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Author  Topic: Size of the universe  
New Cat's Eye Inactive Member 
Gravity bends light... how do you think that is possible?
Oh, I dunno... You can expand a mathematical matrix. You can expand your mind. Anyway, spacetime is where physical properties reside. Even your own rule here takes place within spacetime. Its kind of its own thing, and not necessarily subject to the rules that take place within it.
That question is nonsensical.


Iblis Member (Idle past 2230 days) Posts: 663 Joined: 
The capacity to act as a medium for matter and energy; curvature, as in expansion and gravitation; and vacuum energy in particular is purely a physical property of spacetime itself. The fact that this stuff doesn't make sense to you, or fit into your philosophy, has no bearing on its accuracy. Relativity is one of the most thoroughly tested bodies of theory in all of science. If the terms of the mathematical model were less accurate than the piddly bit of "common sense" your brain can produce, any number of those experiments would have failed miserably. The only point where relativity seems to need some work is in describing the very, very small.


ProtoTypical Member Posts: 1792 From: Ontario Canada Joined: 
So, then, is the concept of a 'void' only a concept? An impossible one at that. Can we logically conceive a 'place' where no 'thing' exists?
Edited by Dogmafood, : No reason given.


cavediver Member (Idle past 1978 days) Posts: 4129 From: UK Joined: 
As we have seen, spacetime is itself a thing, and can quite happily exist with nothing else in it.


ProtoTypical Member Posts: 1792 From: Ontario Canada Joined: 
Can I conclude, then, that space must be infinite?


cavediver Member (Idle past 1978 days) Posts: 4129 From: UK Joined: 
No, not at all. It can be either. Space can be wrapped up such that it is finite but with no boundary  in the way that the surface of the earth has no boundary but is finite.


Seizmik Junior Member (Idle past 3145 days) Posts: 2 From: Edinburgh, UK Joined: 
To all who read this and get the idea that the universe is a sphere, don't. It very well may be, but that isn't what cavediver was eluding to(I think). Keep in mind also that since the socalled 'edges' of the observable universe are 14pc away, this doesn't mean that the universe itself is only 14pc in radius. This can easily be thought of with a completely opaque balloon. If you take the balloon before it is inflated and fill it with a multitude of gases, these gases with start to react(possibly) and you could see a multitude of effects going on, if you were inside the balloon. Now if you fill the room you are in with the same gases the same reactions could happen, but you're inside the balloon, so you can't see them.


ProtoTypical Member Posts: 1792 From: Ontario Canada Joined: 
OK I have successfully cajoled the little grey cells into accepting this. Having done so, I can no longer imagine a 'place' where there is no space.
I think I get what you mean by no boundary along the surface. Regardless of it's shape does the word 'surface' not denote a boundary? On the surface or not on the surface. Above or below the surface. So we exist in a universe that can have a finite space surrounded by an infinite border and infinite space surrounded by a finite border. Am I the only one who has trouble with this? I am not trying to be obtuse .


cavediver Member (Idle past 1978 days) Posts: 4129 From: UK Joined: 
Good.
No, not in the mathematical sense of the word 'surface'. When I refer to a surface, the surface is all that exists  there is no above or below. So the surface of the Earth is a 2dimensional world that is finite but has no boundary. We call it a 2sphere. If you are a 2d creature constrained to live in this 2sphere, you can move forwards/backwards and left/right. If you go far enough you will arrive back where you started from without any deviation from your straight path. The solid Earth is a called 3ball  it is finite and bounded, and it is bounded by the 2sphere surface. A 3sphere is a 3dimensional space that is finite and unbounded. It is very difficult to visualise as we cannot build one in space. But if you lived in one, you could move in all three dimensions, and again, if you go far enough you will arrive back where you started from without any deviation from your straight path. Just to add, a 1sphere is a 1dimensional finite unbounded space that similarly loops back on itself. We call them circles. The interior of the circle is the finite bounded 2ball, or 2disc. And again, the boundary of the 2ball is the 1sphere (i.e. the boundary of a disc is a circle)
No! The Universe can be either finite or infinite, and it is without boundary. It could be infinite in all three spatial dimensions, in which case there is obviously no boundary, or it could be finite in all three spatial dimensions but wrapped into a 3sphere  again, no boundary. It could even be wrapped up into a 3torus, or something even more exotic, but in each case it is finite with *no* boundary. Now, there could be boundaries where the Universe as we know it merges into something else, and we consider this in highly speculative theoretical physics... but that's for another day.


Percy Member Posts: 19039 From: New Hampshire Joined: Member Rating: 3.4 
Yes, the surface of the sphere represents a boundary between the inside and the outside of the sphere, but the analogy is between space and the surface of the sphere itself. You can travel infinite distances along the surface of a sphere and never reach any boundary. If space is unbounded then you can travel infinite distances in space and never reach any boundary. Percy


cavediver Member (Idle past 1978 days) Posts: 4129 From: UK Joined: 
Typical! So to clear up the controvercy, Percy is quite correct in that the surface of the sphere (2sphere) *is* a boundary to the inside and outside of the sphere (3ball). BUT we can have the 2sphere quite independent of any notion of there being a 3ball to which it would be a boundary. In our everyday experience, this is not possible. Every 2sphere has an "inside"  but mathematically, and when we are talking about the geometry/topology of spacetime, this need not be the case. AND you were actually asking the more general question of whether a general surface is a boundary between that "above" and that "below". In this case, we can have a finite unbounded 2dimensional surface that does not form a boundary between an inside and an outside of a 3dimensional space! This is the famous Klein Bottle, whose inside and outside are joined, yet there is no break in the bottle, no opening... imagine a surreally twisted sphere that somehow manages to join its inside to its outside without any break in the sphere! This is another situation where we cannot actually construct a real Klein Bottle in the boring flat 3d space in which we live.


zi ko Member (Idle past 1954 days) Posts: 578 Joined: 
good idea
{I haven't a clue of why this was posted, but don't reply to it  Adminnemooseus} Edited by Adminnemooseus, : Offtopic banner etc.


NoNukes Inactive Member 
Perhaps a key thing to remember that the 2sphere represents a two dimensional curved space. An extra dimension that would move you within or without the sphere is not perceptible to a 2dimensional being. I wouldn't say that a 2sphere has an inside. In a flat two dimensional space, it's easier for most folks to accept that questions about what's going on above and below the flat plane have no meaning. You have to treat the 2sphere in a similar fashion. Edited by NoNukes, : No reason given.


cavediver Member (Idle past 1978 days) Posts: 4129 From: UK Joined: 
Nor would I except when you quotemine me:
Admittedly, there should have been a colon there, not a full stop. And 2sphere should be in quotes.


NoNukes Inactive Member 
"Nor would I except when you quotemine me"
It wasn't meant to be a quote mine. I just wanted to help others who are having trouble understanding what a twosphere is. Edited by NoNukes, : Lighten up the tone a bit.



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