Revisiting Newton's Bucket Experiment: Is Rotation Absolute or Relative?

[novop]

Considering the above set-up, we have a platform that rotates with some angular velocity with respect to the earth. And on this platform, a magical bucket (filled with water) rotates with the same angular velocity, but in the opposite direction.

Now, on the Earth frame, anyone looking at the bucket will see that the bucket and hence the contained water is not rotating, hence the shape of the water will be flat.

However, if a person were to stand on the rotating platform, they would see the bucket rotating, hence the water should appear as concave. (Would the centrifugal force observed in the reference frame of the spinning platform cancel the effects of the rotating bucket on the water, such that the net effect is that the water appears flat in this frame as well?)

How can these two different conclusions be reconciled?

 

[bcrowell]

Rotation in GR is not Machian. You can tell whether your laboratory is rotating without reference to anything external. Some ways you can tell are: (1) a gyroscope, (2) the Sagnac effect, or (3) the bucket of water you described.

GR does, however, allow you to use any coordinate system you choose. If you want to use a rotating coordinate system, you can. In that coordinate system there will be a gravitational field away from the axis. In a frame rotating with the water, this gravitational field is what causes the water to form a concave surface.

 

[I like Serena]

Hi novop!

It's about the difference between so called "inertial frames" and "non-inertial frames".

An inertial frame is a coordinate system in which the laws of Newton apply.
In such a frame there is no centrifugal force, but only the possible lack of centripetal force.

It is possible to apply the physical laws in a rotating frame in which there is a centrifugal force, but in case of doubt, we'll always fall back on an inertial frame in which it is easier to apply the physical laws!

 

[novop]

Thanks for the responses. Something feels quite odd about the notion of absolute rotation though; it doesn't sit well!

 

[Naty1]

Something feels quite odd about the notion of absolute rotation though; it doesn't sit well!

like linear acceleration?

 

[bcrowell]

Hi novop!

It's about the difference between so called "inertial frames" and "non-inertial frames".

An inertial frame is a coordinate system in which the laws of Newton apply.
In such a frame there is no centrifugal force, but only the possible lack of centripetal force.

It is possible to apply the physical laws in a rotating frame in which there is a centrifugal force, but in case of doubt, we'll always fall back on an inertial frame in which it is easier to apply the physical laws!

This is not quite right in the context of general relativity. In GR, frames of reference are local, and coordinate systems are global. In GR, the distinction between preferred and non-preferred frames is not the same as the Newtonian one. In GR, free-falling frame are the preferred frames.

 

[I like Serena]

This is not quite right in the context of general relativity. In GR, frames of reference are local, and coordinate systems are global. In GR, the distinction between preferred and non-preferred frames is not the same as the Newtonian one. In GR, free-falling frame are the preferred frames.

Yes!
Quite right.

So the surface of the water in the bucket would not be flat, nor concave.

It would be convex in the preferred frame!

In a preferred frame that is linearly accelerated, it would be flat.

And in a preferred frame that is rotating, it would be cylindrical, assuming the water won't slop over the edge.

Only in a combination of the last two, would it be concave!

 

[kmarinas86]

Thanks for the responses. Something feels quite odd about the notion of absolute rotation though; it doesn't sit well!

We can't find an absolute non-rotating frame at this time. Our planet rotates, our sun rotates, the galaxy rotates, etc.. It is possible to detect the effects of their non-inertial motions, but as you get to a much larger scale, the effects take much longer to occur, beyond the time scale of limited human observation.

 

[bcrowell]

So the surface of the water in the bucket would not be flat, nor concave.

It would be convex in the preferred frame!

Huh? I don't follow you here.

In a preferred frame that is linearly accelerated, it would be flat.

If you're thinking of free-falling frames in GR as being linearly accelerated, then that isn't really right. Free-falling frames in GR are the natural reference to take as being *unaccelerated*.

And in a preferred frame that is rotating, it would be cylindrical, assuming the water won't slop over the edge.

The preferred (inertial) frames in GR are nonrotating.

 

[bcrowell]

We can't find an absolute non-rotating frame at this time. Our planet rotates, our sun rotates, the galaxy rotates, etc.. It is possible to detect the effects of their non-inertial motions, but as you get to a much larger scale, the effects take much longer to occur, beyond the time scale of limited human observation.

This is incorrect. You don't need astronomical objects in order to define a frame of reference. A nonrotating frame can be established with reference to a gyroscope.

