Newton's Bucket

Al68

It's not hard to claim that all the mass in the universe changed velocity billions of years ago because a small force was applied to a bucket today, if we keep in mind that we are talking about a change in relative velocity.

But we do have to acknowledge that accelerated reference frames are fundamentally different from inertial frames: not only can distant objects exceed c, change velocity with no force applied, etc., but causality itself can be violated, ie effect can precede cause.

Acknowledging that accelerated frames are fundamentally different from inertial frames is equivalent to acknowledging that (proper) acceleration wrt an inertial frame due to applied force is different from coordinate (relative) acceleration due to using a non-inertial frame.

Proper acceleration may not be "absolute", but a change in velocity relative to every other mass in the universe is as close to absolute as it gets.

Max™

The bucket itself has mass, curves spacetime within it's local frame, and should be possible to be identified as rotating/under a rotating gravitational field.


Two bricks could pull a rope taught without rotating if one brick was being accelerated in a straight line more than the other, tie two bricks together, hold one brick, let the other hang free. Naturally this would be distinguishable due to the forces exerted on one brick differing from the other.


Yes a single massive particle would curve spacetime in an empty universe, mass does not arise from groups of particles alone.

Rest Mass represents the amount of energy a body has when in a hypothetically perfect rest frame, it would be like sitting at the bottom of a hill.

Moving it would require pushing it up the hill some, imparting relativistic mass, increasing the total energy of the system.


Note that GR doesn't exclude the concept of an absolute frame, it merely excludes the identification of an absolute frame, as does SR. SR does allow a definition of an inertial frame to be given and used.

GR only allows this in limited cases, not as a global rule due to cases where the curvature of spacetime is large enough to transform the general inertial frame concepts into one of geodesic motions.

I find it easier to just consider the geodesic cases (i.e. free of external forces) than the inertial ones.

If something is rotating, it was acted upon in some way (be it a kinetic impact, or simply it's collapse under gravitation, both impart angular momentum which can be defined), and is no longer considered a valid inertial frame.

MeJennifer

If a universe is rotating or not is simply dependent on what chart you use and is ultimately only a coordinate effect.

And spacetime obviously never rotates.

A-wal

Yea I knew that. I got carried away because I was thinking that if a spinning bucket has force applied to it because the bucket is stationary and the universe is moving around it and therefore has increased mass, then acceleration could be seen as all other objects accelerating relative to you. Even if that could cause the sensation of acceleration it would be different because time dilation would work if reverse. Everything else would be travelling along a longer world line, so you would be ageing faster with respect to everything else rather than slower. I was right about the bucket though.

Anyway, a bucket on it's own couldn't spin because it would have nothing to spin relative to.
What about frame dragging?

Ken G

I would say that "what is rotating" is a purely observer-dependent issue, albeit not a purely coordinate-dependent issue. The distinction I have in mind is that if we are inertial observers, and we attach rotating coordinates to a rotating body, it will be static in those coordinates. However, those coordinates will identify themselves as being rotating, by virtue of fictitous coordinate forces that will appear. But, if the observer is also rotating, then we have a different matter-- the object is no longer rotating with respect to the observer, the rest of the universe is, and now we can attribute the fictitious forces with something real-- the gravity of the rotating universe. The coordinates no longer identify themselves as rotating, as those forces are no longer fictitious. I suppose one might describe that as a Machian view, but I believe it is fully consistent with general relativity.

Buckethead

I have a hard time with this. Doesn't this fly right in the face of Einsteins main reason for rejecting frames of reference when dealing with rotational acceleration, namely , that galaxy way in the distance can suddenly be moving faster than the speed of light if the observer were to be rotating, but be considered non-rotating from its frame of reference and instead the galaxy was considered to be revolving around the observer.

Buckethead

This thread has revealed a lot of really great thought generating ideas and I want to thank everyone for contributing so much. I am going to fully admit right now I am completely obsessed with Netwon's Bucket and I can't get enough of it and all the thoughtful posts have really got my brain working overtime.

There are some things about the Machian view (i.e. the "democracy of mass" in the universe defining a spatial reference to determine whether or not a bucket is actually "spinning" or not) that I would like to get some opinions on.

One thing that I'm having a hard time with is the force or field that might contribute to the metric. I think a lot of us here are assuming that gravity plays the dominant role here, but my problem with this is that if the bucket is rotating because it is rotating against the "stationary" metric, then this is strong evidence that the metric (due to gravity?) has drag. Drag may not be the right word, perhaps "influence" might be more accurate, but I'll say drag to make my point. If the metric is stationary any object flying through the metric at a constant velocity will be subject to the same drag that causes the bucket to show itself as "spinning". The result would be something, such as the object slowing down (which it doesn't) or some other effect.

