Space-time created ahead of matter - how far?

[Saddlestone]

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?

 

[Vanadium 50]

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

 

[Saddlestone]

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?

 

[Chalnoth]

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?

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

 

[Saddlestone]

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.

 

[Chalnoth]

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.

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.

 

[Saddlestone]

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?

 

[Chalnoth]

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?

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.

 

[mrspeedybob]

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.

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.

 

[Drakkith]

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.

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

 

[Chalnoth]

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

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.

 

[Saddlestone]

Two points:
2. There is no difference between saying that the matter recollapses and the space recollapses. The two are one and the same.

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?

 

[Chalnoth]

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.

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).

 

[Saddlestone]

Sorta kinda. There do exist empty space-times. However, you cannot meaningfully separate matter from the space-time it inhabits. Now, you can have an empty universe:

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 definitely 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.

 

[Chalnoth]

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.

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

 

[Saddlestone]

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.

 

[Chalnoth]

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.

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.

 

[Saddlestone]

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.

The fact remains that there is an average density which impacts the rate of expansion.

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)?

 

[Chalnoth]

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

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

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

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.

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)?

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

 

[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

 

[Chalnoth]

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

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.

 

[mrspeedybob]

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

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

 

[Chalnoth]

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

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

 

[Lost in Space]

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

 

[Chalnoth]

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?

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.

Is this not closer to what Hoyle evisaged as a process of 'continuous creation'? If the expansion of space is indeed a 'creative' process, from what is space being created?

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).

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?

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.

 

[Lost in Space]

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.

Couldn't the 'outer surface' be defined as the present?

 

[Chalnoth]

Couldn't the 'outer surface' be defined as the present?

Two points:
1. You can define things however you like, but that doesn't mean the way you've defined things has any real meaning. When I say there is no boundary, I explicitly mean that there is no physical boundary.
2. As relativity shows, there actually is no rigorous definition of "the present". Basically, an observer moving with respect to me will see a very different set of events as happening "now" than I will.

 

[Lost in Space]

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.

By "pre-existing space", do you mean that which existed before spacetime began? Do you think that time and space could have somehow been separated before the Big Bang? Was the BB a convergence of the same? If we run time backwards to the BB doesn't everything converge according to GR? So could this mean that there was a divergence on the other side of the BB?

And if the total amount of energy is increasing I fail to understand how the law of conservation of energy isn't being violated?

 

[Lost in Space]

Two points:
1. You can define things however you like, but that doesn't mean the way you've defined things has any real meaning. When I say there is no boundary, I explicitly mean that there is no physical boundary.
2. As relativity shows, there actually is no rigorous definition of "the present". Basically, an observer moving with respect to me will see a very different set of events as happening "now" than I will.

Yes, I can see how there is no physical boundary condition with relation to space, but surely we have to consider time as well? And yes, two observers are effectively within their own time frame references but the future and the past still exists for them both, doesn't it?

 

[marcus]

... Was the BB a convergence of the same? If we run time backwards to the BB doesn't everything converge according to GR? So could this mean that there was a divergence on the other side of the BB?

There certainly are a lot of researchers who consider that idea worth exploring and trying out math models of it. It comes under the heading of "bounce cosmology" or more generally within the area of "quantum cosmology".

If you do a search of recent research articles on quantum cosmology most of the papers (esp. the highly cited ones) are using a model where this happens: you quantize GR, quantum effects make gr. repellent at extreme high density, resistance to a complete collapse, no "singularity", rebound and reexpansion.

It is possible to derive observable consequences of this---people write articles about what to look for (as instruments get better) in the microwave background. Evidence of a bounce origin, it it happened. So it has become quite an active area of research.

If you ever get interested in this particular area, ask and I'll get some links to online articles and possibly a video presentation. It hasn't been popularized much so there is not a lot of public outreach material about it---but there is some fairly understandable stuff.

And if the total amount of energy is increasing I fail to understand how the law of conservation of energy isn't being violated?

I think what Chalnoth is saying is partly that there simply isn't a "law of conservation of energy" to violate in this context. Laws do not exist in the abstract (as mere strings of words), they need some definite math context. The energy conservation law is something you can PROVE MATHEMATICALLY if you assume a fixed static geometry---non-expanding distances.
So it applies where that is a good approximation---where dynamic geometry effects are so tiny as to be negligible. So we trust it. We know where we can apply it. And it is enormously helpful.

