What Does Newton's Bucket Paradox Reveal About Motion and Inertia?

[Ken G]

I guess the deal is being able to predict what would happen in this sort of experiment.

But that's why I asked if anyone really believed you could not get a dip in a bucket in an otherwise empty universe. I certainly don't believe it. So if you could, then you have to use the bucket to tell you whether or not it's rotating-- the effort to invert that logic is the source of the problem (that's where philosophy enters and muddies the science).

Make a huge concrete ring and suspend it so that the ring is parallel to the ground. Place a non rotating bucket of non rotating water water on the ground in the centre of the concrete ring. Accelerate the ring to a high angular velocity. The surface of the water in the non rotating bucket should start going concave due the curvature of space induced by the rotating concrete ring. I imagine one day they will be able to carry out some sort of real experiment based on this principle or observe it cosmologically.

General relativity predicts the result of that experiment. Why do we need Mach? Don't get me wrong, I realize that asking the questions Mach did helped Einstein think "outside the box". That is generally what I view philosophy is for-- to free our thinking to see what the possibilities are. But we tend to cling to it long after it has ceased its usefulness, and mistake it for part of the theory.

 

[yuiop]

But that's why I asked if anyone really believed you could not get a dip in a bucket in an otherwise empty universe. I certainly don't believe it. So if you could, then you have to use the bucket to tell you whether or not it's rotating-- the effort to invert that logic is the source of the problem (that's where philosophy enters and muddies the science).
General relativity predicts the result of that experiment. Why do we need Mach?

I am just trying to clarify (in my own mind) where Mach and Einstein differ. I get the impression that the mainstream view is that GR and Mach's principle are not compatible while a lot of laypersons and physics popularisations think they are compatible. I do not seem to be able to find a definitive and easy to visulise resolution of the matter.

In other words complete the sentence -

Mach's principle does not work because ...

 

[Garth]

Mach's principle does not work because ...

... GR works.

They are incompatible re the double rotating bucket gedanken.

Alternatively GR 'does not work' (i.e. may need to be modified) because Mach's principle works.

The jury may still be out...

Garth

 

[Mentz114]

Einstein and DeSitter disagreed about the absolute nature of rotation and Einstein eventually agreed there was an element of absolute space in GR. I think he was wrong and should have stuck to his original view. Rotation is not relative, and transforming into the rotating frame does not remove the centripetal acceleration felt by observers at rest in the rotating frame. A non-rotating bucket within a rotating cosmos is not the same situation at all, and is modeled correctly by GR.

Mach's principle is not applicable or relevant to Newton's bucket.

 

[Ken G]

The way I see the difference is that GR is a boundary value problem, because it is a differential theory. Mach's principle is a philosophical statement of how reality must behave. Since a boundary value problem always has the degrees of freedom of what is going on at the boundary, it puts less constraints on the situation than does Mach's principle. So I see the inconsistency between the two as coming from the fact that if the mass is within the solution volume, you still need a boundary condition to do GR whereas Mach's principle indicates the reality is completely determined. That doesn't seem like a big problem unless the boundary condition GR would need in order to work seems unnatural in some way. But if you go to hypothetical situations, like an empty universe, then Mach's principle says reality is undetermined, whereas GR says reality is determined by experiments that determine the appropriate boundary conditions. If that's a fair way to say it, then the incompatibility is the incompatibility of science and philosophy.

 

[Dale]

I don't know much about Mach's principle, but discussions about it always seem to turn into these rather silly "otherwise empty universe" discussions, which makes me question the value of Mach's principle.

Does Mach's principle have any concrete testable predictions? If not, what is its value?

 

[Garth]

Does Mach's principle have any concrete testable predictions? If not, what is its value?

In one version of the principle it suggests the Newtonian Gravitational constant is not actually constant but varies from place to place.

The Brans Dicke theory, which fully incorporates Mach's principle into GR, made observational predictions that do not seem to be consistent with observation.

