Why rotation apparently seems to be absolute ?

[Sushmit Nandy]

First, I would like to say that I have no formal training in physics, so pardon me please, if I am mistaken. I recently thought of something, which has troubled me since, that inside a rotating box, one can always perform an experiment to detect that whether he is the one rotating or the rest of the universe. But in case of uniform translational motion, one cannot. Why does this asymmetry exist in nature?

 

[Demystifier]

Because in rotation you change the direction of motion, i.e. change velocity, i.e. accelerate. Velocity is relative but acceleration is absolute. That's related to the fact that the equations of motion (Newton equation and its relativistic generalization) are second order equations. In other words, the forces determine the acceleration, not the velocity.

 

[Sushmit Nandy]

Because in rotation you change the direction of motion, i.e. change velocity, i.e. accelerate. Velocity is relative but acceleration is absolute. That's related to the fact that the equations of motion (Newton equation and its relativistic generalization) are second order equations. In other words, the forces determine the acceleration, not the velocity.

Sir, but accelerating respect to what ?

 

[Demystifier]

Sir, but accelerating respect to what ?

Acceleration is a change of velocity. A body changes velocity relative to its own velocity a moment before. I know, that's not a satisfying answer. But I don't know how to give a better answer without math.

 

[PeterDonis]

inside a rotating box, one can always perform an experiment to detect that whether he is the one rotating or the rest of the universe.

That's not quite what the experiment is telling you. Inside the box, you can't see the rest of the universe, so you have no idea what it's doing. What you can see is that, for example, an accelerometer attached to you reads nonzero, and you are turning relative to gyroscopes that you carry along with you. Those are observable differences between you and someone who is in uniform translational motion, who will measure zero acceleration with an accelerometer and (at least in flat spacetime) will not measure themselves to be turning relative to gyroscopes they carry with them.

Also, note that those differences do not necessarily match up exactly with your state of motion relative to the rest of the universe. For example, suppose you are on a merry-go-round that is rotating, but otherwise floating in deep space. You measure your local angular velocity of rotation relative to gyroscopes that you carry along with you. But say you also can look at distant stars through a telescope and measure your angular velocity of rotation relative to them. The two angular velocities you measure will not be the same. (This is an example of what is called Thomas Precession.)

If you are in a circular orbit around a gravitating body, there are other effects as well (de Sitter precession, and Lense-Thirring precession if the gravitating body is itself rotating) that make your local measurement of rotation different from your rotation relative to distant stars.

 

[PeterDonis]

accelerating respect to what ?

Proper acceleration, measured by an accelerometer, is not "with respect to" anything. It's a direct observable.

 

[PeterDonis]

change velocity, i.e. accelerate.

Not really, no:

Velocity is relative but acceleration is absolute.

This means that you cannot define acceleration--by which you evidently mean proper acceleration, what is measured by an accelerometer--as "change in velocity", because velocity is relative but proper acceleration is not. If I'm standing on the surface of the Earth, my change in velocity relative to the Earth is zero, but relative to a rock free-falling near me, it's not. But my proper acceleration doesn't change.

 

[Dale]

Sir, but accelerating respect to what ?

Accelerating isn’t with respect to anything. Acceleration is invariant.

 

[Sushmit Nandy]

That's not quite what the experiment is telling you. Inside the box, you can't see the rest of the universe, so you have no idea what it's doing. What you can see is that, for example, an accelerometer attached to you reads nonzero, and you are turning relative to gyroscopes that you carry along with you. Those are observable differences between you and someone who is in uniform translational motion, who will measure zero acceleration with an accelerometer and (at least in flat spacetime) will not measure themselves to be turning relative to gyroscopes they carry with them.

Also, note that those differences do not necessarily match up exactly with your state of motion relative to the rest of the universe. For example, suppose you are on a merry-go-round that is rotating, but otherwise floating in deep space. You measure your local angular velocity of rotation relative to gyroscopes that you carry along with you. But say you also can look at distant stars through a telescope and measure your angular velocity of rotation relative to them. The two angular velocities you measure will not be the same. (This is an example of what is called Thomas Precession.)

