In a static bounded universe, what happens to particles that hit the edge?

Question

Consider a flat universe. The metric tensor is

$$g_{\mu\nu}=\left(\begin{array}{cccc}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)$$

but this is just the topology. Usually, universes with edges are not considered because they are apparently difficult to deal with, but suppose we tried to consider one. If this universe is not expanding (or not expanding very fast), what will happen to fast moving particles like photons that reach the edge?

IIRC there are reasonable cosmologies allowed in GR that have "edges". Not the one we live in, we're pretty sure, but I think the question is still well defined. Going to edit a bit to clarify that it's not about our universe. — Kyle Oman, Apr 19 '16 at 07:18
Edited pretty heavily. @youyou, please make sure you're still happy with the question. If you'd like to go back to the old version, you can use this page. — Kyle Oman, Apr 19 '16 at 07:26
This is not a well-posed question. If you want to consider universes which have edges you need to specify what the laws of physics would be like at the edge: you can't just say 'if there was an edge what would happen?' any more than I could ask 'if the universe was a banana what would happen!'. Once you've given the laws of physics which support the edge or the banana existing, then you can answer questions like this. — , Apr 19 '16 at 14:48
@tfb : no, if you want to consider universes which have edges you go ahead and do it. What you don't do is use some catch-22 reason not to, and to pooh-pooh the question. Answer it instead. — John Duffield, Apr 19 '16 at 20:33
@JohnDuffield unfortunately, not being God, I can only answer questions based on there being proposed laws of physics. — , Apr 19 '16 at 21:48
@KyleOman Thank you for your edition. I still have some questions. 1) why we are sure that our universe has no edge? 2) If our universe is 2+1 dimensional, 'no edge' means that the universe is more like a 2-d sphere rather than a 2-d plane, right? — youyou, Apr 21 '16 at 07:01
@KyleOman 3) If the universe is a sphere, photon traveling in one direction could come back to its original position, this could solve the problem that "photons hit the edge" because there is no edge. But the photons we observe today from the universe may have already finished some loops since the Big Bang ! (if the universe is expanding not so fast.) Is this correct? — youyou, Apr 21 '16 at 07:01
@tfb If our universe is 2+1 dimensional, 'no edge' means that the universe is more like a 2-d sphere rather than a 2-d plane, right? If the universe is a sphere, photon traveling in one direction could come back to its original position, this could solve the problem that "photons hit the edge" because there is no edge. But the photons we observe today from the universe may have already finished some loops since the Big Bang ! (if the universe is expanding not so fast.) Is this correct? — youyou, Apr 21 '16 at 07:04
@youyou re: why are we sure the Universe has no edge: I wouldn't say we're sure, but this is what the standard model of cosmology currently assumes. If you want more detail... well, that could make a decent question on its own. — Kyle Oman, Apr 21 '16 at 07:17
@tfb I disagree that it's ill-posed. You still assume GR, so this is basically asking what happens in a universe described by the GR field equations with an interesting set of boundary conditions and a reasonable stress-energy tensor. Sure, this is probably a currently intractable problem, but just because you can't solve the equations doesn't mean the question is ill posed! — Kyle Oman, Apr 21 '16 at 07:21
@youyou Yes, it's perfectly possible to think about universes that are compact (or compact spatially) but have no boundary. It's the boundary that's a problem. — , Apr 21 '16 at 08:43
@KyleOman It is ill-posed because the boundary conditions -- 'what happens when you hit the edge' -- are not given, there is no physical motivation for picking any, and they are the whole point of such a model. It's easy to see that in such a model, all null geodesics and almost all timelike geodesics intersect the edge both in the past and the future (so it is enormously geodesically incomplete both in the past and the future), which makes the boundary conditions at the edge fantastically important, yet there's just no reason to choose one set over another. — , Apr 21 '16 at 08:50
I think, a "bound" to the Universe could be handled as a constraint, that all fields are zero out of the bounds. In this case, it would be an infinite strong wall, and photons hitting it would be mirrored (it would be also a 100% perfect mirror). — peterh, Dec 12 '16 at 04:11

score -4 · Answer 1 · edited Apr 13 '17 at 12:39

In a static bounded universe, what happens to particles that hit the edge?

I venture to say nobody knows for sure. But it's an interesting question, because we have no evidence whatsoever that our universe is infinite or some kind of hypersphere. See this answer to a related subject. The story goes that in the old days, people could not conceive of a world that was curved. They could only conceive of a world with an edge. Nowadays we have cosmologists who cannot conceive of a world that is not curved, they cannot conceive of a world with an edge.

Consider a flat universe. The metric tensor is $$g_{\mu\nu}=\left(\begin{array}{cccc}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)$$ but this is just the topology. Usually, universes with edges are not considered because they are apparently difficult to deal with, but suppose we tried to consider one. If this universe is not expanding (or not expanding very fast), what will happen to fast moving particles like photons that reach the edge?

Obviously there's no definitive answers to this, merely opinions. And my opinion is based on what Einstein said about space. That it isn't nothing. It's something. Something that you can't see or feel, but nevertheless there's something there, something that can be stressed, something that can have a state which we call a field. Something through which waves propagate. Something which, as per the recent LIGO news, waves.

For an analogy, think of the E=hf photon as a water wave, think of space as water, and think of the universe as a droplet of water. Send a wave towards the edge, and what happens? It doesn't go through the edge. It undergoes total internal reflection. It bounces back. That's what I think will happen to a photon at the edge of the universe. Of course, there's no evidence for this hall of mirrors universe. But who knows, one day there might be. Take a look at the Hubble Ultra Deep Field image. Pick a prominent galaxy, then look over to the right and down a bit. There's a galaxy that looks rather similar. Funny that.

In a static bounded universe, what happens to particles that hit the edge?

1 Answers1