Exploring Newton's Bucket Paradox

[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.

 

[Buckethead]

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.

I tend to agree that even in an otherwise empty universe F=ma will hold but interestingly only because m denotes inertial mass and not the amount of matter. It might just be the case that the amount of matter an object has and it's inertial mass begin to deviate in a universe with increasingly less total matter. The end result in an otherwise empty universe is that a much much smaller force would be needed to accelerate an object to a given velocity relative to the ejected matter. If this is the case then the accelerometer would also have to be recalibrated as it's mass on the spring would be less showing a lower value than the actual increased acceleration (change in velocity relative to the ejected matter) would be.

There are some considerations that need to be taken with regard to the change in inertial mass to amount of matter in on object. For example, I mentioned earlier that it makes sense to consider the persistance of the geodesics when influenced by moving or stationary matter. In an otherwise empty universe one has to consider how long the astronaut sits in his current location before turning on the rocket as it might affect his inertial mass. This goes for rotation as well. If the astronaut turns on rotational jet packs (after sitting for awhile), he will experience a (small) degree of angular momentum and his arms will fly outward, but if he stays in this state for awhile, his arms might just fall back down to his side again as the persistent geodesics would begin to rotate with the astronaut (due to Lense-Thirring effect) rendering him essentially non rotating after awhile (when using the definition of rotation as a feeling of angular momentum).

One more point is that in on otherwise empty universe the object's active gravitational field might remain proportional to it's inertial mass, but again not to it's amount of matter. Therefore an object the size of the Earth in an otherwise empty universe would have a weaker gravitational field and objects would fall more slowly.

 

[Al68]

I tend to agree that even in an otherwise empty universe F=ma will hold but interestingly only because m denotes inertial mass and not the amount of matter.

How is the amount of matter measured other than by mass? Number of atoms, maybe? Would each atom have less mass if there were less mass in the universe? Does the mass of each subatomic particle depend on other mass in the universe?

One more point is that in on otherwise empty universe the object's active gravitational field might remain proportional to it's inertial mass, but again not to it's amount of matter. Therefore an object the size of the Earth in an otherwise empty universe would have a weaker gravitational field and objects would fall more slowly.

Wouldn't the object still fall at 9.8 m/s^2 due to it's proportionally reduced inertial mass offsetting the reduced gravitational mass of earth?

And back to the rocket, since it's being accelerated by the expulsion of reaction mass which itself would have less inertial mass, resulting in less force applied to the rocket, there would be less coordinate acceleration between rocket and reaction mass.

So, even if the mass of each atom were lower, the force used to accelerate the rocket would be proportionally lower due to the reduced reaction mass, and that would leave us with no way to detect any difference caused by "reduced" inertial mass, since inertial mass by definition is resistance to acceleration.

It seems like there would be no way to measure inertial mass in any absolute sense, only in a relative sense. We could only measure the masses of the rocket and reaction mass relative to each other, and their ratio would be the same as they are now.

For example, if a rocket accelerated by "shooting" half its mass in the other direction, in an empty universe the inertial mass of both rocket and reaction mass may be less, but the resulting coordinate acceleration (per unit mass) would be greater due to the lower inertial mass, resulting in the same measured coordinate acceleration (between rocket and reaction mass) as in a "full" universe. And the proper acceleration (felt by observers) would equal the force used to expel the reaction mass, just as it is in our "full" universe. Basically, I see no way to detect any absolute change in the inertial mass per atom, if the change is universal.

If the mass of every atom in the universe is half today of what it was yesterday, how could we tell? Does the concept even make sense?

 

[Buckethead]

How is the amount of matter measured other than by mass? Number of atoms, maybe? Would each atom have less mass if there were less mass in the universe? Does the mass of each subatomic particle depend on other mass in the universe?

The number of subatomic particles can be used to determine mass (see Wiki "mass") as can F=ma (inertial mass), as can gravity and a few other things. Wiki mentions that if any of these prove to be unable to determine mass (because they are the odd one out), then they would be thrown out. In our universe, they all agree, but in an otherwise empty universe, one or more of these may deviate.

