The Expanding Universe: A Scientist's Perspective on Infinite vs Finite Space

[phinds]

Does the LCDM model have anything to say on whether matter/energy are infinite quantities?

No, because it does not say for sure that the universe is infinite in extent. If it is, then they are. If it isn't, then they aren't.

 

[PeterDonis]

it does not say for sure that the universe is infinite in extent

To be clear, the spatially infinite universe is the best fit to the data we have. But given the unavoidable uncertainty in our measurements, it is still possible (though unlikely) that the universe is spatially finite.

Does the LCDM model have anything to say on whether matter/energy are infinite quantities?

If the universe is spatially infinite, then the "total energy of the universe" or "total amount of matter in the universe" are not meaningful quantities. Even if the universe is finite, those quantities aren't really useful. The useful quantities are the energy densities of ordinary matter, radiation, dark matter, and dark energy. Those are the ones that appear in all the equations and the ones we measure or estimate as best we can.

 

[laymanB]

I need someone to explain to me the mechanism of infinite quantities of ordinary matter if we cannot sensibly ask what was happening 20 billion years ago?

 

[laymanB]

Are the energy densities for ordinary matter and radiation decreasing in the universe?

 

[PeterDonis]

I need someone to explain to me the mechanism of infinite quantities of ordinary matter if we cannot sensibly ask what was happening 20 billion years ago?

Imagine an open half-plane, for example, the region $x > 0$ in standard Cartesian coordinates on a Euclidean plane. It extends infinitely both ways in the $y$ direction, but not in the $x$ direction. The $x$ direction is like time in our current model of the universe, and the $y$ direction is like one direction of space (the other two work the same way). The $x = 0$ boundary (which, you will notice, is not part of the region I defined above) would correspond to about 13.7 billion years ago--so there is no region of spacetime in this model that is "older" than that. But the model is still spatially infinite.

Are the energy densities for ordinary matter and radiation decreasing in the universe?

Yes.

 

[laymanB]

Imagine an open half-plane, for example, the region $x > 0$ in standard Cartesian coordinates on a Euclidean plane. It extends infinitely both ways in the $y$ direction, but not in the $x$ direction. The $x$ direction is like time in our current model of the universe, and the $y$ direction is like one direction of space (the other two work the same way). The $x = 0$ boundary (which, you will notice, is not part of the region I defined above) would correspond to about 13.7 billion years ago--so there is no region of spacetime in this model that is "older" than that. But the model is still spatially infinite.

That is a helpful analogy, thanks.

Then, would not the world lines of matter/energy then be finite, radiating out from x > 0?

 

[Grinkle]

Then, would not the world lines of matter/energy then be finite, radiating out from x > 0?

It extends infinitely both ways in the $y$ direction

The region being discussed is spatially infinite. The assertion is the amount of energy / matter in the region is infinite if the region is spatially infinite.

A set with an infinite number of members still has an infinite number of members if you remove half the members. Integers, odd integers, even integers for instance.

Saying there is no model prior to time zero need not make the model for post-time-zero automatically finite.

 

[laymanB]

The region being discussed is spatially infinite. The assertion is the amount of energy / matter in the region is infinite if the region is spatially infinite.

A set with an infinite number of members still has an infinite number of members if you remove half the members. Integers, odd integers, even integers for instance.

Saying there is no model prior to time zero need not make the model for post-time-zero automatically finite.

So they would say that the big bang happened everywhere, but not everywhen?

There are an infinite number of world lines, one for each particle, because it happens everywhere?

Then why have a beginning of time?
Why does the model constrain the time dimension?
What is special about time?

 

[phinds]

The model doesn't constrain time so much as it's just that the model breaks down at 13+billion years back, so has nothing to say about time prior to that.

 

[laymanB]

The model doesn't constrain time so much as it's just that the model breaks down at 13+billion years back, so has nothing to say about time prior to that.

Constrain was probably the wrong choice of words. I'm sure the math and observational data are what are doing the "constraining".

It still leaves me with the question of what is special about time? Is there any consensus about prospective models before time = 0, or what makes 13.8 billion years ago possibly unique with a one-way arrow of time?

 

[phinds]

It still leaves me with the question of what is special about time? Is there any consensus about prospective models before time = 0, or what makes 13.8 billion years ago possibly unique with a one-way arrow of time?

I think you are extrapolating a math model beyond where it was designed to go. I see nothing special about time other that the fact that we don't know what it looked like, if anything, more than 13+ billion years ago, and that is equally true of space.

 

[anorlunda]

Thanks, I read the wiki article to refresh my memory. I am assuming that the information therein is correct. I can't do the math, so everything we discuss using equations will need to be translated into English for me. I am not totally math inept, but my calculus and such is long out of shape due to disuse.