 

[I like Serena]

Huh? I don't follow you here.

In a preferred frame there is no gravity, so the water in the bucket will by cohesion tend to a spherical shape, hence a convex surface.

If you're thinking of free-falling frames in GR as being linearly accelerated, then that isn't really right. Free-falling frames in GR are the natural reference to take as being *unaccelerated*.


The preferred (inertial) frames in GR are nonrotating.

I meant to start with a preferred frame and then shift the frame to one with acceleration in it.
Like we start with a free falling elevator, but then we accelerate the elevator linearly up, creating a kind of artificial gravity.
Now take the frame of the linearly accelerated elevator.
The surface of the water in the bucket will be flat.

Same thing for the rotating frame.

 

[kmarinas86]

We can't find an absolute non-rotating frame at this time. Our planet rotates, our sun rotates, the galaxy rotates, etc.. It is possible to detect the effects of their non-inertial motions, but as you get to a much larger scale, the effects take much longer to occur, beyond the time scale of limited human observation.

This is incorrect. You don't need astronomical objects in order to define a frame of reference. A nonrotating frame can be established with reference to a gyroscope.

Doesn't the gyroscope have to spin sufficiently fast to account for larger scale rotations? A weak-spinning gyroscope obviously can take care of the Earth's rotation, and maybe even its orbit around the Sun. But the galaxy? I don't think so. The weaker the rotational force, then the faster the gyroscope would have to spin, as far as I know. That's correct right?

 

[Quinzio]

Thanks for the responses. Something feels quite odd about the notion of absolute rotation though; it doesn't sit well!

In addition to the methods described, there an even more simple way to detect if your laboratory is rotating. Take two balls you believe they are at rest and connect a sing between them, then let them free. If the spring stretches, the two balls are rotating.

The concept of absolute rotation is not correct and it's confusing. The confusion arises because a spinning object without friction happily continues to rotate forever and seems at rest, but it's not at rest.
Take a rotating disk. Each one of its atoms is in a different inertial frame.
When an object is rotating, it means just that: each slice (a plane passing through the spin axis) is in a different inertial frame. The object is composed by infinite number of inertial frames.

 

[Buckethead]

Considering the above set-up, we have a platform that rotates with some angular velocity with respect to the earth. And on this platform, a magical bucket (filled with water) rotates with the same angular velocity, but in the opposite direction.

Now, on the Earth frame, anyone looking at the bucket will see that the bucket and hence the contained water is not rotating, hence the shape of the water will be flat.

However, if a person were to stand on the rotating platform, they would see the bucket rotating, hence the water should appear as concave. (Would the centrifugal force observed in the reference frame of the spinning platform cancel the effects of the rotating bucket on the water, such that the net effect is that the water appears flat in this frame as well?)

How can these two different conclusions be reconciled?

The water in the bucket will be flat for both observers. The bucket is stationary relative to the stars and the person on the rotating platform is not. The person on the platform will experience non linear acceleration hence they will know they are rotating and they will also know that even thought the bucket is seemingly rotating, in reality it is not rotating at all regardless of who is looking at it.

 

[novop]

I don't agree. If it seems, for the person on the rotating platform, that the bucket is rotating, then it follows that they must see the water in the bucket forming a concave shape.

For an observer standing on the earth, he sees the bucket and its contents as being completely still. So then how can the water be both flat and concave depending on where we look at it from?

I understand that if we "look for a centrifugal force" in the frame of the rotating bucket, we will find one and therefore conclude that the bucket is spinning. The same applied to the rotating platform would lead to the conclusion that the platform is spinning as well.

My question is how I can reconcile the conclusion that the water is both flat and concave, depending on where it is observed from.

 

[Mentz114]

I don't agree. If it seems, for the person on the rotating platform, that the bucket is rotating, then it follows that they must see the water in the bucket forming a concave shape.

For an observer standing on the earth, he sees the bucket and its contents as being completely still. So then how can the water be both flat and concave depending on where we look at it from?

I understand that if we "look for a centrifugal force" in the frame of the rotating bucket, we will find one and therefore conclude that the bucket is spinning. The same applied to the rotating platform would lead to the conclusion that the platform is spinning as well.

You have missed what everyone is telling you - rotation is not relative.

My question is how I can reconcile the conclusion that the water is both flat and concave, depending on where it is observed from.

Have you tried this ? If the bucket is not rotating, then all observers will see the water surface flat. The water acts as a 'rotatometer', and tells us if the bucket is rotating.

