B Infinite vs Expanding Universe: A Physics Conundrum Explained

[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?

 

[jbriggs444]

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

You would have to define "small" in this context. And give a threshold for "quite". It is not clear how one would compare the infinite cardinality of the natural numbers with the positive infinity in the two-point compactification of the real numbers.

In any case, this is irrelevant to the discussion at hand.

 

[phinds]

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

Google "hierarchy of infinities"

 

[Comeback City]

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

It is quite similar to infinity of whole numbers

 

[phinds]

It is quite similar to infinity of whole numbers

I don't get "similar". Since both are cardinalities of sets then either they have the same Aleph number, in which case they are identical not similar, or they have diffrerent Aleph numbers, in which case they are different (and not similar).

 

[Comeback City]

I don't get "similar". Since both are cardinalities of sets then either they have the same Aleph number, in which case they are identical not similar, or they have diffrerent Aleph numbers, in which case they are different (and not similar).

Well, infinity + 1 = infinity, so I'm going to read some more about infinity!

 

[phinds]

Well, infinity + 1 = infinity

Yes, Aleph1 + 1 = Aleph1 and Aleph2 +1 = Aleph2. That does NOT make Aleph1 identical to, or similar to, Aleph2

, so I'm going to read some more about infinity!

Good idea. That will likely dispel your misunderstanding.

 

[Comeback City]

that has nothing at all to do with your statement

Good idea. That will likely dispel your misunderstanding.

You should read more about "comic relief"

 

[phinds]

You should read more about "comic relief"

Doesn't that have something to do with Billy Crystal and Whoopie Goldberg? They are not infinite.

 

[Comeback City]

Doesn't that have something to do with Billy Crystal and Whoopie Goldberg? They are not infinite.

Yeah you got me again

 

[Ken G]

This is not true. Not every physics theory has to have problems.

I never said a physics theory has to have problems, I said they are all known to be incomplete. Which is true.

 

[Ken G]

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

I don't think we can say when a prediction probably isn't correct, we simply have to test it. What is the track record of theories that we thought were probably not correct, versus ones we probably thought were? It's cherry picking, but still I'd say that track record is not good at all. For example:
We thought for thousands of years that geocentric models were probably correct and would not significantly change in the future.
We thought for hundreds of years that Galilean relativity was probably correct, so when Maxwell's equations treated the speed of light as a constant of the theory, most physicists thought that had to be incorrect.
Eddington thought that Chandrasekhar's theory of white dwarfs was probably incorrect because it predicted a maximum mass, above which no static solution was possible without drastic changes to the star. He reasoned that something missing from Chandrasekhar's approach would guarantee stability.
Einstein thought that quantum mechanics had to be wrong because it violated local realism.
And so on.

 

[Comeback City]

Yes, Aleph1 + 1 = Aleph1 and Aleph2 +1 = Aleph2. That does NOT make Aleph1 identical to, or similar to, Aleph2

So do the infinite sets of natural numbers and whole numbers have the same or different Aleph numbers? Wikipedia is saying that natural numbers have an Aleph number of 0 (Aleph-naught). It doesn't mention whole numbers, but whole numbers are just natural numbers with 0. Is it safe to assume infinite series of whole numbers also has Aleph number of 0?

 

[phinds]

So do the infinite sets of natural numbers and whole numbers have the same or different Aleph numbers? Wikipedia is saying that natural numbers have an Aleph number of 0 (Aleph-naught). It doesn't mention whole numbers, but whole numbers are just natural numbers with 0. Is it safe to assume infinite series of whole numbers also has Aleph number of 0?

Yes, they are the same. It's the reals, as I recall, that is the first instance of Aleph1

 

[jbriggs444]

Yes, they are the same. It's the reals, as I recall, that is the first instance of Aleph1

The continuum hypothesis is the statement that the cardinality of the reals is Aleph 1. Its truth or falsity is not decidable (under the usual axioms of set theory).

 

[nikkkom]

For quite a number of various kinds of infinities, look here:

https://en.wikipedia.org/wiki/Ordinal_number