Is acceleration absolute or relative - revisited

[PeterDonis]

I have a sneaking suspicion you knew this all along and watched me slog my way through it

Not at all. We have been trying to figure out (or help you to figure out) what you actually mean. You appear to have changed your mind about that twice now.

 

[PeterDonis]

I think I'm correct to say that only the water is stationary (defining it's reference frame). The bucket must rotate along with the rest of the universe.

No. The bucket and the water are at rest relative to each other in every scenario we have discussed. (Note that we have been ignoring any process of "spinning up" the bucket, i.e., we have been ignoring transients and only considering steady-state situations of one sort or another. During transients the bucket and water can of course move relative to each other; but all such relative motion must disappear by the time a steady state has been reached.)

 

[Peter Leeves]

Not at all. We have been trying to figure out (or help you to figure out) what you actually mean. You appear to have changed your mind about that twice now.

I'm happy to accept that.

Ultimately I wanted to answer "Is acceleration absolute or relative". The answer is, absolute (invariant) no matter which reference frame is used or whether they are inertial or non-inertial, but only within a single spacetime geometry.

Specifically, I wanted to answer, if the water is stationary what would cause the water to climb the walls of the bucket. The answer is, the stationary water is just a different coorinate system (reference frame) in the same spacetime geometry. The acceleration is invariant in all reference frames and hence the observation has to be identical.

I bet you can't wait for my post on the delayed choice quantum eraser experiment

 

[Peter Leeves]

No. The bucket and the water are at rest relative to each other in every scenario we have discussed.

Disagree. The bucket and the water are NOT at rest relative to each other in every scenario we've discussed. The water has to spin up in every scenario and therefore the reference frame can only be with respect to the non-rotating water. If I found my opinion changed by the end of the thread, then potentially anyone else reading this thread could miss the same distinction. It's worth including for accuracy and completeness (things we all value) and costs nothing. I say this even given the immediately following proviso, which is excellent and provides the description required.

(Note that we have been ignoring any process of "spinning up" the bucket, i.e., we have been ignoring transients and only considering steady-state situations of one sort or another. During transients the bucket and water can of course move relative to each other; but all such relative motion must disappear by the time a steady state has been reached.)

I understand and agree.

 

[Peter Leeves]

I haven't had time yet to do those computations in detail, but just looking at the Christoffel symbols, we have $\Gamma_{t \varphi}^{r} \neq 0$, so we would expect a nonzero proper acceleration in the $r$ direction for an object that is rotating about the origin in the $\varphi$ direction. And that means that water in a "non-rotating" bucket in this universe would not have a flat shape! Whereas water in a rotating bucket--one "rotating with the universe"--would have a flat shape!

Good old gut-instinct. I promise not to gloat if it turns out to be correct. It does seem intuitive that water in a rotating bucket in a rotating universe would stay flat. There'd be nothing to cause the water to bulge. On the other hand, if the "hand of god" (or tension in a string) grabbed hold and proper stopped the bucket, the torque I described earlier would be applied causing the water to bulge. The equivalence I've been describing between the two scenarios would be correct. Not that it would negate the coordinate solution discussed earlier. Interesting.

 

[PeterDonis]

The bucket and the water are NOT at rest relative to each other in every scenario we've discussed.

You are mistaken. See below.

The water has to spin up

But you said you understand and agree that we are ignoring the spin-up process and only considering steady state. In steady state the bucket and water are at rest relative to each other.

the reference frame can only be with respect to the non-rotating water

Whether or not the bucket and the water are at rest relative to each other is an invariant; it has nothing to do with any choice of frame and it will be equally true in every frame.

I say this even given the immediately following proviso

I have no idea what you mean by this or why you do not see that your statements are inconsistent with each other, as described above.

 

[PeterDonis]

The equivalence I've been describing between the two scenarios would be correct.

No, it wouldn't. The two spacetime geometries are still different, and that difference will still show up in the two scenarios.

I have not done the detailed computations, but here is what I think they will end up telling us. Note that I am stating everything in terms of invariants and direct observables, with no talk of "frames" at all.

First, we have to be clear about what invariants and direct observables we are talking about. There are actually four:

(1) The proper acceleration of the bucket and the water inside it. This determines the shape of the water's surface (flat for zero proper acceleration, concave for nonzero radial proper acceleration).

