FTL communication and time travel

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Tyndmyr
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Re: FTL communication and time travel

Postby Tyndmyr » Wed Sep 03, 2014 8:07 pm UTC

Hypnosifl wrote:
PsiSquared wrote:Let's take a simple example. Suppose the frame-of-reference in which ansible signals move, is tied to the motion of the center-of-mass of the universe.

Current models of cosmology generally use the assumption that the universe doesn't have any center of mass, see Where is the centre of the universe? from the Usenet Physics FAQ.


I have a degree of trouble with this. Not with the expansion or relative frames of reference. That's all fine. But assuming if the universe is non-infinite, there would have to be a center of mass, yes? Sure, this is just an arbitrary categorization, and a different, smaller categorization would have a different center of mass(I presume the CoM for the solar system would be within, or very close to the sun, for instance), but it should still have one, yes?

Of course, we likely cannot get the information to know exactly where that is...but even the observable universe, as a smaller subset of the entire universe, should have a center of mass.

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Re: FTL communication and time travel

Postby doogly » Wed Sep 03, 2014 8:22 pm UTC

The universe most likely is infinite though. The observable universe has a center of mass, but why should the laws of physics care about that? We might like to talk about it, but we can't assign it any unique significance.
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Re: FTL communication and time travel

Postby Hypnosifl » Wed Sep 03, 2014 8:49 pm UTC

Tyndmyr wrote:
Hypnosifl wrote:
PsiSquared wrote:Let's take a simple example. Suppose the frame-of-reference in which ansible signals move, is tied to the motion of the center-of-mass of the universe.

Current models of cosmology generally use the assumption that the universe doesn't have any center of mass, see Where is the centre of the universe? from the Usenet Physics FAQ.


I have a degree of trouble with this. Not with the expansion or relative frames of reference. That's all fine. But assuming if the universe is non-infinite, there would have to be a center of mass, yes? Sure, this is just an arbitrary categorization, and a different, smaller categorization would have a different center of mass(I presume the CoM for the solar system would be within, or very close to the sun, for instance), but it should still have one, yes?

Of course, we likely cannot get the information to know exactly where that is...but even the observable universe, as a smaller subset of the entire universe, should have a center of mass.

General relativity describes gravity in terms of mass/energy causing 4D spacetime to become curved, and you can also describe 3D space as curved if you pick a particular definition of simultaneity in order to slice 4D spacetime into a stack of 3D instants (there is a particular choice of time coordinate which is most often used in cosmology, which can be though of as the time measured on a set of clocks arranged throughout space that have each remained at rest in the frame of the cosmic microwave background, throughout their entire history). We can't really visualize a curved 3D space, but we can describe it mathematically, and we can also understand it to some degree by analogy with a hypothetical curved 2D universe (I think it helps with the intuition here if you've read Flatland). If the curvature of 3D space is "positive", this is analogous to a 2D surface with the curvature of a sphere, which is also "positively" curved (see here for diagrams of the 2D versions of spaces with zero or negative curvature). In this case space would be finite but unbounded, in the sense that if you travel far enough in any direction you will simply return to your point of origin, just as an ant would when walking as straight as possible along the surface of a globe.

The relevance of this to the center of mass question is that if 2D flatland matter were uniformly distributed on this 2D spherical surface, it wouldn't have any center of mass on that 2D surface, the distribution would be totally symmetrical. Now, you might think it needs to have a center of mass at the center of the sphere, away from the surface of the sphere in the 3D space the sphere is sitting in. But the mathematics used in general relativity, differential geometry, allows one to describe curved surfaces without any reference to a higher-dimensional space for them to be "embedded" in (see the intrinsic versus extrinsic section of the wiki article on differential geometry). And an analogous model is possible with the dimensions raised by one--in this case 3D space is positively-curved and finite, and matter fills it in a uniform way so there is no "center of mass" within our 3D space.
Last edited by Hypnosifl on Wed Sep 03, 2014 8:58 pm UTC, edited 2 times in total.