Wouldn't the object still fall at 9.8 m/s^2 due to it's proportionally reduced inertial mass offsetting the reduced gravitational mass of earth?

I would say no for the same reason that a golf ball and cannon ball fall at the same rate on Earth and both fall at a slower rate on the Moon. A small objects rate of decent toward a planet is not determined by it's mass, only the mass of the planet. But in this peculiar universe in which this happens there may be other factors involved such as the deviation between inertial mass and the amount of matter.

And back to the rocket, since it's being accelerated by the expulsion of reaction mass which itself would have less inertial mass, resulting in less force applied to the rocket, there would be less coordinate acceleration between rocket and reaction mass.

The force would remain constant as this is a given. Therefore the 2 objects of lower mass will accelerate away from each other to a greater degree than than the two objects of greater mass. The expelled propellant would simple shoot out faster offering a greater reaction.

However, you do bring up a good point in that we can't really forsee the effect of this empty universe on all matters of force. For example, if we use a spring to push a cannon ball away from the astronaut, we would expect the accelerations to be greater but only if a given spring produces the same amount of force in this empty universe. Springs work by depending on the electromagnetic force between atoms in the spring. If electromagnetism, and for that matter the weak and strong force are all related to each other and to gravity, then it's possible that if anyone of them is proportionally changed (such as gravity) relative to the amount of matter in an object in an otherwise empty universe that the others could change as well in linear proportion. If this is the case, then this might mean that we could never detect the difference. On the other hand, if the changes between forces is non linear, then we would be able to tell.

Finding the changing relationship of these forces to each other and to the overall mass in the universe might be a pathway to unifying the forces.

If for some reason all forces but one, say gravity, did not change it's strength in this new universe, then I think it could safely be said gravity and the other 3 forces were not related in anyway and unification would be impossible. I doubt that's the case however.

If the mass of every atom in the universe is half today of what it was yesterday, how could we tell? Does the concept even make sense?

Even if all 4 forces were proportionally changed in a linear way relative to the overall mass of the cosmos, it would make a difference on a grand scale because overall mass has to be considered as local. If for example our galactic cluster has a different amount of matter than another galactic cluster in the universe (which no doubt it does), then the inertial mass of particles in our galactic cluster could be different than that of other clusters. This would make interactions between clusters predictable only if these fudge factors were taken into account. Also a particle traveling at a given speed in our galactic cluster, would have a change in velocity when entering another galactic cluster due to the change in it's inertial mass. Measuring the expansion of the universe would be affected as well.

 

[Al68]

The number of subatomic particles can be used to determine mass (see Wiki "mass") as can F=ma (inertial mass), as can gravity and a few other things. Wiki mentions that if any of these prove to be unable to determine mass (because they are the odd one out), then they would be thrown out. In our universe, they all agree, but in an otherwise empty universe, one or more of these may deviate.

Well, I was shooting in the dark predicting the way things might work in an empty universe, but we certainly agree on one thing: We just don't know enough about gravity or mass.

The one thing that seems apparent is that inertial mass and gravitational mass aren't just equal or equivalent, but are in fact the same thing. It would be hard to believe that they are separate things that just coincidentally seem identical in every way (in GR, not in Newtonian physics).

As I'm sure you know, there have been many attempts to detect the hypothesized Higgs boson, theorized to be responsible for the mass of subatomic particles, and there are more planned that might eventually shed some light on the subject. The Large Hadron Collider in Geneva is expected to either confirm or deny its existence once and for all, within a few months, or so they say.

 

[Buckethead]

The one thing that seems apparent is that inertial mass and gravitational mass aren't just equal or equivalent, but are in fact the same thing. It would be hard to believe that they are separate things that just coincidentally seem identical in every way (in GR, not in Newtonian physics).

I think they are the same thing, but of course you will find many that think they are only equivelent.

As I'm sure you know, there have been many attempts to detect the hypothesized Higgs boson, theorized to be responsible for the mass of subatomic particles, and there are more planned that might eventually shed some light on the subject. The Large Hadron Collider in Geneva is expected to either confirm or deny its existence once and for all, within a few months, or so they say.

