Newton's Bucket


by Buckethead
Tags: bucket, newton
Buckethead
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#91
Jun23-09, 12:45 AM
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Quote Quote by Ken G View Post
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
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#92
Jun23-09, 01:48 AM
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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
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#93
Jun23-09, 01:59 AM
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Quote Quote by Buckethead View Post
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
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#94
Jun23-09, 11:44 PM
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Quote Quote by MeJennifer View Post

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
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#95
Jun24-09, 12:09 AM
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Quote Quote by phyti View Post
Quote Quote by 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
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#96
Jun24-09, 03:29 PM
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Did the observer die?
MeJennifer
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#97
Jun24-09, 04:42 PM
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Quote Quote by Buckethead View Post
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
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#98
Jun24-09, 10:23 PM
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Quote Quote by MeJennifer View Post
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 spacial in nature and as such can rotate.
A-wal
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#99
Jun25-09, 11:54 PM
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Quote Quote by Ken G View Post
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.

Quote Quote by Ken G View Post
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
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#100
Jul28-09, 09:05 PM
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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
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#101
Jul28-09, 10:27 PM
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Quote Quote by Buckethead View Post
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
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#102
Jul28-09, 10:36 PM
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Quote Quote by Phrak View Post
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
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#103
Jul28-09, 10:56 PM
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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
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#104
Jul28-09, 11:49 PM
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Quote Quote by Ken G View Post
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
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#105
Jul29-09, 09:17 AM
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Quote Quote by Buckethead View Post
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
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#106
Jul29-09, 11:22 AM
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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
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#107
Jul29-09, 11:59 AM
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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
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#108
Jul29-09, 12:06 PM
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Quote Quote by Al68 View Post
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.


Quote Quote by Al68 View Post
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.


Quote Quote by Al68 View Post
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.


Quote Quote by Al68 View Post
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.


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