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?
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.
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?
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.
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.
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.
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...
http://msowww.anu.edu.au/~charley/papers/LineweaverDavisSciAm.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.
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.
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).
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.
I"d have to say that the surface of the baloon is like space, not space-time, in that analogy. If you still disagree, think about this. The surface of the balloon expands as time passes. In what sort of dimension would space-time expand if space-time were to expand? It couldn't expand as time passes, because time is part of space-time. Let's next go to the literature for some guidance on the terminology. One paper I'm aware of is http://arxiv.org/abs/0707.0380 "Expanding space - the root of all evil". First note the title - it's "Expanding space" not "Expanding space-time". The internals of the paper follow the usage of "expanding space" not "expanding space-time". Aside from the title, I think it's a rather well-written paper on the topic, though there are a few things that it doesn't say that I wish it would say, so while I agree with all the points it makes, I think it misses making at least one important point. It's still worth a read, however (it's not terribly technical for the most part). I'll quote the abstract here to provide some information on what the paper is about, with the hope that it will motivate some people to read it (and I'll repeat that I think that for the most part it's fairly accessible without a lot of math). Finally, I'll provide my own opinion of what I think is missing. I believe that the whole controversy over whether space-time expands or not is an argument about coordinates. Because our space has matter in it, it's sensible to assign coordinates in such a way that the matter appears to be stationary, which leads to the expanding space idea. But it's at least as valid, and more in keeping with everyday experience, to assign coordinates in such a way that space does not expand. This is done for instance, with Fermi-normal coordinates. Cosmologists don't seem to like Fermi-normal coordinates for the most part, perhaps because they're mathematically messy, but they provide an equally valid and just as intuitive framework for understanding the physics involved. Ideally, one would be able to switch to both sets of views, just as one sometimes uses Cartesian coordinates, and other times uses spherical coordinates, without a great deal of angst. Being able to switch with both points of view is particularly important in explaining why Brooklyn is not expanding, even though the universe as a whole is. It would be possible to use coordinates where Brooklyn expands, but they would be inconvenient, and wouldn't represent the physics well. Contra-wise, you can use "Brooklyn" coordinates for cosmology, (the technical name here would be Fermi normal coordinates BTW), but the math gets awfully, horribly, messy - it's just not a good fit.
Dalespam, earlier you wrote: "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.". Well I'm familiar with the concept of the relativity of simultaneity. But when all the space expands. Even the subregions expand together, so the relationship is always the same, so how can you make a comparison between the sub regions? Also does this expanding space only works for curved spacetime? Or is it not related to whether curved or flat? Meaning flat spacetime can expand too?