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How large is the universe?

How large is the Uinverse? - Bigger than big, then a bit.

I suspect, if not infinite, then at least bigger than we will ever be able to know.
 
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It's big all right, and "flat". Some people say that because it's flat it must be infinite. You can even see that on this NASA page. But it's a non-sequiteur, it could be flat and finite. Guys like Neil Cornish have been trying to find patterns in the CMBR to support this idea, arguing that it can't be infinite if the Big Bang was unique. Another thing you hear is that the universe is like the "asteroids" arcade game where if you keep going left you end up coming from the right. Beats me how anybody can justify that. I think a more mundane scenario is that the universe has a straightforward edge. Think of space as water. Think of the universe as a drop of water. Think of electromagnetic waves as ripples in the water. They suffer total internal reflection at the edge. Hence I look at pictures of the Hubble Ultra Deep Field and wonder if there's any double images in there.
 
Feel free to show us a GR solution with an edge Farsight?
 
Sorry edd, here's something on the Einstein field equations, referring to energy density, flux, pressure, and shear stress, but I don't know where to start. Maybe somebody like Kip Thorne could tackle it.
 
edd said:
Feel free to show us a GR solution with an edge Farsight?
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You can consider such things, but the boundary necessarily has its own dynamics that need to be specified - otherwise, it's not a solution to Einstein's equations (so you're correct, strictly speaking, that there are no GR solutions with an edge). You essentially need to invent a new set of laws of physics and impose them at the boundary. That's possible, but it's not justified or required by data, nor is there any theoretical motivation for it I know of.
 
edd said:
Feel free to show us a GR solution with an edge Farsight?
Click to expand...

Farsight said:
Sorry edd, here's something on the Einstein field equations, referring to energy density, flux, pressure, and shear stress,
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That's just some professor's lecture notes introducing Einstein's field equations. edd asked whether you could show us a solution to those equations that has the "straightforward edge" you believe to be present in your "more mundane scenario".

Farsight said:
but I don't know where to start.
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True.

Farsight said:
Maybe somebody like Kip Thorne could tackle it.
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FYI: Kip Thorne is the T in MTW.

On 10 February 2012, you wrote (italics as in the original):
Farsight said:
And MTW is wrong.
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jhunter1163 said:
I've always doubted the expanding-space thing; it seems to me that, to use the raisin-cake analogy again, eventually some raisin would expand beyond our ability to see it. As far as I know, we don't see any galaxies going out.
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I think you should see galaxies going backwards in time. Though trying to prove you are seeing time backwards might be hard.
 
jhunter1163 said:
I've always doubted the expanding-space thing; it seems to me that, to use the raisin-cake analogy again, eventually some raisin would expand beyond our ability to see it. As far as I know, we don't see any galaxies going out.
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In the raisin-cake analogy, the raisins are analogous to galaxies or galactic clusters. Those galaxies/clusters don't expand much because their local gravitational fields dominate the expansion locally and hold them to roughly constant size.

If "galaxies going out" means galaxies travelling away from us, then we do see that phenomenon in the form of red shift. The proportionality of red shift to distance was our first compelling evidence of an expanding universe.

If "galaxies going out" means galaxies fading into invisibility, it would take millions of years to see that entire process. During the short time we've been using sophisticated modern instruments to peer into deep space, we could hope only to see galaxies so faint we can just barely see them. We do see some extremely faint galaxies.
 
sol invictus said:
You can consider such things, but the boundary necessarily has its own dynamics that need to be specified - otherwise, it's not a solution to Einstein's equations (so you're correct, strictly speaking, that there are no GR solutions with an edge). You essentially need to invent a new set of laws of physics and impose them at the boundary. That's possible, but it's not justified or required by data, nor is there any theoretical motivation for it I know of.
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With you there. I certainly wouldn't call that sort of thing 'mundane'.
 
I am not a physicist. Looking at this as a mathematician, it looks easy, even trivial.

sol invictus said:
edd said:
Feel free to show us a GR solution with an edge Farsight?
Click to expand...

You can consider such things, but the boundary necessarily has its own dynamics that need to be specified - otherwise, it's not a solution to Einstein's equations (so you're correct, strictly speaking, that there are no GR solutions with an edge).
Click to expand...
I disagree. I'll describe four trivial solutions for Einstein's field equations with zero cosmological constant:
Rμν - gμν R / 2 = (8 π G / c4) Tμν​
The last of those solutions has a definite edge, and two others might be regarded as having an edge.

Solution 0: Minkowski space, with zero stress-energy tensor.

Solution 1: The subspace of solution 0 with t > 0. Einstein's equations are differential equations. If they hold in an open neighborhood of every point, then they hold everywhere. In solution 1, every point has an open neighborhood that is also an open neighborhood of that point in solution 0 (with the trivial embedding). Since Einstein's equations hold in that open neighborhood in solution 0, they hold for the same open neighborhood in solution 1. Hence solution 1 is a solution.

Solution 2: The subspace of solution 1 with x1 > -1. By the same argument as above, solution 2 is a solution.

