<p>One important concept that has not been mentioned yet is the "cosmological principle."  This is the key simplifying idea for our cosmological models, it says that the universe is the same everywhere on the largest scales at a given age, so alien astronomers 50 billion light years from us that also conclude the universe is 13.8 billion years old will be observing pretty much all the same things we are.  This principle is not proven by data, but the data is consistent with it, most notably the Hubble law and the homogeneity of the cosmic microwave background.  It allows us to understand the past of our own part of the universe by seeing the past of distant parts (a constraint we are stuck with given the speed of light).</p>

<p>So that's why a universe model that is finite in size must curve back on itself-- nothing else would satisfy the cosmological principle.  This doesn't mean the principle is true, it means we are not going to part with it unless we have to.</p>

CC BY-SA 3.0
2016-12-10T21:18:34.093Z
"This principle is not proven by data"... No need to be so modest. No scientific statement can be proven by data (Karl Popper).
kubanczyk
CC BY-SA 3.0
2016-12-08T13:50:04.530Z
2016-12-08T13:50:04.530Z
Ken G
<p>This is one of the most essential questions in cosmology.  The first gedankenexperiment probably. If the universe were finite what could be at the boundary? If there were some sort of wall, what would be on the other side?  Can space just end?  What would stop one from pushing past the end?  If you extend your arm out past the end does your arm cease to exist?  It is because we cannot provide any logically consistent answers to these questions that we accept that there are only two possibilities for the boundaries of the universe: 1) the universe is infinite and has no boundaries or 2) the universe is finite, but bends around and closes in on itself like the surface of a sphere and has no boundaries.  That is, there are no boundaries. Alternative 2 then forces one to contemplate that there is at least one more dimension to space then the known 3.</p>

CC BY-SA 3.0
2016-12-08T13:45:03.147Z
A finite universe with closed curvature does not require another dimension.  It may help us to visualize the curvature to embed it in an imagined fourth dimension, but it is not necessary that the fourth dimension actually be there.
Ken G
CC BY-SA 3.0
2016-12-08T18:08:05.613Z
@KenG I do agree with you.  It is possible that Euclid's postulate for parallel lines is just wrong and the geometry of this universe simply is non-Euclidean.  Or, the universe, if non-Euclidean in 3 dimensions, could be Euclidean in some higher dimension.
eshaya
CC BY-SA 3.0
2016-12-10T22:17:33.927Z
Yes, I think the question is whether Euclid's parallel postulate is regarded as something that has to be true, so if it doesn't hold in 3 dimensions, there must be higher dimensions to embed those in.  Or, if there is no reason why Euclid's parallel postulate needs to be true, then there's also no need to embed what we observe into anything we don't.   The embedding can simply be regarded as a conceptual picture, to help a mind that relates to the parallel postulate, deal with a universe that doesn't.  On the other hand, the universe does appear to be flat, after all.
Ken G
CC BY-SA 3.0
2016-12-07T20:28:59.367Z
2016-12-07T20:28:59.367Z
eshaya
<p>If a universe is finite and is not expanding at a speed equal to or greater than c, what happens when light or another form of electromagnetic radiation traveling reaches the boundary?</p>

