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FRW universe, expanding space or spacetime? 
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#1
Feb2912, 01:51 AM

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In FRW universe, is space expanding or spacetime expanding? If the former... but I know that only spacetime can curve and expand. "Space" doesn't do that. Well?



#2
Feb2912, 02:33 AM

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If spacetime can curve and expand, why can't space? How would you quantify this result?



#3
Feb2912, 02:44 AM

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#4
Feb2912, 05:18 AM

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FRW universe, expanding space or spacetime?
When we say that space is expanding we are talking about a foliation of the spacetime manifold along the time coordinate. We are then comparing different distances in different foliated submanifolds.
Since there is only one spacetime manifold I don't know what meaning could be ascribed to the phrase "expanding spacetime". What comparison is possible? 


#5
Feb2912, 06:04 AM

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#6
Feb2912, 06:42 AM

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I don't know if my terminology is "proper". I certainly don't have any supporting references.



#7
Feb2912, 06:47 AM

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#8
Feb2912, 06:55 AM

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#9
Feb2912, 07:00 AM

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anyway this is what I've been trying to imagine for quite a time. 


#10
Feb2912, 07:16 AM

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Manifolds don't expand or contract in any meaningful sense that I can envision. You can foliate a manifold into a parameterized set of submanifolds and talk about expansion of the submanifolds as a function of the parameter. That would be what I was describing, i.e. expansion of space as a mathematical concept, not a physical concept.
The corresponding physical concept would be that the distances between unbound systems was increasing compared to the size of the bound systems. 


#11
Feb2912, 07:28 AM

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#12
Feb2912, 08:14 AM

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Expanding in time, expanding involve time, spacetime cannot 'evolve', it can BE curved.
Space can evolve or more precisely, a foliation of spacetime gives spacelike submanifolds one for each time... 


#13
Feb2912, 10:05 AM

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http://msowww.anu.edu.au/~charley/pa...DavisSciAm.pdf
"The space we inhabit is itself expanding." The basic entity is curved spacetime. Our notional division of spacetime into space and time can occur in many different ways. Expanding space is a convenient way to describe the curved spacetime of the FRW universe. 


#14
Feb2912, 10:47 AM

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Space can expand because it is scaling up as time passes. Spacetime can't be evolving in time because it already includes time, so it makes no sense to say it is expanding.



#15
Feb2912, 11:10 AM

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#16
Feb2912, 02:00 PM

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Now the orange skin is a manifold representing spacetime, and each circle is a submanifold representing a snapshot of space at a particular time. You could describe what you have as an "expanding circle". You wouldn't describe it as an "expanding orangeskin". P.S. spacetime isn't really orangeshaped, it's more like a trumpet. 


#17
Feb2912, 05:07 PM

P: 381

Going to the orange analogy (I'm familiar with the relativity of simultaneity and it's related to it). But if the entire orange expands, the orangeskin would expand too so we can describe it as "expanding orangeskin". Note that all circles you draw from the pole to the equator expands at the same time. So it has same relationship. It's like the earth expanding and every object, the ground, you and I expanding forever. Can we tell? No. Because we will have same relationship to each other. (btw.. some guy produced a theory where this is what produced gravity because the expanding earth and us keep us close to the ground.. of course I don't believe this but just mentioning this because I just recalled it). 


#18
Feb2912, 05:31 PM

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In the expanding balloon example, time is not on the surface of the balloon, so it is not spacetime that is expanding, it is space that is expanding as time increases.



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