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doogly
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Re: FTL communication and time travel

Postby doogly » Wed Sep 03, 2014 8:56 pm UTC

Hypnosifl wrote: We can't really visualize a curved 3D space.

Well, you can if you do enough general relativity (where "enough" is defined circularly.)

Alternatively, you can approach it from a math angle, and just imagine an n dimensional curved space and set n=3 after all the hard work is done.
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Re: FTL communication and time travel

Postby gmalivuk » Wed Sep 03, 2014 8:58 pm UTC

Tyndmyr wrote:if the universe is non-infinite, there would have to be a center of mass, yes?
No. The surface of a sphere has no center on that sphere.

(I know this was already said, but here's the tl/dr version.)
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drachefly
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Re: FTL communication and time travel

Postby drachefly » Thu Sep 04, 2014 3:12 pm UTC

doogly wrote:It's time to go to the fictional science subforum. Like, the Ender's Game fanfic nadir of the fictional science subforum.


Surely it would be the Hainish Novels end?

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doogly
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Re: FTL communication and time travel

Postby doogly » Thu Sep 04, 2014 3:15 pm UTC

I just remember seeing ansibles in Ender's Game. The Hainish novels never made their way into the fraternity bathroom, so I got no idea what goes on there.
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Re: FTL communication and time travel

Postby gmalivuk » Thu Sep 04, 2014 5:53 pm UTC

Yeah, don't give Orson Scott Card any more credit than he actually earned.
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Re: FTL communication and time travel

Postby lgw » Thu Sep 04, 2014 11:56 pm UTC

I'm sure I saw the term before Card, but damned if I can remember where. Heinlein invented so many SF terms that became widely used, but not this one.

I have noticed that a few people have this strong aversion to the word that I can't explain. It's certainly not tied to Card! There's not a better word for "superluminal communication device", and it's a useful concept for exploring relativity (much like Star Trek transporters are a staple of the philosophical study of identity these days).
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doogly
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Re: FTL communication and time travel

Postby doogly » Fri Sep 05, 2014 12:46 am UTC

Yeah it was LeGuin first, it seems.
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tomandlu
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Re: FTL communication and time travel

Postby tomandlu » Mon Sep 08, 2014 10:39 am UTC

doogly wrote:Yeah it was LeGuin first, it seems.


Definitely. The use in Ender's Game* usage makes reference to the fact that the term comes from an old, fictional book.

* just finished it this AM (never read it before).
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Re: FTL communication and time travel

Postby lgw » Wed Sep 10, 2014 7:26 pm UTC

doogly wrote:The universe most likely is infinite though. The observable universe has a center of mass, but why should the laws of physics care about that? We might like to talk about it, but we can't assign it any unique significance.


gmalivuk wrote:
Tyndmyr wrote:if the universe is non-infinite, there would have to be a center of mass, yes?
No. The surface of a sphere has no center on that sphere.
(I know this was already said, but here's the tl/dr version.)


Well, regardless of the topology of the universe, as long it's bigger than the observable universe, the distribution of mass will be observer-dependent, and the observer is always at the enter of the observable universe. If the universe is homogenous at an appropriate scale, then wherever you go, you're at the center of mass.

The only way you could have a center of mass that observers could agree on is if the universe were smaller than the visible universe (whether that's the surface of a sphere, torus, or one of the vast catalog of other possible shapes) and the mass wasn't evenly distributed. Think of Earth when it had but one continent - you could certainly define a center-of-land then. Of course, we know this universe isn't like that - heck, if there were any sense in which there was an observer-independent center of mass, we'd have observed that by now.

It does seem more and more that our universe isn't actually homogenous on any scale smaller than the visible universe, however, as we keep finding larger and larger "structures". I find that really cool, as it means we might discover evidence of structures larger than the visible universe, giving us observational evidence about the non-observable universe.
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