(2) The vorticity of the bucket and the water inside it. This determines whether the bucket is rotating (nonzero vorticity) or non-rotating (zero vorticity).

(3) The relative angular velocity of the bucket and the water inside it, with respect to the rest of the matter in the universe. Note that this is not the same as (2) above.

(4) The rotation of the rest of the matter in the universe. This is given by the vorticity of the family of worldlines that describe that matter.

Now let's look at four different scenarios and the invariants for each of them (the first two are known, the last two are what I want to verify by computation):

(NN) Non-rotating bucket in non-rotating universe (flat spacetime). The invariants are:

#1: Zero proper acceleration, flat surface.

#2: Zero vorticity, zero rotation.

#3: Zero relative angular velocity relative to rest of universe.

#4: Zero rotation of rest of universe.

(RN) Rotating bucket in non-rotating universe:

#1: Nonzero proper acceleration, concave surface.

#2: Nonzero vorticity, nonzero rotation.

#3: Nonzero angular velocity relative to rest of universe.

#4: Zero rotation of rest of universe.

(NR) Non-rotating bucket in rotating universe (Godel spacetime):

#1: Nonzero proper acceleration, concave surface.

#2: Zero vorticity, zero rotation.

#3: Nonzero angular velocity relative to rest of universe.

#4: Nonzero rotation of rest of universe.

(RR) Rotating bucket in rotating universe:

#1: Zero proper acceleration, flat surface.

#2: Nonzero vorticity, nonzero rotation.

#3: Zero angular velocity relative to rest of universe.

#4: Nonzero rotation of rest of universe.

Note how the first two invariants, which are the "local" ones, are different in each scenario; they cover all four of the possibilities, given that each of the two observables is a binary choice (zero or nonzero). That means no two of these scenarios are equivalent; each one has a different, unique set of observables.

 

[Peter Leeves]

There's no point repeating myself. If you don't wish to consider my viewpoint, that's absolutely fine. The information I felt was of genuine value and ought to be included in this thread, is now included.

But you said you understand and agree that we are ignoring the spin-up process and only considering steady state. In steady state the bucket and water are at rest relative to each other.

I do understand and agree that we are ignoring the spin-up process and only considering the steady state. At the risk of repeating myself (said I wouldn't but I'll give it one try) I feel the spin-up detail was worth including within this thread for both accuracy and completeness. Particularly for the benefit of others reading this thread at a later date. In short, it genuinely adds some value.

Whether or not the bucket and the water are at rest relative to each other is an invariant; it has nothing to do with any choice of frame and it will be equally true in every frame.

Same comment as above. Costs nothing to note the spin-up and we can all sleep better knowing we've been as accuracte and complete as possible.

I have no idea what you mean by this or why you do not see that your statements are inconsistent with each other, as described above.

My statements are consistent. You wrote a concise and excellent description covering spin up of the water and the reasons it can be ignored. It was this description I referred to as "the proviso". Very well put and definitely worth including in the thread.

 

[Dale]

The bucket and the water are NOT at rest relative to each other in every scenario we've discussed.

The traditional Newton's bucket is at rest relative to the water. I.e. the spin-up or spin-down happened a long time ago, viscous forces have caused all of the relative motion between the water and the bucket and between different parts of the water to dissipate.

"When friction between the water and the sides of the bucket has the two spinning together with no relative motion between them then the water is concave."
https://mathshistory.st-andrews.ac.uk/HistTopics/Newton_bucket/

Edit: never mind, I see that you just discussed that for completeness

 

[PeterDonis]

I do understand and agree that we are ignoring the spin-up process and only considering the steady state.

But you apparently do not agree that in the steady state, the bucket and the water are at rest relative to each other?

 

[Peter Leeves]

But you apparently do not agree that in the steady state, the bucket and the water are at rest relative to each other?

Why say that ? To try and make me "wrong" yet again ? Of course in the steady state the bucket and water are at rest relative to each. That defines "steady state". I certainly didn't realize you'd assume every statement I didn't quote would be held against me, like - he didn't answer that bit so therefore I'll simply assume he didn't agree. Once again, I'd prefer to stick to physics rather than semantics.