If you are in a circular orbit around a gravitating body, there are other effects as well (de Sitter precession, and Lense-Thirring precession if the gravitating body is itself rotating) that make your local measurement of rotation different from your rotation relative to distant stars.

Sir, for simplicity we assume that the box is transparent(like made of glass). And sir why does nature favour the box and not the rest of the universe, when both are rotating respect to each other. Why do accelerometers disagree ?

 

[Dale]

both are rotating respect to each other

Rotation is a form of acceleration. It is not with respect to anything. It is invariant.

The box is rotating. The universe is not rotating.

 

[Sushmit Nandy]

Rotation is a form of acceleration. It is not with respect to anything. It is invariant.

The box is rotating. The universe is not rotating.

Sir, sorry to keep questioning, but then wouldn't Newton’s laws need reformulation from coordinate acceleration to proper acceleration. And sir the version of the 2nd law, which you gave for my previous question, does it take into account of this ?

 

[Dale]

the version of the 2nd law, which you gave for my previous question, does it take into account of this ?

Yes, it does. It accounts for all these issues in a systematic fashion. The mathematical framework is not what introductory students are used to, but it has been in use by physicists for a century now.

 

[PeterDonis]

for simplicity we assume that the box is transparent(like made of glass).

Sure.

why does nature favour the box and not the rest of the universe, when both are rotating respect to each other.

What do you mean by "favour the box"?

Why do accelerometers disagree ?

What accelerometers disagree? There is only one accelerometer in the scenario, the one carried by the observer.

 

[PeterDonis]

Rotation is a form of acceleration.

I'm not sure I would put it this way. The standard way of representing these properties in GR is the kinematic decomposition, which includes four things: proper acceleration, expansion, shear, and vorticity. Vorticity is what corresponds to rotation, and it is not the same thing as proper acceleration.

In the particular scenarios under discussion in this thread, it is true that nonzero vorticity goes along with nonzero proper acceleration. But that is not necessarily the case. In the Godel universe, for example, observers at rest in the standard coordinate chart are in free fall, with zero proper acceleration, but they have nonzero vorticity.

 

[PeterDonis]

The box is rotating. The universe is not rotating.

To put this in the language of the kinematic decomposition, the box has nonzero vorticity, but the universe (which we're assuming is flat Minkowski spacetime) has zero vorticity (more precisely the "distant stars" in the universe do). And these are invariant properties which don't depend on any choice of coordinates: we could choose a non-inertial frame in which the rotating box was at rest and the universe appeared to be rotating around it, but that would not change the fact that the box has nonzero vorticity and the rest of the universe has zero vorticity.

 

[Sushmit Nandy]

Sure.


What do you mean by "favour the box"?


What accelerometers disagree? There is only one accelerometer in the scenario, the one carried by the observer.

I mean an accelerometer attached to a distant star and an accelerometer attached with the box. From the box, it seems that the universe is rotating but from the distant stars, we know the box is rotating. The accelerometers deliver their final verdict and say that the box is actually rotating. So why is nature favoring the box, by which I mean isn't Leibniz principle of sufficient reason violated, because when seen from one, the other is rotating, so the experiments must also yield similar results

 

[Dale]

I'm not sure I would put it this way.

It is measured by an accelerometer (the 6 DOF kind).

The mathematical differences you point out are why I said “rotation is a form of acceleration” rather than just saying “rotation is acceleration”.

 

[Dale]

isn't Leibniz principle of sufficient reason violated

If indeed it is violated*, then the universe doesn’t conform to that principle.

The universe also does not appear to conform to Mach’s principle. There are a lot of nice sounding philosophical principles that the universe doesn’t seem to follow, regardless of how appealing they sound to humans

* I don’t think that it is violated

 

[PeterDonis]

It is measured by an accelerometer (the 6 DOF kind).

