Infinite vs Expanding Universe: A Physics Conundrum Explained

[Bandersnatch]

this statement is correct

It is.

 

[phinds]

Could someone please tell me if this statement is correct or is at least believed to be true by some cosmologists?

If the universe is infinite now, it was also infinite one second after the Big Bang.

Yes, as Bandersnatch said, it is true. Finite things can't become infinite and infinite things can't become finite. Whichever one something is, it always has been that way and always will be that way (this statement gets a bit problematic if you allow infinite time but let's not go there).

 

[Ken G]

We should be careful though, there may be types of expansion laws that are solutions to general relativity under the cosmological principle that reach an infinite scale parameter in a finite time, starting from a finite universe. I think the mathematics could allow that, so I don't know that we can say it is logically impossible. But it certainly isn't a type of solution that is under any serious consideration at present. Perhaps all such solutions are open solutions anyway, so could not start out finite.

 

[phinds]

I think the mathematics could allow that, so I don't know that we can say it is logically impossible

The map is not the territory. Not all mathematics can be realized physically. I don't see how something physically finite could become infinite in a finite amount of time.

 

[Ken G]

Yet that's the kind of reasoning we have to watch out for, it's the kind of thing people say when they say they don't understand how an infinite universe could come into being in the first place. A territory is just a different type of map.

 

[phinds]

A territory is just a different type of map.

I don't agree. A map is a DESCRIPTION. A territory is reality.

 

[Ken G]

So when you talk about atoms and forces and other aspects of science, are you talking about maps or territories? And in this thread, when you talk about the universe being finite or infinite, are you doing description or reality? My point is, descriptions are all we ever get, and all science can do with them is test them. We don't tell them in advance what they are allowed to do, we just test them and see what the ones that work actually do. If the equations of general relativity say that the scale factor in an initially finite universe can go infinite in a finite time (I don't know that they can but I don't see why not), then it is not for us to say that cannot happen, any more than it is not for us to say that event horizons cannot form or particles cannot be entangled. All those things are descriptions, none of them are realities, but they are what go into the models and are the only things we could ever test.

 

[phinds]

My point is, descriptions are all we ever get, and all science can do with them is test them.

No argument there, my point is just that (and this is true even GIVEN that all we ever have, really, is maps) it's important not to think that the map IS the reality. I agree that the goal of science is to make maps that are as accurate as possible, I just think it's important to make the distinction. That's particularly true in the case of this discussion because while I can believe that it is possible for math to describe something that goes from finite to infinite, I don't think (and I realize you don't agree w/ me) that reality can do that in a finite amount of time. So in this case, in my point of view anyway, the map can describe something that will never be the territory.

 

[Ken G]

I certainly agree that one's views about differences between maps and territories comes under their personal philosophy, I'm merely saying that this should never impose on the models that we allow ourselves to use to describe reality. If a model tests out well that solves some equations that have the scale parameter going infinite in a finite time, then so be it, that becomes our map. In science, anyway, there should never be a different criteria applied to a map, than to a reality, since the maps are how we understand reality, even if you think those are two different things.

 

[phinds]

I certainly agree that one's views about differences between maps and territories comes under their personal philosophy, I'm merely saying that this should never impose on the models that we allow ourselves to use to describe reality. If a model tests out well that solves some equations that have the scale parameter going infinite in a finite time, then so be it, that becomes our map. In science, anyway, there should never be a different criteria applied to a map, than to a reality, since the maps are how we understand reality, even if you think those are two different things.

Again, no argument, except I would point out that our map of reality includes singularities (black holes, big bang) for which we do NOT say about the math "so be it", we say "this is an unphysical math result".

 

[m k]

"the uverse is infinitely big"
and
"the uverse is expanding"

my understanding is you can't have both

What if you combine two infinities, positives and negatives?

 

[phinds]

What if you combine two infinities, positives and negatives?

You are trying to treat infinity as a number. There ARE areas of math where that works, sort of, but this is not one of them.

 

[Drakkith]

What if you combine two infinities, positives and negatives?

Depends on what you mean by "combine two infinities". For example:
$y=x^2-x$ could represent two infinities as $x→∞$, one positive and one negative. But the combination ($y$) is still a positive infinity because the positive term is squared while the negative term is linear. This is still true if $x→-∞$. You can immediately see this if you graph it, as it's just a parabola that opens upwards.

