experiment so that the gravitational influence of the masses on each other doesn't overwhelm the effect of frame-dragging.

 

Edit: Okay I thought of a way. 1. A bucket spinning inside another bucket... or a spinning mass inside a spherical shell (with a net gravitational attraction of 0) should come to rest relative to the shell. 2. Two masses orbiting each other with such eccentric orbits that they're practically oscillating linearly, but not so much that they collide, should constantly have the size of the orbits reduced and eventually collide. Or maybe the orbits would just become more and more circular.

Edited October 13, 2011 by md65536