Is acceleration absolute or relative - revisited

[PeterDonis]

Impart the right amount of rotation to the chair, and you can end up with a circular motion that uses the rocket thrust to impart centrifugal force.

No, the centrifugal force in this case would not be coming from the rocket. The force of the rocket (pushing on you through the chair) would be pushing you towards the center of rotation, not away from it.

Centrifugal force would appear if you chose coordinates in which you were at rest and the rest of the universe was rotating; it would be required (on the Newtonian view of "force") to balance the force exerted on you by the rocket and keep you at rest.

 

[Dale]

heheh... I can't for the life of me now figure out why I thought/wrote the "elongated" bit, though it made sense at the time. Wait... almost had it... darn, slipped away again. Apparently @Dale and @pbuk understood : maybe they can help.

I didn't worry about it. Elongation is just negative flattening. I don't know the sign, but the amount will be dramatically smaller in the "spinning shell" case than in the "spinning blob" case. Frame dragging is tiny!

 

[Peter Leeves]

Hello Dale, yes I think I've got it straight in my mind now that proper acceleration is invariant (and never relative). Also it's demonstrated by an accelerometer and is true in any coordinate system (I'm now wondering if "coordinate system" has the same meaning in physics as "reference frame" - but that's by-the-by).

Given your next paragraph, do we need to specify whether proper acceleration is invarient in any inertial coordinate system ? Or does it still remain true in a non-inertial coordinate system, hence no need to specify which ?

Focusing on the scenario where the surface is curved, you can describe that in inertial coordinates or in (non inertial) coordinates where the bucket is stationary. In the inertial coordinates the bucket is undergoing coordinate acceleration (the universe is not) and in the co-moving coordinates the bucket is not undergoing coordinate acceleration (the universe is). So coordinate acceleration is relative.

I follow this. Co-ordinate acceleration is relative. Proper acceleration is invariant.

Here you are using the word “rotating” without specifying if you are talking about “proper” or “coordinate”. That is likely the source of the confusion.

I was using the word "rotating" with respect to "proper" (not coordinate).

 

[PeterDonis]

do we need to specify whether proper acceleration is invarient in any inertial coordinate system ? Or does it still remain true in a non-inertial coordinate system, hence no need to specify which ?

"Invariant" means "the same in any coordinate system, period". It is not limited to inertial coordinate systems.

 

[Dale]

It certainly appears (at first sight anyway) that both scenarios would yield identical results.

No, the results are very different. The spinning blob (proper rotation) scenario will produce a very large distortion in the blob shape. The spinning shell (again, proper rotation) scenario will produce a very small distortion in the blob shape.

Of course, in either case you can choose either object as your reference frame. So you can choose coordinates where the shell is fixed regardless of which is undergoing proper rotation, and similarly for the blob. While you can choose either object as your reference frame, the distortion of the shape depends on the invariant facts (which is experiencing proper rotation), not on the relative facts (which is experiencing coordinate rotation).

 

[Peter Leeves]

spacetime geometry is the invariant thing that tells us that it "really" is the bucket that is rotating, not the universe.

You say "it really is the bucket that is rotating". Intutition is telling me this shouldn't be so. It seems directly analagous to saying somehow you can distinguish whether the man really is freefalling in an enclosed lift towards earth, or the man really is in interstellar space. Assuming the observations are identical in both scenarios (emphasis on "assuming" because that's still in question) then surely they would be equivalent and equally valid perspectives, and no preference as to which is "really" rotating ?

 

[Dale]

You say "it really is the bucket that is rotating". Intutition is telling me this shouldn't be so. It seems directly analagous to saying somehow you can distinguish whether the man really is freefalling in an enclosed lift towards earth, or the man really is in interstellar space.

It really is the bucket that is (proper) rotating.

A better analogy would be to have two observers with a relative (coordinate) acceleration between them. You really can identify which of the two observers is (proper) accelerating. The physics (the outcome of any experiment) depends on the proper acceleration, not the coordinate acceleration.

 

[Peter Leeves]

Now wait a moment... are you suggesting that when I switch on a motor to rotate something (like, for example a shaft with a bucket on the end) the motor is actually applying torque to all the rest of the universe causing it to rotate, while the bucket remains still?

