Newton's bucket experiment

[gen x]

If you remove all matter in universe when Newton bucket is spinning(water level is still curved), bucket spins in relation to what?
How we called this frame?

 

[sbrothy]

If you remove all matter in universe when Newton bucket is spinning(water level is still curved), bucket spins in relation to what?
How we called this frame?

Oooh this is an old goodie. I seem to remember something about Newton himself being aware that something was wrong but he went and published (was that the term in those days?) anyway. Also, it's a horse which has been well and truly flogged on here. I can't wait to hear what the new generation makes of it (or if the old will just shut it down in disgust ).

 

[Dale]

If you remove all matter in universe when Newton bucket is spinning(water level is still curved)

Can you provide any experimental confirmation of that claim?

bucket spins in relation to what?
How we called this frame?

Inertial.

 

[Baluncore]

If you remove all matter in universe when Newton bucket is spinning(water level is still curved), bucket spins in relation to what?

Mirror the system. Tie the handles of two similar buckets of liquid together with a string. When the combination is spinning in space, there will be a stationary point on that string.

On the surface of the Earth, when an open container of liquid, spins about a vertical axis, the free surface forms a paraboloid. Without gravity, the liquid surface would form a cylinder. Each part of that liquid surface could be seen as the liquid surface of a small bucket, spinning or swinging about a point on the axis.
https://en.wikipedia.org/wiki/Liquid-mirror_telescope
(Which does mention Isaac Newton).

 

[Andy Resnick]

If you remove all matter in universe when Newton bucket is spinning(water level is still curved), bucket spins in relation to what?
How we called this frame?

If you removed all matter in the universe (other than the spinning bucket), why do you think the surface of the water would still be curved?

In any case, it's a highly interesting thought experiment that seems to require the existence of an absolute frame of reference. The paradoxes of Newton's bucket are countered by Mach's principle (to paraphrase: matter 'there' is required for inertia 'here'). To be sure, Mach's principle hasn't been developed into a quantitative theory (yet).

 

[sbrothy]

It has probably been mentioned before but if so I didn't pay proper attention......

 

[Nugatory]

If you remove all matter in universe when Newton bucket is spinning(water level is still curved), bucket spins in relation to what?

That is the wrong question, because we can call that frame anything we want and the physics will be the same. (And if you’re questioning whether that frame exists, you’re misunderstanding what a frame is. A frame is a rule for assigning coordinates to events, and it is straightforward to find several such rules that work well when applied to a bucket of water).

The right question is “does the surface of the water curve?”; either it does or it doesn’t, no matter what frame we choose and what we call that frame. And the answer to that question is “We don’t know” because we don’t have any spare empty universes hanging around that we can use to perform the experiment.

For what it is worth, both Newtonian physics and special/general relativity say that if we could find an empty universe and insert a rotating bucket of water into it…. The surface of the water would curve.

 

[gen x]

Can you provide any experimental confirmation of that claim?

If you removed all matter in the universe (other than the spinning bucket), why do you think the surface of the water would still be curved?

The right question is “does the surface of the water curve?”; either it does or it doesn’t, no matter what frame we choose and what we call that frame. And the answer to that question is “We don’t know” because we don’t have any spare empty universes hanging around that we can use to perform the experiment.

Water would not be curved like in case when earth(gravity)is below bucket, but without gravity and if bucket has lid water will be rotating on the sides of bucket, in center will be hole. If bucket dont have lid water will goes out of bucket.

Indeed we can try this in free fall, zero g-flight for example...

Why do you think that no matter in universe( zero gravity) will stop water to rotate?

 

[Dale]

Why do you think that no matter in universe( zero gravity) will stop water to rotate?

I didn’t claim that it would stop.

You claimed that it would continue after removing all other matter from the universe. I am asking for you to provide experimental evidence supporting your claim.

My asking you to provide evidence for your claim is not me making the opposite claim.

 

[gen x]

You claimed that it would continue after removing all other matter from the universe. I am asking for you to provide experimental evidence supporting your claim.

My evidence is pure logic, because of inertia water/bucket will continue to spin. Isn't that so trivial?