Garth

 

[aaj]

Hi. First post here. I have no formal math or physics training, but read popular books on physics and am pretty well read as far as that goes. Now for the question.

I'm fascinated by the Newton's Bucket problem and fortunately for me it's cleared my head of the 2 brothers paradox (one on earth, one in ship, ship ages) with regard to which one is considered moving and which is stationary.

For a description of Newton's Bucket, here's a good one:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Newton_bucket.html

I've never liked the traditional idea that the brother that is considered moving (and therefore aging) is the one that is accelerating away because once acceleration stops and the ship continues at near light speed, the aging process continues yet the ship is only moving relative to the Earth and not accelerating away from it.

Newton's Bucket solves that problem by inferring that the ship is moving near light speed relative to either the stars or some universal fabric that is static or almost static relative to the stars.

Newton's bucket implies that if the universe were empty (I suppose this would include dark matter and energy) except for the bucket and a single observer, the bucket would seemingly have to behave strangely. For example, if the observer were spinning around the bucket (and the bucket around the observer) but both in the same direction as far as the two axis of rotation are concerned, the bucket could not be said to be spinning and therefore would not exhibit inertial forces or the resultant concave water. If the observer and bucket were spinning opposite to each other, then what? Would the water then become concave relative to the velocity of the observer? Or is a greater mass (or something else altogether) required such as massive galaxies? And if either or both are causing the water to become concave, then what exactly is causing it. I realize the simple answer is inertia, but this paradox implies that inertia would cease to exist in an empty universe and with the observer and bucket moving in the same direction or possibly in different directions as well.

Inertia would have to cease to exist in an empty universe that contained only a bucket of water and a single observer moving in the same direction around it as there would be absolutely no frame of reference with regard to acceleration. With no inertia, one could not feel any effects of acceleration so if the bucket exploded, or the observer sneezed, which would move relative to the other, and which one would age when applied to the two brother paradox.

Glad to have found this forum.

The way I interpret 'Newton's bucket' experiment is that it does indeed show that there is some absolute reference and that relative motions are not all that matter. Now I don't think, it automatically implies the existence of absolute space, as Newton and most contemporaries thought. Indeed as Einstein showed, the absolute reference turned out to be space-time rather than space.

In space-time, only relative velocities matter but accelerations are still absolute. Hence, that should explain Newton's bucket experiment. There is no ambiguity about whether water in a bucket is rotating or not because rotation is an accelerated motion. Hence, it has nothing to do with gravitational pull of the rest of the universe and so a concave water shape should result in a rotated bucket even if its the only object in the universe.

 

[yuiop]

The way I interpret 'Newton's bucket' experiment is that it does indeed show that there is some absolute reference and that relative motions are not all that matter. Now I don't think, it automatically implies the existence of absolute space, as Newton and most contemporaries thought. Indeed as Einstein showed, the absolute reference turned out to be space-time rather than space.

In space-time, only relative velocities matter but accelerations are still absolute. Hence, that should explain Newton's bucket experiment. There is no ambiguity about whether water in a bucket is rotating or not because rotation is an accelerated motion. Hence, it has nothing to do with gravitational pull of the rest of the universe and so a concave water shape should result in a rotated bucket even if its the only object in the universe.

Can you be sure acceleration is absolute?

Calculations using general relativity have shown that a massive rotating shell would induce a force that causes the surface of stationary water in a stationary bucket at its centre to curve exactly as if the if the water was rotating. The relativistic principle suggests there is no measurement that can destinguish a rotating bucket in a universe of of stationary stars from a stationary bucket in a universe of rotating stars. The mass of the rotating stars will drag spacetime as per the Lense Therring effect causing the water in the stationary bucket to climb up the sides of the bucket as if it was rotating. The stars will not be thrown outward by centripetal forces because the spacetime is co-moving with the stars.

