FRW universe, expanding space or spacetime?

atyy

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.

pervect

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.

waterfall

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?

atyy

Yes, flat spacetime can be described as expanding space - that's the Milne universe.

BTW, read pervect's post #19 and the paper he linked to.

waterfall

I think what atyy is saying is this.

Expanding space produces our universe.
Expanding curved spacetime doesn't produce our universe because it is invalid.
Expanding flat spacetime doesn't produce our universe because it is invalid (Milne).

Hence. Expanding space can either have curved spacetime or flat spacetime embedded in it.

Is this correct analysis?

DrGreg

My orange analogy is different from the balloon analogy.

In the expanding balloon analogy, the 3 dimensions of space are represented by the 2 dimensions of the balloon surface, and time is represented by time.

In my orange analogy, the 3 dimensions of space are represented by just one dimension (circumference) of a circle, and time is represented by the "latitude" of the circle. The 4 dimensions of spacetime are represented by the 2 dimensions of the orange skin. The "North Pole" represents the big bang. The circle expands as it moves down but the orange is static.

waterfall

Also this is what I want to know.

Expanding space (not expanding spacetime) is just curved spacetime.
Spin-2 on flat spacetime produces curved spacetime.
So in the instance of space expanding. It is composed or combinations of the dynamics of spin-2 and flat spacetime. So how does each interact separately with space expanding to produce our universe? Or is there some conceptual flaw somewhere?

DaleSpam

I looked around a bit and was a little disappointed, I didn't really find anything that jumped out at me. There is an example on page 4 of this link, but it is a little technical.

http://luth.obspm.fr/~luthier/gourgo...pohang08-1.pdf

waterfall

Ok. I thought the 4 dimensions of space and time is represented by the 2 dimensions of the balloon surface which expands. But then time is a coordinate, so it should be part of the coordinate of the surface of the baloon (why not)... this is what most know hence assume time also expands.

So the expanding circles are being compared the with preceding smaller circles. I guess this is what Dalespam meant by the comparisons of the submanifolds (to the previous circles).

bcrowell

Could you tell us what your background is in math and physics? I didn't get the impression that you were at the level where you knew what a manifold was. If you don't know what it means, don't throw the word around.

pervect

I think it might be worthwhile to ask a few partially rhetorical questions here:

1) What experiment would you do to tell whether empty space was moving or flowing?

2) What experiment would you do to tell whether or not space is "expanding"

3) What experiment would you do to tell whether empty space was curved?

I'll add my own (spoiler) answers below....
I should also add that the "empty" space I'm envisioning allows you to create and label events in it - it's just that it doesn't have any predefined structure to start with.

I should add the metaphysical point that if there isn't any experiment to test something, the question is philosophical in nature and not scientific. A corollary of this is that you can argue about such questions forever without settling the issue.

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1) Once upon a time, it was thought that you could measure the "ether velocity", but we now expect any experiment that we can perform not to be able to detect the motion of space will have a null result. So, if special relativity is right, there is no apparatus that can detect empty space moving. So it's possible to imagine an experiment that could detect moving space, but relativity says that all such experiments will show that it's not moving.

2) None - as far as I know, at least, there isn't any experiment (at least none compatible with relativity) to tell whether or not empty space is expanding or not. This may be debatable, I suppose - just because I've never seen it doesn't mean it exists. But if we can't tell that empty space is moving, how would we tell that it's expanding?

3) A lot of people aren't aware of the details, but this can in fact be measured. To tell if a plane is curved, for example, you'd construct a quadrilateral with four equal sides and equal diagonals, and measure the diagonals to make sure they're sqrt(2).

This presuposes that you do know how to measure distances - it's necessary to define how you measure distances before you can measure curvature.

A good example is using this technique to detect the fact that the surface of a sphere is curved.

You should be able to do something similar with the diagonals of a cube in 3d - check if they are both sqrt(3).

Someone posted a good reference in the literature about a different geometric construction to measure spatial curvature by measuring only distances, but I'm forgetting both the poster. ((I think it was some book by Synge))

It's also easy to to find constructions if you're confident in your ability to measure angles, but measuring distances is really more fundamental IMO.

waterfall

I imagine a manifold as like a map of the earth with coordinates or latitudes or longitudes. In the case of spacetime, manifolds composed the nodes, points, spaces and time without any matter. It's like the graph of the surface of things in graphics program without any details. Spacetime is like a manifold because it is not really solid but just composed of coordinates. I understand spacetime as just coordinates and general covariance proves it is not a thing. Hence something that is not a thing is better called a manifold with coordinates than a solid object.

waterfall

Hi, I have read your shared paper "Expanding space - the root of all evil" for more than an hour. But it still hasn't answered my simple question.. which is...

Since expanding space is automatically curved spacetime (right?).. and since curved spacetime is just spin-2 field on flat spacetime. Then expanding space is composed of spin-2 field and flat spacetime. Therefore expanding space is related to expanding space&spin-2 field and expanding space&flat spacetime. How does one imagine or model expanding space&spin-2 field for example? Or expanding space&flat spacetime which is a Milne model that isn't valid. Can one say that when one adds spin-2 to Milne model. It becomes valid? Does anyone see if there is something wrong with my analysis and directly address what I'm talking about. Thanks.

Mentz114

I think your logic is wrong in that not all curved spacetime is expanding. The expanding spacetimes of GR are a special class where spatial parts of the metric depend on t.

Also field gravity is not the same as GR. They are two different theories, both claim to explain the observed cosmological phenomena but in different ways. In fact I don't think FTG needs expanding space but supposes a fractal distribution of mass.

So you can't talk about splicing them together in the way you suggest.

waterfall

Thanks for it. It's usefull enough. I'm familiar with hypersurfaces as I learnt this in the topic on relativity on simultaneity. So you are saying the hypersurfaces sort like expand against a constant time, and the differences is between them at a previous time and them at a latter time. I think some GR educator must build the very basic graphics of this exact details on expanding space, so all laymen would get some idea what in the world it means. Maybe those who have seen this.. pls share the vital link and images. Thanks.

waterfall

Yes, that's what I'm asking how to imagine space expanding in Field Theory of Gravitation. I think atyy didn't understand my question that's why he kept mentioning about the milne universe and stuff. But in FTG if space didn't expand. Then in the first planck milliseconds from the Big Bang where space was still just the size of a football field. How then does space expanded when there was nothing out there. Unless you are assuming space already existed? But I think this was already refuted by say the redshift and other matters (think why else would they propose space indeed expands if they could just state space already existed).

bloby

You seem to think the big bang happened in some place, it's wrong...