It is not possible to remove all matter in universe, but we can do this test in elevator in free fall, in free fall gravity is zero and that is very similar situation as there is no matter in universe. But again this test is so trivial that is not need to be tested at all.

If we can't remove all matter from universe that is not reason that we can't conclude will water continue to spin or not.

Point of my question is what was Newton conclude wrong it this experiment? I don't understand.

 

[Roberto Pavani]

The Riemann tensor of the spinning bucket is a coordinate-invariant fact, sourced by the bucket+water's own $T_{\mu\nu}$ (the angular momentum shows up as gravitomagnetic terms).
The distant stars contribute nothing to it, so removing them changes nothing local: the water surface stays curved.
The bucket never spun "relative to the stars", it spins relative to the local inertial frame set by free-falling gyroscopes, which is defined with or without any distant matter.
That's why Mach's idea fails here as a physical claim.

 

[Dale]

My evidence is pure logic,

That isn’t evidence. Many things are logically possible and experimentally false.

we can do this test in elevator in free fall, in free fall gravity is zero and that is very similar situation as there is no matter in universe

Yes, we can do the experiment in an elevator, but we have no basis by which to claim that is very similar to an empty universe. We simply cannot know that.

If we can't remove all matter from universe that is not reason that we can't conclude will water continue to spin or not.

I agree. We can make firm conclusions about what would happen here.

Point of my question is what was Newton conclude wrong it this experiment? I don't understand.

Newton was not wrong in his prediction for the outcome of the experiment. What do you feel like you do not understand?

(If it is about this universe I will try to answer)

 

[Sagittarius A-Star]

it spins relative to the local inertial frame set by free-falling gyroscopes, which is defined with or without any distant matter.

Via the Lense–Thirring effect, gravity influences the orientation of free-falling gyroscopes in an Earth orbit relative to the stars. (related experiment: Gravity probe B). Therefore, distant matter should have an influence in the definition of local inertial frames. I think it is still not known, if this effect can support/ explain Mach's principle.

 

[Dale]

The distant stars contribute nothing to it, so removing them changes nothing local

Do you have any experimental evidence to support this claim? Please post the reference where the experimenters removed the distant stars and demonstrated the absence of any local change.

 

[Roberto Pavani]

@timmdeeg @Dale, Let me put it more carefully by superposition. To linear order the local inertial frame gets two contributions: the bucket's own stress-energy, plus the integrated effect of all distant matter (Lense–Thirring summed over the cosmos):

$\Omega_{\text{local inertial}} = \Omega_{\text{bucket}} + \int (\text{distant matter contribution})$

The bucket term is there regardless. Distant matter only changes the conclusion if that integral is nonzero. So the whole Machian question reduces to a single well-defined quantity: does $\int \frac{G}{c^2}\frac{\rho}{r} \,dV$ vanish or not?

I shouldn't have claimed "removing the stars changes nothing", that presupposes the integral is negligible, which I can't show. In fact Sciama's estimate suggests it's of order unity for the observed density, which would support Mach. So I'll retract that.

But there's a point that holds regardless of that integral, and it's the core one: the spinning bucket has one Riemann tensor, the static bucket has another, and changing the reference frame does not turn one into the other. The Riemann tensor is a tensor: its components transform covariantly, but the curvature invariants (e.g. the Kretschmann scalar $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$) are the same numbers in every coordinate system. Hence "stars rotating around a static bucket" and "bucket at rest" are the same physical system in two coordinate charts, same Riemann, same invariants. "Bucket physically spinning" is a different stress-energy tensor, different Riemann, different invariants, real gyroscope precession, curved surface. No change of frame can map one into the other, because no change of frame can alter an invariant scalar.

That distinction stands whether or not the Machian integral vanishes; whether the inertial frame itself is fixed locally or by the cosmic integral is the separate open question, and Timmdeeg is right that GP-B / Lense–Thirring is exactly the term that could make that integral matter.

If rotation could be removed by a change of frame, the Kerr metric would be diffeomorphic to Schwarzschild, but it isn't. They have different curvature invariants (the Kretschmann scalar depends on $a$), Kerr has an ergosphere and frame-dragging that Schwarzschild lacks, and angular momentum $J$ is an invariant charge, not a coordinate artifact. A rotating source and a static one are genuinely different spacetimes.

