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General Relativity

Perpetual Student said:
I have never heard of a theory involving a rotating universe. Is there such a theory?
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Every thing we observe in the universe is surely rotating, or has angular momentum/velocity?
Is it incorrect to say the universe is rotating?
 
sol invictus said:
How do you conduct an experiment "in" a frame?

Frames are just human labeling conventions . They have no more connection to reality or intrinsic meaning than the sequence of symbols C-A-T does to the animal it describes in English.

If anything, an experiment is conducted "in" every possible frame simultaneously, and the laws of physics - used correctly in any one of those frames - will always correctly predict the results.
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Here:

Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.
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and

The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.
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FROM: LINK
 
Skwinty said:
Every thing we observe in the universe is surely rotating, or has angular momentum/velocity?
Is it incorrect to say the universe is rotating?
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Rotation picks out an axis. If you said "the universe is rotating", most people would take that to mean that there is a special axis in the universe, and that at least some physical phenomena depend on distance from that axis. But there isn't any evidence for such an axis in the part of the universe we can see.

Of course as we've been discussing you're free to choose a frame in which there is such an axis of rotation - but you'd find that when you compute anything physical (i.e. measurable in an experiment), the distance from the axis always miraculously cancels out.
 
Perpetual Student said:
Here:



and



FROM: LINK
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I don't see anything in there I disagree with (although I would word some things differently), or anything that disagrees with what I've said here, or that explains how to perform an experiment "in" a frame.

By the way nothing in that article applies to the universe, because it's all for the special case of flat spacetime. The universe cannot be described by an inertial frame - no such frame exists.
 
Perpetual Student said:
If the universe wee rotating as a whole we would detect it in the CBMR.
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Surely to assert that, then In 5000 years time,you would need to send another space craft to the exact last location and perform a recording.

A comparison could then made.
 
sol invictus said:
I don't see anything in there I disagree with (although I would word some things differently), or anything that disagrees with what I've said here, or that explains how to perform an experiment "in" a frame.

By the way nothing in that article applies to the universe, because it's all for the special case of flat spacetime. The universe cannot be described by an inertial frame - no such frame exists.
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I don't understand your objection to the word "in." I am moving along "in" my spaceship relative to local stuff around me. I throw a ball up and it comes straight down. That is my experiment "in" my inertial frame. If I were "in" an accelerating frame it would not come straight down.
 
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sol invictus said:
Rotation picks out an axis. If you said "the universe is rotating", most people would take that to mean that there is a special axis in the universe, and that at least some physical phenomena depend on distance from that axis. But there isn't any evidence for such an axis in the part of the universe we can see.

Of course as we've been discussing you're free to choose a frame in which there is such an axis of rotation - but you'd find that when you compute anything physical (i.e. measurable in an experiment), the distance from the axis always miraculously cancels out.
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.... which is basically what I said earlier (and that you disagreed with then).

If the universe is rotating "around Phobos," then there's an axis that goes through Phobos, and some physical phenomena depend on distance from Phobos. Since the opening post talked about "the whole universe as revolving around Phobos," I feel comfortable restricting our attention to large-scale phenomena (i.e. we're not talking about a Phobon basketball game where the purely local gravity well dominates our measurements or something like that.)

By your own admission, if we set up such a system (formally), we find that the distance cancels out. This is exactly what Occam said could be ignored -- entities (in this case, "the distance to the axis through Phobos) that are not necessary for understanding should not be multiplied.

I would also point out that the hypothesis that the universe is revolving around Phobos involves at least three free parameters that have no effect on any of our calculations -- two in the orientation of the axis, and one in the rotational speed. Again, Occam suggests that free parameters with no effect should be discarded.

Occam's razor therefore tells us that the hypothesis that the universe is revolving around Phobos is not parsimonious and can be rejected.
 
Perpetual Student said:
Here:

Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.
Click to expand...
and

The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.
Click to expand...

and

FROM: LINK
Click to expand...


Wasn't this the exact problem GR was designed to solve?
 
Skwinty said:
Surely to assert that, then In 5000 years time,you would need to send another space craft to the exact last location and perform a recording.
Click to expand...

