I Is acceleration absolute or relative - revisited

[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.

 

[Peter Leeves]

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.

What's the purpose of this forum if not to willingly share knowledge and increase understanding - both of the learner and perhaps also the teacher, through his efforts to educate ?

I've done my best to keep up and have re-read each and every post SEVERAL times to try and understand better (and follow suggested links !). If I made you repeat yourself, that can be frustrating and I apologise (sincerely this time). I've done nothing but try to grasp a LOT of new terminology and take on a HEAP of new concepts (Christoffel symbols anyone ?) in a very short space of time. All of this may well be "baby talk" to you. I assure you it's not to me. As mentioned earlier, a lot of people contributing to this thread have helped enormously - but also with patience and good grace. Strikes me as a much nicer way of doing business for all.

This has gone way too far off physics now. I'm not going to respond further to anything other than the OP and physics.

 

[PeterDonis]

What's the purpose of this forum if not to willingly share knowledge and increase understanding

Yes, that is the purpose, and that's what we've been doing. If the discussion has helped you, that's good.

 

[Peter Leeves]

To all contributors, I made the following summary for my own (educational) benefit. Since it's merely a quick "copy and paste", I thought it might be of value to anyone coming across the thread in the future.

There's no need to read it, and it might be better if there are no further responses / clarifications / corrections / arguments etc. I'm definitely not expecting anything else. I thank you ALL for your time and patience sharing your knowledge.

I fully accept that the two scenarios are NOT equivalent and the observations would NOT be identical. Further, within the reference frame (excuse my little play on words) of my limited abilities, I have understood both the reasoning and the proof.

My take from this thread (what I now understand - or think I do, lol):

Proper "anything" means it is independent of coordinate system / reference frame, it is not relative and it can't be transformed away. eg proper acceleration or proper rotation.

Invariant means the same / unchanging in all reference frames, and is not limited to inertial coordinate systems. eg. Proper acceleration or charge on an object.

Relative means changing depending on the reference frame. eg. Velocity

A coordinate system typically consists of one coordinate for time and three mutually perpendicular coordinates for space.

Proper acceleration (aka absolute acceleration, aka invarient acceleration) is invariant (unchanging in all coordinate systems / reference frames). It is physically measured by an accelerometer. The physics (the outcome of any experiment) depends on the proper acceleration, not the coordinate acceleration. All observers agree on proper acceleration.

Relative acceleration (aka coordinate acceleration) is dependent on a coordinate system/reference frame and is the second derivative of the space coordinates with respect to time.

In an inertial frame, the coordinate acceleration and the proper acceleration are the same (at non-relativistic velocities). They can be very different in non-inertial frames.

An object falling to Earth has coordinate acceleration (reference frame is Earth) but no proper acceleration (subject to no forces). An object on the Earth's surface has proper acceleration (upwards force from the ground).

With respect to equivalence of rotating bucket / rotating universe scenarios - this is only true as a statement about choices of coordinates for the same spacetime geometry; it is not true as a statement about invariants. As far as invariants are concerned, "rotating bucket in non-rotating universe" is not the same as "rotating universe with non-rotating bucket"; the latter would be a different spacetime geometry from the former. [This concludes the two scenarios are NOT equivalent and the observations would NOT be identical, for the stated reason.]

The equivalence principle is local, not the entire universe. [Thought only - if the entire universe was proper rotating / proper angular accelerating, would this make the equivalence principle non-local ?]

The global equivalence of different choices of coordinates on the same spacetime geometry is called "general covariance", not the equivalence principle. So the bucket thought experiment is an illustration of general covariance, not the Equivalance Principle.

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).

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.

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

It really is the bucket that is rotating.

Einstein’s 1918 lecture was based on coordinate acceleration, not proper acceleration.

For equivalence it must not merely have some influence, it must have the exact same influence. It does not. [Conclusion that the two scenarios are NOT equivalent and the observations would NOT be identical].