Now imagine a universe with a one stationary bucket and one atom at the edge of the universe visible from the bucket. The atom is rotating around the bucket at very high speed but there is no way that the mass of a single atom at such a great distance can induce any significant gravitational field or curvature in the surface of the water in the bucket. By invoking the principle of relativity, rotating the bucket and water relative to the distant stationary atom will not induce any curvature in the surface of the water. The single atom is an aproximation of an "otherwise empty universe"

The same can be said for linear acceleration. There is no difference between a rocket accelerating in a stationary universe and a stationary rocket in an accelerating universe. The rocket engine is simply resisting the gravitational field that is drawing the rest of the universe into an event horizon behind the rocket.

Further evidence that gravitational fields might be the source of inertia is this. A perfectly elastic ball is placed in a box and set bouncing from side to side horizontally. The box is far out in space. As the box is gradually lowered towards a large massive body we would expect that if the inertial mass is increasing with increasing proximity to a massive body and if momentum is conserved, that the ball would slow down. That is exactly what we do observe (from a distance). When we bring the box back up we note the ball has speeded up again. Similar experiments accelerating objects horizontally would show they behave as if they have greater inertial mass lower down nearer the massive body, suggesting Mach's principle of inertia being a function of the total gravity of the all the surrounding mass is not far off the mark. Now when we take the box infinitely far away from the massive body (or a long way away, anyway) that the ball still has inertia seeming to contradict Mach's principle. The solution is that in our universe, you can not get infinitely far from any massive body without getting closer to other massive bodies. There is always a "zero point" gravitational field wherever you are and although we might find it mathematically convenient to call this residual gravitational potential zero, it is not in fact zero and this could account for baryon particles having a non zero inertial mass, when seemingly at a zero gravitational potential. Even in the largest of voids, the surrounding mass ensures the gravitational potential is never zero and so the inertial mass is never zero.

So my argument is that if we take a take an informal description of Mach's principle as "Inertia of a body is a property of its motion relative to the fixed stars" and restate it as "Inertia of a body is a property of its motion relative to the spacetime determined by the distribution and motion of matter in space" then Mach's principle is pretty compatible with relativity. The important notion is that inertia is not an intrinsic property of mass, independent of its surroundings.

 

[aaj]

The important notion is that inertia is not an intrinsic property of mass, independent of its surroundings.

This is interesting. Just as a curiousity, has there been any experiment conducted to verify this notion? I haven't thought over this much but should it not be possible to simply test this out by performing an experiment on an object, once with no heavy object close by and once more with many heavy objects in its immediate surrounding? By observing whether the object responds differently to the same force, it might be possible to test out the hypothesis that inertia is not an intrinsic property of mass. Ofcourse, I can quite guess that technical limitations might be a big reason why we cannot achieve the sensitivity required for the above kind of experiment.

On another line of thought, if the hypothesis of inertia not being an intrinsic property of mass is true, how come we have never quite observed this effect through astronomical observations? I mean galaxies also move through space. Has it ever been observed that the inertia of an entire cluster of stars has changed simply because of their changed position in the universe? If it hasn't and they have changed position, it would imply that the mass density of the universe is pretty even in all directions.

 

[Mentz114]

The idea that inertia is a reaction between mass and some field is explored in this paper, which is published in Physics Letters A and on the arXiv

http://arxiv.org/abs/physics/9802031

The authors ascribe inertia to the EM ZPF, but actually it would work with any ZPF that interacted with baryons. here's a brief extract -

If correct, this concept would substitute for Mach’s principle and imply that no further mass-giving Higgs-type fields may be required to explain the inertia of material objects, although extensions to include the zero-point fields of the other fundamental interactions may be necessary for a complete theory of inertia.

Which sounds like Kev's proposal.

 

[aaj]

The important notion is that inertia is not an intrinsic property of mass, independent of its surroundings.

Its also intetresting to note that the above hypothesis seeks to make a clear distinction between mass and inertia. Most common definitions of mass itself are in terms of inertia. For instance, 1kg of mass may be defined as that mass which accelerates at 1m/s^2 in response to a force of 1N. Now if we delink mass and inertia as per the quoted hypothesis, how then do we define mass?