Spot on. In the sense that it is equivalent (and will show identical observations and therefore be an equally valid perspective). This is the very principle that Einstein used in a lecture in 1918 when he was asked to resolve the Twin Paradox. I'm not smart enough to think this stuff up on my own. I just saw that you could apply the same answer, but rotationally, to the Newton's Bucket scenario to explain why the water would still become concave if you rotated the universe and the bucket/water remained stationary.

Don't get stuck on the size of the torque necessary to rotate the entire universe with all it's mass. It seems that would take ridiculous amounts of energy. Not at all. The torque required to rotate the entire universe to produce identical observations on the bucket/water system, is precisely equivalent to that generated by the motor (not that much).

You may be thinking of a different question

No, I'm not thinking of a different question.

 

[Dale]

This is the very principle that Einstein used in a lecture in 1918 when he was asked to resolve the Twin Paradox.

Note that the principle you are referring to in Einstein’s 1918 lecture was based on coordinate acceleration, not proper acceleration.

One problem with applying the same strategy to a rotational problem is that rotating coordinates very quickly lose any semblance of physical meaning. Even with a rotation rate of just 1 Hz, the moon is moving at v>c and the rotating coordinate time no longer describes anything that could be measured with a clock. Talking about the rotation of the universe as a coordinate transform is non-trivial if you intend for the coordinates to have a physical interpretation.

Usually, when physicists talk about a rotating universe this is not what we mean. What we mean is that we locally make sure that we are not (proper) rotating and then we look at the distant stars and galaxies. If those are rotating around us then we say the universe is rotating. This is not a coordinate effect.

 

[Peter Leeves]

but the amount will be dramatically smaller in the "spinning shell" case than in the "spinning blob" case. Frame dragging is tiny!

I agree it will be dramatically smaller - when you're only considering the inluence caused by the mass of the Earth rotating. But that's not the case I've described. It's the frame dragging due to the rest of the entire mass of the visible universe rotating (I choose those words very carefully) that influences the "stationary blob"of water, to produce identical squishing of the blob.

Why did I specify "the entire visibile universe" ? Because gravity works at the speed of light in a vacuum. Anything beyond that can't gravitationally influence the water blob. Every bit of mass within that sphere does influence every other bit of mass in that sphere.

 

[Dale]

I agree it will be dramatically smaller - when you're only considering the inluence caused by the mass of the Earth rotating. But that's not the case I've described. It's the frame dragging due to the rest of the entire mass of the visible universe rotating (I choose those words very carefully) that influences the "stationary blob"of water, to produce identical squishing of the blob.

The mass of the Earth is easier to analyze because you can simply place an accelerometer on it and because you can use rotating coordinates that cover both the blob and the Earth. But the qualitative conclusion does not change if you go to the universe as a whole. This is, IMO, a way that Mach's principle fails although I am sure there are other opinions (Mach's principle is too loosely defined to have definitive answers).

Suppose that we have a situation where an observer/blob looks out and sees that the distant stars and galaxies are rotating around the observer/blob. It is possible that the universe is rotating (observer has no proper rotation) or it is possible that the observer is rotating (observer has proper rotation). The blob will be greatly distorted if the blob is rotating and the blob will barely distort if the universe is rotating. They are physically different scenarios with physically different outcomes, even though the relative motion is the same.

 

[PeterDonis]

You say "it really is the bucket that is rotating". Intutition is telling me this shouldn't be so.

Your intuition is faulty and needs to be retrained. Go back and read my posts about spacetime geometry again, carefully.

It seems directly analagous to saying somehow you can distinguish whether the man really is freefalling in an enclosed lift towards earth, or the man really is in interstellar space.

It isn't. Go read my post about what the equivalence principle does and doesn't say again, carefully.

Assuming the observations are identical in both scenarios (emphasis on "assuming" because that's still in question)

It shouldn't be. Changing your choice of coordinates doesn't change the results of any observations or measurements. That has never been a point at issue in this discussion.

then surely they would be equivalent and equally valid perspectives, and no preference as to which is "really" rotating ?

Go back and read my post about what "equivalent and equally valid perspectives" is and is not asserting again, carefully.

 

[PeterDonis]

This is the very principle that Einstein used in a lecture in 1918 when he was asked to resolve the Twin Paradox.

