Is acceleration absolute or relative - revisited

[Peter Leeves]

TL;DR Summary

Can the spinning bucket of water be used to argue that acceleration is relative, and not absolute ?

Hello all, I just joined this group after stumbling over a post from 2003 on this topic. The issue I'd like to deal with is the spinning bucket of water and why the water will still climb up the sides of the bucket if the bucket is stationary.

In the original post an Absolutist put it like this, "If the bucket of water is stationary and the entire universe rotates it's axis, why does the water climb up the sides ?" This question wasn't answered directly (at least I don't think so) but I believe I can.

Water climbs up the sides of the stationary bucket due to the gravitational field of the rotating universe. It is the strenth of the gravitational field and the fact it's rotating that influences the water (via the curved distortion of space-time) and causes it to climb up the sides of the bucket. This is completely consistant with the observation and can be regarded as proof that acceleration is relative.

I haven't come down on one side or the other yet, but I do at least see the argument that acceleration is relative.

 

[PeroK]

Summary:: Can the spinning bucket of water be used to argue that acceleration is relative, and not absolute ?

Hello all, I just joined this group after stumbling over a post from 2003 on this topic. The issue I'd like to deal with is the spinning bucket of water and why the water climbs up the sides of the bucket if the bucket is truly stationary.

In the original post an Absolutist put it like this, "If the bucket of water is stationary and the entire universe rotates it's axis, why does the water climb up the sides ?" This question wasn't answered directly (at least I don't think so) but I believe I can.

Water climbs up the sides of the stationary bucket due to the gravitational field of the rotating universe. It is the strenth of the gravitational field and the fact it's rotating that influences the water and causes it to climb up the sides of the bucket. This is completely consistant with the observation and can be regarded as proof that acceleration is relative.

I haven't come down on one side or the other yet, but I do at least see the argument that acceleration is ACTUALLY relative.

As far as modelling the universe is concerned, there is no need to postulate that the universe is rotating. That takes you into deep waters if nothing else.

If we take the simplest model of our universe, therefore, then proper acceleration can be measured and is invariant. See, for example:

https://en.wikipedia.org/wiki/Proper_acceleration#In_curved_spacetime

 

[Peter Leeves]

As far as modelling the universe is concerned, there is no need to postulate that the universe is rotating. That takes you into deep waters if nothing else.

If we take the simplest model of our universe, therefore, then proper acceleration can be measured and is invariant. See, for example:

https://en.wikipedia.org/wiki/Proper_acceleration#In_curved_spacetime

Thank you for the input PeroK. Had a quick look at that page and it looks like I have some serious bedtime reading to do tonight !

But it does seem you simply dismissed the very point of my post :( My purpose is to gain some understanding about our universe. Responding "there is no need to postulate that the universe is rotating" is simply disregarding that it might be an entirely legitimate view point, and is not a constructive argument. If acceleration is relative, then the description I gave of the rotating universe is equally as valid as your notion that the universe doesn't rotate.

I suppose the reason I posted is to hear arguments on both sides (rather than instant dismissal as wrong) to improve my understanding. i.e. Whether acceleration absolute or relative.

 

[FactChecker]

This question is related to Mach's principle. This is over my head, but I believe that GR and frame-dragging do indicate that a massive spinning shell would cause such an effect at the center. I would appreciate hearing the PF expert opinion on this.

 

[PeroK]

Thank you for the input PeroK. Had a quick look at that page and it looks like I have some serious bedtime reading to do tonight !

But it does seem you simply dismissed the very point of my post :( My purpose is to derive some "truth" about our universe. Responding "there is no need to postulate that the universe is rotating" is simply disregarding that it might be an entirely legitimate view point, and is not a constructive argument. Compounded when you talk about "proper acceleration". If acceleration "truly" is relative, then the description I gave of the rotating universe is equally as valid as your notion that the universe doesn't rotate.

I suppose the reason I posted is to hear arguments on both sides (rather than instant dismissal as wrong) to get me closer to the correct version of reality. i.e. Whether acceleration absolute or relative.

There is no "absolute truth" in physics, only mathematical models that successfully predict natural phenomena.