I am guessing it would be in terms of the ability to curve spacetime. So depending on the surroundings, an object's inertia may be different but are we saying that its ability to curve spacetime around itself would be unaffected?

So would a universe consisting of only one atom still be curved in the vicinity of the atom?

It seems we would then we forced to have to have two masses for each object. a) The Inertial mass which would be a measure of the inertia of the object and which the hypothesis says depends on its surroundings and b) the curvature mass which would be a measure of the ability of the object to curve spacetime.

But then, gravity is a manifestation of curvature so we are harking back tothe times when we had the concept of inertial and gravitational masses. And so many experiments have showed that these two masses have always been found to be the same with ever increasing accuracy. If this is the case, we are left with two conclusions:

a) The two masses seem to be equal because inertia is indeed and intrinsic property of the body and is determined by the same quantity that curves spacetime and is unaffected by its surroundings

b) Inertia may be determined by surroundings but we have never noticed any fluctuation because the universe is very even in all directions to an astonishing degree.

But then point b still begs the question why it is that the quantity which determines inertia is so so nearly equal to the quantity which is responsible for curving spactime in the vicinity of the object?

 

[Mentz114]

aaj

But then point b still begs the question why it is that the quantity which determines inertia is so so nearly equal to the quantity which is responsible for curving spactime in the vicinity of the object?

If the ZPF hypothesis is true, then both inertia and gravity result from the very same cancellation effect - and so must be identical. This is one of the best points about this hypothesis, unification of gravitational mass and inertial mass.

 

[Ken G]

What bothers me about this idea is that it seems to require that the presence of gravity alters the physics of a system in a way other than due its tidal effects, which seems to violate the principle of equivalence. In other words, if you put a box around a system, then the effect of gravity on the internal workings of that system should only come in via its tidal influences. But if you put a force on a point particle in that box, and claim that gravity from external sources are responsible for the way it accelerates, then you cannot have the equivalence principle. Note there is not a problem with kev's thought experiment about a ball bouncing back and forth in a box, because tidal stresses across that box must be responsible for the behavior observed, but inertia itself is a property of a point particle.

 

[Mentz114]

I agree that it would be a major flaw if the gravitational mass and inertial mass changed according to some local field strength. I think the authors of the cited paper assume an absolute vacuum, one that looks the same to all inertial observers and is in fact the source of inertial and gravitational effects when interacting with matter.

I'm keeping an open mind about this. No one else has attempted to 'explain' F=ma and it is an ingenious idea that maybe could give rise to a decent theory.

 

[Ken G]

I see something of a "Catch 22" here. If it responds to a local field strength, inertia seems to refute relativity, but at least you have a falsifiable theory. If it does not, then how will you ever establish the connection? It sounds a lot like the claim "the total distribution of mass in the universe is why the speed of light is what it is"-- how could anyone falsify that claim? I see Mach's principle as a way to break one's mind out of a box that might limit you to missing a theory like general relativity, but having the theory of GR, I'm not sure where we need Mach's principle. It's true that GR is a differential theory, so needs the external application of some kind of boundary conditions (does it not?), and one might then say we use Mach to inform the boundary conditions. But even that would be backwards logic-- we always apply whatever boundary conditions that seem to work, so if Mach hadn't worked we would use a different boundary condition. It doesn't establish that Mach informs our boundary condition-- getting results that agree with experiment do that. This is the fundamental problem of mixing philosophical principles into physics-- science just isn't done that way, except in the "inspiration" phase.

 

[Mentz114]

..., but at least you have a falsifiable theory.

We aren't talking about fully-fledged theory but an hypothesis. When I said a 'decent' theory, I mean it must be falsifiable. I don't consider what Haisch et al have presented to anything like correct.

This is the fundamental problem of mixing philosophical principles into physics-- science just isn't done that way, except in the "inspiration" phase.

If you're talking about Mach's conjecture, I agree. I've never seen any use for it.

 

[Buckethead]

Can you be sure acceleration is absolute?