Solution 3: The subspace of solution 2 with x1 >= 0. Here we have to allow manifolds with boundary to qualify as a spacetime manifold, but that's just a matter of the definitions you prefer, and has nothing to do with whether the space is a solution of Einstein's equations. Note that Hawking and Ellis consider manifolds with boundary (§2.1), although they require models of spacetime to be inextendible (§3.1). That inextendibility condition has nothing to do with whether the space is a solution of Einstein's equations; historically, there have been several important solutions that are extendible (e.g. Schwarzschild, Eddington-Finkelstein, Lemaître).

sol invictus said:
You essentially need to invent a new set of laws of physics and impose them at the boundary. That's possible, but it's not justified or required by data, nor is there any theoretical motivation for it I know of.
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Agreed.

With solutions 1, 2, and 3 above, there are geodesics that go off the reservation, which presumably violates some conservation laws.

That happens for realistic solutions as well, but only at singularities. With solutions 1, 2, and 3 above, there are no singularities to blame for the violation of physical laws.
 
W.D.Clinger said:
FYI: Kip Thorne is the T in MTW. On 10 February 2012, you wrote (italics as in the original): And MTW is wrong.
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I know who Kip Thorne is, Clinger. And as you know, I referred to him when we were talking about time travel a few of days back, saying two out of three authors of MTW believe in time travel. I said MTW is wrong re black hole Kruskal-Szekeres coordinates which gloss over a trip to future infinity and back. It isn't all wrong.
 
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sol invictus said:
You can consider such things, but the boundary necessarily has its own dynamics that need to be specified - otherwise, it's not a solution to Einstein's equations (so you're correct, strictly speaking, that there are no GR solutions with an edge). You essentially need to invent a new set of laws of physics and impose them at the boundary. That's possible, but it's not justified or required by data, nor is there any theoretical motivation for it I know of.
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I disagree. We've had data for a long time that tells us the universe has been expanding from a relatively small size for 13.7 billion years. More recent data from WMAP says the universe is "flat", so it isn't a hypersphere. If it was infinite the stress-energy (akin to pressure) of space would be confined and couldn't cause the universe to expand. I think the data points to the universe being say a sphere of space expanding in no space, something like a squeezed-down stress ball expanding when you unclench your fist. My reference to Kip Thorne shows that he's been teaching elasticity, which relates to the shear stress in the EFE, and fluid mechanics, wherein the boundary conditions might be something like surface tension.
 
Farsight said:
W.D.Clinger said:
FYI: Kip Thorne is the T in MTW. On 10 February 2012, you wrote (italics as in the original): And MTW is wrong.
Click to expand...
I know who Kip Thorne is, Clinger. And as you know, I referred to him when we were talking about time travel a few of days back, saying two out of three authors of MTW believe in time travel.
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FYI: John Archibald Wheeler is dead. I doubt whether he believes anything at all about time travel, or anything else.

As for your link to Kip Thorne's article: That article is uncontroversial. It says travel backwards in time is probably impossible, but the so-called Twin Paradox makes it theoretically possible for a resident of earth to travel away from earth at high speed and then to revisit earth arbitrarily far into earth's future but only a few years into the traveller's future.

Farsight said:
I disagree. We've had data for a long time that tells us the universe has been expanding from a relatively small size for 13.7 billion years. More recent data from WMAP says the universe is "flat", so it isn't a hypersphere.
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Okay so far, but...

Farsight said:
If it was infinite the stress-energy (akin to pressure) of space would be confined and couldn't cause the universe to expand. I think the data points to the universe being say a sphere of space expanding in no space, something like a squeezed-down stress ball expanding when you unclench your fist.
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:boggled:
 
I know Wheeler's dead, and you know I know, so stow the wisecrack comments. This is the Kip Thorne article on time travel that's junk.

What's the problem with the universe being an expanding ball of space? Space has its vacuum energy. The "empty space" of a gravitational field comprises energy that "shall act gravitatively in the same way as any other kind of energy". On the large scale the universe is "flat", so you don't you go thataway and come back thisaway. To the best of our knowledge the universe has been expanding from a small size for 13.7 billion years, so it can't be infinite. Doesn't leave much room for manoeuvre, does it?
 
Farsight said:
I disagree. We've had data for a long time that tells us the universe has been expanding from a relatively small size for 13.7 billion years. More recent data from WMAP says the universe is "flat", so it isn't a hypersphere.
Click to expand...

Nope - the data simply says that if it's a hypersphere (or hyperbolic 3-space, or anything else with uniform curvature), the radius of curvature is about 10x the current Hubble radius. And if the curvature is not assumed uniform, it tells us almost nothing about what's beyond the Hubble horizon.

If it was infinite the stress-energy (akin to pressure) of space would be confined and couldn't cause the universe to expand.
Click to expand...

Nonsense.

I think the data points to the universe being say a sphere of space expanding in no space, something like a squeezed-down stress ball expanding when you unclench your fist. My reference to Kip Thorne shows that he's been teaching elasticity, which relates to the shear stress in the EFE, and fluid mechanics, wherein the boundary conditions might be something like surface tension.
Click to expand...

More nonsense.
 
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