Beyond that, your question relates more to metaphysics and philosophy, which are off limits here.

 

[Dale]

Summary:: Can the spinning bucket of water be used to argue that acceleration is relative, and not absolute ?

I do at least see the argument that acceleration is ACTUALLY relative.

Before you make that argument one way or the other it is important to clarify what you mean by acceleration. There are at least two distinct concepts of acceleration: proper acceleration and coordinate acceleration. Which are you discussing?

 

[Peter Leeves]

Beyond that, your question relates more to metaphysics and philosophy, which are off limits here.

I'm busy reading through a whole pile of earlier threads on this topic (on this forum). It seems many others consider this a question of physics rather than philosophy. But I do appreciate your time and thoughts.

 

[Dale]

It seems many others consider this a question of physics rather than philosophy.

Well, this is a tricky line. It is a topic that can be discussed physically, but it does have a tendency to degenerate into philosophy quite easily. @PeroK was reasonably objecting to words like “ACTUALLY” “truth” “truly” and “reality” which tend to push the topic away from the science and towards the philosophy.

Those terms can all be taken to imply that there is some hidden facts that may be in contradiction to our measurements. So they are best avoided if you do in fact wish to have a scientific rather than a philosophical discussion.

I don’t think that the discussion is inherently problematic, but please do be aware of the risk and do what you can to steer the conversation in the right direction.

 

[Peter Leeves]

Before you make that argument one way or the other it is important to clarify what you mean by acceleration. There are at least two distinct concepts of acceleration: proper acceleration and coordinate acceleration. Which are you discussing?

Dale, as you'll no doubt guess I'm a complete amateur, just trying my best to get a handle on reality. My current understanding of acceleration is that Force = Mass x Acceleration, hence Acceleration = Force / Mass). I have a little knowledge of Special and General Relativity and that's why I can see the argument for acceleration being relative and not absolute. Do you have the time / patience to briefly explain the difference between the two concepts you mentioned ? Or I can do some googling myself. Then I can answer your question as to which one I'm discussing.

 

[Peter Leeves]

@PeroK was reasonably objecting to words like “ACTUALLY” “truth” “truly” and “reality”

Thanks Dale, noted and I'll be sure to avoid using such terms in the future. Hopefully my original question was a physics one.

I've arrived at this point (is acceleration absolute or relative) due to the Twin Paradox and the asymmetry used to explain why one twin gets older and the other younger. It seems it comes down to whether the acceleration is absolute or relative (does the spaceship twin move, or could the universe accelerate away from the spaceship). I can certainly see the argument that acceleration is relative (hence my answer to the spinning bucket example).

 

[Dale]

Do you have the time / patience to briefly explain the difference between the two concepts you mentioned ? Or I can do some googling myself. Then I can answer your question as to which one I'm discussing.

Sure. That is probably the best place to start this discussion.

When we do physics we often use a coordinate system. This is a set of four numbers that identify every event, typically one for time and three for space. The coordinate acceleration is then the second derivative of the space coordinates with respect to time.

In contrast, the proper acceleration is the acceleration that is physically measured by an accelerometer. By “accelerometer” I mean one of those six degree of freedom inertial measurement units, but that is a lot to write. In an inertial frame the coordinate acceleration and the proper acceleration are the same (at non-relativistic velocities), but they can be very different in non inertial frames.

 

[Peter Leeves]

When we do physics we often use a coordinate system.

In contrast, the proper acceleration is the acceleration that is physically measured by an accelerometer.

Thank you. That's an extremely clear and concise explanation.

I can now say the acceleration in my original post considers the latter type - proper acceleration, as measured by an accelerometer. Since the water in the bucket is influenced by the rotating gravitational field (hence water climbs up the sides of the bucket), so would an accelerometer be influenced. Hence, this appears to confirm that acceleration (of the accelerometer type) is indeed relative.

Can I ask if you'd agree, or do you have some argument that my conclusion is incorrect ? I'm honestly just trying to increase my understanding.

 

[PeroK]

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

The key example from GR is to contrast an object on the Earth's surface and one in freefall towards the Earth's surface.

In a reference frame in which the Earth's surface is at rest, the falling object has coordinate acceleration. But, according to GR, it has zero proper acceleration.

