Exploring Newton's Bucket Paradox

[Buckethead]

First of all Mach's principle is hard to prove or refute because it it is not clear what exactly is meant by that principle and there are no "Mach's principle equations" to calculate exactly what it predicts or exactly how it differs from General Relativity..

Yes, which I think is very exciting as it makes this subject undiscovered territory. :)

Reading between the lines I get the impression the principle that Mach was trying to establish was a fully relativistic notion of acceleration that only has meaning relative to other objects. Einstein of course was drawn to Mach's idea because of its relativistic nature but ultimately he rejected that notion in formulating his final version of GR. So here is the surprise. General Relativity is not fully relativistic. Here is an example. Say you are a universe like ours but it contains only you and a glowing particle many light years away. The particle appears to circumnavigate a large circle once every minute. Now is it you rotating at 1 rpm or are you stationary and the particle is orbiting you? Mach's principle would seem to indicate that either view point of view is equally valid (the fully relativistic idea). However if we assume for a moment that it is you that is stationary (after all by the democracy of mass your mass is orders of magnitude larger) then the particle would be orbiting at velocity much greater than the speed of light. This is why I think Einstien rejected the fully Machian universe. Much as Einstein liked the idea of everything being fully relativistic, he really hated the idea of anything exceeding the speed of light, so he settled for a not fully relativistic description of the universe which gives an absolute nature to accelerating motion which includes rotation.

If this is what Mach intended, then I would have to disagree with him as well. I do believe that there is a framework as you and Einstein are suggesting, but I think i differ with Einstein in that the framework is not static but instead is a product of the motion of, and the mass of the bodies in the framework. Therefore it is to a degree fluid.

In your example, the particle would never go faster than light. If both you and the particle start out stationary and you decide to rotate at 1 rpm, your efforts would be fruitless. Since you hold most of the mass, you would not feel any inertial forces on you as the spacetime around you (the Machian frame) would rotate with you. This would force the particle to follow your rotation and both of you would end up stationary (relative to each other) regardless of your efforts to circumvent it.

Here are some other points to consider. The Schwarzschild metric describes the spacetime around a non-rotating body in an "otherwise empty universe" and the Kerr metric describes the spacetime around a rotating body in an "otherwise empty universe". (Both metrics assume an uncharged body). Whether or not the body is rotating or not, is relative to the spacetime it is embedded in and is not relative to any other bodies. The Schwarzschild or Kerr body curves and shapes the spacetime around it. The vacuum outside of the body is not entirely nothing. After all you cannot curve and shape nothing

Since the spacetime is being curved by the body, this supports my definition of Machian space nicely. In other words, it is the body and not just "absolute space" that defines the space around the body. This is good news.

In modern cosmology it is known that distant galaxies are receding at velocities that greatly exceed the speed of light. However, this is not considered a violation of General Relativity because the distant receding galaxies are stationary with respect to the expanding spacetime that they are embedded in. Again, what looks like a vacuum is not entirely nothing because a pure vacuum that is entirely nothing can not expand or do anything else for that matter. This sort of relates to the ZPE field that Mentz referred to. It is also generally accepted that if a body accelerates sufficiently quickly that it will see virtual particles popping out of the vacuum. This is the "Unruh effect" and again it only requires that a body is accelerating relative to the vacuum or spacetime and is not relative to any other bodies. Again the vacuum should not be thought of as entirely nothing.

In my definition of Machian space allows for dynamic changes in the space at large distances and sizes. It is possible to have a Machian space surrounding a galactic cluster and this space is moving away relative to another Machian space millions of ly away. In fact, it is almost necessary to have multiple Machian spaces ( or at least a fluid continuum of spaces) otherwise if you had a cluster embedded (and not moving relative to) a static space then a neighboring cluster expanding would mean that it would be moving relative to it's own space since that space were part of a "static, non expanding continuum" of the neighboring cluster.

With regard to the Unruh effect, a Machian space would be sufficient to allow for this as such a space would allow for a small moving object to move relative to it as long as there were a larger mass that was defining the space position and rotation.

