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

[laymanB]

I have read some of the other posts about this topic but am still left unsatisfied. Could just be me.

Did the universe, one minute after the big bang, consist of a finite volume of spacetime?

If so, then is it not logically inconsistent that the universe can possibly be infinite now? If we say that spacetime is expanding into nothing, and that nothing is what is infinite, does not language itself make that a nonsensical statement? Isn't that like saying I have an infinite amount of 0 dollars in my bank account? I have not really said anything at all.

Thanks for the replies.

 

[PeterDonis]

Did the universe, one minute after the big bang, consist of a finite volume of spacetime?

Not according to our best current model, no. According to our best current model, the universe is and always has been spatially infinite.

Our observable universe had a very small, finite volume one minute after the Big Bang; but it has a (much, much larger) finite volume now.

If we say that spacetime is expanding into nothing, and that nothing is what is infinite

Our cosmological model does not say that.

 

[laymanB]

Thanks PeterDonis, I appreciate the reply.

What are you saying is the best current model? I am not up to date on all this stuff. How much consensus does this view have?

If the current consensus model states that the universe is eternally spatially infinite, then why do so many take the theory of inflation to be an explanation of flat geometry? It would seem to me to render that cause and effect relationship of inflation to geometry unnecessary?

Thanks

 

[PeterDonis]

What are you saying is the best current model?

The Lambda-CDM model:

https://en.wikipedia.org/wiki/Lambda-CDM_model

How much consensus does this view have?

The full details of the model are always being refined, but the part about the universe being spatially infinite is pretty solid.

If the current consensus model states that the universe is eternally spatially infinite, then why do so many take the theory of inflation to be an explanation of flat geometry?

Because "spatially infinite" and "spatially flat" are not the same thing.

 

[Anushka Umarani]

Stephen Hawking's book A brief history of time explains the following.
According to Netwon, every body of certain mass attracts another body of certain mass, and this force of attraction is propotional to square of their masses. So, shouldn't asteroids and meteorites and all other space stuff be colliding onto the Earth or vice-versa?
That's where infinite universe comes into play. Masses don't collide onto each other because if the universe is infinite, there would not be a center for all the masses to collide onto! And observation shows that the universe is expanding, providing for the big bang theory of "infinitely small" particle. (Expanding universe in the sense it must have been all together at some point, that's why "infinitely small" particle!)
Hope that suffices :D

 

[PeterDonis]

Stephen Hawking's book A brief history of time explains the following.

Unfortunately, pop science books even by very deservedly famous scientists aren't good sources from which to learn actual science.

Masses don't collide onto each other because if the universe is infinite, there would not be a center for all the masses to collide onto!

This argument is not correct, because it ignores the fact that even if the universe were spatially finite, it would have no center. The spatial topology of a spatially finite universe is that of a 3-sphere; there is no point within a 3-sphere that is its "center", just as there is no point on the surface of the Earth--an example of a 2-sphere--that is the "center" of that surface.

 

[Anushka Umarani]

True, I get it
Gracias!

 

[laymanB]

The Lambda-CDM model:

https://en.wikipedia.org/wiki/Lambda-CDM_model

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.

The full details of the model are always being refined, but the part about the universe being spatially infinite is pretty solid.

What are the properties of what you are calling the universe? What does it mean that it is spatial? I realize that we are not talking about the observable universe with it's radiation, matter, and four dimensions of spacetime.

Because "spatially infinite" and "spatially flat" are not the same thing.

What other geometry besides a Euclidean flat geometry could be infinite? I'm not talking unbounded, but in what other geometry do two parallel lines not intersect at some point? How could we detect a geometry other than flat if it was infinite?

 

[Bandersnatch]

What other geometry besides a Euclidean flat geometry could be infinite? I'm not talking unbounded, but in what other geometry do two parallel lines not intersect at some point? How could we detect a geometry other than flat if it was infinite?

Hyperbolic geometry:

Detection method is the same as for spherical geometry - measurement of internal angles of large triangles.

 

[laymanB]

Hyperbolic geometry:
Detection method is the same as for spherical geometry - measurement of internal angles of large triangles.