The Higgs field, which is responsible for giving mass to all particles including the Higgs boson itself might be a candidate for the Machian effect, but I don't know the properties of the Higgs field enough to have an opinion on this. Perhaps someone with more knowledge of this field can chime in.

The field or effect that I am searching for would have these properties, and these are based on gravity and mass being the same thing and not just eqivalent. Some of these properties seem contradictory, but they are not contradictory, they are simply peculiar.

1. It uniformly saturates galaxtic clusters and it's density is dependent on the total galactic mass.
2. It's density decreases near massive objects which may imply mass absorbs it.

3. It's density changes when a massive object is accelerated through it with the leading edge having a higher density. This change in density looks like gravity from behind
4. If it's density is non uniform across an object, then the object will accelerate (gravity) toward the less dense region.

5. It's density does not change if an object moves through it at a constant velocity.
6. It offers no resistance to an object, as long as it's density is uniform across the object

7. It interacts with each and every particle in an accelerating object. (A 1 kg disc for example offers no more resistance than a 1 kg spear, both of which are traveling at the same speed)

8. It is defined as a geodesic and the geodesics are shaped by both mass and by the acceleration of a given mass. The greater the gravity or the greater the acceleration, the greater the distortion in the geodesic.

9. The shapes of the geodesics are persistent and the degree of persistance is proportional to the amount of mass, and duration of the mass in a specific location or the degree of acceleration of a mass.

10. If the geodesic rotates as a whole, this causes a change in density across the objects within it, causing the objects to accelerate rotationally until they match the rotation of the geodesic as a whole.

11. Light curves if passing through an area of density change (such as near a planet, or near an accelerating object.

Number 11 has some predictive properties. For example, light will bend near an accelerating object in the same way it would near a gravitational mass.

Number 3 makes a prediction as well. If a massive cylinder is rotated at a high speed, the density would increase inside the cylinder due to angular acceleration. The inside of the cylinder would be the leading edge of the accelerating cylinder and therefore the gravity inside the cylinder would be higher than Earth gravity. A particle passing through the cylinder would have an increase in mass for the duration of it's time in the cylinder. It would also slow down entering the cylinder due to the change in density, but speed up again on exiting so these effects would cancel. The increase in mass however and it's associated decrease in speed due to it's mass change would be measurable.

Number 7 is particularly interesting because in a traditional gravitational field all the particles in an object are affected by all the particles in the large body. This is why two objects of different mass fall at the same rate, the amount of force on each particle in the two objects are the same which follows f=ma.

These properties are bizaar to say the least, and I have racked my brain trying to come up with something that could possibly have such properties, but fall short. Whatever it is, it's different than what we can commonly imagine. If something can be found to match these properties, then we have found what gravity is and what inertia is and also solve Newton's bucket.

 

[inflector]

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.

I know this thread is six months old, but I see a problem with the above logic.

In particular, unless I'm missing something important, the reach of gravity could be infinitely larger than that of photons/electromagnetic energy.

Consider this. The oldest light we can see is from the CMB which is about 15 billion years old. This is some 400 thousand years after the Big Bang. The reason we have this limit is because before this time, the universe was opaque to photons.

It was not, however, opaque to gravity.

Therefore, if gravity propagated at the speed of light beginning with the Big Bang, it seems possible that we are currently feeling the gravitation of a much greater proportion of the matter in the universe, perhaps even all of it. This is in contrast with the light we can see which is limited due to the fact that we can only see back to about 400,000 years after the big bang.

So, it may be that the gravitational effects of the entire universe dominate even when on the surface of the Earth from the perspective of Newton's Bucket.

- Curtis

 

[utesfan100]

Let's take two bricks tied together by a rope and define that the bricks are not spinning (one face of each brick always faces the other). If there is tension on the rope, then one can say the bricks are revolving about each other. But in an empty universe, this would mean the system would be revolving relative to absolute space. If there is no absolute space, then there could be no tension on the rope since the objects are not rotating relative to anything (not even to each other if their faces are stationary)

I like this version. In an empty universe a spinning bucket of water would send out water uniformly in a big mess that I don't want to clean up.

