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

[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.

 

[vin300]

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.

Yes that's true,Einstein said this to mach-
"it... turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton's pail experiment... If one rotates [a heavy shell of matter] relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity)."

 

[M Grandin]

As I wrote some year earlier in aquainted thread, I myself was fully satisfied and did no longer regard "Newton's Bucket" as a "paradox", when I realized this:

The rotation must be judged from comparing with particles left free moving at the place of rotation. Then there is no paradox and no need talking about "fixed stars" as reference.

Then the task is reduced to answer why free moving particles are moving as they do at that place. Probably they appear moving straight and slowly at the speed they were launched.

So there is no paradox. The rotation of bucket has not much with this to do, it is simply calculated from centripetal acceleration in relation to the free moving particles, defining
a kind of "equilibrum" at that place and instance.

 

[Buckethead]

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.

Even if you take the absolute value (in other words, ignore cancellation) of all the gravity in the cosmos and sum it together the strength of the gravitational force would be much weaker than the gravitational field near Earth. I say this because you can use all the light from all the stars as a weak but usable analogy. Even though there are magnitudes more light being emitted by all the stars than say the sun, the sun easily washes out the starlight and light is a good example as it doesn't suffer from cancellations in the same way gravity does.

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.

This is true, but is not relevant in the Newton's bucket problem.

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.

Again, this is not part of the bucket problem. If gravity directly defined the reference frame used to determine the outcome of the bucket problem, then the rotation of the Earth and it's overwhelming gravitational field near the bucket would completely determine the concavity of the bucket.

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.

Yes, this is true and was a study done with regard to Mach's principle.

 

[Ken G]

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?

As far as I could say, yes, I'm no GR expert. Also, I would hesitate taking the spacetime grid too literally, as we could fall into the same semantic difficulties as claims that "space is really expanding" in the Big Bang. Instead, as with that common Big Bang description, we have a language for telling a story that is not itself verifiable, but which is a workable picture for getting to the results that are verifiable. Reality kind of emerges from the smoke of the conceptual sparks of our calculations, involving grids and space and so forth.

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.

Yes, the effect from the Earth would be too small to worry about, but perhaps the effect from the rest of the universe is another way to talk about that "footprint" that the universe has left on our spacetime environment. In other words, Lense-Thirring may have to do with the mechanism whereby the footprint gets left, but if we just say "all roads lead to Mach", we needn't necessarily have a specific mechanism like that in mind.

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.

I think this gets to the issue of what we mean by gravity. Some would say that gravity is only curvature, so only tidal gravity (with zero divergence where there is no mass) matters. But I prefer a more general meaning, saying essentially that gravity is the mechanism by which fictitious forces are generated in any coordinate system. So in that more general meaning, the centrifugal force is gravity, and so forth, even though it exists and has a nonzero divergence even in the absence of mass. I believe (but don't know) the issue of what decides the "inertial frame" for Newton's bucket, is of this more general type of gravity, which I think is what you are saying too. The elements might break down into something like the local curvature constraints, and the global boundary constraints, that sort of thing. It's all pretty vague until one can actually solve some equations to show what is really being said, and I haven't done any of that hard work.

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.

I recall Einstein himself, when considering his general relativity, saying words to the effect that one needs an aether. He was not talking about an invariant aether like was imagined before relativity, so I think he meant it needs to be more like a mutable aether that appears a bit different for each observer.

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.

It sounds like you are getting into the realm of unification of gravity. I agree that philosophical considerations can provide helpful guidance, if one uses the right philosophy, so that's why these philosophical musings are actually pretty important. I suspect that whoever does achieve unification will at some point be aided in finding the right path by largely philosophical thinking, just as Einstein was.

 

[Buckethead]

As far as I could say, yes, I'm no GR expert. Also, I would hesitate taking the spacetime grid too literally, as we could fall into the same semantic difficulties as claims that "space is really expanding" in the Big Bang. Instead, as with that common Big Bang description, we have a language for telling a story that is not itself verifiable, but which is a workable picture for getting to the results that are verifiable. Reality kind of emerges from the smoke of the conceptual sparks of our calculations, involving grids and space and so forth.