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.
Where equation 2.1.30 (rotating bucket in the bucket's frame) [missing equation] has but equation 2.10.2 (rotating universe in the bucket's frame) has [missing equation]. [Proof the two scenarios will NOT yield identical observations - but see later comment that "this is not a good way of looking for influences"].

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. [Conclusion the two scenarios will NOT yield identical observations].

*** This is the proof that the two scenarios are NOT equivalent ***

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 and the vorticity is . 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.
*************************************************************

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.

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.

I should avoid using words like “ACTUALLY” “truth” “truly” and “reality” as they can be misconstrued.

PeroK considers the notion of a proper rotating universe being equivalent to a proper stationary universe (now properly discounted) to be mysticysm / metaphysics / philosophy.

And my final take is ... "There is no spoon"

Things I didn't understand and need to further research:

Proper acceleration can be written mathematically as a covariant derivative (?).

What Einstein was calling a gravitational field is technically the Christoffel symbols. Those are indeed relative to the individual frame. The Christoffel symbols do not affect the proper acceleration (?).

What you are describing here is not frame dragging. It is those Christoffel symbols (?).

Acceleration type is related to Mach's Principle (?).

The shape of water's surface would be subject to Lorentz contraction the same as any other shape. Doesn’t change the measured proper acceleration though... we’re looking at the geodesic deviation between adjacent volumes of water in the bucket (?).

In an empty universe a particle can still undergo inertial forces because Minkowski spactime solves the field equations of an empty universe (?).

This is all about Mach's principle. The question is: does the (inertial) mass m of the water depend on all the other mass M of the universe? Mach believed so; he believed that, whatever m(M) is, the inertial property of it should vanish if M vanishes. It's not clear if and how the (inertial) mass of the water is fully determined by all the other (inertial) mass in the universe (?).

The family of worldlines describing the motion of objects "at rest relative to the universe" will be integral curves of a timelike Killing vector field that is hypersurface orthogonal (which is what "static" translates to in more technical GR language); whereas the family of worldlines describing the motion of the bucket will be integral curves of a timelike Killing vector field (assuming the bucket's angular velocity of rotation relative to the universe is constant) that is not hypersurface orthogonal (in more technical jargon, the bucket's motion will be stationary but not static) (?).

Links followed (or yet to be followed):
https://en.wikipedia.org/wiki/Proper_acceleration#In_curved_spacetime
Mach's principle.
https://en.wikipedia.org/wiki/Brans–Dicke_theory
https://arxiv.org/abs/0904.4184

P.S. I knew you couldn't resist reading it

 

[PeterDonis]

A coordinate system typically consists of one coordinate for time and three mutually perpendicular coordinates for space.

This is not correct.

First, there are many spacetimes in GR for which it is impossible to find such a coordinate chart globally at all.

Second, there are many spacetimes for which, even if such a coordinate chart is possible, there will be scenarios where a different coordinate chart is more useful.

The only actual requirements on a coordinate chart are that all four coordinates are real functions on spacetime, that the functions are continuous, and that the mapping of coordinate 4-tuples to points in spacetime is one-to-one. There is no requirement that one coordinate be timelike and the other three spacelike, and there is no requirement that the coordinate "grid lines" be orthogonal. (In fact, as noted, there are cases where these last two things are not even possible.)

if the entire universe was proper rotating / proper angular accelerating, would this make the equivalence principle non-local

First, the concepts of "proper acceleration" and "proper rotation" make no sense with respect to the universe. They only make sense with respect to individual objects in the universe.

That said, the EP is always local. No choice of spacetime geometry can change that.

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.

I think the caveats that I stated in my earlier exchange with @Dale about this are important. The fact that this heuristic happens to work in the particular cases discussed in this thread is a matter of being fortunate in the choice of coordinates that the Catalog of Spacetimes happens to have made for those cases. It cannot be extended to a general rule that always works. The general rule that always works is to look at the invariants I specified, proper acceleration and vorticity, as described later on in your post.

 

[Peter Leeves]

This is not correct.

First, there are many spacetimes in GR for which it is impossible to find such a coordinate chart globally at all.