Finally a little thought experiment. Imagine an Earth sized body in an "otherwise empty universe" that is rotating so fast that it oceans would be flung into space by centripetal forces but from the Machian viewpoint it is "unaware" that it rotating and retains its oceans and perfectly spherical shape. Now imagine a single particle popping up anywhere in this otherwise empty universe due to some quantum fluctuation. Would the Earth like body suddenly lose its oceans as a result of the appearance of this single tiny particle? That seems unlikely.

Agreed. The particle, as soon as it appeared, would find itself rotating around the Earth such that it would appear that the Earth was not rotating relative to the particle. In other words, in such a universe, it would be impossible for the Earth to ever spin since it holds most of the mass and therefore would force the Machian frame to rotate along with it.

My intuition is that unlike Special Relativity which is fully relativistic and where motion only has meaning relative to other bodies, General Relativity has an absolute nature relative to spacetime as far as rotation and linear acceleration are concerned. It would seem to me that in General Relativity a body has an existence relative to the spacetime around it, even in an otherwise "apparently empty" universe.

I am mostly in agreement with this to the limitation that it is still the masses in the universe that define this spacetime. I don't believe you could ever have a scenario for example where all the mass in the universe was moving (in the same direction) relative to the underlying space time.

Thanks for joining in.

 

[Ken G]

I agree that vacuum isn't nothing, but I don't think it could be quite said that GR isn't fully relativistic. Instead, I would say that GR requires some boundary condition at infinity to get a solution, but that's common in physics-- we always need to impose some manual constraint on anything we do. So it is that manual constraint that breaks the relativity, not GR itself-- we must tell GR what the boundaries are doing. If we say the boundaries are rotating with the Earth, then the spacetime is rotating with the Earth, which is a lot like saying the Earth isn't rotating. Spacetime is only as "real" as the boundary conditions we impose on it, but what is "real" about them? At some point it seems you would have to trace back to an initial condition, and it is in that initial condition where Mach's principle would enforce some constraint, or not.

 

[phyti]

Newton's bucket

Tidal forces - clarification:
An object in a gravitational field experiences greater acceleration at the near end than at the far end, thus elongation in the vertical. The convergence to the center of the field causes the horizontal dimension to contract. A sphere would become an ellipsoid as it falls. Research tides to see if it's the water that is distorted, not the earth. In general the less
massive objects are accelerated before the more massive.

Absolute rotation:
If the rotation of the water in the bucket can be equivalently attributed to the rotating
universal mass, then two counter rotating buckets would require the universe to rotate
simultaneously in opposite directions, i.e. a net rotation of zero. What if two buckets
rotated on perpendicular axes?

The shell theorem demonstrates zero gravity inside a hollow mass. If the universal mass is
approximately uniformly distributed, the net gravitational effect would average zero. With
the current (miniscule) angular motion of distant masses, would any effect be detectable?

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction.
If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the
equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

The case of linear motion with an acceleration is shown in the drawing. The same argument
applies, the remote objects would have had to start moving in the past at a time proportional to their distance. On the left, person-a accelerates, on the right, the rest of the universe accelerates. If considering multiple objects, this idea becomes nonsense.

If acceleration has no relative counterpart, it can be considered absolute.

https://www.physicsforums.com/attachments/17923

 

[Al68]

A better example of Mach's Principle may be Einstein's spinning globes: Imagine two fluid masses, each rotating wrt the other, with a common axis. Now imagine that one and only one of the globes has a bulging equator. If the situation is analyzed as a "closed" system, without regard to any distant masses, how can the bulging equator be explained? What causes the bulging equator on one globe but not the other?

Einstein's conclusion was that the cause must lie outside the system. (only one of the globes is rotating relative to the "fixed" stars).

As a closed system, there is no way to explain a cause for the empirically measured bulge of only one equator. And an observer on each globe would agree which one bulged, but no cause of the preferential bulge would exist within the system.

 

[Buckethead]

Tidal forces - clarification:
An object in a gravitational field experiences greater acceleration at the near end than at the far end, thus elongation in the vertical. The convergence to the center of the field causes the horizontal dimension to contract. A sphere would become an ellipsoid as it falls. Research tides to see if it's the water that is distorted, not the earth. In general the less
massive objects are accelerated before the more massive.