 

[Peter Leeves]

The traditional Newton's bucket is at rest relative to the water. I.e. the spin-up or spin-down happened a long time ago, viscous forces have caused all of the relative motion between the water and the bucket and between different parts of the water to dissipate.

"When friction between the water and the sides of the bucket has the two spinning together with no relative motion between them then the water is concave."
https://mathshistory.st-andrews.ac.uk/HistTopics/Newton_bucket/

Edit: never mind, I see that you just discussed that for completeness

I understand every word of that.

If you don't wish to work towards accuracy and completeness (especially when it costs nothing), that's absolutely fine. The issue I tripped up over is now included MANY times (many more than necessary now) so I'm all good.

 

[Dale]

especially when it costs nothing

Actually including the spin-up or spin-down would cost an enormous amount. Fluid dynamics are messy, especially when you have to include viscosity. But I see that you are not actually including them, just mentioning them in passing. That is fine. I don't think that it adds anything substantive to the discussion precisely because we are not actually analyzing those periods, but it does no harm either to just mention them.

 

[Peter Leeves]

Actually including the spin-up or spin-down would cost an enormous amount.

Wrong context. Didn't mean "cost anything" with respect to fluid mechanics (something I'm more familiar with by profession). I meant it doesn't "cost anything" but our toil and the sweat of our brows to strive for completeness and accuracy

Here's the context. I said "If you don't wish to work towards accuracy and completeness (especially when it costs nothing), that's absolutely fine." On reflection I'm sure you'll agree there's nothing in there hinting at fluid mechanics. No need to reply.

 

[PeterDonis]

Why say that ?

Because from your previous post that's what it seemed like you were saying. Now you have clarified that it wasn't, which is good.

You need to seriously take a step back and consider the possibility that the way you are phrasing things might be misleading.

 

[Peter Leeves]

Because from your previous post that's what it seemed like you were saying.

"Seemed" ?

Physics please. The physics in this thread is absolutely fascinating.

 

[Peter Leeves]

You need to seriously take a step back and consider the possibility that the way you are phrasing things might be misleading.

Purposely misconstrued is also a possibility. But please, can we stick to physics ?

 

[PeterDonis]

Purposely misconstrued is also a possibility.

No, it isn't. I am not purposely trying to misunderstand what you mean. I am honestly having difficulty understanding what you mean. You really should stop assuming that that is not possible.

 

[PeterDonis]

can we stick to physics ?

The things you are saying that I am having trouble understanding are about the physics. So I have to clarify them if we are going to talk about the physics.

 

[Peter Leeves]

I confess although I've heard of the Coriolis force/effect, it's been a long time so I looked it up:

"In physics, the Coriolis force is an inertial or fictitious force that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame."

This does sound exactly as I described earlier this evening, "We agreed just before post #87 all matter in the visible universe communicates gravitationally with all other matter at the speed of light c in a vacuum, and this must have some influence on the water. In a proper stationary universe [edit for clarity - containing a proper stationary bucket], this would likely have little (or no) net influence on the water, especially if you choose to assume matter is more or less evenly distributed. Perhaps just a tiny, quite possibly imperceptible, bulge in all directions would be my guess.

It then occurred that if the entire visible universe was proper rotationally accelerated, the effect on the [edit for clarity - proper stationary] water [further edit for clarity - but proper rotating WITH RESPECT TO the now proper rotating universe] might be far from net zero. Now the entire universe's mass would exert a circumferential torque on the water."

For my description to equate to a coriolis effect, the water would be the object in motion within a frame of reference that rotates WITH RESPECT TO an inertial frame (the entire universe). Here's the killer chaps ... WITH RESPECT TO the entire universe's reference frame (which is proper rotating), the water reference frame IS proper rotating.

Furthermore, the observation (water bulging) MUST be identical in both scenarios for the reason I also gave. The proper acceleration is invariant in one scenario so it MUST remain in the other scenario. Literally all you're doing is choosing whether to view from the water reference frame or the entire universe reference frame.

It's actually similar (in fact equivalent) to the coordinate solution you provided earlier. The proper acceleration is invarient so remained identical. All we had to do was choose the water as the stationary reference frame. Nothing more, and nothing less.