No, it isn't.

Einstein said that when the traveling twin fires his rocket to turn around, this can be viewed as creating a gravitational field in which the stay-at-home twin is at a much higher altitude than the traveling twin, and this accounts for the stay-at-home twin's much greater elapsed time during the period when the field is present (i.e., when the traveling twin is firing his rocket).

Einstein did not say that the traveling twin firing his rocket was applying a force to the stay-at-home twin. This is obviously false since (a) the stay-at-home twin is in free fall the whole time, and (b) the traveling twin's rocket can't apply a force to the stay-at-home twin, that would violate causality.

I'm not smart enough to think this stuff up on my own.

Unfortunately, you are also apparently not well informed enough to correctly interpret what you are reading.

 

[PeterDonis]

It's the frame dragging due to the rest of the entire mass of the visible universe rotating (I choose those words very carefully) that influences the "stationary blob"of water, to produce identical squishing of the blob.

And this is wrong. In the spacetime geometry in question, there is no frame dragging. Frame dragging is not a coordinate effect; it is an effect of the spacetime geometry, and only certain kinds of spacetime geometries have it.

You really need to take several steps back at this point. As far as I can tell, pretty much everything you think you know about this topic is wrong.

 

[Peter Leeves]

This is, IMO, a way that Mach's principle fails although I am sure there are other opinions (Mach's principle is too loosely defined to have definitive answers).

I think I read yesterday that Einstein agreed with Mach (I'm not suggesting Einstein was infallible, but he did get quite a bit right). Sorry, I should stick to physics.

I hope you agree gravity travels at the speed of light in a vacuum and every piece of mass within our visible universe necessarily influences every other piece of mass. At big distances this is imperceptible (the distortion of space-time would be tiny) but nonetheless there. Considering there's quite a lot of mass in the universe (at varying distances from the bucket) it could nevertheless add up to have some influence when totalled (put Jupiter in Mars' location and see what happens on Earth, lol). It must have some influence, if you agree with the first sentence.

Suppose that we have a situation where an observer/blob looks out and sees that the distant stars and galaxies are rotating around the observer/blob. It is possible that the universe is rotating (observer has no proper rotation) or it is possible that the observer is rotating (observer has proper rotation). The blob will be greatly distorted if the blob is rotating and the blob will barely distort if the universe is rotating. They are physically different scenarios with physically different outcomes, even though the relative motion is the same.

Well described and I follow your description. For completeness, it's also possible the blob is proper rotating and the universe is proper rotating. In this case, the blob would squish mostly due to it's own proper rotation but also must be influenced to some lesser degree (due to gravitational frame dragging) by the universe's proper rotation. If the rotations were coincident I suppose the blob would be squished a tiny bit more. If opposite, then a tiny bit less (frame dragging countering the centripetal effect). Any other direction could have a small net disorting effect (depending on net distribution of the universe's mass).

In the bucket/water scenario (prior to releasing the bucket) the shape of the water is accurately determined by the shape of the bucket, the Earth's gravity sucking the water to the bottom of the bucket, the location of the centre of Earth's gravity at Earth's centre (hence slight curvature of the water surface due to it's radial distance), the proper rotation of the Earth and resulting centripetal forces plus ... ta da ... the tiny net influence of the remaining mass in the visible universe and any proper rotation of the universe (if any). [There's a couple other influences like surface tension and atmospheric pressure but I think we can say irrelevant to this case].

Release the bucket and the tension in the string causes the universe to rotatationally accelerate (bucket/water stationary co-ordinate system). Frame dragging by the visible universe's mass increases significantly, distorting the water such that it mimics the centripetal force.

Dale, at this stage (your patience has been very much appreciated) are you able to say agree, disagree or indeterminate ? I think I should probably drop this now for everyone's sanity, lol.

 

[PeterDonis]

I think I read yesterday

Where? Please give a reference.

I hope you agree gravity travels at the speed of light in a vacuum

With appropriate qualifications, yes. But see below.

every piece of mass within our visible universe necessarily influences every other piece of mass

Yes, but this doesn't mean what you think it means. For example, it does not mean there is "frame dragging" on a bucket that is rotating relative to the rest of the universe.

The way that the rest of the matter in the universe influences the bucket is by determining the spacetime geometry.