The object on the Earth's surface, however, has a proper acceleration upwards.

This matches the data that the object in freefall is subject to no forces, but the object on the ground measures an upward force from the ground. Measurable force equates to proper acceleration.

 

[Dale]

I can now say the acceleration in my original post considers the latter type - proper acceleration, as measured by an accelerometer. Since the water in the bucket is influenced by the rotating gravitational field (hence water climbs up the sides of the bucket), so would an accelerometer be influenced. Hence, this appears to confirm that acceleration (of the accelerometer type) is indeed relative.

On the contrary, proper acceleration is invariant. All reference frames and all observers agree on the proper acceleration.

Proper acceleration can be written mathematically as a covariant derivative, which is specifically designed to produce only invariant results.

Can you explain why you think proper acceleration is relative?

 

[Peter Leeves]

On the contrary, proper acceleration is invariant. All reference frames and all observers agree on the proper acceleration.

Proper acceleration can be written mathematically as a covariant derivative, which is specifically designed to produce only invariant results.

I apologise but the above is over my head, so I'm not able to comment.

Can you explain why you think proper acceleration is relative?

Two reasons.

The first is simple logic. You can place yourself in both reference frames (the bucket/water is inertial, or the universe is inertial) and make the same (correct) observations in both cases.

The second is that in a lecture in 1918 Einstein used the propogation of a universal gravitational field to explain the Twin Paradox. In that case the field was linear in direction of the travel (+ in the outward travel and - in the return travel). I just put that same gravitational field in a circular context to suit the spinning bucket/water example.

It might help to clarify that the universal gravitational field that Einstein proposed, only exists to the stationary twin and only for the duration of the acceleration. The Earth (and universe) which accelerate away from the stationary twin, do not feel this new gravitational field - only the stationary twin.

 

[reinhard55]

If there is no difference then there is no difference otherwise there must be a difference
If we cannot differ between a rotating bucket and a rotating universe around the bucket then reality must be the same otherwise reality is not the same.
So the final question is: Is there a difference between a rotating bucket and a rotating universe arround the bucket?
If yes which?

 

[PeroK]

So the final question is: Is there a difference between a rotating bucket and a rotating universe arround the bucket?
If yes which?

What happens if you have two buckets rotating in different directions? Or, a rotating bucket on a rotating Earth?

 

[Peter Leeves]

Is there a difference between a rotating bucket and a rotating universe around the bucket?

Beautifully put.

That really gets to the crux of it. Logic says if you get the same observations in both cases there's no difference and proper acceleration is relative.

I believe there would be no difference in the observations (for the reasons I've already described) - but happy to be shot down so long as someone can do it with logic I can comprehend.

 

[Peter Leeves]

What happens if you have two buckets rotating in different directions?

The answer is, it's only the spinning bucket that experiences the new gravitational field and only for the duration of the acceleration, not the rest of the universe or any other bucket. I did make that clarifcation above, but as an edit. Possibly you didn't see it.

Two spinning buckets would each see a new gravitational field propogate but rotating in different directions. Same for a 3rd rotating bucket on a rotating earth. It is the only thing that would feel it's own rotating gravitational field.

I think I see why Einstein invoked this emerging gravitational field to explain the twin paradox. It seems to be the principle of equivalence. Something accelerating in one direction away from something static, is equivalent to the static one saying he is accelerating away and the other one stays static.

 

[Dale]

You can place yourself in both reference frames (the bucket/water is inertial, or the universe is inertial) and make the same (correct) observations in both cases.

The fact that you can use different frames and get the same proper acceleration is precisely what makes it invariant. It would be relative if the two different frames got different results.

The second is that in a lecture in 1918 Einstein used the propogation of a universal gravitational field to explain the Twin Paradox. In that case the field was linear in direction of the travel (+ in the outward travel and - in the return travel). I just put that same gravitational field in a circular context to suit the spinning bucket/water example.

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.

 

[Nugatory]

Logic says if you get the same observations in both cases there's no difference...

yes, that is a reasonable position (to be on absolutely solid ground you’d also want to exclude the possibility that different mechanisms that coincidentally produce the same effect on the water are involved - that’s an unnecessary distraction here). However, it does not follow that

... and proper acceleration is relative.