How would you know if you can only measure angles within the observable universe? Does not the geometry appear flat in the observable universe where you can actually use objects to construct a triangle? Do not the angles sum to 180 degrees using objects at the "edge" of the observable universe?

 

[Bandersnatch]

How would you know if you can only measure angles within the observable universe? Does not the geometry appear flat in the observable universe where you can actually use objects to construct a triangle? Do not the angles sum to 180 degrees using objects at the "edge" of the observable universe?

They do in our universe (within error bars), and that's an indication it's flat or with sufficiently small curvature that we can't detect it. They wouldn't add up to 180 if it the universe weren't flat.
The curvature is intrinsic - it's detectable from inside the space.

 

[laymanB]

They do in our universe (within error bars), and that's an indication it's flat or with sufficiently small curvature that we can't detect it. They wouldn't add up to 180 if it the universe weren't flat.
The curvature is intrinsic - it's detectable from inside the space.

When you say that the curvature is intrinsic, are you talking about the localized curvature due to gravitational fields from energy and matter?

 

[jbriggs444]

When you say that the curvature is intrinsic, are you talking about the localized curvature due to gravitational fields from energy and matter?

"Intrinsic" curvature is curvature which is detectable using instruments purely within the space being measured. For example, by laying out three points connected by shortest paths (i.e. a triangle) and seeing that the sum of the internal angles is not 180 degrees.

By contrast, "extrinsic" curvature involves representing the space you are interested in by "embedding" it in a higher dimensional space. For instance, a plane that is embedded in a three dimensional volume and rolled into a tube. That plane is an example of a two-dimensional space with non-zero extrinsic curvature but zero intrinsic curvature.

We can measure and talk about curvature without needing to ask what is causing it.

 

[PeterDonis]

What does it mean that it is spatial? I realize that we are not talking about the observable universe with it's radiation, matter, and four dimensions of spacetime.

The four dimensions of spacetime in the Lambda CDM model describe the entire universe, not just the part of it that we can observe. When we say the universe is "spatially flat", what we mean is that spacelike hypersurfaces of constant time for comoving observers (observers that see the universe as homogeneous and isotropic) are flat--i.e., they are Euclidean 3-spaces.

 

[laymanB]

By contrast, "extrinsic" curvature involves representing the space you are interested in by "embedding" it in a higher dimensional space. For instance, a plane that is embedded in a three dimensional volume and rolled into a tube. That plane is an example of a two-dimensional space with non-zero extrinsic curvature but zero intrinsic curvature.

I'll have to think on that example for a while. Is this bringing in ideas from higher dimensional theories like string theory or is this dimensional idea encapsulated within LCDM?

We can measure and talk about curvature without needing to ask what is causing it.

Well, you know how to stifle a curious mind.

 

[laymanB]

The four dimensions of spacetime in the Lambda CDM model describe the entire universe, not just the part of it that we can observe. When we say the universe is "spatially flat", what we mean is that spacelike hypersurfaces of constant time for comoving observers (observers that see the universe as homogeneous and isotropic) are flat--i.e., they are Euclidean 3-spaces.

I do appreciate all the responses. I'll have to think on this one for a while. Would the language then be inaccurate to say that spacetime from the big bang was expanding into eternal spacetime with the same four dimensions. In other words, if this view was correct, does not space have something to expand into? Thanks.

 

[PeterDonis]

Would the language then be inaccurate to say that spacetime from the big bang was expanding into eternal spacetime with the same four dimensions.

Yes. Spacetime doesn't "expand". The spacetime model that describes the universe is a single 4-dimensional geometry that includes the Big Bang and our current universe. When we say the universe is "expanding", we just mean that this 4-dimensional geometry has a particular shape.

does not space have something to expand into?

No. Spacetime is a 4-dimensional geometry that doesn't expand at all--see above. So it's meaningless to even ask whether it has something to expand into.

 

[jbriggs444]

I'll have to think on that example for a while. Is this bringing in ideas from higher dimensional theories like string theory or is this dimensional idea encapsulated within LCDM?

Nothing so fancy. This is as simple as rolling up a piece of graph paper into a tube and noticing that the geometry of lines on paper is unaffected. That's "extrinsic" curvature.

Well, you know how to stifle a curious mind.