This holds because of gravity. It is not affected by my version of Mach's principle as the principle only affects objects in relative linear and/or rotational motion.

Absolute rotation:
If the rotation of the water in the bucket can be equivalently attributed to the rotating
universal mass, then two counter rotating buckets would require the universe to rotate
simultaneously in opposite directions, i.e. a net rotation of zero. What if two buckets
rotated on perpendicular axes?

Two rotating buckets opens up some very wild phenomenon. For example, from above, a bucket on the right spins counterclockwise and a bucket on the left spins clockwise. Between the two buckets any atoms in between the two buckets will pass from top to bottom at a constant velocity. Interestingly atoms to the right of the right bucket or to the left of the left bucket will also flow in the same direction, from top to bottom (against the directions of the buckets on these sides) and to a lesser degree than the atoms in the middle of the buckets. Far to the left or right of the buckets the movement of atoms falls off so that a distant observer at rest will not see either bucket moving relative to himself but will see atoms near the buckets moving past them. In other words there will be a curve in the spacetime in the area of the two spinning buckets.

In addition the water in the buckets will be flat. If the rotation of the buckets however is increased, the water will move toward the bottom (-y) direction of the two buckets for as long as the acceleration in applied.

If the bucket on the right changes direction so that both buckets are now spinning clockwise, then from the overall frame of the universe both buckets will precess around each other at 1/2 the rotational speed of the buckets in a counterclockwise direction. In otherwords an observer at rest far away from the two buckets will see them precessing around each other.

In addition I believe the water in the two buckets will ride up a wall of the bucket on the side opposite it's direction of motion as if it were accelerating in a straight line.

For two buckets where one is on a z axis, similar anomolies will occur although I have not yet worked out exactly what those anomolies would be.

The shell theorem demonstrates zero gravity inside a hollow mass. If the universal mass is
approximately uniformly distributed, the net gravitational effect would average zero. With
the current (miniscule) angular motion of distant masses, would any effect be detectable

The net gravitational effect is zero, but the Machian frame is not determined by gravity alone, it is determined by the relative velocites and rotations of all the bodies in question. If all the masses in the universe seem at rest relative to the center of all these masses, then this center is also at rest and an object placed here will resist movement relative to the stars.

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction.
If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the
equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

In my version of the Machian frame, If an observer rotates relative to a distant star, he may percieve a star moving around him, but this would only be an illusion. The observer would be rotating relative to the Machian frame and the star would remain stationary.

PLEASE NOTE: I'm obviously expressing my opinion here and not stating a fact. I am suggesting that if a Machian frame behaves according to the individual velocites and rotations of masses then the above observations would be the likely result. It's all just a mind experiment. I don't want to come off as some kind of pompous head, just a buckethead.

 

[Al68]

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction.
If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the
equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

This is incorrect. The speed of light is not limited to c wrt an accelerating (or rotating) reference frame. It can have any value up to infinity.

 

[Ken G]

What causes the bulging equator on one globe but not the other?

Einstein's conclusion was that the cause must lie outside the system. (only one of the globes is rotating relative to the "fixed" stars).

I guess Einstein tended to see causes and effects as a fundamental requirement of any description of reality, though of course one might also view them as effective constucts, shadows of some deeper principle, with no such fundamental status.

As a closed system, there is no way to explain a cause for the empirically measured bulge of only one equator. And an observer on each globe would agree which one bulged, but no cause of the preferential bulge would exist within the system.

This raises a possibility to imagine alternate approaches whereby, if that universe truly were a closed system, either observer might claim the other globe bulged. In our universe, the issue would need to be resolved by the action of the distant masses. That would seem to be the fully Machian/relativistic approach to these hypothetical possibilities. Alternately, of course, one might simply state that the bulging does not require a cause, it just is, but the fact that it is there decides which globe is "really" rotating. In short, we interpret rotation because of the presence of the bulge (and other things that come with it), rather than the other way around.