I do take this grid very seriously as there is an interim mechanism between gravity (or some other mass related force) and the effect on Newton's bucket. I realize that some take this grid as a mathamatical construct to simply define and describe gravity, but your point about history (historical inertia?) is a crucial one. For example, Earth distorts spacetime, but as the Earth moves, so does the spacetime (no history). But the Earth moving also leaves a footprint as you said although it is small since it is fighting against a much larger history of the cosmological footprint. Another way to say this is that gravity is immediate, but there is a substance or field that can take note of it and be influenced by it over time. This is more than just a math model of gravity it seems to me.

Yes, the effect from the Earth would be too small to worry about, but perhaps the effect from the rest of the universe is another way to talk about that "footprint" that the universe has left on our spacetime environment. In other words, Lense-Thirring may have to do with the mechanism whereby the footprint gets left, but if we just say "all roads lead to Mach", we needn't necessarily have a specific mechanism like that in mind.

Perhaps, but it's important to note Lense-Thirring brings into the spotlight the importance of not dismissing movement (angular in this case, but linear movement as well) on the shape of the overall curvature of the cosmos. In other words, it's not just mass, but mass and movement that affects the current footprint.

I think this gets to the issue of what we mean by gravity. Some would say that gravity is only curvature, so only tidal gravity (with zero divergence where there is no mass) matters. But I prefer a more general meaning, saying essentially that gravity is the mechanism by which fictitious forces are generated in any coordinate system. So in that more general meaning, the centrifugal force is gravity, and so forth, even though it exists and has a nonzero divergence even in the absence of mass. I believe (but don't know) the issue of what decides the "inertial frame" for Newton's bucket, is of this more general type of gravity, which I think is what you are saying too. The elements might break down into something like the local curvature constraints, and the global boundary constraints, that sort of thing. It's all pretty vague until one can actually solve some equations to show what is really being said, and I haven't done any of that hard work.

I tend to think of tidal gravity and this general gravity as the same thing, both influencing fictitious forces which works quite well if you consider that we are talking about bodies that are in motion and bodies that are stationary. A tidal force can have a strong influence on the fictitious forces but only for a short time because the body in question is always moving away from it's area of influence a moment earlier, whereas gravity in areas of low (or no?) divergence tends to be stationary. It's eqivelent to a camera taking a picture with a long exposure in low light or a short exposure with a flash. And like photographic paper, this only works if we are talking about ficticious forces (or grid or what have you ) that have memory otherwise long range low level gravity would not have the same influence as short range intense gravity.

I vote the term ficticious forces not be used as it implies that the grid (or whatever) has force and I don't think it does. It does seem it defines geodesic shapes and movements, and it has persistance. How about Persistant Geodesics (PG) or something like that.

I'm going to make a big leap here now and say the first property of PG is that is has persistance.

I recall Einstein himself, when considering his general relativity, saying words to the effect that one needs an aether. He was not talking about an invariant aether like was imagined before relativity, so I think he meant it needs to be more like a mutable aether that appears a bit different for each observer.
It sounds like you are getting into the realm of unification of gravity. I agree that philosophical considerations can provide helpful guidance, if one uses the right philosophy, so that's why these philosophical musings are actually pretty important. I suspect that whoever does achieve unification will at some point be aided in finding the right path by largely philosophical thinking, just as Einstein was.

I couldn't agree more. I think math is used far too much to create theories, when it should really only be used to solve theories. Theories must be created philosophically or they end up running the risk of having no basis in reality.

 

[Ken G]

I do take this grid very seriously as there is an interim mechanism between gravity (or some other mass related force) and the effect on Newton's bucket.

This is a tricky question in metaphysics-- what separates a construct from something real? At one level, we can say with certainty that everything is a construct, but we can also agree that some constructs seem a lot "closer" to the reality than others. Nevertheless, in any case this tends to be a "moving target". My discounting the "realness" of the spacetime grid was more along the lines of discounting the realness of the electromagnetic field, on the grounds that ten theorists will use ten different descriptions of what this field "really is", it very much seems to depend on how it is treated in the theory that person applies regularly. I've even heard it rumored that there are equivalent formulations of GR that make all the same predictions without invoking any concept of spacetime at all, but I could not give details. I feel that we have the predictions we make and test, and the stories we tell about those predictions (which we do not test, other than pedagogically), so it behooves us to keep these two magisteria separate.