Physics is not just about the amazing flashing lights. It also about understanding the simple stuff so that you can appreciate the amazing flashing lights. Curved space or curved space-time is more meaningful if you know what "curved" means first.

 

[laymanB]

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...

 

[laymanB]

Yes. Spacetime doesn't "expand". The spacetime model that describes the universe is a single 4-dimensional geometry that includes the Big Bang and our current universe. When we say the universe is "expanding", we just mean that this 4-dimensional geometry has a particular shape.
No. Spacetime is a 4-dimensional geometry that doesn't expand at all--see above. So it's meaningless to even ask whether it has something to expand into.

Do either of these ideas depend on the existence of the multiverse, as opposed to our universe being the only one?

 

[PeterDonis]

Do either of these ideas depend on the existence of the multiverse, as opposed to our universe being the only one?

No. The term "spacetime" in what I posted means our universe; whether or not it is the only one does not affect the model I described.

 

[laymanB]

Nothing so fancy. This is as simple as rolling up a piece of graph paper into a tube and noticing that the geometry of lines on paper is unaffected. That's "extrinsic" curvature.

That makes sense in making a distinction between intrinsic and extrinsic curvature. Thanks.

 

[laymanB]

No. The term "spacetime" in what I posted means our universe; whether or not it is the only one does not affect the model I described.

Okay, thanks. So if I am understanding you correctly, based on the current consensus model, the proponents would NOT say that space and time were created in the big bang? As this seems to be the common explanation in popular understanding and teaching?

They would say that the eternal, infinite spacetime takes on a particular shape and geometry in our observable universe?

 

[phinds]

Okay, thanks. So if I am understanding you correctly, based on the current consensus model, the proponents would not say that space and time were created in the big bang, as this seems to be the common explanation in popular understanding and teaching?

No, that is not what the BB Theory says at all. It says that the universe is, and has been and will continue to be, expanding from a dense hot plasma starting at the time designated as the end of inflation (which is itself speculative but likely). It is silent on what went before that.

 

[laymanB]

phinds, I am referencing the ongoing discussion with PeterDonis in which he appears to be asserting that spacetime is eternal and infinite, according to the consensus view of the LCDM model.

 

[laymanB]

Is spatially infinite spacetime one solution to the equations of this model or just an assumption to make it easier to deal with? What type of observations would be required to verify that this solution (or assumption) corresponds to reality?

 

[PeterDonis]

So if I am understanding you correctly, based on the current consensus model, the proponents would NOT say that space and time were created in the big bang?

Some might say that in pop science discussions, but I would say that the concept of space and time being "created" doesn't make sense. Spacetime just is. It doesn't "change".

They would say that the eternal, infinite spacetime takes on a particular shape and geometry in our observable universe?

They would say that spacetime has a particular geometry.

 

[PeterDonis]

Is spatially infinite spacetime one solution to the equations of this model or just an assumption to make it easier to deal with?

It's an exact solution.

What type of observations would be required to verify that this solution (or assumption) corresponds to reality?

The observations that have established spatially infinite spacetime as our current best fit model.

 

[laymanB]

Thanks for the education.

 

[Hendrik Boom]

In a hyperbolic space, there are more than one parallel to a given line through a given point. And the sum of the angles of a triangle is less than 180 degrees. The discrepancy increases with the size of the triangle. So if our space were to be hyperbolic, it would mean that all the triangles we have to measure are very small.

 

[laymanB]

So, if spacetime is spatially infinite, could we ask what was happening 20 billion years ago?

Can we assume that fields, zero-point energy, and quantum fluctuations were occurring?

 

[PeterDonis]

if spacetime is spatially infinite, could we ask what was happening 20 billion years ago?

Not according to our best current model, because in our best current model there is no region of spacetime corresponding to "20 billion years ago". This has nothing to do with whether spacetime is spatially infinite or not.

 

[laymanB]

Not according to our best current model, because in our best current model there is no region of spacetime corresponding to "20 billion years ago". This has nothing to do with whether spacetime is spatially infinite or not.

So spatially infinite does not presuppose eternality?

 

[PeterDonis]

So spatially infinite does not presuppose eternality?

No.

 

[laymanB]

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

 

[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.