# Space-time created ahead of matter - how far?

1. Oct 8, 2011

As the universe expanded after the big bang it was expanding into nothingness, ie even the fabric of space-time itself didn't exist.

How far ahead of the expanding matter was space-time being created for it to expand into?

2. Oct 8, 2011

Staff Emeritus
Zero. Space expands and carries matter into it. There is no explosion into pre-existing space. (Even space preexisting for one second)

3. Oct 8, 2011

Space expands and carries matter into it.

So just after the big bang, as the ultra-hot matter was starting to expand, was an expanding space-time sphere being created in anticipation of matter filling that newly created space?

4. Oct 9, 2011

### Chalnoth

Um, no. Space doesn't expand into anything at all. The expansion itself is the creation of new space.

5. Oct 9, 2011

Ok I see that. But what is the shape of the new space-time? Is it an expanding sphere, or is its shape dependent on the perhaps non-uniform outer surface of the expanding matter.

I'm trying to understand the relationship between the shape of space-time and the shape of the matter that exists in it.

The question isn't just relevant to the early universe: I could ask what is the shape of space-time right at the edge of the existing old universe. Is it uniformly spherical, or is it related to the old matter that is right at the outer edge of the universe.

6. Oct 9, 2011

### Chalnoth

There is no reason to believe that there is any "outer surface". And the space-time itself is defined by the matter that is within it. The two are not fundamentally separate things.

7. Oct 9, 2011

Ok I think I get that.

Up to a few years ago the view was that the expansion of the universe would slow down and it would eventually start to contract, leading to a Big Crunch. Would it have only been the matter in the universe that would have collapsed inwards, or space itself?

8. Oct 9, 2011

### Chalnoth

Two points:
1. That was not the view a few years ago. The view about 12-15 years ago was that we didn't know the ultimate fate of the universe, but the amount of matter out there seemed to be quite a bit too little to make the universe recollapse. Recollapse was still considered a possibility, but it was seeming less likely.
2. There is no difference between saying that the matter recollapses and the space recollapses. The two are one and the same.

9. Oct 9, 2011

### mrspeedybob

There is no edge to the universe. The current view is that the universe is either infinite or wraps back on itself. Think of the surface of a ball. Is is finite, yet has no edge. Add 1 more dimension and you get a hypersphere. The surface is 3 dimensional instead of 2. Your next logical question could be 'what is inside the hypersphere and what is outside it?' My answer would be the past and the future respectively.

10. Oct 9, 2011

### Drakkith

Staff Emeritus
I don't think the universe wrapping around back onto itself requires it to exist in 4d. Not sure though.

11. Oct 9, 2011

### Chalnoth

No, it doesn't. A simple example of how this can work is the old arcade game Asteroids:
http://www.play.vg/games/4-Asteroids.html

This is a flat, two-dimsional space that wraps back on itself, without existing in any sort of higher, three-dimensional space.

12. Oct 9, 2011

I can understand the inter-connection between matter and space-time in the volumes of space where matter exists. But how about the vast volumes of space where there is no matter. Clearly space-time exists in these volumes.

As far as I can see matter needs space-time, but space-time doesn't need matter.
Just like fish need water, but water doesn't need fish.

If matter and space are so interdependent, then how did this empty (of matter) space-time come into existence, and how would it recollapse if there were no nearby recollapsing matter?

13. Oct 9, 2011

### Chalnoth

Sorta kinda. There do exist empty space-times. However, you cannot meaningfully separate matter from the space-time it inhabits. This can be seen heuristically in Einstein's equations (constants omitted for clarity):

$$G_{\mu\nu} = T_{\mu\nu}$$

The left hand side, $G_{\mu\nu}$, is the Einstein tensor. This describes the space-time. So when you are using words like "the space-time expands", you're talking about what this tensor is doing.

The right hand side of the equation, $T_{\mu\nu}$, is the stress-energy tensor. This is the matter content of the universe. Or, rather, it is the properties of matter to which gravity responds (energy, momentum, pressure, and shear).

Now, you can have an empty universe: one where the stress-energy tensor is identically zero everywhere, and the left hand side of the equation can still be a large number of different things. But the left hand side isn't completely arbitrary. For the most part, it's limited to the specific $G_{\mu\nu}$ defined by the matter, with the addition of gravitational waves. So aspects of the universe like expansion and contraction have a direct one-to-one relationship between the left-hand side description (space is expanding/contracting) vs. a right-hand side description (matter is getting closer together/further apart).

14. Oct 9, 2011

It seems to me that the universe we inhabit is ALMOST empty of matter, ie the average density of matter is very low. But it is FULL of space-time. Therefore there doesn't seem to be a strong correlation between matter existing and space-time existing. Although, as you say, you can't separate matter from the space-time it inhabits, you can definately separate space-time (because it's everywhere) from matter (because it isn't everywhere).

