Does the Big Bang Model Support Instantaneous Inflation in an Infinite Universe?

[SW VandeCarr]

The Big Bang model describes a smoothly expanding universe from a point where the current laws of physics break down. However if the universe is infinite, it would be infinite down to this point and presumably before it. This would imply instantaneous inflation from 0 to infinity. The universe would not pass through any intermediate stage. Is this a proper understanding of Alan Guth's original proposal, or would it have be substantially revised for an infinite universe?

EDIT: I'm including the inflation period in the description "smoothly expanding" since I assume there are no discontinuities in the Big Bang description from the point where it starts. In the infinite case, the universe would already be infinite at this point so instantaneous inflation would have had to come before.

 

[friend]

The Big Bang model describes a smoothly expanding universe from a point where the current laws of physics break down. However if the universe is infinite, it would be infinite down to this point and presumably beyond it. This would imply instantaneous inflation from 0 to infinity. The universe would not pass through any intermediate stage. Is this a proper understanding of Alan Guth's original proposal, or would it have be substantially revised for an infinite universe?

EDIT: I'm including the inflation period in the description "smoothly expanding" since I assume there are no discontinuities in the Big Bang description from the point where it starts. In the infinite case, the universe would already be infinite at this point so instantaneous inflation would have had to come before.

It seems to me that if the universe were truly infinite, then there would no since of scale. There would be no stopping point to inflation and we would still be expanding as fast as ever. Since that's obviously not the case, then the universe cannot be infinite.

 

[SW VandeCarr]

It seems to me that if the universe were truly infinite, then there would no since of scale. There would be no stopping point to inflation and we would still be expanding as fast as ever. Since that's obviously not the case, then the universe cannot be infinite.

I think most cosmologists are hoping the universe is closed, but no one can tell nature what is should be. All the current evidence is pointing to a flat universe. The bias is toward positive curvature, but its a very close thing. The fact is the possibility must be considered with some very weird consequences, but apparently little effect on key physical theories such GR. For example, it has been proposed by physicist Max Tegmark that an infinite number of copies of everyone (and apparently everything in the visible universe and beyond) would exist in an infinite universe.

My question is regarding inflation in the context of an infinite expanding universe.

EDIT: Current evidence is that expansion is accelerating.

 

[matt.o]

You seem to have the (common) misconception that initially the entire Universe had zero size. The current thinking is that the observable Universe, i.e., that bit we have access to, is embedded in an infinite Universe. In this scenario, it was the observable Universe which had zero size -- the Universe was always infinite.

 

[SW VandeCarr]

You seem to have the (common) misconception that initially the entire Universe had zero size. The current thinking is that the observable Universe, i.e., that bit we have access to, is embedded in an infinite Universe. In this scenario, it was the observable Universe which had zero size -- the Universe was always infinite.

Does the infinite universe have a beginning? Is it expanding?

 

[sylas]

Does the infinite universe have a beginning? Is it expanding?

Some ideas for an infinite universe have beginnings, others don't. Everything we see is expanding. Almost certainly everything far beyond could ever be observed from Earth is expanding.

Going back to the OP:

The Big Bang model describes a smoothly expanding universe from a point where the current laws of physics break down. However if the universe is infinite, it would be infinite down to this point and presumably beyond it. This would imply instantaneous inflation from 0 to infinity. The universe would not pass through any intermediate stage. Is this a proper understanding of Alan Guth's original proposal, or would it have be substantially revised for an infinite universe?

EDIT: I'm including the inflation period in the description "smoothly expanding" since I assume there are no discontinuities in the Big Bang description from the point where it starts. In the infinite case, the universe would already be infinite at this point so instantaneous inflation would have had to come before.

One problem is speaking of the singularity as if it is a defined value. Don't think of it as zero, but as 0/0. It's not anything. It is truly undefined, not finite or infinite, just a discontinuity. In particular, it is not a point where the universe has a size of zero, in any model.

Apart from that, you've got it. Everything else is smooth, in the classical account. Of course, the nice smooth descriptions break apart as you approach scales where quantum effects apply for an the entire Hubble volume, and even well before that we need to combine ideas from quantum physics with relativistic physics ... which we can do pretty effectively in many ways.