The water in the bucket is a form of accelerometer, a device that measures proper acceleration. There’s nothing relative about its behavior - the shape of the surface is what it is, and it is the same for all observers everywhere.

 

[Peter Leeves]

The fact that you can use different frames and get the same proper acceleration is precisely what makes it invariant. It would be relative if the two different frames got different results.

Once again I'm at a loss. Can you please explain what invarient means in the context of acceleration / this discussion ? Not familiar with the term so unable to comment.

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.

Same as above. I'm not familar with Chistoffel or his symbols.

I can clarify that Einstein didn't mention that during his answer to the twin paradox. It was the propogation of a new gravitation field (only existing for the stationary twin) for the duration of the acceleration / deceleration. I'm pretty sure Einstein was saying that regarding the Earth twin as static and the spaceship twin as moving was only one of two possible (but equally real) perspectives. The other being the spaceship twin remained static and the Earth (and destination point and rest of the entire universe) was moving away. His assertion that the two scenarios were equivalent and equally valid does seem logical. A bit like the guy in a lift in free fall above the Earth being equivalent to a guy deep in space experiencing no gravitational acceleration really.

 

[David Lewis]

...the shape of the surface is what it is, and it is the same for all observers everywhere.

I believe the shape of the surface would be subject to Lorentz contraction the same as any other shape.

 

[Nugatory]

I can clarify that Einstein didn't mention that during his answer to the twin paradox.

Some of the difficulty here is because the popular treatments oversimplify the history until it disappears. Relativity did not spring out of Einstein’s brain fully formed in 1905; it took many years to distill the clean mathematical form of the theory from his initial brilliant insight and then to reformulate special relativity as the flat-space special case of the more general theory of General relativity. Just about anything you read from that era is going to contain a number of unmarked wrong turns.

Thus, it’s most effective to learn the modern form of the theory and then apply that understanding to the history, rather than trying to work forward from the writings of Einstein and his contemporaries.

 

[Nugatory]

I believe the shape of the 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.

 

[Peter Leeves]

I can't help but feel I'm the one causing confusion here. I'm probably using terms like absolute or relative acceleration, inertial and non-inertial reference frames without really understanding the terms well enough. Throwing even more into the pot (variance, proper or co-ordinate acceleration, Christoffel symbols etc) isn't helping much, lol (although I really am trying to take more onboard and will look up stuff I'm unfamiliar with later). It's easier (for me) to speak in layman's terms, which I hope can still be used to make a coherent argument.

So, earlier we seemed to arrive at the core issue. Will there be any observed difference between a rotating bucket in a static universe or a rotating universe around a static bucket ? I think not because I believe one scenario is directly equivalent to the other (mechanism described earlier). Can anyone shoot this conclusion down (preferably in layman's terms) ?

 

[haushofer]

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. I.e. water in the bucket shouldn't become concave in an otherwise empty universe. Newton would disagree; he defined acceleration w.r.t. space.

And Einstein...well, Einstein believed Mach's principle was true, but his own theory of General Relativity is not fully Machian. Yes, inertial properties of a test mass are defined by other masses; they curve spacetime. But in an empty universe a particle can still undergo inertial forces because Minkowski spactime solves the field equations of an empty universe.

In the end, this remains an open question, mostly because neither Mach, Einstein or other people can tell you exactly what m(M) is. Thats's also why nowadays most physicists lost their interest in the topic.

 

[PeroK]

And Einstein...well, Einstein believed Mach's principle was true, but his own theory of General Relativity is not fully Machian.

To give Einstein a taste of his own medicine: "God does not play roulette with the universe"!

 

[haushofer]

I can't help but feel I'm the one causing confusion here. I'm probably using terms like absolute or relative acceleration, inertial and non-inertial reference frames without really understanding the terms well enough. Throwing even more into the pot (variance, proper or co-ordinate acceleration, Christoffel symbols etc) isn't helping much, lol (although I really am trying to take more onboard and will look up stuff I'm unfamiliar with later). It's easier (for me) to speak in layman's terms, which I hope can still be used to make a coherent argument.