Perhaps, but it's important to note Lense-Thirring brings into the spotlight the importance of not dismissing movement (angular in this case, but linear movement as well) on the shape of the overall curvature of the cosmos. In other words, it's not just mass, but mass and movement that affects the current footprint.

Indeed, that's already true in Schwarzschild, because of the role of pressure.

I tend to think of tidal gravity and this general gravity as the same thing, both influencing fictitious forces which works quite well if you consider that we are talking about bodies that are in motion and bodies that are stationary.

I just don't know enough GR to separate how tidal effects accumulate over large distances, versus what is an independent boundary condition.

I vote the term ficticious forces not be used as it implies that the grid (or whatever) has force and I don't think it does. It does seem it defines geodesic shapes and movements, and it has persistance. How about Persistant Geodesics (PG) or something like that.

Yes, it's an antiquated term when dealing with GR, what you need to know are the geodesics.

Theories must be created philosophically or they end up running the risk of having no basis in reality.

This is also a very sticky question-- I know as many who would agree with as those who would replace "philosophically" with "mathematically"! I thnk there is less of line between those then most people recognize-- mathematics is essentially philosophy-by-numbers, and philosophy is mathematics-with-rhetoric.

 

[Al68]

If gravity directly defined the reference frame used to determine the outcome of the bucket problem, then the rotation of the Earth and it's overwhelming gravitational field near the bucket would completely determine the concavity of the bucket.

I think you misunderstood what I was saying. The inertial path each water molecule would take in the absence of applied force is strongly affected by Earth's gravity, but very weakly affected by Earth's rotation (frame dragging).

It is that path being opposed by the bucket wall that causes the concavity. But thinking of a fluid sphere rotating (bulging equator) in deep space might be a better example than the bucket.

The simplest example of the same concept is just a single object in inertial motion that accelerates relative to the rest of the universe if a force is applied. Why does an applied force cause an object (rock, water molecule, etc.) to accelerate relative to the rest of the universe?

Answering that question would answer the rest. (And get you a Nobel Prize).

 

[Buckethead]

This is a tricky question in metaphysics-- what separates a construct from something real? At one level, we can say with certainty that everything is a construct, but we can also agree that some constructs seem a lot "closer" to the reality than others. Nevertheless, in any case this tends to be a "moving target". My discounting the "realness" of the spacetime grid was more along the lines of discounting the realness of the electromagnetic field, on the grounds that ten theorists will use ten different descriptions of what this field "really is", it very much seems to depend on how it is treated in the theory that person applies regularly.

Yes, this is so true. I guess my point was that this construct we are dealing with here has some additional properties that we are not for the most part aware of. Persistence for example being one of them. I would be perfectly happy to tag this property onto what we currently call gravity or equally happy identifying some new force or field in nature that is influenced by gravity that causes the same effect with regard to the bucket. All I'm saying is that there is something here that I think is being overly ignored and if it were addressed it would bring out some new discoveries about the nature of our universe.

I've even heard it rumored that there are equivalent formulations of GR that make all the same predictions without invoking any concept of spacetime at all, but I could not give details. I feel that we have the predictions we make and test, and the stories we tell about those predictions (which we do not test, other than pedagogically), so it behooves us to keep these two magisteria separate.

This doesn't surprise me. It's six of one and half dozen of the other. If two theories predict the same thing then I guess these two theories are saying the same thing but in different ways. It's probably best to take the simpler theory.

Indeed, that's already true in Schwarzschild, because of the role of pressure.

Can you explain this further?

This is also a very sticky question-- I know as many who would agree with as those who would replace "philosophically" with "mathematically"! I thnk there is less of line between those then most people recognize-- mathematics is essentially philosophy-by-numbers, and philosophy is mathematics-with-rhetoric.

I was being just a bit pompous here. I agree with you on this.

 

[Buckethead]

I think you misunderstood what I was saying. The inertial path each water molecule would take in the absence of applied force is strongly affected by Earth's gravity, but very weakly affected by Earth's rotation (frame dragging).

It is that path being opposed by the bucket wall that causes the concavity. But thinking of a fluid sphere rotating (bulging equator) in deep space might be a better example than the bucket.

I did understand what you were saying, but this is just Newtonian mechanics. The real issue with the Newton's bucket goes beyond this because it questions what a inertial line of travel actually means. The molocules want to go in a straight line and this is the Newtonian aspect, but the question is what is a straight line? For the most part a straight line means a path right to a stable star. Or does it? That is the problem. Mach says yes, others say no.