 

[A.T.]

I shouldn't have claimed "removing the stars changes nothing"

What is removing them now supposed to prove anyway? The information determining which local frames are inertial could have been imprinted on space-time before the expansion, when all those distant stars were not distant.

 

[gen x]

I agree. We can make firm conclusions about what would happen here.

And what is your conclusion?

Newton was not wrong in his prediction for the outcome of the experiment. What do you feel like you do not understand?

If we don't have matter in universe, does we have only one possible frame?

 

[Roberto Pavani]

A universe with a single mass admits either the Schwarzschild or the Kerr metric, depending on whether it is static or rotating, and the two metrics are different.

 

[Dale]

And what is your conclusion?

Before release there is no relative rotation between the bucket and the water, and the water is flat. Shortly after release there is relative rotation, and the water is flat. Some time after that there is no relative rotation, and the water is curved.

Going beyond Newton’s scenario, while in the last state, the bucket could be suddenly stopped and there would again be relative rotation between the bucket and the water, and the water would be curved.

I conclude that the curved surface of the water does not depend on the relative rotation of the water and the bucket. Rotation is not relative.

If we don't have matter in universe, does with have only one possible frame?

Yet again, we have no evidence for how a universe without matter would behave.

 

[Roberto Pavani]

@A.T. I didn't mean removing them now; I meant a universe that never had any other matter, a single object from the beginning of time. So the imprinting story doesn't apply: there's no past epoch when those stars were nearby and dense, because they never existed at all.

And GR still answers unambiguously: that lone object has a Riemann field that is Kerr if it rotates and Schwarzschild if it doesn't. Rotation and the local inertial structure are defined with no distant matter ever, past or present, to refer them to.
That's the point: the invariant distinction survives even in the one case where no Machian imprinting is possible even in principle.

 

[gen x]

Some time after that there is no relative rotation, and the water is curved.

Why Newton didn't conclude, now water rotate in relation for example Earth frame? I think he wrote, that water rotate in relation to absolute space

I conclude that the curved surface of the water does not depend on the relative rotation of the water and the bucket. Rotation is not relative.

Rotation is acceleration, so Newton did not notice that speed is relative and acceleration is absolute?

Yet again, we have no evidence for how a universe without matter would behave.

Why would not behave same as places where gravity is zero (almost zero)?

 

[Sagittarius A-Star]

Frame-dragging near the rotating Earth (about 30.7 milliarcseconds per year) was recently measure with a relative uncertainty of about 0.2 percent, using the satellites LARES-2 and LAGEOS.

Source:
https://www.gfz.de/en/press/news/de...nen-zeigen-wie-die-erde-die-raumzeit-mitzieht

related paper:
https://www.nature.com/articles/s41586-026-10715-0

 

[Roberto Pavani]

I think it's simple: do we want to keep GR, or not?

If we keep GR, the answer is unique, change the mass distribution, solve Einstein's equations, get the geometry.

If we don't keep GR, then we first have to define the new physical laws, and then derive the outcomes from them.

 

[Dale]

Why Newton didn't conclude, now water rotate in relation for example Earth frame?

As he said in his scholium, he believed in absolute space, and he wanted to provide the bucket example in support of absolute space. He was not interested in the Earth frame (which he did not consider to be the absolute frame).

Rotation is acceleration, so Newton did not notice that speed is relative and acceleration is absolute?

I don't know Newton's writing on that topic enough to say.

Why would not behave same as places where gravity is zero (almost zero)?

We simply don't know how empty universes behave. They might behave the same as empty space in this universe, or they might not. We just don't know.

 

[Dale]

If we keep GR, the answer is unique, change the mass distribution, solve Einstein's equations, get the geometry.

Almost. We also have to specify the boundary conditions. Only with the mass distribution and the boundary conditions is the answer unique.

The other issue is about keeping GR. We don't know if GR is the high-matter limit of some other more general law for gravitation. If so, then GR would not be the appropriate law for an empty universe.

For those two reasons any discussion of empty universes is pointless for physics in this universe. Solutions like Minkowski or Schwarzschild can and should be understood as representing an isolated patch of this universe rather than making claims about empty universes.