Calculations using general relativity have shown that a massive rotating shell would induce a force that causes the surface of stationary water in a stationary bucket at its centre to curve exactly as if the if the water was rotating. The relativistic principle suggests there is no measurement that can destinguish a rotating bucket in a universe of of stationary stars from a stationary bucket in a universe of rotating stars. The mass of the rotating stars will drag spacetime as per the Lense Therring effect causing the water in the stationary bucket to climb up the sides of the bucket as if it was rotating. The stars will not be thrown outward by centripetal forces because the spacetime is co-moving with the stars.

This last sentance is astonishing to me, a real eye opener. If spacetime moves with the stars, then doesn't this automatically imply that the spatial location of the stars (by stars I do mean all matter in the universe) and spacetime itself are one in the same thing? Doesn't this mean that Mach's principle and the idea of absolute spacetime are the same thing?

Now imagine a universe with a one stationary bucket and one atom at the edge of the universe visible from the bucket. The atom is rotating around the bucket at very high speed but there is no way that the mass of a single atom at such a great distance can induce any significant gravitational field or curvature in the surface of the water in the bucket. By invoking the principle of relativity, rotating the bucket and water relative to the distant stationary atom will not induce any curvature in the surface of the water. The single atom is an aproximation of an "otherwise empty universe"

I'm not convinced that there is a relationship between gravity and absolute spacetime/Mach's principle as wouldn't we see a change in inertia if we were far out in space away from strong forces of gravity? Whatever spacetime is "made of" it has to be fairly uniform across the universe. It must be influenced by either virtual particles, dark energy, dark matter, or some strange type of pervasive field.

It seems about half of the posts here have argued that a bucket can be said to spin if and only if the water is climbing it's side independant of whether or not there is other matter in the universe and I'm assuming also independant of any absolute spacetime (if it can exist without matter). But in the very minimum, an absolute spacetime must exist or the idea of rotation reduces to simply a "seemingly stationary bucket with water in a concave shape". I could not conclude that anything was spinning from this observation. This would lead me to believe that some outside force such as gravity or otherwise was surrounding the bucket and forcing the water into this shape. This is the reason I do not think that a bucket in an empty universe (or in a universe without an absolute spacetime) can have a concave shape. This implies a lack of inertia (no more Newton's laws).

This lack of inertia does indeed bring up some additional strange observations. For example, what would happen if you shone a laser beam? If nothing unusual happened (it's light propagated out in a straight line) then we have a good argument as to why the water should go concave. If a straight line were definable by a laser, then certainly a bucket could be said to spin (and could be observed going concave) as it's water molocules tried to follow the path of the laser light. But without the presence of absolute spacetime, light could not propagate in a line or in any definable fashion.

It seems to me there can be nothing logical happening to light, a spinning bucket, or a linearly accelerating object unless these things are happening in a frame of reference and in the very least this frame of reference must be a grid of spacetime and at most could be the relative position of all matter in the universe.

To get back to Kev's comment about the stars not being affected by centrifugal forces: If this were indeed true, then spacetime's rotational velocity is defined by the location of the matter in the universe and follows it exactly. This would imply that Mach's principle is true. If Kev's comment were not true, then this would imply that spacetime and the matter in the universe were rotating relative to each other and centrifugal forces would be acting on stars in strange ways and it would also imply that spacetime must be made up of some form of matter or field that defined a grid by which inertia is subject. I'm not sure I can buy that, but I suppose it's possible.

I wish I had time to respond to more of the comments in this thread, but I am very much enjoying all that I am reading and I appreciate that this thread is being kept alive.

 

[newTonn]

Hi. First post here. I have no formal math or physics training, but read popular books on physics and am pretty well read as far as that goes. Now for the question.

I'm fascinated by the Newton's Bucket problem and fortunately for me it's cleared my head of the 2 brothers paradox (one on earth, one in ship, ship ages) with regard to which one is considered moving and which is stationary.