To get into the details of Guth's proposals does in fact require quantum physics as well as relativity. But you can explain quite a lot of the end result pretty simply.

The vast majority of what we discuss about cosmology in this forum can be managed by trying to help people get to grips with the simple models in which the universe is approximated as a smooth uniform fluid. You can give simple numbers like matter density and dark energy density and rate of expansion and so on, and this takes you a long way into understanding cosmology, and inflation as well; particularly slow-roll inflation (I think).

The simple answers (which always leave someone curious and wanting more, of course, and rightly so) can be as follows.

• Is the universe infinite? We don't know.
• Is the universe expanding? Everything we see and also far beyond the range of anything we can see is all expanding. What happens when you go for absolutely everything; we don't know.
• Assuming the universe is infinite, does it have a beginning? We don't know. There's certainly a beginning of that volume which includes everything we see and a lot more beside, in the sense that a finite time ago all of that was tightly compressed and in a state that we don't understand all that well, before it began to be something we can now recognize as the universe.

People who want to speculate about resolutions of the unknowns often cannot shake some simple presumptions which seem so obvious to them they don't even see that they are making presumptions.

For example, on space. Many beginners to the topic think in terms of a vast canvas, and the expanding universe occupying a part of it, and something else occupying other parts. But the expansion is not an expansion within a space, like stuff spreading out over a large canvas. Space itself swells to contain the expanding stuff of the universe. Resolutions of the unknown in relation to the extent of the whole universe are going to involve rethinking what you think about space at all.

For example, on time. Many beginners to the topic think in terms of an endless progression of events, with the bang occurring then, and us occurring now, and want to know about before, and after. But time itself is not that straightforward. Resolutions of the unknown in relation to the origins of the universe are going to involve rethinking what you think about time at all.

Inflation occupies a kind of middle ground in these matters. There are a number of different forms of inflation being considered. Inflation itself doesn't tell you about the origin of the universe. And inflation itself doesn't tell you whether the whole universe is finite or infinite.

Cheers -- sylas

 

[twofish-quant]

This would imply instantaneous inflation from 0 to infinity. The universe would not pass through any intermediate stage. Is this a proper understanding of Alan Guth's original proposal, or would it have be substantially revised for an infinite universe?

No. Alan Guth's original proposal is that if the universe expanded very rapidly at some point it's past then a lot of problems with the big bang model would be fixed. Now it could be the rapid expansion happened after time zero, or it could be that the rapid expansion eliminates the need for there to be a time zero, but the basic idea doesn't really involve talking about what happened at time zero, but rather what happened very, very shortly afterwards.

Also, I find it more useful to think not so much in terms of an infinite universe, than a universe that is so much larger than what we can see that we can't detect if there is an "edge" and if there is one, it's so far away that it doesn't matter to us.

 

[twofish-quant]

To get into the details of Guth's proposals does in fact require quantum physics as well as relativity. But you can explain quite a lot of the end result pretty simply.

One very important point is that Guth's ideas do involve quantum physics, but it doesn't involve *weird* quantum physics. If you start talking about "time zero" you can basically make up pretty much anything because we really don't have any clue about what rules the universe followed at "time zero." Guth's ideas of inflation happened a very short time after "time zero" and at that point the universe in a situation where we can make educated guesses about what the universe was like since it's starts getting to the point were we can think of taking the results of experiments we have done, and extrapolating it into the inflationary era.

As the universe cools, we start getting into physics that we know more and more about. The inflationary era is hot enough so that we are doing some educated guesses, but it's not so hot that we can make up anything.

 

[sylas]

One very important point is that Guth's ideas do involve quantum physics, but it doesn't involve *weird* quantum physics.

Yes, exactly!

Inflation does not need or use the so far unattained grand unification of relativity and quantum physics. It uses the relativity and the quantum physics we have right now, theories which have been used with great success to model all kinds of physical phenomena. We don't know the nature of the inflaton field, but many of its properties can be inferred and constrained from observations, particularly of the background radiation. For example, the small inhomogeneities in the very early universe. Some models of inflation (including Guth's earliest proposals in the late 1970s) are falsified. Indeed, Guth knew they had to be wrong from the start, but still had the insight and confidence to present the constraints anyway, along with the problems, in the expectation that there was something work looking into here. He was right; there was.