It makes me wonder which is more difficult; to understand the concepts intuitively or to solve the equations and program the computer models to simulate them? Brain needs rest...

You have lots of company. Many people are math phobic. But you said that you had calculus once. Let me suggest that it would be easier for you to learn it the right way with equations. Watching PF, I have come to believe that many people exaggerate their problems with math and they go to great trouble trying to understand with verbiage which is actually more difficult.

Fortunately, there is a free and excellent way to do that. Leonard Susskind's video course on Cosmology, available on youtube and itunes. A link to lecture 1 is below. In that course, Susskind does everything on the blackboard with drawings and equations, but the math is pretty elementary, nothing esoteric. Give it a try. Then post again and let us know how it worked for you.

 

[laymanB]

Fortunately, there is a free and excellent way to do that. Leonard Susskind's video course on Cosmology, available on youtube and itunes. A link to lecture 1 is below. In that course, Susskind does everything on the blackboard with drawings and equations, but the math is pretty elementary, nothing esoteric. Give it a try. Then post again and let us know how it worked for you.

Thanks, I'll have to do that.

 

[PeterDonis]

would not the world lines of matter/energy then be finite, radiating out from x > 0?

No. Remember that the $x$ direction is the "time" direction. That means the worldlines of matter/energy are horizontal open half-infinite lines (open at the $x \rightarrow 0$ end, infinite in the positive $x$ direction). They're all parallel in this analogy; they don't "radiate" anywhere.

But what about expansion? you ask. Remember that we are talking about a curved 4-dimensional spacetime; there's no way to accurately represent all of its properties in a single diagram. What I've described is basically a "conformal" diagram of spacetime in our best current model; "expansion" in this diagram appears as a change of scale along the horizontal worldlines, i.e., a given increment of $x$ along those worldlines does not correspond to a constant increment of proper time along them. Also, a given increment of $y$ (the "spacing" between two worldlines) does not correspond to a constant increment of proper distance between two worldlines "at the same time"--that increment of proper distance increases with time.

 

[laymanB]

but the math is pretty elementary, nothing esoteric.

I did enjoy the cosmology lectures by Susskind, but esoteric is a relative term to the groups we run with.

Give it a try. Then post again and let us know how it worked for you.

I like the lectures and think Susskind is a good teacher, but it has forced me to go back and try to relearn my calculus so I can better understand the derivations of the equations. I was a little disappointed that Susskind did not address my thread topic more directly in these lectures, although I'm sure he has lectured or written on it more in depth in other places. He makes a few passing comments about space being created maybe not being a meaningful question to him. And then really just leaves it at that space was expanding exponentially during inflation and the geometry was changing but I got the feeling that many sitting in his class were still perplexed if space was created or not. Or if the scalar change in geometry relates to something metaphysical, not just our coordinate system changing. He does say that the human mind has a hard time of conceiving of things not embedded in higher dimensions in order to visualize what is going on. The learning continues.

 

[Grinkle]

I got the feeling that many sitting in his class were still perplexed if space was created or not.

Anyone who takes such a class expecting physics is going to answer that question for them is likely to struggle with the homework assignments. ;-)

 

[PeterDonis]

I got the feeling that many sitting in his class were still perplexed if space was created or not.

That's because the question is meaningless, so it doesn't have a well-defined answer. Since it doesn't have a well-defined answer, of course Susskind couldn't give one.

 

[laymanB]

That's because the question is meaningless, so it doesn't have a well-defined answer. Since it doesn't have a well-defined answer, of course Susskind couldn't give one.

Is the question meaningless because what we call space is not well defined?

If we say that space has structure which can be curved and warped, can we not then talk about its properties?

If there is dark energy with a constant density, does not space have mass?

 

[phinds]

If we say that space has structure which can be curved and warped ...

WE don't say that. Pop-science presentations say that. What we say is space is just geometry. The "bent / warped" stuff is a pop-sci misrepresentation of the fact that things travel on geodesics which are straight lines in pseudo-Riemann geometry, which is the correct math for describing space-time and these geodesics are curved lines if looked at from the point of view of our more familiar Euclidean geometry.

 

[laymanB]

One of the concepts I find hard to reconcile is talking about the universe being dense at the Big Bang and at the same time talking about space being spatially infinite. To me, being dense has to imply being smaller in volume. Maybe just a consequence of expanding an already existing infinity I suppose?

 

[laymanB]

WE don't say that.

I do have to be careful about who WE are.

 

[phinds]

One of the concepts I find hard to reconcile is talking about the universe being dense at the Big Bang and at the same time talking about space being spatially infinite.