For a description of Newton's Bucket, here's a good one:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Newton_bucket.html

I've never liked the traditional idea that the brother that is considered moving (and therefore aging) is the one that is accelerating away because once acceleration stops and the ship continues at near light speed, the aging process continues yet the ship is only moving relative to the Earth and not accelerating away from it.

Newton's Bucket solves that problem by inferring that the ship is moving near light speed relative to either the stars or some universal fabric that is static or almost static relative to the stars.

Newton's bucket implies that if the universe were empty (I suppose this would include dark matter and energy) except for the bucket and a single observer, the bucket would seemingly have to behave strangely. For example, if the observer were spinning around the bucket (and the bucket around the observer) but both in the same direction as far as the two axis of rotation are concerned, the bucket could not be said to be spinning and therefore would not exhibit inertial forces or the resultant concave water. If the observer and bucket were spinning opposite to each other, then what? Would the water then become concave relative to the velocity of the observer? Or is a greater mass (or something else altogether) required such as massive galaxies? And if either or both are causing the water to become concave, then what exactly is causing it. I realize the simple answer is inertia, but this paradox implies that inertia would cease to exist in an empty universe and with the observer and bucket moving in the same direction or possibly in different directions as well.

Inertia would have to cease to exist in an empty universe that contained only a bucket of water and a single observer moving in the same direction around it as there would be absolutely no frame of reference with regard to acceleration. With no inertia, one could not feel any effects of acceleration so if the bucket exploded, or the observer sneezed, which would move relative to the other, and which one would age when applied to the two brother paradox.

Glad to have found this forum.

Dear all
let us view it in another angle.a liquid(water here)will exert presurre in all direction to the walls of the container(radially).when the bucket starts rotating,the extreme end molecule of water which is pressed against the wall will be moved together with the wall,because it is pressed against the wall,this in turn will be transferred to the next molecule and so on...upto the centre.
when a molecule near to centre starts to move in a circular path,it will exert more pressure tangentially and in fact ,it will be tranfered to the next layer of molecules(which is already pushing the other layer molecule due to circular motion) and forces added so on... and that force is not enough to break the wall of the bucket,but enough to raise the external molecule to a small height against the atmospheric pressure and gravity which is pulling it down.
When this external molecule is elevated,the penultimate will occuppy its space and so on.ultimately the surface will become concave..
Now when even the bucket stops rotating,the water will continue spinning because the water molecules still possesses kinetic energy and the pressure exerted to the walls of bucket is tangetial instead of normal as in the begining.gravity and atmospheric pressure of course will take some time to act against this spinning ,ultimately to halt it
Please correct me if i am wrong in understanding actual problem

 

[Buckethead]

Dear all
let us view it in another angle.a liquid(water here)will exert presurre in all direction to the walls of the container(radially).when the bucket starts rotating,the extreme end molecule of water which is pressed against the wall will be moved together with the wall,because it is pressed against the wall,this in turn will be transferred to the next molecule and so on...upto the centre.

This is the reason that water flows up the side of the bucket, but this is not the problem. The problem is determining how the water knows that it is moving in the first place and hence moving up the side of the bucket.

 

[Buckethead]

But that's why I asked if anyone really believed you could not get a dip in a bucket in an otherwise empty universe. I certainly don't believe it. So if you could, then you have to use the bucket to tell you whether or not it's rotating-- the effort to invert that logic is the source of the problem (that's where philosophy enters and muddies the science).
General relativity predicts the result of that experiment. Why do we need Mach? Don't get me wrong, I realize that asking the questions Mach did helped Einstein think "outside the box". That is generally what I view philosophy is for-- to free our thinking to see what the possibilities are. But we tend to cling to it long after it has ceased its usefulness, and mistake it for part of the theory.

