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

[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.

 

[PeterDonis]

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".

"Most people" is not the appropriate criterion here. The appropriate criterion is, how is the term "big bang" used in actual textbooks and peer-reviewed papers in the field of cosmology? I think you will find that they use the term as I defined it. That is the actual scientific usage, which is what we are concerned with here at PF; what is said in pop science books and articles and websites is irrelevant.

what was inflating prior to the big bang?

The universe.

Now you seem to be saying no, the big go was actually contained in something else.

No, that's not what our current best model says.

 

[PeterDonis]

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.

I think you should not be making such criticisms unless and until you thoroughly understand what the current best model physicists are using actually says. It does not seem like you do.

And I do think you can't always hide behind "gee that's pop science so go away".

Why not?

 

[Ken Ucarp]

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.

I see. So I think what I said originally is still correct, just poorly worded. According to cosmologists who accept the theory of inflation, there was actually an "era" prior to the big bang that was as you described. And you said "the universe was cold and dark...". The important piece is, it was the universe that went through this inflationary era, not some entirely different thing that then became the universe that we know and love during the big bang. The thing that was inflating was our universe itself including the actual "rulers and clocks" themselves. The thing that was inflating was not itself contained in a higher dimensional set of rules and clocks. Do I have that description right?

 

[PeterDonis]

The thing that was inflating was our universe itself including the actual "rulers and clocks" themselves. The thing that was inflating was not itself contained in a higher dimensional set of rules and clocks. Do I have that description right?

As far as our best current model is concerned, yes. If you talk to string theorists, they will start talking your ear off about "a higher dimensional set of rules and clocks". But all of that is speculative at this point.

 

[Ken Ucarp]

I think you should not be making such criticisms unless and until you thoroughly understand what the current best model physicists are using actually says. It does not seem like you do.
Why not?

Criticisms? Please. No criticism intended. A race car driver can provide input to the mechanics even though he may not understand the engine like they do. And yes, I do think it's very easy to simply write a non-expert off under the guise of "pop science". I'm a computer programmer. Sometimes the users describe what an application is doing in some pretty funky terms. If I merely wrote them off because they don't know "modern programming techniques" I'd probably end up losing my job.

 

[Ken Ucarp]

As far as our best current model is concerned, yes. If you talk to string theorists, they will start talking your ear off about "a higher dimensional set of rules and clocks". But all of that is speculative at this point.

Ok thank you. I get the part about string theorists. SO...the end point of my whole post was that I was watching a show where the cosmologist said at like a trillionth of a second after the big bang, the universe was approximately one centimeter across. I don't know if he meant the big bang era or the inflationary era. What struck me as odd was that as I mentioned, I thought the "rulers" themselves were expanding. So in what way can something be a centimeter across. Centimeter is only a centimeter in reference to a larger measurement. Or was THIS and example of a cosmologist just trying to explain something about relative size in terms the layman might relate to?

 

[PeterDonis]

No criticism intended.

I meant "criticism" in the sense of presenting a counter-argument, not in the sense of expressing a judgment of value.

I'm a computer programmer. Sometimes the users describe what an application is doing in some pretty funky terms. If I merely wrote them off because they don't know "modern programming techniques" I'd probably end up losing my job.

I don't think your implied analogy here is valid. A computer programmer has to meet the requirements of his users, because the users are the reason he's writing the program in the first place. But science does not have to meet the requirements of people who don't understand science (except in the sense, irrelevant to this discussion, that scientific knowledge underlies our technology). If scientific theories that work happen to be expressed in terms that are hard for lay people to understand, that's just a fact about science that has to be accepted and dealt with; and if pop science presentations distort the science so that they don't provide a proper understanding of it, that's also a fact that just has to be accepted and dealt with.

I do think it's very easy to simply write a non-expert off under the guise of "pop science".

We're not "writing off" the non-expert; we're just pointing out that he's a non-expert who doesn't properly understand the science, and that reading pop science won't fix that condition. You have to look at the actual science--the textbooks and peer-reviewed papers that describe, in precise technical language and math, what the best current scientific theories actually say. Again, that's just a fact about science that has to be accepted and dealt with; complaining that a non-expert is being "written off" when this unpleasant fact is pointed out to him doesn't change the fact.

 

[phinds]

Ok thank you. I get the part about string theorists. SO...the end point of my whole post was that I was watching a show where the cosmologist said at like a trillionth of a second after the big bang, the universe was approximately one centimeter across. I don't know if he meant the big bang era or the inflationary era. What struck me as odd was that as I mentioned, I thought the "rulers" themselves were expanding. So in what way can something be a centimeter across. Centimeter is only a centimeter in reference to a larger measurement. Or was THIS and example of a cosmologist just trying to explain something about relative size in terms the layman might relate to?

That is NOT a description of the universe. It is, and he most likely did not know this, a description of the OBSERVABLE universe which is a totally different thing. This is the kind of crap you get in pop science.

 

[PeterDonis]

I was watching a show where the cosmologist said at like a trillionth of a second after the big bang, the universe was approximately one centimeter across. I don't know if he meant the big bang era or the inflationary era.

Strictly speaking, he meant neither. Those times quoted by cosmologists are not actually times in the current best model; they are times in an idealized model in which there is no inflation and the "big bang" is indeed an idealized "initial singularity" (which does not appear at all in the current best model). Basically, what the cosmologists are doing is taking the temperature of the universe at some point in time in the actual best current model, looking at the idealized model to see at what time after the "initial singularity" that temperature occurs, and then giving that time as though it was an actual time in the actual best current model.

(The comment by @phinds regarding what the "size" given actually refers to is also valid.)

Yes, this means cosmologists routinely use confusing and misleading language (at least it's misleading if you're trying to understand what's actually going on). And yes, these are actual cosmologists, actual experts in the field. This is a good illustration of why you cannot trust pop science sources, even when they are written by actual scientists.

 

[mfb]

What struck me as odd was that as I mentioned, I thought the "rulers" themselves were expanding.

It depends on the type of rulers. Are they made out of freely floating particles in space? Then they expand. Are they made out of a solid material (neglecting that there was nothing solid back then)? Then they do not.
The length of a second is defined based on fundamental quantities (here: in cesium atoms - they didn't exist either back then, but let's ignore practical details), and a centimeter is based on the length time travels in a defined length of time. That allows a measurement of a centimeter no matter where you are. The observable universe today had a diameter of something like a centimeter back then. The precise value depends on the model and the question which point in time exactly you consider.

Criticisms? Please. No criticism intended. A race car driver can provide input to the mechanics even though he may not understand the engine like they do. And yes, I do think it's very easy to simply write a non-expert off under the guise of "pop science". I'm a computer programmer. Sometimes the users describe what an application is doing in some pretty funky terms. If I merely wrote them off because they don't know "modern programming techniques" I'd probably end up losing my job.

In this analogy the race car drivers are professional astronomers.
You are someone who has seen descriptions of car races made for people who have never seen them.