CC BY-SA 3.0
2016-05-16T05:57:23.300Z
"Bounded" and "has a boundary" are distinct concepts.  You can have one without the other.
zibadawa timmy
CC BY-SA 3.0
2016-05-16T07:59:04.207Z
That's my thoughts on this as well.  The models that I know of for a bounded universe, it's curved in on itself, so light wouldn't reach a boundary but would ultimately travel back to where it started, but that would take a very long time.
userLTK
CC BY-SA 3.0
2016-05-16T09:42:10.850Z
Thanks, zibadwa timmy. For the purposes of my question, does the distinction make a difference? I am not trained at all in astrophysics.
gwofatlanta
CC BY-SA 3.0
2016-05-16T09:45:21.870Z
Thanks, userLTK. Can you point me to a layman's description of the models you refer to?
gwofatlanta
CC BY-SA 3.0
2016-05-16T11:41:06.323Z
@gwofatlanta Yes, it makes a difference, as physical behaviors are linked to the geometry they occur in, and a "boundary" has dimension one lower than the rest of space.  I feel like you're not the first person to make this mistake on this site, and some answers were given in an earlier case that addressed the mathematical distinction and some possible physical implications, but I haven't been able to find that Q&A so far.  Maybe it got deleted or I'm picking the wrong search items...
zibadawa timmy
CC BY-SA 3.0
2016-05-16T21:38:15.837Z
@gwofatlanta I couldn't find a good link, it's more something I've read here and there.   Wikipedia touches on it, and says that universes with "edges" are rarely considered https://en.wikipedia.org/wiki/Shape_of_the_universe#Bounded_and_Unbounded
userLTK
CC BY-SA 3.0
2016-05-17T01:24:18.207Z
@zibadawa timmy - I don't know which concept about the universe and its boundary or its boundedness is most accepted today but is there an answer to the gist of my question for whatever concept that is, or the answer for each distinction? Or is my question not meaningful in any of the concepts and it is not possible to explain in layman's terms why it is not meaningful?
gwofatlanta
CC BY-SA 3.0
2016-05-17T01:41:56.487Z
@userLTK thanks. The Wikipedia article is very helpful. The statement that spaces with edges are conceptually and mathematically difficult is made without explication, although it seems intuitively not difficult so I assume the reason is very technical.  I wonder if the concepts about universe shapes and edges are *defined* in such a way that my question's assumption (light catches up with the 'edge' of the universe) cannot occur or if for other reasons, the concepts do not *produce* a result where light reaches an edge.
gwofatlanta
CC BY-SA 3.0
2016-05-17T09:24:15.490Z
@gwofatlanta I'll see if I can put together a response in the near future.  I think some of your concerns have been addressed in other Q&A's here or on the Physics.SE, but I'll have to hunt them down and write up whatever I can't find that I think I can explain properly.  A lot of the nitty gritty boils down to studying a mathematical discipline known as "differential geometry", namely the basics of manifolds (of which there are those without boundary, and those with boundary), and what "boundary conditions" are in physics (and differential equations).
zibadawa timmy
CC BY-SA 3.0
2016-05-17T09:40:42.740Z
@zibadawa timmy, thanks for the offer to prepare an extensive response but I don't wish you to go through that effort. I am in over my head, I realise, and can accept that my simplistic conception of the 'problem' of light reaching the 'end' of the universe is not compatible with current models of the universe. My thought expressed in my comment to userLTK about whether the models are constrained from such 'edge' events or simply do not produce such edge events is of more interest to me now.
gwofatlanta
CC BY-SA 3.0
2016-05-18T14:51:02.957Z
Compare *"In a finite universe, what happens when light reaches the boundary?"* with *"on the surface of a finite planet (say, like Mars but smooth), what happens when a mars-buggy drives over the boundary?"*
RedGrittyBrick
CC BY-SA 3.0
2016-05-19T02:52:20.853Z
@RedGrittyBrick the mars-buggy will always be on the (surface) boundary so not sure that is analogous? Does light approaching normally to a point of  the finite universe's boundary bend to be tangent with the boundary at that point and is then trapped forever propagating along the boundary?
gwofatlanta
CC BY-SA 3.0
2016-05-19T08:43:19.897Z
@gwofatlanta: The point of the 2D analogy for a 3D universe is that the universe can be finite yet boundless. You (or light) may travel forever without reaching any boundary.
RedGrittyBrick
CC BY-SA 3.0
2016-05-20T00:21:02.023Z
@RedGrittyBrick thanks, I think I have it now after re-sending Wiki article.
gwofatlanta
CC BY-SA 3.0
2016-12-08T14:37:07.317Z
The old Asteroids game universe is finite and boundless. objects that reach the boundary simply reappear at a different place on the boundary, on the other side of the screen.
Wayfaring Stranger
<universe><light><radiation>
In a finite universe, what happens when light reaches the boundary?
gwofatlanta
# In a finite universe, what happens when light reaches the boundary?

(Asked by: username_0 on 2016-05-16)

If a universe is finite and is not expanding at a speed equal to or greater than c, what happens when light or another form of electromagnetic radiation traveling reaches the boundary?