So, earlier we seemed to arrive at the core issue. Will there be any observed difference between a rotating bucket in a static universe or a rotating universe around a static bucket ? I think not because I believe one scenario is directly equivalent to the other (mechanism described earlier). Can anyone shoot this conclusion down (preferably in layman's terms) ?

We don't know, because 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.

Maybe I missed the mechanism you mentioned; I haven't read all posts yet.

 

[Dale]

Once again I'm at a loss. Can you please explain what invarient means in the context of acceleration / this discussion ?

There are generally two classes of physical quantities that are relevant to this discussion: relative and invariant. Relative quantities are quantities that depend on the reference frame. For example, velocity. The velocity of a given object is a relative quantity because different reference frames will disagree on the quantity. Invariant quantities are quantities that do not depend on the reference frame. For example, charge. The charge on an object is an invariant quantity because different reference frames will all agree on the quantity.

So when you say that something is the same for different reference frames then that thing is an invariant thing, rather than a relative thing.

The term “absolute” is often used in a philosophical sense, so instead I use the term invariant to avoid any accidental philosophical implications.

I can clarify that Einstein didn't mention that during his answer to the twin paradox. It was the propogation of a new gravitation field (only existing for the stationary twin) for the duration of the acceleration / deceleration.

Sure. I know exactly the passage you are describing. It is written for a non-technical audience and I am telling you the corresponding technical terminology. Hopefully that will help with your studies at some point.

I'm pretty sure Einstein was saying that regarding the Earth twin as static and the spaceship twin as moving was only one of two possible (but equally real) perspectives. The other being the spaceship twin remained static and the Earth (and destination point and rest of the entire universe) was moving away. His assertion that the two scenarios were equivalent and equally valid does seem logical.

Yes, both are equivalent and valid. However that does not change the fact that the Christoffel symbols (Einstein’s gravitational field) are relative. Relative quantities are legitimate and valid, but it is still important to recognize them as relative. Particularly since that is the topic of the thread.

 

[Peter Leeves]

So when you say that something is the same for different reference frames then that thing is an invariant thing.

The term “absolute” is often used in a philosophical sense, so instead I use the term invariant to avoid any accidental philosophical implications.

My thanks again. Understanding these new terms is helping enormously. So:

Changes in different reference frames (example velocity) = relative
Same in different reference frames (example charge on an object) = invarient (absolute)

Velocity is relative. Are you able to say if acceleration (of the proper type) is relative or invariant (absolute) ?

 

[PeroK]

Are you able to say if acceleration (of the proper type) is relative or invariant (absolute) ?

In SR/GR, proper acceleration is an invariant.

 

[Sagittarius A-Star]

I can clarify that Einstein didn't mention that during his answer to the twin paradox. It was the propogation of a new gravitation field (only existing for the stationary twin) for the duration of the acceleration / deceleration.

No. That new "gravitational field" was only existing for the traveling twin and during acceleration (in the direction of the stationary twin). Also a deceleration is an accaleration (in the opposite direction). If you are in an accelerating rocket, you feel the artificial "gravitational" field. In this accelerating frame, the clock of the "stationary" twin ticks faster than that of the travelling, due to a different hight in the "gravitational field".

The scenario is asymmetric for both twins.

Source (see in the middle of the page):
https://en.wikisource.org/wiki/Translation:Dialog_about_Objections_against_the_Theory_of_Relativity

 

[Nugatory]

Are you able to say if acceleration (of the proper type) is relative or invariant (absolute)?

Proper acceleration is invariant; if you are holding an accelerometer we can use any frame to calculate the reading on the accelerometer and we’ll get the same answer. Coordinate acceleration is relative; something may have zero coordinate acceleration relative to you and non-zero coordinate acceleration relative to me.

 

[Peter Leeves]

In SR/GR, proper acceleration is an invariant.

Then returning to my original post, having determined that proper acceleration is invariant (and accepting the postulates of SR/GR), we can deduce there would be no observed difference whether you consider the bucket is rotating in a static universe, or a static bucket is in a rotating universe. Because the acceleration must be the same (equivalent) in both reference frames