Maybe this is something that humans just don't know how to do yet. Maybe there is some way to generalize the law mathematically, to extend it to cover the situation with dynamic geometry. Maybe there is a way to redefine "energy" so it is conserved. Right now we even have trouble defining energy in a GR context. we can only define it in local patches that aren't doing anything funny. (but "local" can include galaxies!)

It's possible that the cosmological constant is simply another constant of Nature, like Planck constant or Newton G constant. It very possibly is simply NOT a form of energy. There may be nothing one can reasonably call "dark energy". that could be hype basically.
It sounds exciting. But it might simply be a constant curvature that belongs where Einstein originally put it, on the left side of the GR equation (our law of geometry/gravity).
It is only when you drag it over to the other side of the equation and multiply it by other stuff that it acquires units of an energy density. And then people make a big fuss about "dark energy".

The evidence continues to accumulate through observation that it IS constant and can simply be treated as such---not as an "energy field", just more like we treat Newton's G (which is certainly not a "dark" anything )

If you google "why all these prejudices against a constant?" you will get a link to an article by Bianchi and Rovelli that debunks the big "dark energy" fuss.
If googling that doesn't work for you, let me know and I'll fetch a link.

 

[Chalnoth]

By "pre-existing space", do you mean that which existed before spacetime began?

No. I'm purely talking about an expanding universe here. So the pre-existing space is the space that existed slightly earlier in the expansion.

If we run time backwards to the BB doesn't everything converge according to GR?

Yes, that is the case according to GR. Which is one reason why we know GR is wrong. Because GR is wrong here, we can't conclude anything about the very early universe based solely upon this sort of analysis.

And if the total amount of energy is increasing I fail to understand how the law of conservation of energy isn't being violated?

As marcus pointed out, that law doesn't apply here. Conservation laws stem from symmetries. The symmetry which energy conservation stems from is symmetry in time. The expansion of the universe violates that symmetry.

 

[Chalnoth]

Yes, I can see how there is no physical boundary condition with relation to space, but surely we have to consider time as well? And yes, two observers are effectively within their own time frame references but the future and the past still exists for them both, doesn't it?

This is why I talked about the fact that there is no such thing as a global now. If there is no such thing as a global now, then the present cannot be considered any sort of physical boundary.

 

[DaveC426913]

I think the topic has drifted away from Saddlestone's original question, which I'm not sure has been adequately answered in the spirit in which it was asked (i.e. in layperson's terms).

Let me try.

If the Big Bang had created only a whopping two particles, each flying away from the other at .5c which, after 2 years, are now 1 light year apart, what would the shape of spacetime be?

- a 1D line, 1 light year long, one particle wide (only exists where the particles are)
- a 3D sphere, 1 light year in diameter (only expands with particles' speed)
- a 3D sphere 2 light years in diameter (expanding at c, along with any EM)

If the BB had actually made 3 particles, and the first two as before whizzed away at .5 c, but the third bopped around in between the first two, would space time be formed as that particle moved, say perpendicular to the other two?

i.e does space time exist anywhere where matter has not made it yet?

 

[Lost in Space]

This is why I talked about the fact that there is no such thing as a global now. If there is no such thing as a global now, then the present cannot be considered any sort of physical boundary.

It's hard for me to get my head round this but does that mean then that different parts of the universe can be in front of or behind each other in terms of the time that has passed, and if so would there be any kind of limit as to how much? In other words are there areas of the universe that are already existing but as far as we're concerned they're in our future and we likewise are in their past?

We locally share a common history of the past. And as far as I'm aware there's no way for us to determine anything that lies in our future but I think I'm correct in saying that from what you say it seems to indicate that in other areas of the universe our future has already happened?

 

[Chalnoth]

It's hard for me to get my head round this but does that mean then that different parts of the universe can be in front of or behind each other in terms of the time that has passed, and if so would there be any kind of limit as to how much?

No, it means that when you are dealing with points separated by some distance, there is no non-arbitrary way to say whether a particular time at one point is ahead or behind a particular time at another. You always can write down a global "now", but it is always arbitrary: somebody else could come up with a completely different definition that would be every bit as valid.

Fundamentally, this means that the past and the future must exist in the exact same way as the present. Reality cannot be a sort of wave moving from the past into the future, but instead the flow of time is merely a result of our perception of it.