 

[Al68]

I guess Einstein tended to see causes and effects as a fundamental requirement of any description of reality, though of course one might also view them as effective constucts, shadows of some deeper principle, with no such fundamental status.
This raises a possibility to imagine alternate approaches whereby, if that universe truly were a closed system, either observer might claim the other globe bulged. In our universe, the issue would need to be resolved by the action of the distant masses. That would seem to be the fully Machian/relativistic approach to these hypothetical possibilities. Alternately, of course, one might simply state that the bulging does not require a cause, it just is, but the fact that it is there decides which globe is "really" rotating. In short, we interpret rotation because of the presence of the bulge (and other things that come with it), rather than the other way around.

Einstein definitely viewed physics very differently than most do today, that is obvious from his writings.

Stating that we don't need to know the cause of the bulge is fine, maybe we don't need to know. Maybe some would be satisfied with just a mathematical description..

Einstein obviously was not, fortunately.

 

[phyti]

Buckethead;

The net gravitational effect is zero, but the Machian frame is not determined by gravity alone, it is determined by the relative velocites and rotations of all the bodies in question. If all the masses in the universe seem at rest relative to the center of all these masses, then this center is also at rest and an object placed here will resist movement relative to the stars.

Don't quite understand this part.
Currently a mass anywhere in the universe offers inertial resistance.

 

[Ken G]

Stating that we don't need to know the cause of the bulge is fine, maybe we don't need to know.

Indeed, I think it could be said that Einstein was ultimately unsuccessful in identifying a "cause" of the bulge. Though of course, the effort to do so certainly resulted in many other useful things!

 

[Al68]

Indeed, I think it could be said that Einstein was ultimately unsuccessful in identifying a "cause" of the bulge.

You're right, at least not to his satisfaction. But just the conclusion that the cause must lie outside the system (containing just the globes) is significant to the issue of Newton's bucket, and it's a simpler example, since it's not complicated by the downward force of gravity holding water in the bucket.

 

[Ken G]

Yes, it's an excellent example, and it's certainly a conclusion that is relevant here, but I think we are still left to wonder if Einstein and Mach were actually right about that external cause. I can agree the cause isn't internal to the globes, but my feeling is that the whole concept of cause and effect is simply not a useful one in that context. I suppose that would put me in the "motion is as motion does" school of thought, whereby what we identify as motion is a kind of shadow of some much deeper phenomenon that we are mostly oblivious to and therefore cannot successfully apply our simplified concepts like cause and effect. We have only demonstrated a use in applying them to the concept of a change in motion, starting from an initial condition of some kind, but we are always left to wonder what was the cause of the initial condition. Such is the basic structure, and limitation, of physics thinking.

 

[Buckethead]

Yes, the whole approach to the "center of mass" of a system is very much a kind of "vote", as you say. It still has strange properties though-- as you say, if we have a spinning bucket with 99% of the mass of the universe, and an outside observer with 1% of the mass, the spinning bucket could "vote" that the observer is actually in orbit and the bucket is not spinning at all, and we conclude the bucket is 1% spinning and the observer is 99% orbiting. Hence we only expect a 1% bulge in the water in the bucket. Now in a universe where the observer had a million times more mass, the bulge is back to its usual scale. But the problem is, this would hold no matter how small those masses actually are, so the gravitational constant G would have to be "renormalized" based on the mass in the universe, otherwise the influences would be too small with our current G to do anything. I prefer to think of G as a fundamental constant, and only the nature of spacetime is influenced by the mass. That's why I think you need the rest of the universe to have essentially infinite mass for Mach's principle to seem reasonable, because then the gravitational influence is not negligible, it "anchors" the spacetime. Nevertheless, I could not argue that your way of renormalizing G to whatever is the total mass is impossible or wrong.

I wonder if G really is a fundamental constant. A few years ago I was researching the various experiments being performed around the world to measure this constant and at the time none of the numbers matched. Experimental error of course is the first thing to look at, yet I got the sense that these experimenters were more baffled than accepting of errors they may have made. But even with this aside and more to the point, SR says the mass of an object increases with it's velocity, hence it's gravitational attraction increases. If this speeding object were suddenly to find itself in an almost empty universe, would it's graviational attraction (and it's increased mass) remain, or would it's gravity return to an expected value, or more interestingly, would it's gravity suddenly become zero? The possibility of it becoming zero is related to your observation that ("a third possibility might be") the spinning bucket in a universe with a distant particle, might show a reduced curve for a given relative rotational rate. Because of the equivelency principle, this reduced curve(mass?) might also come with it a reduced gravitational pull. Hence G may not be constant but instead may relay heavily on the total number of particles (I was going to say total mass, but that would be a non-sequiter) in the universe.