Release the bucket and the tension in the string causes the universe to rotatationally accelerate (bucket/water stationary co-ordinate system). Frame dragging by the visible universe's mass increases significantly, distorting the water such that it mimics the centripetal force.

All of this is wrong--not about what happens to the water in the bucket, but about why it happens. There is no "frame dragging" by the universe's mass in this scenario.

 

[Dale]

I think I read yesterday that Einstein agreed with Mach

Well, philosophically he definitely wanted to agree with Mach, but his actual theory does not. Of course, it is a little difficult to exactly pin down what Mach’s principle means in an empirical sense.

It must have some influence, if you agree with the first sentence.

Certainly, it does have some influence. But for equivalence it must not merely have some influence, it must have the exact same influence. It does not.

Frame dragging by the visible universe's mass increases significantly, distorting the water such that it mimics the centripetal force.

No. What you are describing here is not frame dragging. It is those Christoffel symbols.

Dale, at this stage (your patience has been very much appreciated) are you able to say agree, disagree or indeterminate ?

Sorry, what is the question at this stage?

 

[Peter Leeves]

Sorry, what is the question at this stage?

Will a PROPER rotating bucket in a static universe give identical observation (water pushed out towards the circumference) as a static bucket in a PROPER rotating universe, as the acceleration is invariant in both cases ? Or in the PROPER rotating universe would the water remain as-is since there's nothing to push the water outwards ?"

 

[PeterDonis]

Will a rotating bucket in a static universe give identical observation (water pushed out towards the circumference) as a static bucket in a rotating universe

It depends on what you mean by "a static bucket in a rotating universe". That phrase can mean one of two things:

(1) You have the same spacetime geometry, you've just changed coordinates. This is the case I think we have been discussing. In this case, all observations are the same since the spacetime geometry is the same (as well as the relative motion of bucket and rest of universe). You're just describing the same observations using a different choice of coordinates. However, as I have already pointed out, the phrase "static bucket in a rotating universe" is not really a good one to describe this case, since there is an invariant sense in which the bucket is rotating and the universe is not.

(2) You have a different spacetime geometry, one in which there is an invariant sense in which the universe is rotating and the bucket is not. In this case, observations will be different because the spacetime geometry is different. Taken literally, this is what "a static bucket in a rotating universe" describes, but I don't think it's what you intended to describe in your earlier posts in this thread.

These answers were already given in an earlier post, which I asked you to go back and read carefully. Apparently you didn't.

 

[Dale]

Will a rotating bucket in a static universe give identical observation (water pushed out towards the circumference) as a static bucket in a rotating universe

Disagree, as I described in detail in post 81.

as the acceleration is invariant in both cases ?

These are two different situations, not one situation described from two frames. The (proper) accelerations are different in the two different spacetimes.

 

[PeterDonis]

These are two different situations, not one situation described from two frames.

This is one possible interpretation, and I agree (based on what I said in post #89) that it's what the phrase "static bucket in a rotating universe" describes if interpreted literally based on a correct technical understanding of the issues involved. However, I don't think it's the interpretation the poster intended--and that is the real issue that the poster needs to understand, that these words he's throwing around don't mean what he thinks they mean, and what he thinks he knows about this topic is wrong and he needs to unlearn it.

 

[Peter Leeves]

Unfortunately, you are also apparently not well informed enough to correctly interpret what you are reading.

Quite so, and I came here to better my understanding by asking questions. Many here have helped with patience and good grace. Others not so much.

 

[Dale]

I don't think it's the interpretation the poster intended--and that is the real issue that the poster needs to understand

It is indeed hard to tell since, although I explained the importance and the terminology, he does not consistently specify "proper" or "coordinate". However each time that he has been asked to clarify he has answered "proper" so I assumed that he meant it in that sense. It would be better to specify since you and I interpreted it differently, and neither is a wrong interpretation of the unspecified terms.

 

[Dale]

Certainly, it does have some influence. But for equivalence it must not merely have some influence, it must have the exact same influence. It does not.