From what I understand Einstein first bonded with Mach's idea, but then fell back on just accepting that there is an absolute universe. When Einstein talks about curvature of spacetime due to gravity in GR, what exactly is he referring to? (not mathamatically, but philosophically). One couldn't say it's a gravitational field because the warping of space is a result of gravitation. Is he referring to the virtual frame of reference that is created when all the mass and it's revolving/positional properties are taken into account (which would be Mach's principle)? I cannot accept that he is simply referring to a mathamatical virtual spacetime that has no physical basis in the real world. This would be nonsense.

So please, without a physical spacetime with which to say a water molocule is moving relative to, how can you still conclude that the water in the bucket will take a concave shape? The answer to this question is in my opinion very important to this discussion.

 

[Buckethead]

I don't know much about Mach's principle, but discussions about it always seem to turn into these rather silly "otherwise empty universe" discussions, which makes me question the value of Mach's principle.

Does Mach's principle have any concrete testable predictions? If not, what is its value?

I think it may. For example, if it can be shown that massive objects (or some other form of matter in the universe) and it's relative rotation/speed to an object determines the inertia (or mass) of the object, then this would indicate that counter structures could be built to alter the mass of objects. Having control over the mass/inertia of on object can open up all sorts of doors. More efficient ways to propel ships through space and countering gravity being a couple.

 

[Mentz114]

So please, without a physical spacetime with which to say a water molocule is moving relative to, how can you still conclude that the water in the bucket will take a concave shape? The answer to this question is in my opinion very important to this discussion.

Rotation can only be meaningfully defined for an extended object ( the water). Parts of the water are moving relative to other parts. There is no need to invoke physical space-time.

 

[Buckethead]

Rotation can only be meaningfully defined for an extended object ( the water). Parts of the water are moving relative to other parts. There is no need to invoke physical space-time.

I don't believe it's true when you say parts of the water are moving relative to other parts. They are all aligned and moving together. Let me restate this Newton's bucket in another way to eliminate the rotation.

Imagine a long straight stiff rod lying in empty space. Near one end of the rod and with it's nozzel parallel to it is a canon with a tennis ball inside. Just behind the tennis ball inside the canon is a laser pointing in the same direction as the nozzle of the canon.

The canon is fired, and shortly after that the laser is also fired. Two questions. Is the trajectory of the tennis ball parallel to the rod and secondly does the laser beam strike the rear of the tennis ball?

The seemingly obvious answers are yes in both cases, but I'm not so sure these are the correct answers. The reason being there is no physical relationship between the rod and the tennis ball or between the tennis ball and the laser beam.

The tennis ball can be thought of as representing water molocules in the bucket, and if it cannot be determined that the tennis ball will move parallel to the rod, then it cannot be determined that the molocules of water in the bucket will try and move tangent to the rotation of the water.

 

[newTonn]

This is the reason that water flows up the side of the bucket, but this is not the problem. The problem is determining how the water knows that it is moving in the first place and hence moving up the side of the bucket.

Can you please explain it further?water is moving because it is pressed against a moving object(bucket).since it cannot break the walls of bucket ,it is taking the next easiest path,that is tangentially with a small horizontal angle upwards.
I cannot understant why physical space time is necessary to explain this experiment.

 

[Mentz114]

Buckethead:

I appreciate that you're trying to make a subtle point, but your example fails in the first sentence.

Imagine a long straight stiff rod lying in empty space...

How do you define 'straight' ? You need some kind of reference to compare the rod with ( line of sight ?).
I don't see how this relates to the rotating water, sorry.

It is the inertial mass of the water that makes it climb the sides of the bucket, so I think it all boils down to this - will a solo object possesses inertia ?

In my opinion it will. It is simpler to believe that inertia is a local thing, either an intrinsic property of matter, or the result of a local interaction.

 

[yuiop]

What bothers me about this idea is that it seems to require that the presence of gravity alters the physics of a system in a way other than due its tidal effects, which seems to violate the principle of equivalence. In other words, if you put a box around a system, then the effect of gravity on the internal workings of that system should only come in via its tidal influences. But if you put a force on a point particle in that box, and claim that gravity from external sources are responsible for the way it accelerates, then you cannot have the equivalence principle. Note there is not a problem with kev's thought experiment about a ball bouncing back and forth in a box, because tidal stresses across that box must be responsible for the behavior observed, but inertia itself is a property of a point particle.