However, the mechanism to make to the two scenarios equivalent is different in each case, centripetal in one (proper stationary universe with proper rotating water), coriollis in the other (proper rotating water WITH RESPECT TO a proper rotating universe). Just like Einstein's thought experiment after all.

This would also verify both scenarios take place in a single spacetime geometry. I did say that earlier, but was informed in no uncertain terms I was wrong and confusing reference frames with spacetime geometries. That I could only be proposing two spacetime geometries. That was incorrect.

I appreciate there are a lot of statements above. I am not qualified to know if those statements are correct or not. I am just asking if this is the conclusion currently being considered ?

 

[PeterDonis]

I looked it up

Where? Please give a reference.

the Coriolis force is an inertial or fictitious force

Note that this means it is not a "proper" force--it is an artifact of choosing a particular reference frame, and you can make it vanish by choosing a different frame. It is not an invariant.

That means it can't be the same as anything that happens because of "proper rotation", because "proper rotation" is an invariant.

I am just asking if this is the conclusion currently being considered ?

No, for the reason given above. Physics is contained in invariants. If you go back and read my post #149, you will see that I described four different scenarios, corresponding to the four possible ways of combining the two binary variables "bucket/water not rotating vs. rotating" and "the rest of the matter in the universe not rotating vs. rotating". I described those scenarios entirely in terms of invariants; you won't see "Coriolis force' or "centrifugal force" or any other frame-dependent thing anywhere in my descriptions. I strongly suggest that you read those descriptions carefully and think carefully about what they are telling you.

(Btw, for clarity, what you and @Dale have been calling "proper rotation" is the same as what I called "nonzero vorticity" in that post.)

 

[vanhees71]

How would it imply that? In science the “correct” quantity is the one that matches experiment.

Well, yes, and the empirical evidence is that the universe is not rotating.

 

[anuttarasammyak]

As for the words "Is acceleration absolute ?”, say the referring (local) system or frame of reference does not satisfy Newton's first law, i.e. free objects change speed with time, the FR is not a (local ) IFR. In the sense that everybody in any FR agrees with this observation, we may say it is not a (local) IFR absolutely.

 

[anuttarasammyak]

Stars are moving against each other with proper speed. We may well consider their proper speeds to make them rotate uniform. We should do it for dark matter also. No other place but the bucket on the Earth is chosen to Origin of the rotation. Say all the stars start to rotate at the same time for Origin, farther star starts to rotate earlier. Far stars of more than c/$\omega$ distance move with speed more than c in current IFR which might be retained by closer stars which does not start rotation yet. Now farther stars have radial coordinate speed > c due to inflation of the universe. How should we do... They are a part of difficulties to do experiment of rotating universe. If we were lucky enough new comer stars beyond the event horizon could be rotating uniform to effect the bucket.

 

[Peter Leeves]

If correct how do they verify that their universe is rotating?

I have a thought with respect to "their universe is rotating". If this is "old news" please just ignore. I'm an amateur and most of the physics in this thread is new to me. But I can see two possible uses of the phrase "proper rotating universe".

1) Reality
Neglecting local effects and ongoing expansion, I don't think it's ever possible to claim the entire universe as a reference frame is proper rotating in reality. An acceleromoter (proper acceleration) and gyroscope (proper rotation) should always confirm this (as long as they avoid local effects). The only way this could be wrong is if the entire universe reference frame sat inside some larger reference frame (to which it was causally connected at speed of light c in a vacuum) and was proper rotating with respect to it. In that case, you could legitimately say reality shows the larger reference frame to be proper stationary and the visible universe is indeed proper rotating - but is now merely a local effect within the larger construct. However, since there is nothing larger (causally connected at speed of light c in a vacuum) than our entire visible universe (Earth as a datum), we can never say "in reality" the universe is rotating.

In short, everything within the largest available causily connected reference frame, moves with respect to it. This is both logical and reflects our reality.

2) Thought Experiment
However, I may see a case for saying "the entire universe is proper rotating" in a thought experiment, should you desire, but only if it adds something of value to physics.