Yes, as I have said here before I too have a hard time getting my head around this, BUT ... if the universe was not spatially infinite at the beginning of the big bang descriptive era (that portion of time starting immediately after inflation) then it is not spatially infinite now and THAT means there is a "shape" to the universe and what the hell would THAT be? I find that just as hard to get my head around.

 

[PeterDonis]

Is the question meaningless because what we call space is not well defined?

No, it's because "space being created" is not well-defined.

If we say that space has structure which can be curved and warped

If we're careful, we don't say that. We say that spacetime has structure which can be curved and warped. "Space" is then just a "slice" we take out of spacetime--a 3-dimensional spacelike surface that is part of the overall 4-dimensional geometry. "Space" at different times is just different slices. Nothing gets "created" or "changed"; the 4-dimensional geometry is just there.

 

[PeterDonis]

Maybe just a consequence of expanding an already existing infinity I suppose?

No. It's a consequence of taking intuitions that work for a finite, isolated piece of matter, like the gas inside a balloon (denser gas means the balloon is smaller), and trying to apply them in a domain where they don't work, like our best current model of the universe.

 

[Ken Ucarp]

I apologize for chiming in late. Interesting thread. If I could take it back to the basics for a sec. Earlier it was said that the universe was spatially infinite, but the observed universe was not. In laymen's terms I take that to mean the big bang was a limted event inside an unlimited something. But I thought the big bang was actually the beginning of literally everything, space and time itself. It's not that an infinitessimally small "ball" came into existence in a big room, it's that the room itself came into existence. Or put another way, the rulers and clocks themselves came into existence. Have things changed in the twenty or so years since I followed cosmology?

 

[laymanB]

Earlier it was said that the universe was spatially infinite

We don't know. It could be finite; spatially infinite is just the assertion and consensus using the best current model, LCDM.

But I thought the big bang was actually the beginning of literally everything, space and time itself.

That was my initial understanding and the reason for starting this thread. @PeterDonis is saying that the phrase "space was created" is not well-defined, so it is hard to talk about and could be a meaningless statement.

Have things changed in the twenty or so years since I followed cosmology?

Mind bending, isn't it? I personally think that there is still a flaw in the logic of spatially infinite, but it is really hard to pin down when trying to conceive of something so foreign to the perception of time and space our minds are used to. Part of the problem for me is going from mathematical abstractions of geometry and scalar expansions of coordinate systems to describing what the physics is trying to model.

 

[Drakkith]

Earlier it was said that the universe was spatially infinite, but the observed universe was not. In laymen's terms I take that to mean the big bang was a limted event inside an unlimited something. But I thought the big bang was actually the beginning of literally everything, space and time itself. It's not that an infinitessimally small "ball" came into existence in a big room, it's that the room itself came into existence.

While that is the common description of the big bang, even by cosmologists themselves, I think it is far more helpful to view the big bang as being the state of the universe just prior to the point that our models and theories break down. In other words, the big bang would be the state of the universe just after t=0. After all, our models are built by looking backwards from the present into the past, and we cannot see any conclusive evidence that there was ever some sort of creation event. All we know is that our model, in which we model the universe as expanding from an extremely hot and dense state, is the best match to our observations so far.

All the talk of spacetime popping into existence or being created at t=0 is the result of our model breaking down when the underlying math starts giving us infinities as answers at t=0. Given the likelihood that we are lacking some knowledge of physics at the immense temperature and densities at this early stage of the universe, I prefer to wait before saying that the universe was created at this time.

 

[PeterDonis]

In laymen's terms I take that to mean the big bang was a limted event inside an unlimited something.

No, that's not what it means. It just means that, because of the finite age of the universe and the finite speed of light, we can't see the entire universe, we can only see a portion of it.

I thought the big bang was actually the beginning of literally everything, space and time itself.

That's not quite what our best current theory says, for two reasons:

(1) The term "big bang", strictly speaking, does not refer to an idealized "initial singularity", but to the hot, dense, rapidly expanding state of the universe at the end of inflation (at least, inflation is our best current theory for what preceded it). So it's not quite "the beginning of literally everything".

(2) We don't currently know whether, when we go back further than the "big bang" as defined above, into the inflation era, we will find an "initial singularity" (a literal beginning to spacetime) or not. There are proposed models that have this feature, and other proposed models that don't. We don't have enough evidence at this point to decide between them; it's an open area of research.

 

[laymanB]

What observational data could confirm that space has infinite geometry?

What observational data could confirm that space has finite geometry?

 

[PeterDonis]

What observational data could confirm that space has infinite geometry?

What observational data could confirm that space has finite geometry?