It is my understandings that GR allows great flexibility in selecting reference frames. Mach's principle can be viewed as stating that we can use a rotating reference frame in classical mechanics.

This produces complicated curvature to the space-time that reduces to the pseudo-forces in classical rotating frames.

For a localized system I would think that a reference frame that minimized the curvature at infinity would offer a preferred reference frame. I suspect this convention would eliminate rotating reference frames and frames where the net momentum of the system of interest is not 0.

As for a non-mathematical explanation of scalars and tensors ... I'll provide that once you provide me with a non-mathematical explanation of integrals.

Tensors are generalizations of scalars, vectors and matrices to an arbitrary dimension of indexes. GR is written in the language of Riemannian Geometry, and this would be a good place to start.

 

[Buckethead]

I know this thread is six months old, but I see a problem with the above logic.

In particular, unless I'm missing something important, the reach of gravity could be infinitely larger than that of photons/electromagnetic energy.

Consider this. The oldest light we can see is from the CMB which is about 15 billion years old. This is some 400 thousand years after the Big Bang. The reason we have this limit is because before this time, the universe was opaque to photons.

It was not, however, opaque to gravity.

Therefore, if gravity propagated at the speed of light beginning with the Big Bang, it seems possible that we are currently feeling the gravitation of a much greater proportion of the matter in the universe, perhaps even all of it. This is in contrast with the light we can see which is limited due to the fact that we can only see back to about 400,000 years after the big bang.

So, it may be that the gravitational effects of the entire universe dominate even when on the surface of the Earth from the perspective of Newton's Bucket.

- Curtis

I thought light was opaque from the earliest universe because it is traveling away from us faster than light, and 2) because it's frequency is too low (actually negative) because of this. Gravity would fall into the same category.

 

[Buckethead]

It is my understandings that GR allows great flexibility in selecting reference frames. Mach's principle can be viewed as stating that we can use a rotating reference frame in classical mechanics.

This produces complicated curvature to the space-time that reduces to the pseudo-forces in classical rotating frames.

For a localized system I would think that a reference frame that minimized the curvature at infinity would offer a preferred reference frame. I suspect this convention would eliminate rotating reference frames and frames where the net momentum of the system of interest is not 0..

I agree with all you are saying here and it would be fine to just stop at that if it weren't for what I see as a possibility that there might be a case where a complicated curvature to space time does not reduce to the pseudo-forces in a classical rotating frame. What if there are curvatures caused by the movements of concentrated masses in the universe that lagged or were otherwise out of phase with the pseudo-forces we observe? A lag for example between a spacetime curvature and the pseudo-forces in a rotating galaxy would give the appearence of a the galaxy having a flattened rotational curve which we are currently attrributing to being caused by dark matter.

 

[matheinste]

I thought light was opaque from the earliest universe because it is traveling away from us faster than light, and 2) because it's frequency is too low (actually negative) because of this. Gravity would fall into the same category.

Can you elaborate on what you mean by light being opaque and of negative frequency.

Matheinste.

 

[Buckethead]

Can you elaborate on what you mean by light being opaque and of negative frequency.

Matheinste.

Sorry, my response was a little obscure. At the furthest reaches of the universe (the earliest times) there is a horizon where, due to expansion, the universe is theorized as moving away from us faster than light. Because of this the light past this point cannot ever be seen by us. I took this to be what you meant by "opaque". The frequency of the light just on this side of the horizon would be below the microwave frequency, at the horizon it would be zero, so beyond that it would be a negative frequency if we could see it which we can't so it's really a nonsense term that I threw out there for illustrative purposes. Since gravity from the earliest universe is also beyond this horizon and also traveling at the speed of light, it cannot reach us either.

 

[Al68]

I thought light was opaque from the earliest universe because it is traveling away from us faster than light, and 2) because it's frequency is too low (actually negative) because of this. Gravity would fall into the same category.

The universe was opaque to light because of its density. Gravity is much different, because unlike light, there is no opaqueness, and we can't rule out the possibility that we could be under the gravitational influence of masses that are not even part of our universe at all, or that predate our universe.