However, it occurs to me from earlier discussion, this is merely changing choice of reference frame (coordinate systerm). I'm still struggling with this, but it does seem to be just saying "lets pretend the universe is proper rotating" - but that statement has no physical impact whatsover on anything happening within the reality of the thought experiment. Even in the thought experiment, the universe remains the largest reference frame we have, and the thing that everything within moves with respect to. Given that it changes nothing physical within, I can see no purpose whatsoever to consider a proper rotating universe, not even in a thought experiment.

Conclusion
Everthing within the largest available causily connected reference frame, moves with respect to it. This reflects reality. Any measurement by accelerometer (proper acceleration) and gyroscope (proper rotation) within, is a local effect. There is no case for considering the universe to be proper rotating, either in reality or thought experiment.

I believe this to be the correct conclusion. I also look forward to being shot down

 

[timmdeeg]

I have a thought with respect to "their universe is rotating".

Please note that my post 173 refers to the Godel universe which has been discussed between @Dale and @PeterDonis. So your conclusions seem to fail in this respect.

I believe this to be the correct conclusion. I also look forward to being shot down

Don't worry I've no gun.

 

[Peter Leeves]

Please note that my post 173 refers to the Godel universe

Timmdeeg, I've literally never come across the term "Godel universe" before this thread. Every time I come across it I've let it go for the moment a) because I'm lazy and b) because I find the physics in this thread fascinating and difficult to find time to break away and research (Google etc).

Do you have time to briefly define "Godel universe" here ? If not, just tell me to stop being lazy and go look it up.

Also, thanks for letting me know my idea contradicts Godel. I don't mind if I'm wrong. I just have a thirst to learn. In the meantime I'll go back and re-read #173

No, nothing in #173 defining Godel universe. I'll go to Google.

 

[PeterDonis]

Do you have time to briefly define "Godel universe" here ?

The Godel universe is a spacetime geometry--a known mathematical solution to the Einstein Field Equation. It was originally discovered by Godel, hence the name.

Several papers describing this spacetime geometry have already been linked to in this thread.

 

[PeterDonis]

my idea contradicts Godel

More precisely: the Godel spacetime is a valid mathematical solution to the Einstein Field Equation, so it is a perfectly valid basis for a thought experiment. So your statement in post #176 that there is no valid basis for considering a "rotating universe" as a thought experiment is wrong. We have been using the Godel spacetime as the basis for considering "rotating universe" thought experiments in this thread.

However, as multiple people have posted, our observational evidence is not consistent with the Godel spacetime as a description of our actual universe; so your statement in post #176 that there is no valid basis for considering a "rotating universe" in reality is correct.

 

[Peter Leeves]

Several papers describing this spacetime geometry have already been linked to in this thread.

Doing a thread search on Godel now, and will catch up on what I skipped over earlier (time restraints etc). Thank you.

 

[PeterDonis]

if the entire universe reference frame sat inside some larger reference frame (to which it was causally connected at speed of light c in a vacuum)

This doesn't make sense. Reference frames are human abstractions, not real things. Reference frames can't be causally connected to anything; they aren't real things. The actual universe is not a reference frame.

 

[PeterDonis]

I don't think it's ever possible to claim the entire universe as a reference frame is proper rotating in reality. An acceleromoter should always confirm this

You don't detect proper rotation with an accelerometer; an accelerometer detects proper acceleration, not proper rotation. You detect proper rotation with gyroscopes.

 

[Peter Leeves]

The actual universe is not a reference frame.

My mistake. I thought reference frames could be inertial and non-inertial and the entire visible universe could be regarded as the largest of all available inertial reference frames. I stand corrected and thanks again.

 

[PeterDonis]

I thought reference frames could be inertial and non-inertial

They can. But either way, they're human abstractions.

There is a separate concept of inertial vs. non-inertial motion of an object; "inertial motion" means "zero proper acceleration", and "non-inertial motion" means "nonzero proper acceleration". But that concept has nothing to do with reference frames.

 

[PeterDonis]

the entire visible universe could be regarded as the largest of all available inertial reference frames

In a curved spacetime, such as the spacetime of our actual visible universe, there are no global inertial frames. The global frame we use to describe our universe is not inertial. Objects at rest in this frame are moving inertially (zero proper acceleration), but the frame as a whole is not inertial.