 

[Buckethead]

Hi,


Reading between the lines I get the impression the principle that Mach was trying to establish was a fully relativistic notion of acceleration that only has meaning relative to other objects. Einstein of course was drawn to Mach's idea because of its relativistic nature but ultimately he rejected that notion in formulating his final version of GR. So here is the surprise. General Relativity is not fully relativistic. Here is an example. Say you are a universe like ours but it contains only you and a glowing particle many light years away. The particle appears to circumnavigate a large circle once every minute. Now is it you rotating at 1 rpm or are you stationary and the particle is orbiting you? Mach's principle would seem to indicate that either view point of view is equally valid (the fully relativistic idea). However if we assume for a moment that it is you that is stationary (after all by the democracy of mass your mass is orders of magnitude larger) then the particle would be orbiting at velocity much greater than the speed of light. This is why I think Einstien rejected the fully Machian universe. Much as Einstein liked the idea of everything being fully relativistic, he really hated the idea of anything exceeding the speed of light, so he settled for a not fully relativistic description of the universe which gives an absolute nature to accelerating motion which includes rotation. .

(regarding bold text:) My take on this is that in this scenario, it would not be possible for the bucket to rotate at any speed (very very slowly perhaps due to the particle having some small mass). Due to democracy of mass, if the bucket attempted to rotate (strap on those jets) the entire frame would rotate along with it including the particle, rendering the bucket essentially non-rotating. The particle could revolve around the bucket however, and it's speed would be limited to c. Another thing to observe here (if my take on this is correct) is that it would also be impossible for the bucket to "go concave" (over and above that small amount allowed by a revolving particle) .

If we now start adding stars to this universe, giving democracy of mass to the stars, and if the bucket started spinning (which it now could) relative to the stars, it would go concave, it would actually be "spinning" and it would not make sense to say it was the particle that was actually moving and the bucket being at rest. So in either scenario, nothing would ever travel faster than light.

Here are some other points to consider. The Schwarzschild metric describes the spacetime around a non-rotating body in an "otherwise empty universe" and the Kerr metric describes the spacetime around a rotating body in an "otherwise empty universe". (Both metrics assume an uncharged body). Whether or not the body is rotating or not, is relative to the spacetime it is embedded in and is not relative to any other bodies. The Schwarzschild or Kerr body curves and shapes the spacetime around it. The vacuum outside of the body is not entirely nothing. After all you cannot curve and shape nothing.

I'm not sure what your point was here. I personally think though that the Kerr metric would not make sense in an otherwise empty universe, as rotation (rotation being defined as a non zero centrifugal force) would not be possible for an object in such a universe.

In modern cosmology it is known that distant galaxies are receding at velocities that greatly exceed the speed of light. However, this is not considered a violation of General Relativity because the distant receding galaxies are stationary with respect to the expanding spacetime that they are embedded in. Again, what looks like a vacuum is not entirely nothing because a pure vacuum that is entirely nothing can not expand or do anything else for that matter. This sort of relates to the ZPE field that Mentz referred to. It is also generally accepted that if a body accelerates sufficiently quickly that it will see virtual particles popping out of the vacuum. This is the "Unruh effect" and again it only requires that a body is accelerating relative to the vacuum or spacetime and is not relative to any other bodies. Again the vacuum should not be thought of as entirely nothing.

(Interesting about the virtual particles) I don't consider the vacuum as being entirely nothing as certainly in the Machian view, the large masses are communicating with all other objects through some means, filling the universe. This would be through the motions of gravitons or some yet undiscovered (dark matter/energy) particle, or possibly something even more mysterious such as the non-local particle interaction phenomenon.