All your input relating to multiple alternatives duly noted and agreed, other than my statement being incorrect. I didn't say "only", but "typical". The most familiar coordinate system to all humans is the one in which we live, which is orthagonal and consists of the 4 coordinates stated - hence it is typical. "Typical" also specifically requires there to be other types. It cannot imply "only", by definition. It would have been more accurate if you'd begun, "Yes, that's one familiar coordinate system, and here are some others ..." Or even better, just don't set out to make me appear incorrect when I'm not, in the first place.

First, the concepts of "proper acceleration" and "proper rotation" make no sense with respect to the universe.

Your comment suggests you're failing to grasp this thread is about a thought experiment, not reality. My idea (now answered) was essentially - Is it possible to devise a thought experiment in which a proper rotating universe might be considered eqivalent and produce identical observations to reality, and therefore be considered equally valid ? The fact you proved it can't isn't the point.

My idea was never about literally proper accelerating the universe to observe the influence on a proper stationary bucket. A spaceship firing it's rocket does not in reality remain proper stationary against a proper accelerating linear gravitational field magically generated by the rocket firing, and thus accelerate the entire universe away from the spaceship. Einstein merely proposed that it was equivant. Your comment is the same as telling Einstein, "don't be an idiot - firing a spaceship rocket cannot cause the entire universe to accelerate". Whether he was right or wrong doesn't matter. He was entitled to devise his ridiculous concept and ask - would this be equivalent ? I was just as entitled to ask if my thought experiment might work, particularly as they share some similar (though not identical) concepts.

Yes, you have disproved my idea for which I will be eternally grateful. But in the context of my thought experiment, a true rotating universe does make sense. After all, how did you manage to disprove something that "makes no sense" to you ? The answer is, it did make sense to you. Once again, it appears the real purpose of your comment was to make me appear wrong, not to make a valid contribution.

I think the caveats that I stated in my earlier exchange with @Dale about this are important.

I agree. An answer providing a general rule for all cases is preferable.

 

[Dale]

This is not correct.

I disagree. I think “typical” is an accurate description. After all, such a coordinate system is in fact the prototypical coordinate system, and how can the prototypical system not be considered typical. Your point regarding global coordinates is correct, but even in such spacetimes you can and often do construct local coordinates. When you do, they are typically as described.

First, the concepts of "proper acceleration" and "proper rotation" make no sense with respect to the universe. They only make sense with respect to individual objects in the universe.

This is terminology that I introduced, and I think your assertion goes too far. There are some spacetimes where the concepts may make no sense, but many where it makes perfect sense.

When I say that I am undergoing proper acceleration or rotation I mean that an accelerometer at rest with respect to my body and located in or on my body will measure said acceleration or rotation. Similarly, if an accelerometer is at rest with respect to the matter of the universe then it can be said to measure the proper acceleration or rotation of the universe. In the Goedel spacetime the universe has rotation in this sense.

Obviously, some universes have material that is not at rest with respect to other material, in which case you can specify the local distribution of matter and see if that rotation or acceleration is homogenous throughout the universe. Other universes are vacuum solutions, where there isn’t any matter to be at rest with respect to. For those I agree that it wouldn’t make sense.

 

[weirdoguy]

Your comment suggests you're failing to grasp this thread is about a thought experiment, not reality.

Thought experiments can't be in contradiction with known physics. If they are, we have no basis to analyse them.

 

[Peter Leeves]

Thought experiments can't be in contradiction with known physics.

Nonetheless, it remains valid to ask "Is this thought experiment in line with known physics ?". It's equally valid to receive the answer "No, and here's why not". And the person asking the question has increased their knowledge in a meaningful way.

Perhaps you meant to say, "Successful thought experiements won't be in contradiction with known physics." ?