 

[Ken G]

Again, no argument, except I would point out that our map of reality includes singularities (black holes, big bang) for which we do NOT say about the math "so be it", we say "this is an unphysical math result".

But that's just it, we don't always say that. For example, no lesser expert on general relativity than Kip Thorne takes entirely seriously the singularity that the mathematics says forms in a black hole. He holds that if the mathematics says it is so, and the mathematics seems to be a reliable guide, then so be it, there is a singularity in a black hole. Others think there are all kinds of things behind the veil of an event horizon, even dragons there. But no one can say with any confidence that there isn't a singularity inside a black hole, simply on the grounds that it would be "unphysical." Our track record for telling our mathematics when it is doing something impossible is not very good, as it includes things like Einstein telling Bohr that God doesn't play dice, or Eddington telling Chandrasekhar that white dwarfs cannot undergo unstable gravitational collapse.

On the other hand, I grant you that no one could ever do an observation and say, "see, there really is a singularity there," but they could say, "there is no better way to treat this result than as a singularity." We have things like photons that are moving in frames that no observer is allowed to enter, and some might say "that means photons can't really have zero rest mass and can't really move at the speed of light", but that isn't actually what we say. We seem rather arbitrary about what types of singularities we will tolerate, and what types we will regard as unphysical, but our best theories still do include singularities, whether we disbelieve them or not.

 

[nikkkom]

Actually, BH singularity is somewhat problematic. Mathematically, it represents a boundary on the space-time manifold: for objects inside horizon, any possible future worldline ends on the singularity. The problem is that it really ENDS there, it does not continue (it does not have any valid continuation after it hits singularity). The time coordinate just stops there.

Imagine that someone tells you that today, after 23:59:59, tomorrow will not arrive. Time will just... end. 23:59:59 second will be the last second of time, ever.
Sounds ridiculous, right?

 

[Ken G]

I don't see anything necessarily ridiculous about that, I only see people who are used to thinking in one particular way. And isn't that exactly what people say about the origin of the universe in the Big Bang model? Certainly there are those who attempt to "continue" existence before the origin, but most people accept that the most striking feature of the Big Bang model is that it implies a time origin, before which time might not make sense. So how is that any more problematic running forward than backward? The point is, we are students of reality, and all our understanding of it comes from models that seem to work. But as soon as we say one model "could not be," all it means is that we are already married to a different model. And the track record of that style of thinking, in science, is pretty spotty!

 

[nikkkom]

I don't see anything necessarily ridiculous about that, I only see people who are used to thinking in one particular way. And isn't that exactly what people say about the origin of the universe in the Big Bang model? Certainly there are those who attempt to "continue" existence before the origin, but most people accept that the most striking feature of the Big Bang model is that it implies a time origin, before which time might not make sense. So how is that any more problematic running forward than backward?

It is equally problematic, and there is no reason to think that such approximation backwards is valid. Standard Model's math certainly breaks down at _finite_ density and thus loses its validity at this point. We don't have reliable predictions before this moment.

 

[Ken G]

The issue is not if there is a reason to think it is valid, it is if there is a reason to think it is not valid. Falsification is the beating heart of science. The evidence in favor of a model is all a model ever has going for it, we never get evidence that the model is correct. All we do is, use a model until found to be contradicted by observation, and that's just as true for atoms as it is for black hole singularities.

 

[nikkkom]

The issue is not if there is a reason to think it is valid, it is if there is a reason to think it is not valid.

Hey, check this out. I did a little experiment:
When I run "dd bs=1024 count=9 </dev/urandom >FILE", this creates FILE 9 kbytes long.
When I run "dd bs=1024 count=99 </dev/urandom >FILE", this creates FILE 99 kbytes long.
When I run "dd bs=1024 count=9999 </dev/urandom >FILE", this creates FILE 9999 kbytes long.

It's obvious!
Clearly, if I'd run
"dd bs=1024 count=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 </dev/urandom >FILE",
this will surely create FILE 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 kbytes long.

What can possibly go wrong? Why should I think there might be some "new" things at play if I'd go this far?

 

[Ken G]

I can't tell if you are trying to be ironic, or if you are being serious. Of course a computer can hit a limit and be unable to function beyond that. That's my point-- the same could happen to the universe, and if the math of our best theory predicts that will happen (hypothetically), then we would have no logical basis to claim no it won't! That was Einstein's error, that was Eddington's error.