**Tags:** universe, light, radiation

> **Comments:**
> **username_1**: "Bounded" and "has a boundary" are distinct concepts.  You can have one without the other.  
> **username_2**: That's my thoughts on this as well.  The models that I know of for a bounded universe, it's curved in on itself, so light wouldn't reach a boundary but would ultimately travel back to where it started, but that would take a very long time.  
> **username_0**: Thanks, zibadwa username_1. For the purposes of my question, does the distinction make a difference? I am not trained at all in astrophysics.  
> **username_0**: Thanks, username_2. Can you point me to a layman's description of the models you refer to?  
> **username_1**: @username_0 Yes, it makes a difference, as physical behaviors are linked to the geometry they occur in, and a "boundary" has dimension one lower than the rest of space.  I feel like you're not the first person to make this mistake on this site, and some answers were given in an earlier case that addressed the mathematical distinction and some possible physical implications, but I haven't been able to find that Q&A so far.  Maybe it got deleted or I'm picking the wrong search items...  
> **username_2**: @username_0 I couldn't find a good link, it's more something I've read here and there.   Wikipedia touches on it, and says that universes with "edges" are rarely considered https://en.wikipedia.org/wiki/Shape_of_the_universe#Bounded_and_Unbounded  
> **username_0**: @username_1 - I don't know which concept about the universe and its boundary or its boundedness is most accepted today but is there an answer to the gist of my question for whatever concept that is, or the answer for each distinction? Or is my question not meaningful in any of the concepts and it is not possible to explain in layman's terms why it is not meaningful?  
> **username_0**: @username_2 thanks. The Wikipedia article is very helpful. The statement that spaces with edges are conceptually and mathematically difficult is made without explication, although it seems intuitively not difficult so I assume the reason is very technical.  I wonder if the concepts about universe shapes and edges are *defined* in such a way that my question's assumption (light catches up with the 'edge' of the universe) cannot occur or if for other reasons, the concepts do not *produce* a result where light reaches an edge.  
> **username_1**: @username_0 I'll see if I can put together a response in the near future.  I think some of your concerns have been addressed in other Q&A's here or on the Physics.SE, but I'll have to hunt them down and write up whatever I can't find that I think I can explain properly.  A lot of the nitty gritty boils down to studying a mathematical discipline known as "differential geometry", namely the basics of manifolds (of which there are those without boundary, and those with boundary), and what "boundary conditions" are in physics (and differential equations).  
> **username_0**: @username_1, thanks for the offer to prepare an extensive response but I don't wish you to go through that effort. I am in over my head, I realise, and can accept that my simplistic conception of the 'problem' of light reaching the 'end' of the universe is not compatible with current models of the universe. My thought expressed in my comment to username_2 about whether the models are constrained from such 'edge' events or simply do not produce such edge events is of more interest to me now.  
> **username_3**: Compare *"In a finite universe, what happens when light reaches the boundary?"* with *"on the surface of a finite planet (say, like Mars but smooth), what happens when a mars-buggy drives over the boundary?"*  
> **username_0**: @username_3 the mars-buggy will always be on the (surface) boundary so not sure that is analogous? Does light approaching normally to a point of  the finite universe's boundary bend to be tangent with the boundary at that point and is then trapped forever propagating along the boundary?  
> **username_3**: @username_0: The point of the 2D analogy for a 3D universe is that the universe can be finite yet boundless. You (or light) may travel forever without reaching any boundary.  
> **username_0**: @username_3 thanks, I think I have it now after re-sending Wiki article.  
> **username_4**: The old Asteroids game universe is finite and boundless. objects that reach the boundary simply reappear at a different place on the boundary, on the other side of the screen.  

---

## 2 answers

### Answer by username_5 on 2016-12-08. Score: 3

One important concept that has not been mentioned yet is the "cosmological principle." This is the key simplifying idea for our cosmological models, it says that the universe is the same everywhere on the largest scales at a given age, so alien astronomers 50 billion light years from us that also conclude the universe is 13.8 billion years old will be observing pretty much all the same things we are. This principle is not proven by data, but the data is consistent with it, most notably the Hubble law and the homogeneity of the cosmic microwave background. It allows us to understand the past of our own part of the universe by seeing the past of distant parts (a constraint we are stuck with given the speed of light).

So that's why a universe model that is finite in size must curve back on itself-- nothing else would satisfy the cosmological principle. This doesn't mean the principle is true, it means we are not going to part with it unless we have to.

> **Comments:**
> **username_6**: "This principle is not proven by data"... No need to be so modest. No scientific statement can be proven by data (Karl Popper).  

---

### Answer by username_7 on 2016-12-07. Score: 0

This is one of the most essential questions in cosmology. The first gedankenexperiment probably. If the universe were finite what could be at the boundary? If there were some sort of wall, what would be on the other side? Can space just end? What would stop one from pushing past the end? If you extend your arm out past the end does your arm cease to exist? It is because we cannot provide any logically consistent answers to these questions that we accept that there are only two possibilities for the boundaries of the universe: 1) the universe is infinite and has no boundaries or 2) the universe is finite, but bends around and closes in on itself like the surface of a sphere and has no boundaries. That is, there are no boundaries. Alternative 2 then forces one to contemplate that there is at least one more dimension to space then the known 3.

> **Comments:**
> **username_5**: A finite universe with closed curvature does not require another dimension.  It may help us to visualize the curvature to embed it in an imagined fourth dimension, but it is not necessary that the fourth dimension actually be there.  
> **username_7**: @username_5 I do agree with you.  It is possible that Euclid's postulate for parallel lines is just wrong and the geometry of this universe simply is non-Euclidean.  Or, the universe, if non-Euclidean in 3 dimensions, could be Euclidean in some higher dimension.  
> **username_5**: Yes, I think the question is whether Euclid's parallel postulate is regarded as something that has to be true, so if it doesn't hold in 3 dimensions, there must be higher dimensions to embed those in.  Or, if there is no reason why Euclid's parallel postulate needs to be true, then there's also no need to embed what we observe into anything we don't.   The embedding can simply be regarded as a conceptual picture, to help a mind that relates to the parallel postulate, deal with a universe that doesn't.  On the other hand, the universe does appear to be flat, after all.  

---