No it seems to me that what we are looking at here is some makeup of the metric that can influence a rotating body without interfering with a body that is not accelerating but instead moving at any given velocity. Can gravity fit this effect?

One thought I have on this is that an object moving at a constant velocity is similar to a DC magnetic field. For example a wire can pass through a magnetic field and as long as the field strength or polarity don't change, no work is done and no electric current is induced in the wire. A rotating body first pushes against a stationary gravitational field then pulls on it, an AC movement through the gravitational field, which might induce resistance.

Another thought is that it's not gravity we are dealing with here, but some other field that can create a metric that is sensitive to acceleration but has no other effect on matter, and also a field that is created by matter.

I'd love to hear speculative opinions about this.

Ken G

I don't know to what extent Einstein "rejected frames of reference", I think he tried pretty hard to keep general relativity a completely relative description of motion. I believe the prevailing view is that he did not succeed in keeping motion entirely relative to other masses, but he did keep it entirely relative to other masses and/or to the fields that are proxies for those masses, thinking of inertia as a kind of interaction with a gravitational field. But what I'm saying is, if we place the observer at the top of the food chain, such that even the fields are subordinate to the perspective of the observer, then we can have the whole universe rotating for any given observer, and galaxies and even planets in our own solar system can move faster than c. There are already galaxies receding from our vantage point at speeds greater than c, cosmologically, so why should we object?

Buckethead

This may not necessarily be true. If the universe is expanding, it indicates a separation of local spacetimes that surround galaxy clusters. Certainly if spacetime in clusters can move relative to spacetime in other clusters, it also has the freedom to rotate relative to the spacetime of other clusters.

Buckethead

I didn't mean to be vector specific. I was just taking the sum total of the relative placement of the stars in general and any particle that was stationary (or moving at a constant velocity) relative to the sum of these stars would resist change, so yes that's right that this body in question could be anywhere in the local spacetime.

Hal King

Did the observer die?

MeJennifer

Space can, given the appropriate chart and/or solution, rotate, however spacetime cannot. Spacetime includes time and rotation is something that obviously happens in time.

Buckethead

I don't think this is correct. Spacetime is a construct that can describe the motions of bodies or energies through space taking time into account. For example: Light passes by the sun and deflects. Pure space would not allow for this, but spacetime describes this bending. Spacetime is a geometric shape that uses time to define the geometric form. It is still spacial in nature and as such can rotate.

A-wal

If the observer is rotating and the universe is rotating around the observer at the equivalent rate then there is no rotation.

In a straight line? Does that imply false red shifting or is special relativity only local? I didn't think it had a range.

Buckethead

So something has been bothering me about using gravitational attraction of stars as the "web" that defines the "absolute space" that is used as a reference point for determining whether or not Newton's bucket is spinning.

I was reading a section of "Matter and Motion" by James Clerk Maxwell and he talks about Newton's bucket on the north pole of the Earth. If the bucket is made to spin with the Earth, once every 24 hours relative to the stars, and then against the earth again once every 24 hours, the bucket would show the same amount of concaveness in either direction indicating that the velocity of the overwhelming gravitational field of the earth has zero effect on the bucket. Since rotation of the bucket relative to the stars (or the stars relative to the bucket) is the reason for the water's concaveness, and since the rotating gravitaional field of the Earth is not influencing the bucket and since the rotating gravitational field of the Earth is several magnitudes stronger than the rotating gravitational fields of the stars, it seems to me this indicates that it is not a gravitational field that determines the outcome of Newton's water.

Even if we just consider the buckets position relative to the Earth we have a problem. If for example the bucket were orbiting the earth with it's surface parallel to it's plane of rotation and not spinning relative to the stars (in other words the face of the bucket walls change from the viewpoint of the earth), it would not be concave even though the gravitational pull of the Earth is much stronger than any residual gravity in space from the stars.

It is clear that whatever it is that defines what is stationary and what is rotating in the universe is NOT defined by gravitational influence.

Phrak

You are assuming that 'gravitational influence' is reduced by distance. You assume a bunch of massive stars at a distance have less effect on determining outcome, rather than a small amount of gravitational influence from a much closer Earth. It appears to me that you are basing this on what one can imply from the inverse ralationship of Newtonian gravity, but this is the relativity folder, so I would be perplexed by this calculation.

The force in question is not due to proximity and distance of masses, but the velocity of masses as well.

Buckethead

Since the strength of gravity does follow the inverse square law and since the strength of gravity has a direct correlation with the amount of distortion in spacetime, where is the flaw in my logic?