 

[Quinzio]

I think his question is: why in the universe is there a "rotatometer" but not a "speedometer" ?
The answer is because rotation is made by pair of differential inertial frames (pairs of frames moving at +v and -v).

 

[PAllen]

I think his question is: why in the universe is there a "rotatometer" but not a "speedometer" ?
The answer is because rotation is made by pair of differential inertial frames (pairs of frames moving at +v and -v).

Rotation is acceleration (change in velocity; that speed is constant is irrelavant). The proper linear comparison is with uniform acceleration. So there are both 'rotatometers', to use your word, and accelerometers. In fact, the simplest accelerometer will respond to all types of acceleration, including rotation: attach a ball to a flexible spring and hold the other end of the spring. The spring will have tension and point away from the center of rotation (if you are rotating, but otherwise in free fall). If you have other acceleration components, they will sum producing some total magnitude and direction; the spring->ball will be point opposite the total acceleration direction, and the tension will be proportional to the magnituge.

 

[novop]

If the bucket is not rotating, then all observers will see the water surface flat. The water acts as a 'rotatometer', and tells us if the bucket is rotating.

Didn't Newton's bucket experiment show this to be wrong as well? If you let a bucket attached to a coiled rope spin, once the rope uncoils itself the bucket will stop spinning for a moment, but the water will continue to spin... meaning that the bucket would not be rotating at that moment, but the water would definitely be concave.

 

[Buckethead]

Didn't Newton's bucket experiment show this to be wrong as well? If you let a bucket attached to a coiled rope spin, once the rope uncoils itself the bucket will stop spinning for a moment, but the water will continue to spin... meaning that the bucket would not be rotating at that moment, but the water would definitely be concave.

Don't confuse Newton's Bucket or any other experiment involving rotating objects with releativity as described by Special Relativity or with the general idea of 2 objects moving relative to each other in a linear fashion such as 2 coasting spaceships passing each other in the night. It is not correct to say that platform A rotating relative to platform B is the same as platform B rotating relative to platform A. Newtons bucket and your experiment involve one thing and one thing only and that is the question of what is rotating relative to the Earth (loosely speaking) or more correctly relative to the distant stars. In the case of your experiment the observer on the platform is rotating and the bucket is not, period, there is no other way to look at it. In the case of Newton's bucket the question is whether the water itself is rotating or not, nothing else matters, not the bucket or the observer. If the water is rotating relative to the Earth (actually stars) then it will be concave to everyone looking at it, if it is not rotating relative to to the Earth (actually stars) then it is flat to everyone looking at it. This is not a question of relativity between the water and any observers, this is only a question of relativity between the water and the stars.

 

[Mentz114]

Didn't Newton's bucket experiment show this to be wrong as well? If you let a bucket attached to a coiled rope spin, once the rope uncoils itself the bucket will stop spinning for a moment, but the water will continue to spin... meaning that the bucket would not be rotating at that moment, but the water would definitely be concave.

The water would be concave because it is spinning. The point is that if the water, or anything, is rotating, this is not relative. The forces created locally by the rotation make the surface concave.

 

[harrylin]

Considering the above set-up, we have a platform that rotates with some angular velocity with respect to the earth. And on this platform, a magical bucket (filled with water) rotates with the same angular velocity, but in the opposite direction.

Now, on the Earth frame, anyone looking at the bucket will see that the bucket and hence the contained water is not rotating, hence the shape of the water will be flat.

However, if a person were to stand on the rotating platform, they would see the bucket rotating, hence the water should appear as concave. (Would the centrifugal force observed in the reference frame of the spinning platform cancel the effects of the rotating bucket on the water, such that the net effect is that the water appears flat in this frame as well?)

How can these two different conclusions be reconciled?

Did you read the original discussion by Newton, with which Mach later disagreed?
You can find it here (just click on "cancel"!):
http://gravitee.tripod.com/definitions.htm

Scroll down to "Scholium" and search for "vessel".
Enjoy

Harald

 

[Mentz114]

Did you read the original discussion by Newton, with which Mach later disagreed?
You can find it here (just click on "cancel"!):
http://gravitee.tripod.com/definitions.htm

Scroll down to "Scholium" and search for "vessel".
Enjoy

Harald

Newton got it right first time. Rotation is absolute and can be distinguished from relative motion by the forces. Not surpring since he discovered the laws of inertia as well.