 

[acidmatic]

It is important to stop thinking the universe is expanding into somewhere. The universe itself is somewhere. It is the same difference as with any, let's say surface, because we can imagine surfaces. If we only knew our Earth and nothing about outer space, since the universe doesn't have an outer space, we would only knew the Earth's surface. Why shouldn't it get bigger and bigger without any reference to getting bigger into something? The surface is all we have, and it might get bigger. O.k. not the Earth as a solid rock, but for imagination it's sufficient.

The universe is estimated to have an expansion of about 45 billion light years in each direction (see Wikipedia). But that doesn't mean it's shaped like a ball. We simply don't know how it is shaped. All we know is, that it is almost flat, so either it is really big, or indeed flat. And it doesn't need a boundary as our Earth's surface doesn't have a boundary either. So infinitely big should better be read as without boundary.

It works in our consciousness limits only, I guess... I tend to suppose that we are all looking at some simple structure that is just beyond our mind... Similar to an ant watching at a computer monitor or chimpanzee making sex.

 

[nikkkom]

I can't tell if you are trying to be ironic, or if you are being serious. Of course a computer can hit a limit and be unable to function beyond that.

No, it will function. The last command will not make computer break. Just the result of this command will be different from your naive extrapolation - because new factors are in play now.

if the math of our best theory predicts that will happen (hypothetically), then we would have no logical basis to claim no it won't!

You misunderstand me. I'm not claiming that for sure, there is no singularity. I'm saying our math just breaks down and stops being valid. It predicts nothing. We don't have logical basis to claim *anything*.

 

[Ken G]

You misunderstand me. I'm not claiming that for sure, there is no singularity. I'm saying our math just breaks down and stops being valid. It predicts nothing.

You framed your remarks as though they were disagreeing with what I said above. I never said we could "claim" a truth that is not observed, I said we could not place preconditions on what is possible to happen. For example, if GR predicts a singularity, and GR is our best current theory, then the singularity is our best current working hypothesis. Science then demands we attempt to test that working hypothesis, in terms of predictions it makes. We never know if our predictions will occur, but we must not say they cannot occur because they are somehow logically impossible. That's what I meant about Einstein and Eddington, they both thought what the best theory was telling them was logically impossible, and it turned out that it wasn't. Ergo, predictions are not "problematic," they are just predictions that require testing.

 

[nikkkom]

You framed your remarks as though they were disagreeing with what I said above. I never said we could "claim" a truth that is not observed, I said we could not place preconditions on what is possible to happen. For example, if GR predicts a singularity, and GR is our best current theory, then the singularity is our best current working hypothesis.

GR is the currently best theory of gravity, yes.

However. It also is known to be incomplete, it is an approximation of some better, but currently unknown theory, since we know that GR is incompatible with quantum field theory.

You are trying to use GR predictions exactly in the situation where it is known to be incomplete, and insist that that prediction is valid.

 

[Ken G]

All physics theories are known to be incomplete, so all you are saying is that GR is a physics theory. I don't see how that let's us know that the universe cannot expand to infinity in a finite time, or contract to a singularity. There is nothing special about a theory that leads to surprising consequences, almost all of them do, and some have been found to be observed, others have not. The only thing we know for certain is the folly of placing preconditions on successful theories, and this is what I said above. I certainly never "predicted" anything, I think you should read it again.

 

[Drakkith]

For example, if GR predicts a singularity, and GR is our best current theory, then the singularity is our best current working hypothesis.

Hi Ken. What are your thoughts on when we can reasonably say that the predictions of GR probably aren't correct?

 

[nikkkom]

All physics theories are known to be incomplete, so all you are saying is that GR is a physics theory.

This is not true. Not every physics theory has to have problems. A physics theory can exist which has no theoretical problems, and matches all current observations (and thus be a candidate to be a final theory in its field). SM comes quite close to this gold standard.

GR has the first problem - it has a theoretical problem. It is incompatible with quantum physics, which in turn is supported by experiments.

 

[Chronos]

I trust that is not to say the QM is utterly flawless, it is not. Your former assertion was accurate - there is no perfect theory.

 

[Comeback City]

This debate has been going on for about 20 posts and the only discrepancy is your interpretations of GR. If GR predicts a BH singularity, then it predicts a BH singularity. But, it is also true that there is no experimental evidence to back it up. I agree with what @Chronos said also, as no theory can be perfect.

 

[m k]

You are trying to treat infinity as a number. There ARE areas of math where that works, sort of, but this is not one of them.

Would you say that infinity of natural numbers is quite small among infinities?