Cheers -- sylas

 

[SW VandeCarr]

Also, I find it more useful to think not so much in terms of an infinite universe, than a universe that is so much larger than what we can see that we can't detect if there is an "edge" and if there is one, it's so far away that it doesn't matter to us.

I think most cosmologist want to believe that the universe is not infinite with its weird consequences. See my response #3 in this thread and my post "Questionable article in Scientific American" on this board. I provide a link to a summary of the article. You can pay to read the whole article if you don't subscribe to SA.

 

[twofish-quant]

I think most cosmologist want to believe that the universe is not infinite with its weird consequences.

My personal experience has been that most cosmologists don't have any opinion on the topic. It also turns out that most physicists have a high tolerance for "weird consequences."

See my response #2 in this thread and my post "Questionable article in Scientific American" on this board. I provide a link to a summary of the article. You can pay to read the whole article.

This is why I stopped reading Scientifc American, because it has lousy science journalism. Cosmologists like most other physicists have weird speculative ideas which they often talk about. This is a good thing. What's not a good thing is when an article gives an impression that one person's ideas are generally shared in the community.

One problem with a lot of popular science descriptions of cosmology is that it makes it seem weirder and stranger than it is. There are some weird parts of it, but a lot of it *isn't* very weird. We see galaxies expanding away from each other. If you run the movie backwards, the universe starts to contract. When you compress gases, they get hot. The more you compress them, the hotter things get. We know more or less how hot gasses behave.

 

[twofish-quant]

Inflation does not need or use the so far unattained grand unification of relativity and quantum physics.

Which means that we can assume certain things about the inflationary period. Space has three dimensions. Gravity is attractive. The fundamental constants aren't weird values. One important part about inflation is that while you have to assume some unknown energy field, the assumption is that the unknown energy field is something that behaves the same way as known energy fields.

Basically what inflation says is that if you assume that something dumped a lot of energy that caused the universe to expand, a lot of problems with the big bang model go away.

Some models of inflation (including Guth's earliest proposals in the late 1970s) are falsified. Indeed, Guth knew they had to be wrong from the start, but still had the insight and confidence to present the constraints anyway, along with the problems

Guth's original idea was that inflation was caused by the energy field that is associated with the strong nuclear force. After working on the idea for about six or seven years, it became clear that this was not going to work, since we know enough about the strong nuclear force to know that it just didn't fit. So at that point people gave up trying to fit the inflation energy field to known energy fields and started figuring out what the unknown field would act like.

One other thing is that in the late-1970's, one important idea was "supersymmetry" which were a set of theories that predicted a *lot* of new particles, so assuming that there was some unknown particle wasn't a big deal at that time. Since we haven't found any of these new unknown particles, theories that predict new particles would have slightly more skepticism today.

 

[SW VandeCarr]

My personal experience has been that most cosmologists don't have any opinion on the topic. It also turns out that most physicists have a high tolerance for "weird consequences."



This is why I stopped reading Scientifc American, because it has lousy science journalism. Cosmologists like most other physicists have weird speculative ideas which they often talk about. This is a good thing. What's not a good thing is when an article gives an impression that one person's ideas are generally shared in the community.

Yes, especially if the broadcast media gets a hold of it.

I don't personally believe that the consequences described in the summary are forced by the mathematics (infinite number of copies of everything). An infinite set cannot have any repeat elements in standard set theory. However it can have an infinite number of distinct infinite subsets. But is this not forced. In principle, the set of natural numbers is sufficient to uniquely label every discrete object in an infinite universe from sub atomic particles to composite objects up to rocks, individual life forms, planets, stars and galaxies. There need not be any identical copies although they are allowed provided they can be distinguished in some way. Of course I can't speak to any purely scientific argument Max Tegmark might have. I only read the summary.