The simplest example of the same concept is just a single object in inertial motion that accelerates relative to the rest of the universe if a force is applied. Why does an applied force cause an object (rock, water molecule, etc.) to accelerate relative to the rest of the universe?

Answering that question would answer the rest. (And get you a Nobel Prize).

Indeed! The beauty of the Newton's bucket problem is that one eventually winds up with the most abstract questions. For example, does inertia exist or have any meaning in an otherwise empty universe? If inertia does exist, is it possible to accelerate (with a rocket for example)? Does light travel in a straight line in an empty universe? What is a straight line?

 

[Ken G]

Perhaps the cleanest statement is to break the issue into two pieces, one is whatever determines the geodesics, and the second is whatever causes particles to deviate from geodesics. We can agree that other forces, like bucket walls, create the deviations from geodesics, based on whatever constraints those forces must satisfy, so the real issue here is, what makes the geodesics? Some might say that spacetime is in some sense "comprised" of the geodesics, and gravity is only a kind of tidal modification to those geodesics. To me, the heart of Mach's principle is avoiding such a dichotomy, and saying that the action of the mass of the universe is not just to create tidal modifications, but rather the whole concept of a geodesic is specified by the action of the mass and fields. We model that influence in two stages, one is the boundary conditions on the geodesics, and the other is the tidal modifications that link the boundary conditions.

It seems to me people tend to take the first part for granted and only call the second part "gravity", whereas Mach's principle would seem to involve the unification of both parts. That's the personal take of a non-expert who has not done the hard work of actual calculations, so is subject to correction by those who do.

 

[Buckethead]

I think you misunderstood what I was saying. The inertial path each water molecule would take in the absence of applied force is strongly affected by Earth's gravity, but very weakly affected by Earth's rotation (frame dragging).

I'm going to re-reply to this as I wasn't clear the first time.

The trajectory taken due to gravity alone is Newtonian mechanics, but the frame dragging is part of the Newton's bucket problem because it has a direct impact on the universal frame of reference (the geodesics) that is at the core of the problem. My earlier point was that it was surprising to me that the overwhelming gravitational field of the Earth doesn't have a stronger effect on influencing the geodesic in the vicinity of the strong gravity. My mistake was in assuming that the strength of the gravity could alter the geodesic due to it's sheer strength, when it's more likely that the geodesic is only influenced by gravity over time. Since the Earth is in constant motion around the sun it is not in one spot long enough to alter the geodesic in it's immediate vicinity. And that is also why the frame dragging is so weak. I would guess that if the Earth was stationary in space and spinning (the faster the better) that the outcome of Newton's bucket at the north pole would be measurably different

 

[Buckethead]

Perhaps the cleanest statement is to break the issue into two pieces, one is whatever determines the geodesics, and the second is whatever causes particles to deviate from geodesics.

Excellent! With regard to the first, gravity seems to be a prime candidate. If this is the case then we might also say the degree to which the shape of a geodesic can be altered is proportional to the total mass in the universe. If gravity is not a prime candidate (if Mach was wrong), then the geodesic has a given "density" and mass has nothing to do with it's existence, only it's shape, movement, and position.

I would guess that the 3 forces (gravity not inclued) cause particles to deviate from the geodesic, but of equal significance is that a distortion (change in density?) in the geodesic could cause a particle to accelerate, either linearly or in an angular fashion and movment of the geodesic might be the definition of frame dragging.

It might be useful to add a third part to the two: What are the properties of the geodesics? Persistance seems to be one, Does a geodesic have the ability to flow into a mass? Is it the movement of a geodesic that determines the trajectory of an object passing near a mass? What is the nature of a geodesic with regard to constant motion through space (why isn't there resistance?). What is the nature of a geodesic with regard to reality (is it just a math construct or does it resemble a real life construct with a physical reality such as virtual particles)? I realize here that I might be deviating from your philosophy as I think if I'm not mistaken that you are more inclined to think of geodesics as being less based in reality than I do and more as just a construct to describe the forces and motions of masses. But that's OK.