But as I understand it, it's pretty much meaningless to speak of the "exact last location" together with "in 5000 years time" since there's no preferred coordinate system in which to have a fixed location. You could certainly specify a coordinate system and revisit the point that, 5000 years later, had the same coordinates. But there are an infinite number of equally-valid coordinate systems, and in general they'll diverge pretty quickly.
 
sol invictus said:
I don't see anything in there I disagree with (although I would word some things differently), or anything that disagrees with what I've said here, or that explains how to perform an experiment "in" a frame.

By the way nothing in that article applies to the universe, because it's all for the special case of flat spacetime. The universe cannot be described by an inertial frame - no such frame exists.
Click to expand...

Why couldn't the CBMR be the basis of such a frame?
 
Perpetual Student said:
I don't understand your objection to the word "in." I am moving along "in" my spaceship relative to local stuff around me. I throw a ball up and it comes straight down. That is my experiment "in" my inertial frame. If I were "in" an accelerating frame it would not come straight down.
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That makes no sense at all. If by "in" a frame you mean "at rest in", then the ball would not come back down, it would bounce off the inside of your ship.

If I show you two maps of the earth that use different projections, which one are you "in"?

drkitten said:
.... which is basically what I said earlier (and that you disagreed with then).

If the universe is rotating "around Phobos," then there's an axis that goes through Phobos, and some physical phenomena depend on distance from Phobos.
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Nope. Not one physical phenomenon depends on that distance - not if we're talking about the universe we actually live in, at least (which is rotating around Phobos in some set of frames).

By your own admission, if we set up such a system (formally), we find that the distance cancels out. This is exactly what Occam said could be ignored -- entities (in this case, "the distance to the axis through Phobos) that are not necessary for understanding should not be multiplied.
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It's impossible to set up a coordinate system in which there are no distances that cancel out. But anyway, I never claimed the Phobocentric coordinates are the simplest ones to describe the large scale structure of the observable part of our universe.

I would also point out that the hypothesis that the universe is revolving around Phobos involves at least three free parameters that have no effect on any of our calculations -- two in the orientation of the axis, and one in the rotational speed. Again, Occam suggests that free parameters with no effect should be discarded.
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All frames contain free parameters - an infinite number of them, actually.

Occam's razor therefore tells us that the hypothesis that the universe is revolving around Phobos is not parsimonious and can be rejected.
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No, it tells us absolutely nothing of the kind. It's completely useless for deciding this question, actually - because what you refer to as a "hypothesis" is no such thing, since it's completely equivalent to the "hypothesis" that the universe is not revolving around Phobos. (Again, let me make clear that I am talking about different choices of frame in the same universe.)
 
I don't understand the fuss. Aren't we just talking about arbitrary frames of reference?


How fast am I currently moving? :eye-poppi


ETA- If Phobos is not as valid as any other place to call rest, are you all saying that people standing on Phobos will feel as if they are moving and accelerating in some strange fashion that you wouldn't feel anywhere else in the universe on a body of equal size and mass?
 
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Raze said:
I don't understand the fuss. Aren't we just talking about arbitrary frames of reference?
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That's kind of the point of Occam. If you have two apparently arbitrary ways to describe the same data, pick the one with the fewest entities.
 
Perpetual Student said:
I don't understand your objection to the word "in." I am moving along "in" my spaceship relative to local stuff around me. I throw a ball up and it comes straight down. That is my experiment "in" my inertial frame. If I were "in" an accelerating frame it would not come straight down.
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Just to add to what sol invictus posted, this is a perfect example.

Both your examples are inertial reference frames (as he pointed out). There's no way to distinguish if one, both, or neither are at rest or in motion (without outside references). With the ball coming stright down, you coul dbe at rest within a gravity field, or at a constant acceleration straight up. The second, you could be accelerating across a gravity field, or at rest at an angle to a gravity field, or just accelerating.
 
sol invictus said:
That's the point. Depending on what one wishes to describe, different frames will allow more or less complex descriptions. There isn't a single one that's simple for everything - quite the contrary.
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Sure, but that doesn't make everything equivalent. You can call a road race of Phobos equivalent to a road race on earth. But once you introduce cosmology, well, you really do have something unique and special. There may be an absurd number of possible road races in the universe, each with its simplest reference frame, but there's only one cosmos. And there's only one co-moving reference frame for that one cosmos. On a certain level, yes, it's not any more valid than any other reference frame. And Occam's razor is ultimately about convenience, not truth. But nonetheless, there still remains one reference frame which is unique for everyone, everywhere. I don't think you can construct any other reference frame which is similarly unique for everyone.
 
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