It is actually fairly simple to show that it does not exert the same influence. We can just look up the Christoffel symbols in the Catalog of Spacetimes: https://arxiv.org/abs/0904.4184

Where equation 2.1.30 (rotating bucket in the bucket's frame) has $\Gamma_{tt}^{r}=-\omega^2 r$ but equation 2.10.2 (rotating universe in the bucket's frame) has $\Gamma_{tt}^{r}=0$.

 

[Peter Leeves]

It is indeed hard to tell since, although I explained the importance and the terminology, he does not consistently specify "proper" or "coordinate". However each time that he has been asked to clarify he has answered "proper" so I assumed that he meant it in that sense. It would be better to specify since you and I interpreted it differently, and neither is a wrong interpretation of the unspecified terms.

Dale, I've not hidden the fact that a lot of the terms used in this thread are new to me. I also hope you'll see that my knowledge has increased somewhat. I did follow your explanation of "invariant" and the fact that acceleration is invariant (not relative) etc. When asked proper or coordinate I answered to the best of my ability (and think "proper" was the correct answer). As previously mentioned, thanks for your patience with an amateur. Genuinely appreciated

But I didn't come here to give anyone a hard time, or have a hard time myself. I came here to learn. With that I'll end my questions and thank all contributors very much for their input. I've learned a lot from all your responses And yes, I still have a long way to go, lol.

 

[Peter Leeves]

It is actually fairly simple to show that it does not exert the same influence. We can just look up the Christoffel symbols in the Catalog of Spacetimes: https://arxiv.org/abs/0904.4184

Where equation 2.1.30 (rotating bucket) has $\Gamma_{tt}^{r}=-\omega^2 r$ but equation 2.10.2 (rotating universe) has $\Gamma_{tt}^{r}=0$.

Perfect. That indisputably kills off the idea. One is NOT equivalent to the other. Thank you !

 

[Nugatory]

I think I read yesterday that Einstein agreed with Mach

Not quite... Einstein did find Mach's approach to be intuitively appealing, so he was initially somewhat disappointed to find that GR, the relativistic throry of gravity, was non-Machian.

 

[timmdeeg]

@Peter Leeves, sorry that I interfere as a layman. First the water in the bucket is flat. Then you start to rotate it and the water becomes concave which proves that as a local phenomenon. Now you can chose the coordinates such that the bucket stands still and the universe rotates. But I don't think that you can explain that you managed to rotate the universe. The whole thing is that regarding the bucket we talk about proper acceleration which is invariant. That's all in my opinion.

 

[Peter Leeves]

(1) You have the same spacetime geometry, you've just changed coordinates.

(2) You have a different spacetime geometry, one in which there is an invariant sense in which the universe is rotating and the bucket is not.

These answers were already given in an earlier post, which I asked you to go back and read carefully. Apparently you didn't.

I meant (2), not just coordinate change. I've edited my earlier post to say "proper rotating bucket" and "proper rotating universe". Hopefully this clarifies my intent.

You are correct. I haven't had time to go back and re-read carefully. But I promise I will (when I can find time if that's ok).

 

[PeterDonis]

I came here to better my understanding by asking questions.

You haven't just been asking questions, though. You've been making definitive statements, many of which are wrong.

I meant (2), not just coordinate change.

In which case even more of what you are saying is wrong. If you meant (2), then the two situations are not equivalent, as @Dale has already explained: the shape of the water in the bucket will be very different in the two cases. So if you meant (2), your original claim in the OP of this thread that "the gravitational field of the rotating universe" will make the water in the bucket climb up the sides of the bucket is wrong.

Not only that, but if by "rotating universe" you mean a different spacetime geometry, then to really have a well specified scenario, you have to specify which one. The term "rotating universe" does not pick out a single spacetime geometry. It so happens that, because any spacetime geometry you pick will have to be locally flat, if you specify that the bucket itself is not rotating (in the invariant sense of that term), then the surface of the water in the bucket will be flat to a very good approximation, no matter what the global spacetime geometry is. But if you want to add in tiny effects of "frame dragging" due to the spacetime geometry induced by the "rotating universe", you have to know which "rotating universe" spacetime geometry you are using.

 

[PeterDonis]

We can just look up the Christoffel symbols

This is not a good way of looking for "influences", since those are supposed to be invariant but the Christoffel symbols are not. "Influences" should be described by invariants. The relevant invariants to look at would be the proper acceleration and vorticity of the congruence of worldlines describing the bucket.