 

[vanhees71]

Concerning the question whether the universe rotates or not, afaik, what's meant is the question whether the large-scale averaged spacetime is described by a standard FLRW solution of Einstein's equations or whether it's described by a solultion "with spin" (like Gödel's solution). Also I think today there's no hint of such a rotating universe from observations, but it's a possible cosmological model within standard GR, and it's also empirically investigated (e.g., by evaluating CMBR observables). Here is a not too old paper about this issue. I don't know, whether there are newer ones with newer measurements.

https://arxiv.org/abs/0902.4575
https://doi.org/10.1088/0004-637X/703/1/354

 

[Peter Leeves]

Dale, may I pose a question to you directly, as it relates to your Post #87 ? (all welcome to comment of course).

Prior to Post #87, I asked if the mass of the entire visible univese (proper rotating) would have any influence at all on the water ? You replied "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."

I fully take onboard that statement. Particularly the "It does not." bit. And yet confirming there would be some influence is like a red rag to a bull.

Given there is some influence on the water (though not identical), implies we may simply not be considering the correct magnitude of gravitational field or the correct magnitude of proper angular acceleration or some combination of both. Maybe if the gravitational field were stronger or we proper rotated it faster (or both) it might have identical influence on the water after all. I merely seek to close out this possibility.

Can you please clarify that no magnitude of gravitational field and no magnitude of proper rotational acceleration (or combination of both) could ever duplicate the obervation ?

 

[Dale]

Given there is some influence on the water (though not identical), implies we may simply not be applying the correct magnitude of gravitational field or the correct magnitude of proper angular acceleration or some combination of both.

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

 

[Peter Leeves]

How would it imply that?

How one thing implies the other:

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 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 water might be far from net zero. Now the entire universe's mass would exert a circumferential torque on the water. (I'm not certain, but that seems to be a description of rotational frame dragging, by-the-by, forget it). So when you confirmed, yes, there would be some influence - but not the same, it occurred upon subsequent re-reading that perhaps we were just not considering a large enough gravitational field or a large enough proper rotational acceleration (or both). The question then becomes, is there any magnitude that would apply an indentical torque to the water and so produce an identical observation ?

That's my best shot at explaining the implication.

As ever, this is a question and not a statement. I also thought clarifying there was no magnitude that could ever duplicate the obervation would close the issue and add even more value to this thread.

(I also considered a slim chance that on reflection you might agree. That if there was some influence, then adding more might well produce an indentical influence - but shhhh, don't tell anyone. For me, I can't shake that proper acceleration (and the resulting observation) is invarient and MUST be present in all reference frames. If the proper rotating universe is a legitimate reference frame then, by definition, it MUST contain the same proper acceleration and identical observation. That's just simple logic. If that's correct then it's possible I've borrowed from Einstein and described the mechanism by which it works - as an equivalent, not as a reality. Nonetheless, both would be equivalent and therefore equally valid viewpoints).

 

[Dale]

That's my best shot at explaining the implication.

That is pretty far from an implication. X implies Y means that if X is true then logically Y must also be true.

As I mentioned above, the "correct" value for a quantity in physics is the value that matches experiments. So the desire to produce something that matches some philosophical desideratum has nothing whatsoever to do with the correctness of a physical quantity. In this case, you have very little room to change anything. GR has exactly 1 tuneable parameter, and it cannot take any value other than what it is without departing from experimental observations.

 

[PeterDonis]

GR has exactly 1 tuneable parameter

Are you referring to the gravitational constant $G$?

 

[Peter Leeves]

That is pretty far from an implication. X implies Y means that if X is true then logically Y must also be true.

I gave it my best shot. My reasoning was logical, even if it didn't amount to what you consider to be a legitimate implication. Your definition is incorrect/incomplete. X implies Y, could equally mean that if X is true then logically Y must be untrue. It's a completely muddled and frankly pointless definition. Can we please stick to physics rather than definitions of words which is adding little ?

Is a rotating universe a legitimate frame of reference ? If the answer is yes, then given proper acceleration (and resulting observation) is invarient, then it (plus the corresponding observation) must by definition also exist in the rotating universe reference frame. Therefore your answer can only be no, a rotating universe is not a legitimate reference frame ?