Of course that's pretty speculative, but I'm only saying we can't rule it out based on the opaqueness of the universe prior to 400,000 years after the big bang, like we can with light. And we can't rule out the existence of masses beyond the "horizon" that aren't moving away from us faster than light.

We can only rule out light from such masses because of the previous opaqueness (density) of the universe, but that wouldn't apply to gravity.

 

[Buckethead]

The universe was opaque to light because of its density. Gravity is much different, because unlike light, there is no opaqueness, and we can't rule out the possibility that we could be under the gravitational influence of masses that are not even part of our universe at all, or that predate our universe.

Of course that's pretty speculative, but I'm only saying we can't rule it out based on the opaqueness of the universe prior to 400,000 years after the big bang, like we can with light.
.

I might be wrong here but it seems to me that if the density of the early universe (that is not going faster than light) was so high that it would block light, then the energies must have been so high that everything emited light and the sky would be a wash with light. If the time of this opaque universe was beyond the horizon, then there wouldn't be a wash, but there would also be no effect of gravity at this distance since gravity also travels at c.

And we can't rule out the existence of masses beyond the "horizon" that aren't moving away from us faster than light.

What would be traveling slower than light beyond the horizon, since everything in this area of the universe started from the big bang?

 

[Al68]

I might be wrong here but it seems to me that if the density of the early universe (that is not going faster than light) was so high that it would block light, then the energies must have been so high that everything emited light and the sky would be a wash with light. If the time of this opaque universe was beyond the horizon, then there wouldn't be a wash, but there would also be no effect of gravity at this distance since gravity also travels at c.

What would be traveling slower than light beyond the horizon, since everything in this area of the universe started from the big bang?

I was referring to the speculative, but very real possibility that our universe, the result of the big bang, isn't all that exists or ever existed. Our universe could be subject to the gravitational influence of masses that aren't part of our universe, and predate the big bang.

The previous opacity of our universe restricts any light we can detect to sources within our universe's horizon, but gravitational influence cannot be ruled out the same way.

Of course, this probable belongs in the cosmology or string theory forums instead of SR/GR.

 

[Buckethead]

I was referring to the speculative, but very real possibility that our universe, the result of the big bang, isn't all that exists or ever existed. Our universe could be subject to the gravitational influence of masses that aren't part of our universe, and predate the big bang.

The previous opacity of our universe restricts any light we can detect to sources within our universe's horizon, but gravitational influence cannot be ruled out the same way.

Any gravity that would be present previous to the big bang from other universes would be accompanied by light from those universes as well since again, they both travel at light speed. However, we are getting into a very speculative area here, not so much the extra universes, but the physics of what is allowed before the big bang. Does light or gravity even propagate in a pre-big bang univserse?

Not to loose the point of this discussion, I was speculating whether or not gravity is the carrier of the Newton's bucket effect. Is the web of fields generated by the gravity of distant stars the reason behind Newton's bucket, and if so, what particular property of gravity is it? It can't be the sheer strength because Newton's bucket is unaffected by the gravity of the Earth, but rather the gravity (or something else) of the stars. This is very peculiar. It more likely is caused by an effect of gravity, a shadow or echo of gravity, a residual that is more persistent than the gravity of the Earth that moves with it's orbit around the sun. Or it could be something other than gravity, a new force maybe that has different characteristics than gravity such as persistance. I've no idea, but it's clearly not just the gravitational pull itself.

 

[A-wal]

Can't this simply be explained be inertia? If you swing an object round then it wants to go in a straight line away from you but you've got hold of it so it can't, but it flies off as soon as you let go. The forward energy of the water in a spinning bucket has to go somewhere so it pushes the sides up because the water wants to go in a straight line outwards.

 

[Pythagorean]

Can't this simply be explained be inertia? If you swing an object round then it wants to go in a straight line away from you but you've got hold of it so it can't, but it flies off as soon as you let go. The forward energy of the water in a spinning bucket has to go somewhere so it pushes the sides up because the water wants to go in a straight line outwards.