In the first case, "rotating bucket in static universe", we describe the bucket using the Langevin congruence in flat Minkowski spacetime. The proper acceleration of this congruence is $- \omega^2 r / \left( 1 - \omega^2 r^2 \right)$ and the vorticity is $\omega / \left( 1 - \omega^2 r^2 \right)$. The proper acceleration is what accounts for the curved shape of the water surface inside the bucket, and the vorticity is what tells us the bucket is rotating.

In the second case, "static bucket in rotating universe", now that that OP has clarified that he intends this to mean an actual change in spacetime geometry, we describe the bucket using a Fermi-Walker transported congruence centered on a comoving worldline in the Godel spacetime. The proper acceleration and vorticity of this congruence are both zero. The zero proper acceleration tells us that the surface of the water in the bucket is flat, and the zero vorticity tells us that the bucket is not rotating.

 

[Dale]

This is not a good way of looking for "influences", since those are supposed to be invariant but the Christoffel symbols are not. "Influences" should be described by invariants. The relevant invariants to look at would be the proper acceleration and vorticity of the congruence of worldlines describing the bucket.

I don’t disagree in principle, but in practice I think that it is sufficient for this thread. As the OP was interested in “gravitational fields” (ala Einstein’s lecture) $\Gamma_{tt}^r$ is the “gravitational field” associated with a spinning frame, such as a traditional rotating space station’s artificial gravity.

It is clear that such a “gravitational field” leads to a flattened blob. Of course the details can be computed in a fully invariant manner, and that would be more satisfying. But I am lazy and only wanted to point out that there is a difference in the easiest way possible.

 

[Peter Leeves]

You haven't just been asking questions, though. You've been making definitive statements, many of which are wrong.

My post started by describing a scenario and suggesting a possible answer. Quote "I haven't come down on one side or the other yet, but I do at least see the argument that acceleration is relative."

My understanding of acceleration types was completely wrong at that time (probably still is) as I didn't have a clear understanding of what relative meant and what absolute (invariant) meant. I definitely used relative incorrectly there. I was trying to say "acceleration is invariant" (and might therefore apply equally in both scenarios - pehaps).

Throughout the entire thread, I don't think it was necessary to punctuate every sentence with a "?" to establish my contributions as a "question". It must be obvious to all but the blind, if I start off by saying "I don't know which is true, can you please help me understand ?" that all following discussion is trying to dig further to (hopefully) arrive at a conclusion. Yes, some of that dialogue is made in the form of statements without question marks. You can have my apology for not stating the "bleeding obvious".

 

[PeterDonis]

As the OP was interested in “gravitational fields” (ala Einstein’s lecture) $\Gamma_{tt}^r$ is the “gravitational field” associated with a spinning frame, such as a traditional rotating space station’s artificial gravity.

It is clear that such a “gravitational field” leads to a flattened blob.

Only with the appropriate caveats about the choice of coordinates. But one of the key points of discussion during this thread has been that all choices of coordinates are equally valid, and that actual physical observables must be described by invariants. That point is all the more important now that the OP has clarified that he intends the two scenarios to be different in an invariant sense, not just as a matter of choice of coordinates.

To put it another way, the concept of "gravitational field" as embodied in the Christoffel symbols is a coordinate-dependent concept; but the OP has said he's not interested in coordinate-dependent concepts, but in two scenarios that have an invariant difference between them. So the difference should be described in terms of invariants.

 

[PeterDonis]

Throughout the entire thread, I don't think it was necessary to punctuate every sentence with a "?" to establish my contributions as a "question". It must be obvious to all but the blind, if I start off by saying "I don't know which is true, can you please help me understand ?" that all following discussion is trying to dig further to (hopefully) arrive at a conclusion.

Yes, you said you wanted to improve your understanding, but if your method of doing that is to state what your current understanding is in definitive statements--and that is the method you adopted in this thread--then the only way for us to help you improve your understanding is for us to tell you when your statements are wrong, in the same definitive manner that you used to make the statements. Which is what I did. And when I make such a statement about something you've said, and then you make a subsequent post that says the same wrong thing, definitively, that I've already told you is wrong, you can expect me to remind you, definitively, that I've already told you it's wrong. Which is what I did.