Finally a little thought experiment. Imagine an Earth sized body in an "otherwise empty universe" that is rotating so fast that it oceans would be flung into space by centripetal forces but from the Machian viewpoint it is "unaware" that it rotating and retains its oceans and perfectly spherical shape. Now imagine a single particle popping up anywhere in this otherwise empty universe due to some quantum fluctuation. Would the Earth like body suddenly lose its oceans as a result of the appearance of this single tiny particle? That seems unlikely.

I agree it would be unlikely. The reason being that since it is showing no bulging or flinging, the Earth could not be said to be spinning. In other words, spinning in this universe is impossible. If a particle were suddenly to appear, it would not be spinning relative to the Earth or the Earth to it, so flinging would still not happen. As I mentioned above, I think that once the particle appeared, due to democracy of mass, the Earth could still not spin as the whole frame (particle included) would spin right along with it if it tried, rendering the whole thing as non-spinning. The particle could BTW revolve around the Earth, limited by lightspeed relative to the inertial frame (defined by the Earth), but the Earth could not spin.

My intuition is that unlike Special Relativity which is fully relativistic and where motion only has meaning relative to other bodies, General Relativity has an absolute nature relative to spacetime as far as rotation and linear acceleration are concerned. It would seem to me that in General Relativity a body has an existence relative to the spacetime around it, even in an otherwise "apparently empty" universe.

I absolutely agree.

 

[A-wal]

My intuition is that unlike Special Relativity which is fully relativistic and where motion only has meaning relative to other bodies, General Relativity has an absolute nature relative to spacetime as far as rotation and linear acceleration are concerned. It would seem to me that in General Relativity a body has an existence relative to the spacetime around it, even in an otherwise "apparently empty" universe.

I absolutely agree.

I completely but respectfully disagree. All movement is relative. These are just my thoughts:

Absolute rotation:
If the rotation of the water in the bucket can be equivalently attributed to the rotating
universal mass, then two counter rotating buckets would require the universe to rotate
simultaneously in opposite directions, i.e. a net rotation of zero. What if two buckets
rotated on perpendicular axes?

From one frame it would rotate in one direction, while it would be rotating in a different direction from the other frame. If the were on different axes then the universe would rotate on different axes from the different frames. You could argue that the fact that they can't both be right at the same time proves that the buckets must be spinning, or at least one of them must be, but you can always say things look different from other frames.

In Max Born's book on SR, he mentions Mach's principle in an attempt to provide a symmetrical view of the rotating observer. It appears he ignores postulate 2. When the observer rotates, he instantaneously perceives the universal background to rotate in the opposite direction. If a star is 1000 ly distant, it would have had to start moving 1000 yr ago to produce the equivalent perception, but this is before the observer was born! What if two people rotated at different rates?

Yes they would have to of started moving before you were born. That doesn't mean they didn't. Maybe they were thrown back in time due to the fact that they're moving faster than c. The further away they are, the faster their relative movement, so the further back in time they go, which is handy. That was either really cool or I need to lay off the smoke. What if two people rotated at different rates? See above.

The case of linear motion with an acceleration is shown in the drawing. The same argument applies, the remote objects would have had to start moving in the past at a time proportional to their distance. On the left, person-a accelerates, on the right, the rest of the universe accelerates. If considering multiple objects, this idea becomes nonsense.

No, it just becomes relative to the observer.

If acceleration has no relative counterpart, it can be considered absolute.

The counterpart of acceleration is the acceleration of everything else in the universe at the perfect individual timing to coincide exactly with your position in space-time when you can be said to be accelerating. It's not an alternative, it's exactly the same.

In a universe with just the bucket, there would be no other matter to move round the bucket with increased mass brought about by increased the relative velocity, and therefore nothing to pull the water up the sides of the bucket. That's basic Galilean relativity surely?

 

[Al68]

Yes they would have to of started moving before you were born. That doesn't mean they didn't. Maybe they were thrown back in time due to the fact that they're moving faster than c. The further away they are, the faster their relative movement, so the further back in time they go, which is handy. That was either really cool or I need to lay off the smoke.

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]

GR can tell us if the universe is rotating or not.

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 traveling 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.

And spacetime obviously never rotates.

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 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.

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]

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.

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]

And spacetime obviously never rotates.