We can agree that other forces, like bucket walls, create the deviations from geodesics, based on whatever constraints those forces must satisfy, so the real issue here is, what makes the geodesics? Some might say that spacetime is in some sense "comprised" of the geodesics, and gravity is only a kind of tidal modification to those geodesics. To me, the heart of Mach's principle is avoiding such a dichotomy, and saying that the action of the mass of the universe is not just to create tidal modifications, but rather the whole concept of a geodesic is specified by the action of the mass and fields. We model that influence in two stages, one is the boundary conditions on the geodesics, and the other is the tidal modifications that link the boundary conditions.

Yes, some give far to little importance to geodesics instead using them just to model gravity but without regard to their creation (whether that be a math construct or a real construct) or their real significance with describing the universe.

Since I'm taking geodesics as a real substance I'm going to go as far as to say that geodesics cause most of what we see and are not simply just a way to describe gravity or the motions of objects or of light. What if a change in density in a geodesic (due to mass) causes a particle to move towared a massive object. What if that is what gravity actually is? Not just a description of gravity, but the actual gravitational mechanism. If distortion and movement are able to deflect particles (cause acceleration), then it seems to me gravity is an extension of this.

It seems to me people tend to take the first part for granted and only call the second part "gravity", whereas Mach's principle would seem to involve the unification of both parts. That's the personal take of a non-expert who has not done the hard work of actual calculations, so is subject to correction by those who do.

I too am hoping someone else will do the math!

 

[Al68]

Indeed! The beauty of the Newton's bucket problem is that one eventually winds up with the most abstract questions. For example, does inertia exist or have any meaning in an otherwise empty universe? If inertia does exist, is it possible to accelerate (with a rocket for example)?

Is it possible to accelerate relative to what? Reaction mass maybe, but that would make the universe non-empty. I would say no, since without reaction mass, there could be no "force" of acceleration felt, and nothing to accelerate relative to. No proper acceleration and no coordinate acceleration.

If we allowed reaction mass in a previously empty universe, we could have both proper acceleration (reaction mass providing the applied force) and coordinate acceleration (relative to the reaction mass).

How to build the rocket in an empty universe is a different question.

 

[Buckethead]

Is it possible to accelerate relative to what? Reaction mass maybe, but that would make the universe non-empty. I would say no, since without reaction mass, there could be no "force" of acceleration felt, and nothing to accelerate relative to. No proper acceleration and no coordinate acceleration.

If we allowed reaction mass in a previously empty universe, we could have both proper acceleration (reaction mass providing the applied force) and coordinate acceleration (relative to the reaction mass).

How to build the rocket in an empty universe is a different question.

I'll allow reaction mass in this question. That being the case, one has to be careful about assuming that there will be an acceleration in the traditional sense, namely something that shows a reading on a mechanical accelerometer. There may be a separation over time between the reaction mass and the body in question, but will there be a reading on the accelerometer? This may seem like a silly question but it's not if one questions the concept of inertia in an otherwise empty universe. Inertia shows it's face when mass finds itself changing it's velocity with respect to Machian space. If there is no Machian space, no frame of reference with which to determine if a change in velocity is taking place, then there may be no such thing as traditional acceleration or more precisely, inertia. This is an analogous situation to Newton's bucket in that both depend on inertia to determine their outcome, and it is the question of what determines inertia (the stars?) that is at the heart of it. Oh and you get the rocket from Jerry's Rocket Shop as he will transport it to an empty universe for you.

 

[Al68]

I'll allow reaction mass in this question. That being the case, one has to be careful about assuming that there will be an acceleration in the traditional sense, namely something that shows a reading on a mechanical accelerometer. There may be a separation over time between the reaction mass and the body in question, but will there be a reading on the accelerometer?

Should be, since the universe is not empty, it contains both the rocket and the reaction mass. The rocket's coordinate acceleration relative to its reaction mass should even be proportional to the proper acceleration read on an accelerometer, ie, F=ma. This leaves the question of what value m would have, since mass is the measure of the rocket's inertial opposition to acceleration, and as you've pointed out, the inertial mass may itself depend on the other mass in the universe.

But assuming we have the same laws of physics, as long as the universe contains some (reaction) mass, the rocket's inertial mass will be non zero, so acceleration should be proportional to the force applied (and felt), even if the ratio (inertial mass) is very different than in the real universe.

If reaction mass is not allowed, there would be no physical way to provide acceleration, no way to apply any force to be "felt", and no other masses to establish a reference frame to measure coordinate acceleration.