The point is about where inertia comes from. Mach's principle is that it comes from all the other mass in the universe.

 

[Buckethead]

Can't this simply be explained be inertia? If you swing an object round then it wants to go in a straight line away from you but you've got hold of it so it can't, but it flies off as soon as you let go. The forward energy of the water in a spinning bucket has to go somewhere so it pushes the sides up because the water wants to go in a straight line outwards.

In addition to what Pathagorean said it is also a matter of what defines a "straight" line. If you swing an object on a string around your head and you let it go, where exactly will it go? If Mach's principle holds, then it will head out toward whatever star it was pointing to when it was released and continue on to that star even if that star and all other matter in the universe moves out of position relative to "empty" space. If Mach's principle does not hold, then it will head out toward a star, but miss the star if the star (and all other matter) moves. In other words, the "straight" line will be straight in only one of those scenarios, but it is not clear which one. I'm a Machian person, so I think the object will follow the stars. Keep in mind that light will follow only one of these trajectories as well, so in either case the path of the object will be parallel to beam of light that is projected parallel to the initial path of the object when it is released, which is why it will look "straight" regarless of which path it is following.

 

[A-wal]

The point is about where inertia comes from. Mach's principle is that it comes from all the other mass in the universe.

I thought inertia was simply due to the fact that an object doesn't have a true rest state, or do you mean why an object with a relatively different velocity carries a force with it that's transferred to anything it hits? Machs principle says that it's because of the rest of the mass in the universe?



@Buckethead:
"Does light or gravity even propagate in a pre-big bang univserse?"

There's no space in a pre-big bang universe, so no.


"If Mach's principle holds, then it will head out toward whatever star it was pointing to when it was released and continue on to that star even if that star and all other matter in the universe moves out of position relative to "empty" space. If Mach's principle does not hold, then it will head out toward a star, but miss the star if the star (and all other matter) moves."

There's no such thing as movement relative to empty space. If everything moves by the same amount then nothing moves.


"In other words, the "straight" line will be straight in only one of those scenarios, but it is not clear which one. I'm a Machian person, so I think the object will follow the stars. Keep in mind that light will follow only one of these trajectories as well, so in either case the path of the object will be parallel to beam of light that is projected parallel to the initial path of the object when it is released, which is why it will look "straight" regarless of which path it is following."


Why would it always look straight? Light doesn't, it always follows at least a slightly curved path, just not locally.

 

[Buckethead]

I thought inertia was simply due to the fact that an object doesn't have a true rest state, or do you mean why an object with a relatively different velocity carries a force with it that's transferred to anything it hits? Machs principle says that it's because of the rest of the mass in the universe?.

Mach's Principle speculates that inertia, or a body's resistance to acceleration is directly caused by all of the matter in the universe. No matter, no resistance.

"If Mach's principle holds, then it will head out toward whatever star it was pointing to when it was released and continue on to that star even if that star and all other matter in the universe moves out of position relative to "empty" space. If Mach's principle does not hold, then it will head out toward a star, but miss the star if the star (and all other matter) moves."

There's no such thing as movement relative to empty space. If everything moves by the same amount then nothing moves..

Indeed! Which makes me wonder why the debate about Mach's principle is still going on. Nevertheless it is, and (correct me if I'm wrong) the alternative to Mach's principle is acceleration relative to background spacetime (Minkowski spacetime?)? Sorry, but I can't say I really understand what is meant by acceleration relative to spacetime. This doesn't make much sense to me.

"In other words, the "straight" line will be straight in only one of those scenarios, but it is not clear which one. I'm a Machian person, so I think the object will follow the stars. Keep in mind that light will follow only one of these trajectories as well, so in either case the path of the object will be parallel to beam of light that is projected parallel to the initial path of the object when it is released, which is why it will look "straight" regardless of which path it is following."

Why would it always look straight? Light doesn't, it always follows at least a slightly curved path, just not locally.

Are you talking about light bending due to gravity? If so then I'll clarify by saying that a straight path (used in this context of a released object) can be defined as the path light takes when unaffected by gravity. And this can be considered the path that the object in question would take if it were also unaffected by gravity.