The observational data is, first, that the universe is spatially flat, to the best accuracy we can observe, and that we see no signs of it having a spatial topology more complicated than $R^3$ (i.e., Euclidean 3-space).

What tells us that the universe is spatially infinite, based on that observational data, is the fact that the only spatially flat FRW spacetimes (i.e., the solutions to the Einstein Field Equation that are relevant for describing the universe as a whole) with spatial topology $R^3$ are spatially infinite.

 

[Ken Ucarp]

No, that's not what it means. It just means that, because of the finite age of the universe and the finite speed of light, we can't see the entire universe, we can only see a portion of it.
That's not quite what our best current theory says, for two reasons:

(1) The term "big bang", strictly speaking, does not refer to an idealized "initial singularity", but to the hot, dense, rapidly expanding state of the universe at the end of inflation (at least, inflation is our best current theory for what preceded it). So it's not quite "the beginning of literally everything".

(2) We don't currently know whether, when we go back further than the "big bang" as defined above, into the inflation era, we will find an "initial singularity" (a literal beginning to spacetime) or not. There are proposed models that have this feature, and other proposed models that don't. We don't have enough evidence at this point to decide between them; it's an open area of research.

I think we're making language mistakes here. You make it sound like there were two periods, one called inflation, then one called the big bang. I think most people would just call the whole thing "the big bang". Afterall, what was inflating prior to the big bang? Or let's call the combination of inflation and big bang the "big go". And this "big go" is the start of the universe. And so what I've been asking is, was the "big go" inside something? I used to think it wasn not inside anything, it was the start of the thing itself - space and time itself. Now you seem to be saying no, the big go was actually contained in something else. Which then doesn't make sense. The whole point of relativity, I thought, was that there was no "big room of clocks and rulers" against which everything is measured or in which the big go occurred.

 

[phinds]

I think we're making language mistakes here.

No, we are not. You just don't like the language that physicists use and seemingly would prefer the language of pop-science.

You make it sound like there were two periods, one called inflation, then one called the big bang.

Yes, that is correct. Inflation is an unproven period prior to the beginning of the big bang era.

I think most people would just call the whole thing "the big bang".

Irrelevant. We are not here to debate pop-science but to discuss real science.

Afterall, what was inflating prior to the big bang?

Good question. Answer it and I can guarantee you a Nobel prize.

Or let's call the combination of inflation and big bang the "big go".

No, let's not. New terminology is not needed.

And so what I've been asking is, was the "big go" inside something?

Good question. Answer it and I can guarantee you a Nobel prize.

 

[Ken Ucarp]

No, we are not. You just don't like the language that physicists use and seemingly would prefer the language of pop-science.

Yes, that is correct. Inflation is an unproven period prior to the beginning of the big bang era.

Irrelevant. We are not here to debate pop-science but to discuss real science.

Good question. Answer it and I can guarantee you a Nobel prize.

No, let's not. New terminology is not needed.

Good question. Answer it and I can guarantee you a Nobel prize.

Not true at all. I love the language physicists use. But I do think it's very possible for them to miss the forest for the trees if they don't sometimes step out from behind the equations and consider things from a different perspective. And I do think you can't always hide behind "gee that's pop science so go away".

You are saying there are some who believe the Universe (or its history to be precise) consists of two periods, inflationary era and big bang era. However you wordsmith it, those two are periods of a single thing evidently. And it's that single thing I'm asking about in terms of whether or not it was contained in another thing or not. Unless you are saying these two periods do not relate to a single thing called the universe.

 

[phinds]

You are saying there are some who believe the Universe (or its history to be precise) consists of two periods, inflationary era and big bang era. However you wordsmith it, those two are periods of a single thing evidently.

No, they are not. The Big Bang theory describes (VERY well, I might add) the period of the universe starting at the end of what we call Inflation. Inflation is NOT a fact, it is conjecture. It is pretty successful conjecture but conjecture none-the-less.

 

[laymanB]

You make it sound like there were two periods, one called inflation, then one called the big bang. I think most people would just call the whole thing "the big bang".

I think most cosmologists, as best I understand them, who accept the theory of inflation, which are most, would say that the universe was cold and dark during the epoch of inflation and that the potential energy of the inflaton field was converted into heat, radiation, and matter and that is the beginning of what most people refer to as the big bang. I think inflation is a theory which set out to explain various problems areas in the current cosmological model of its day based on what they observed. A lot of physics proceeds by creating the mathematics to describe the observations instead of being derived from prior theories. Think of the example of the ultraviolet catastrophe where the mathematics was constructed to explain the observations. Then you take the physics you have just developed and test them to see if they hold true in all experiments and can be thus generalized. Cosmology is a little different because you can't rerun the experiment.