Ah, so in terms of kinematic decomposition, it should actually be called an acceleration-plus-vorticity-ometer.

 

[PeterDonis]

I mean an accelerometer attached to a distant star and an accelerometer attached with the box.

Ok. Yes, in that scenario, an accelerometer attached to a distant star would read zero. And if we used the 6 DOF kind of accelerometer that @Dale described, which also measures vorticity, that would read zero as well.

From the box, it seems that the universe is rotating but from the distant stars, we know the box is rotating.

No. We know the box is rotating because it has nonzero vorticity, and we measure that using devices attached to the box. We can do that even if we can't observe the distant stars at all.

Similarly, we know the distant stars are not rotating because devices attached to them read zero vorticity.

why is nature favoring the box

Nature isn't "favoring" anything. We are specifying the scenario such that the box has nonzero vorticity. But we could also imagine a scenario where the box has zero vorticity and the distant stars have nonzero vorticity. We don't live in such a universe, but we could model it mathematically using the laws of physics.

isn't Leibniz principle of sufficient reason violated

Why would you think that? What in the scenario do you think does not have a sufficient cause?

because when seen from one, the other is rotating, so the experiments must also yield similar results

This does not follow at all, because you are shifting the meaning of "rotating" between the two parts of your sentence. "Seen" to be rotating by some other outside observer is not the same thing as rotating defined by nonzero vorticity.

 

[Dale]

Ah, so in terms of kinematic decomposition, it should actually be called an acceleration-plus-vorticity-ometer.

I like it! I think the technical term is “inertial measurement unit”. But people just know them as accelerometers.

 

[PeterDonis]

I like it! I think the technical term is “inertial measurement unit”. But people just know them as accelerometers.

Yes, I agree that's a lot easier to pronounce than what I said.

 

[Sushmit Nandy]

Ok. Yes, in that scenario, an accelerometer attached to a distant star would read zero. And if we used the 6 DOF kind of accelerometer that @Dale described, which also measures vorticity, that would read zero as well.


No. We know the box is rotating because it has nonzero vorticity, and we measure that using devices attached to the box. We can do that even if we can't observe the distant stars at all.

Similarly, we know the distant stars are not rotating because devices attached to them read zero vorticity.


Nature isn't "favoring" anything. We are specifying the scenario such that the box has nonzero vorticity. But we could also imagine a scenario where the box has zero vorticity and the distant stars have nonzero vorticity. We don't live in such a universe, but we could model it mathematically using the laws of physics.


Why would you think that? What in the scenario do you think does not have a sufficient cause?


This does not follow at all, because you are shifting the meaning of "rotating" between the two parts of your sentence. "Seen" to be rotating by some other outside observer is not the same thing as rotating defined by nonzero vorticity.

Thanks a lot sir for patiently answering my questions, especially to someone who has no formal training in physics. In between, I had got lost in the complex mathematical terms, except that vorticity is something I had read in fluid mechanics.

 

[Demystifier]

@PeterDonis and @Dale , how to explain the notion of proper acceleration at a popular physics level, to someone without a physics background?

 

[Sushmit Nandy]

@PeterDonis and @Dale , how to explain the notion of proper acceleration at a popular physics level, to someone without a physics background.

@PeterDonis and @Dale , how to explain the notion of proper acceleration at a popular physics level, to someone without a physics background?

Sir, I think proper acceleration is that, which introduces some kind of stress in a material, which is the principle on which accelerometers work(which means an accelerometer cannot be a point object). Please correct me, if I am wrong

 

[Demystifier]

Sir, I think proper acceleration is that, which introduces some kind of stress in a material, which is the principle on which accelerometers work(which means an accelerometer cannot be a point object). Please correct me, if I am wrong

You are not wrong. But that's how proper acceleration manifests, not what proper acceleration is.

To compute the proper acceleration in relativity theory, one needs to know the metric tensor of spacetime. So it could be said that proper acceleration is "relative" to the metric. But that's quite abstract, I don't know how to explain that at a popular physics level.