I therefore get back to the theme of the thread: At the big bang - Is it possible that space-time was created ahead of matter - and if so how far? By "ahead of" I mean spacially. The question of how far isn't too important.

15. Oct 9, 2011

### Chalnoth

The phrase "full of space-time" doesn't make any sense. And by what measure is it "almost empty"?

16. Oct 9, 2011

By "full of space-time" I mean that every point in the universe exhibits properties of space-time.

By "almost empty" I mean that most points in the universe are devoid of matter.

I'm sorry that I don't have mathematical ways of expressing this. It just seems to me that the relationship between matter and space-time isn't necessarily symmetrical if one (space-time) can exist without the proximity of other (matter).

My fish and water analogy explains what I'm thinking.

17. Oct 9, 2011

### Chalnoth

Given that matter is made up of point-like particles, you could say this no matter the epoch. The fact remains that there is an average density which impacts the rate of expansion.

18. Oct 9, 2011

By "an empty universe" I take this to be a universe with no matter in it.

I'm assuming that if you know the average density of the universe, then you can calculate its expansion rate.

How fast would an empty (of matter) universe expand compared with our universe which has some amount of matter in it (and hence an average density greater than zero)?

19. Oct 9, 2011

### Chalnoth

Yes. But also no radiation or other form of energy.

Not quite. The matter density only sets the rate of change of the expansion. It doesn't set the expansion itself. You also have to define some sort of initial condition to get the current rate. This is the equivalent of defining either the expansion rate at any particular time, or the spatial curvature.

If there is nothing in the universe at all, then expansion itself is meaningless.

20. Oct 9, 2011

### marcus

I would only take issue with you on a fine point, Chalnoth. To start with, something you may agree with me about or at least understand my preference, I like to think of G and Lambda as two CONSTANTS of the theory (not as forms of matter )

They are the only two constants allowed by the symmetries governing the theory, so according to the usual practice in physics they have to be there.

So I think of Lambda as just a constant on the lefthand side of Einstein equation. A constant curvature or reciprocal area. And not a big deal! Some people get all in a sweat about it but it is just a constant of nature like Newton G is. What in hell did we expect?

So then we have to acknowledge the deSitter solution that is a perfectly good solution to Einstein equation, but has no matter.

It seems to me that you have been suggesting that we cannot have dynamically varying geometry (following Einstein equation) unless there is some matter included. But deSitter solution (vintage 1917, I think) does not have matter. You would only have to introduce a tiny little test particle to be an observer---one imagines that an observer must somehow be material. But test particles are a formality and not part of the dynamics.

Feel welcome to disagree. It's not something to argue about, not important. I agree to disagree ahead of time

Last edited: Oct 9, 2011
21. Oct 10, 2011

### Chalnoth

Well, yes, but in the case of a pure de Sitter or anti-de Sitter space-time, the expansion is also meaningless because the properties of the space-time are invariant with respect to time. You have to have at least some matter for the expansion to be meaningful.

22. Oct 10, 2011

### mrspeedybob

It may not require it but I don't think anyone will argue that the universe we live in has at least 3 spacial dimensions and 1 time-like dimension. That makes 4.

23. Oct 10, 2011

### Chalnoth

I believe the context makes it clear he's talking about a fourth spatial dimension.

24. Oct 16, 2011

### Lost in Space

Ok. So if the expansion of space is increasing at a faster rate, doesn't that in turn imply that this creation is an ongoing and accelerating process? Is this not closer to what Hoyle envisaged as a process of 'continuous creation'? If the expansion of space is indeed a 'creative' process, from what is space being created? Or could it be some kind of energy conversion? The reason I ask is because otherwise the total energy of the system increases with the expansion as the total volume increases, doesn't it?

25. Oct 16, 2011

### Chalnoth

Sort of. It depends upon what you mean by "accelerating". Yes, if you take the distance between two far-away objects in our current universe, that distance gets larger at an accelerating rate.

From the pre-existing space. There is no conserved "amount" of space, so there's no need to talk of any sort of conversion process. The amount of space simply changes as the universe expands (or contracts).

In a way, yes. The difficulty here is that in General Relativity, there simply isn't any rigorous, non-arbitrary way to define "total energy". This means that while you can, in some specific cases, come up with a definition of total energy, somebody else could come up with a different definition that is equally valid. And because there is no non-arbitrary way to define it, total energy cannot be conserved. So yes, when you take a naive definition of total energy (say, the energy in the matter contained within an expanding volume), then the total energy absolutely does change with time.

In the early universe, when our universe was dominated by radiation energy, this definition of energy leads to the conclusion that the total energy in an expanding volume was decreasing. As the radiation redshifted away, the normal matter and later dark energy came to dominate. When the normal matter dominated, energy, by this definition, was (more or less) conserved. And then when dark energy took over, the amount of energy in an expanding volume started to once again grow.