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]

The net gravitational effect is zero, but the Machian frame is not determined by gravity alone, it is determined by the relative velocites and rotations of all the bodies in question. If all the masses in the universe seem at rest relative to the center of all these masses, then this center is also at rest and an object placed here will resist movement relative to the stars. .

Don't quite understand this part.
Currently a mass anywhere in the universe offers inertial resistance.

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]

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.

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]

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

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 spatial in nature and as such can rotate.

 

[A-wal]

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.

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

There are already galaxies receding from our vantage point at speeds greater than c, cosmologically, so why should we object?

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]

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.

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]

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

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?

 

[Ken G]

I think the flaw is that you have to look at spacetime itself, not just its local curvature. Even in the complete absence of any local gravity, so nowhere near the Earth or any star, we still have the Newton's bucket problem. We still need the spacetime itself to tell us if the bucket is rotating. So it seems to me we have two possibilities-- either spacetime is "real", all on its own (the non-Machian view), or spacetime is just a proxy for the history of motion of matter and fields through the universe (the Machian view). The Machian view holds even if all that matter is very far away and is not creating any noticeable local curvature-- it is more like a boundary condition on the spacetime than a local curvature effect, like the "real gravity" of the Earth that you are talking about. In short, Mach's principle is a whole new way that gravity affects spacetime, by giving it a history.

 

[Buckethead]

I think the flaw is that you have to look at spacetime itself, not just its local curvature. Even in the complete absence of any local gravity, so nowhere near the Earth or any star, we still have the Newton's bucket problem. We still need the spacetime itself to tell us if the bucket is rotating. So it seems to me we have two possibilities-- either spacetime is "real", all on its own (the non-Machian view), or spacetime is just a proxy for the history of motion of matter and fields through the universe (the Machian view). The Machian view holds even if all that matter is very far away and is not creating any noticeable local curvature-- it is more like a boundary condition on the spacetime than a local curvature effect, like the "real gravity" of the Earth that you are talking about. In short, Mach's principle is a whole new way that gravity affects spacetime, by giving it a history.

OK, this is very well put and makes sense. In other words (going with the Machian view), a "spacetime grid" exists and is capable of bending, rotating, and moving in some direction all of which will be completely responsible for the outcome of Newton's bucket. In addition, there is no meaning to the strength of the grid as it is not a force but rather as you say, a placemat capable of position only and it's bending, rotating and moving are defined by the history of gravity moving across the universe over time. Did I get that right?

I have to bring in the Lense-Thirring effect (frame dragging), as it seems this effect will indeed move the grid to a limited degree around something like a rotating planet. the effect is small which would mean it's washed out by the grid created by distant stars and would therefore have little effect on the north pole issue.

If all this is correct, then this does mean that this grid and gravity are two entirely different phenomenon. In other words, one can't say that gravity itself is responsible for the bucket problem directly but one can say that gravity is able to manipulate and define the shape of an absolute universe and it is this mutable universe that is responsible for the bucket effect.

One has to take this one step further and ask what is it that is being mutated? We are not talking about gravity, as we have already stated it won't affect the bucket, we are talking about something like an aether (but not really of course), something that has properties.

If I were to take a stab I might say that virtual particles might play a part. Or a new force that has the characteristic of changing slowly over time when hit with gravitational fields. It would be helpful to at least list the properties of such a spacetime "substance" which might help to identify it.

 

[Al68]

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.

Why would you say this? It's true that the net gravitational "force" due to all of the stars is zero, but that's just because it's the same in every direction. And if the bucket were in freefall, it would also feel no overall "force" from Earth's gravity.

The concavity of the water in a spinning bucket is due to each water molecule trying to travel an inertial trajectory. The reason for the concavity is the same as the reason any object will follow an inertial path, or a geodesic.

The reason the direction of rotation relative to Earth's rotation is (almost) irrelevant is that while Earth's location affects the inertial path each water molecule would take in the absence of the bucket, its rotation doesn't, neglecting Earth's non-uniform mass distribution and frame dragging effects.

I think I remember someone modeling the effect of frame dragging of a rotating universe on a "stationary" bucket and found that the concavity would be the same as if the bucket were spinning in a stationary universe. But don't hold me to that, because I'm not sure.