# FRW universe, expanding space or spacetime?

by waterfall
Tags: expanding, space, spacetime, universe
 P: 381 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?
 P: 1,937 If space-time can curve and expand, why can't space? How would you quantify this result?
P: 381
 Quote by Matterwave If space-time can curve and expand, why can't space? How would you quantify this result?
spacetime as a differential manifold can curve and expand because spacetime is a mathematical entity and it is a model of our world. Space is our actual world and hence may not truly curve and expand. That's the distinction i learnt for many years after also learning it from a physicist that only spacetime can curve, space doesn't curve.. i may have to look for the reference if you object to my statements.

Mentor
P: 15,617

## 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 sub-manifolds.

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?
P: 381
 Quote by DaleSpam 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 sub-manifolds. 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?
Are you saying the proper term is "expanding space" and not "expanding spacetime"? Can others confirm this? Objections?
 Mentor P: 15,617 I don't know if my terminology is "proper". I certainly don't have any supporting references.
P: 381
 Quote by DaleSpam I don't know if my terminology is "proper". I certainly don't have any supporting references.
Let's discuss it then by logic or common sense then. So in expanding spacetime, what comparison is it made with. How about matter. If the universe was as big as the earth. We would know we can't see far. If it expands further. We can see more distance from earth. Hence it is in comparison to matter.
Mentor
P: 15,617
 Quote by waterfall So in expanding spacetime, what comparison is it made with. How about matter. If the universe was as big as the earth. We would know we can't see far. If it expands further. We can see more distance from earth. Hence it is in comparison to matter.
How is that different from "expanding space"? What do you mean by "expanding spacetime"? It sounds like your description of "expanding spacetime" is the same as my description of "expanding space". I just don't understand the distinction you are trying to make between the two terms.
P: 381
 Quote by DaleSpam How is that different from "expanding space"? What do you mean by "expanding spacetime"? It sounds like your description of "expanding spacetime" is the same as my description of "expanding space". I just don't understand the distinction you are trying to make between the two terms.
spacetime expanding is the differential manifold expanding, we who live in physical space would for mysterious reason just feel space is expanding... so one is mathematical, the latter physical.

anyway this is what I've been trying to imagine for quite a time.
 Mentor P: 15,617 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.
P: 381
 Quote by DaleSpam 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.
Do you know of sites with the illustrations of what you are talking about? They seldom describe this in Big Bang expansion illustrations. So it's like an orange being a manifold and the pieces inside the submanifolds expanding regionally... or a direct site graphics would say a thousand words. Thanks.
 P: 50 Expanding in time, expanding involve time, space-time cannot 'evolve', it can BE curved. Space can evolve or more precisely, a foliation of space-time gives space-like sub-manifolds one for each time...
 Sci Advisor P: 7,410 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.
 P: 743 Space can expand because it is scaling up as time passes. Space-time can't be evolving in time because it already includes time, so it makes no sense to say it is expanding.
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P: 3,930
 Quote by Khashishi Space can expand because it is scaling up as time passes. Space-time can't be evolving in time because it already includes time, so it makes no sense to say it is expanding.
To understand how the spacetime is experienced by observers it is necessary to use local coordinates of some observer. The holonomic (coordinate) frame is an abstraction. In the FRW model it is possible to find a class of observers for whom all distant objects are moving away.
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P: 1,772
 Quote by waterfall Do you know of sites with the illustrations of what you are talking about? They seldom describe this in Big Bang expansion illustrations. So it's like an orange being a manifold and the pieces inside the submanifolds expanding regionally... or a direct site graphics would say a thousand words. Thanks.
If you want an analogy with an orange, try this. Take an orange and draw a small circle round its "North Pole". Then draw a larger circle around that. Then draw an even larger circle around that. Keep going until you get to the "equator".

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 orange-skin".

P.S. spacetime isn't really orange-shaped, it's more like a trumpet.
P: 381
 Quote by DrGreg If you want an analogy with an orange, try this. Take an orange and draw a small circle round its "North Pole". Then draw a larger circle around that. Then draw an even larger circle around that. Keep going until you get to the "equator". 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 orange-skin". P.S. spacetime isn't really orange-shaped, it's more like a trumpet.
The thing is this (and to Dalespam too), we are taught that Big Bang is like the baloon expanding and the surface like spacetime, therefore everywhere expand at the same time, so how can any comparison be done when all is expanding together.

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 orange-skin would expand too so we can describe it as "expanding orange-skin". 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).
 Sci Advisor P: 7,410 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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