 

[sylas]

I don't personally believe that the consequences described in the summary are forced by the mathematics (infinite number of copies of everything). An infinite set cannot have any repeat elements in standard set theory. However it can have an infinite number of distinct infinite subsets. But is this not forced. In principle, the set of natural numbers is sufficient to uniquely label every discrete object in an infinite universe from sub atomic particles to composite objects up to rocks, individual life forms, planets, stars and galaxies. There need not be any identical copies although they are allowed provided they can be distinguished in some way. Of course I can't speak to any purely scientific argument Max Tegmark might have. I only read the summary.

Except that there are only a finite number of particles you can fit into a given volume at a reasonable density, and only a finite number of ways to arrange them, and only a finite number of possible microstates at a given temperature.

Your requirement that all copies must be distinguishable is what seems to be far more weird to me. It doesn't make sense to me. Why would you insist two arrangements of atoms can always be distinguished? It runs counter to everything I know about the quantum nature of objects as finite collections of discrete indistinguishable particles, with strictly finite numbers of distinguishable states.

Some of what Tegmark does is odd, but not the particular step you are objecting to. Given an infinite universe, in the sense of an unbounded flat expanding homogenous field of galaxies, the existence of repeating "twins" is an unexceptional consequence. There's nothing intrinsically inconsistent between this and inflation, or the Big Bang.

If pressed for a view, I'd say that I doubt the universe is infinite in that sense, but I think it might be infinite in something more like what Tegmark calls the "level 2" multi-universe. But as twofish_quant notes, this is really something on which it makes sense to be somewhat agnostic.

Regardless, if the universe is infinite in the "level 1" sense, being flat and topologically simple and with an infinite spatial extent, then the mathematics does indeed give you the consequences described, of repeating "twins". A "twin" is simply a volume of space that is indistinguishable by any measurement; my "twin" in this sense is an arrangement of atoms that would a middle aged guy tapping on a laptop on his kitchen table on a sweltering summers day.

FWIW I don't share quite the same negative view of Scientific American. (On the other hand, don't get me started on New Scientist.) It's not a science journal, and I don't actually read it much myself; but as a magazine giving popular explanations of science to a lay audience it seems okay to me. But may be speaking out of turn; as I say, it is not something I read myself.

Cheers -- sylas

 

[SW VandeCarr]

Your requirement that all copies must be distinguishable is what seems to be far more weird to me. It doesn't make sense to me. Why would you insist two arrangements of atoms can always be distinguished? It runs counter to everything I know about the quantum nature of objects as finite collections of discrete indistinguishable particles, with strictly finite numbers of distinguishable states.

Cheers -- sylas

I was referring to distinct spatio-temporal positions of otherwise identical objects, particularly as it refers to composite objects, meaning made of atoms. The concept does break down at the sub atomic level. So every carbon atom for example would get a number as well as any higher composite which contains this particular carbon atom. With an infinite supply of numbers, there's no problem. I was indicating that even a simple infinity like the natural numbers can be sufficient to uniquely label everything in an infinite universe. However, sets cannot contain identical elements, so we must distinguish them is some way. If you couldn't do this, the concept of an infinite number of identical copies breaks down.

 

[twofish-quant]

However, sets cannot contain identical elements, so we must distinguish them is some way. If you couldn't do this, the concept of an infinite number of identical copies breaks down.

The problem is that it appears that particles really are indistinguishable. It turns out that you can't label an electron. Let me just give a weird example. Suppose you have two coins that are indistinguishable. What is the chance that you flip them and get one coin heads and one coin tails. Well if you can label the coins, then the odds of getting one heads and one tails is 1/2, since there are four possible states HH, HT, TH, TT. If the coins are really indistinguishable, then the odds of getting one heads and one tails is 1/3. since there are only three possible states, HH, HT, TT.

Now if you do the experiments with particles, it turns out that you really do get behavior that says that electrons are indistinguishable. There are also some really weird restrictions on what you can do with particles (google the no-cloning theorem).

 

[SW VandeCarr]

Well, I said the idea breaks down at the sub-atomic level and possibly for isolated atoms as well. I was really thinking of composite objects, like copies of myself. Identical except by spatio-temporal position.