I would just like to point out I was talking about a ball bouncing back and forth horizontally in the box so tidal stresses do not come into that thought experiment, because tidal stresses are vertical.

Having given some more thought to the subject it seems that GR is not fully compatible with Mach's principle as pointed out by Garth. (By the way, you have to admire Garth's honesty and intellectual integrity in his handling of his own theory with respect to the GPB experiment). It would seem that inertial mass is influenced by it environment (the distribution of mass around it) but there is also a residual intrinsic inertial mass independent of its surroundings, just as there is a residual invariant rest mass/ energy. It could be thought of as Mach's principle is partly incorporated into GR but Einstein did not go the whole way. In other words, in GR a rotating bucket in a universe of "fixed stars" is not exactly the same thing as a stationary bucket in a universe of stars rotating around it, and GR can tell us if the universe is rotating or not. Mach's principle on the other hand can not tell a rotating universe from a static universe. That is my interpretation anyway, but welcome the input of the experts here ;)

 

[Buckethead]

Buckethead:

I appreciate that you're trying to make a subtle point, but your example fails in the first sentence.
How do you define 'straight' ? You need some kind of reference to compare the rod with ( line of sight ?)

The rod was manufactured just before the universe suddenly vanished. It was determined to be straight using a laser which had a straight beam when the universe existed (I'm actually not being sarcastic here even though it might sound that way)

I don't see how this relates to the rotating water, sorry.

There are three factors involved in the water rising in a bucket. 1) The water is in motion relative to something. 2) The water has mass. 3) Anything in motion with mass wants to move in a straight line. If it can be shown that inertia (mass) vanishes, or the ability to move in a "straight" line vanishes or relative motion vanishes, then the water in the bucket will have a problem. In a spinning bucket, the issue of relative motion can be answered because the water is being forced to deviate from a "straight" line, so I have removed this as being a factor and instead am just focusing on the definition of a "straight" line in my new example. The issue of inertia is also a factor, but my example is just focusing on the definition of a straight line in empty space since if a straight line becomes undefined in an empty universe this is enough of a reason for the water to be confused.

It is the inertial mass of the water that makes it climb the sides of the bucket, so I think it all boils down to this - will a solo object possesses inertia ?

In my opinion it will. It is simpler to believe that inertia is a local thing, either an intrinsic property of matter, or the result of a local interaction.

I think that inertia for objects with "mass" or more properly objects that are made of matter is a long standing assumption. I think objects are given the property of inertia because of something acting on those objects, not because inertia is an inherent property of matter.

 

[Mentz114]

JesseM:

In other words, in GR a rotating bucket in a universe of "fixed stars" is not exactly the same thing as a stationary bucket in a universe of stars rotating around it, and GR can tell us if the universe is rotating or not. Mach's principle on the other hand can not tell a rotating universe from a static universe.

Well put. That's what motivates me to call it 'Mach's conjecture'. Why is it a 'principle' if our best theory of gravity clearly disagrees ?

Buckethead:

I think objects are given the property of inertia because of something acting on those objects, not because inertia is an inherent property of matter.

Let's hope some future experiment can decide this, and lay Mach's thing to rest.

 

[Ken G]

I would just like to point out I was talking about a ball bouncing back and forth horizontally in the box so tidal stresses do not come into that thought experiment, because tidal stresses are vertical.

No, tidal stresses in a central gravitational field are not vertical on a box. This is why the Moon makes tides on the Earth-- it stretches the Earth along the Moon-Earth line, and squashes it in directions perpendicular to that line. Both effects are about equally important in making tides. In other words, I predict the effect you describe would not happen in the constant gravitational field of a huge plane of mass. If I'm right, that invalidates the argument. (And I think I am, or else your effect would occur in a reference frame in constant acceleration relative to the box, and that doesn't come out of my Lorentz transformation.)