An infinite vs a finite universe.

[geordief]

I understand we can't say which might apply.

If one was ,or was shown to be the case and the other was not ,would it make any practical or philosophical (or any other sort of) difference?

 

For instance would it make any difference to how we understand our own "place in the world" ? (and is that a weighty question?)

[Genady]

Just a technicality, but I think the question is not "infinite vs finite" but rather "bounded vs unbounded".

[geordief]

37 minutes ago, Genady said:

Just a technicality, but I think the question is not "infinite vs finite" but rather "bounded vs unbounded".

I think I see that.Would you say that a bounded universe can contain physical infinities?

 

Should I change the title to reflect that?

Edited July 3, 2023 by geordief

[studiot]

1 hour ago, geordief said:

I understand we can't say which might apply.

If one was ,or was shown to be the case and the other was not ,would it make any practical or philosophical (or any other sort of) difference?

 

For instance would it make any difference to how we understand our own "place in the world" ? (and is that a weighty question?)

Yes indeed it makes a difference.

 

Because there is more than one infinity.I will use the word infinity / infinite to follow you.

 

There are an infinity of counting numbers  -  1, 2, 3, ......   and so on.

Each one is a whole complete package.

But there is a more numerous infinity of real numbers  -  1, 1.1, 1.11, 1.111   and so on.

We say that this greater amount is the infinity of the continuum.

 

Aah! the continuum.

 

So is the Universe  granular ie made up of lots of individual, indivisible pieces of space (eg the Planck length or whatever) or is it actually infinite as the real numbers ie indefinitely divisible?

Because if it is granular we can count the total number of grains, even if they are infinite.

But if it is continuous we can't.

 

Incidentally be careful of genady's suggestion.

Bounded v unbounded are not quite the same as infinite v finite.

Didderent combinations of these two qualities are possible.

 

[Genady]

Technicalities aside, back to the original question,

5 hours ago, geordief said:

would it make any practical or philosophical (or any other sort of) difference?

I don't think it will make any immediate difference, but it is something that is good to know. Might become handy at some point. Like extra savings in the bank.

[wtf]

1 hour ago, Genady said:

I don't think it will make any immediate difference, but it is something that is good to know. Might become handy at some point. Like extra savings in the bank.

In the mathematical study of the infinite, there are many important questions that are independent of the standard axioms, and whose ultimate truth value, if there even is such a thing, is currently unknown. The Continuum hypothesis is the most famous one of these questions.

It seems to me that if physicists are serious about the possibility that the universe is infinite, then questions of mathematical infinity thereby become questions about the physical universe, in principle amenable to experiment.

Therefore, no matter how much cosmologists blather about an infinite multiverse or an infinitely spatial universe, until physics postdocs apply for grants to investigate the Continuum hypothesis and other set theoretic questions, I will not believe they are serious.

Indeed when physicists use the word infinite, they generally mean "finite but very large," or perhaps "unbounded."

I saw a video interview with Leonard Susskind, one of the superstar physicists. He was talking about the multiverse. The interviewer asked him whether there are infinitely many universes in the multiverse. Susskind replied that there are "ten to the five hundred types of universes." But 10 to the 500 is of course a finite number; and as large finite numbers go, not a very big one. It's dwarfed by Skewes's number, Graham's number, Tree(3), and many other huge finite numbers known to computer scientists and mathematicians. It's only infinite to a physicist using a non-mathematical definition.

To show that this was no one-off casual error, I read one of Susskind's short papers on a related subject. He made the same mistake, conflating the very large finite with the infinite. It turns out that even rock star physicists do not understand mathematical infinity.

We see the same thing in the speculative theory of eternal inflation, which posits that time had a beginning but no end. The physicists say that in that case, the universe is spatially infinite. But this is false. What they mean is that the universe is finite today, and it will be finite tomorrow, and it will be finite in a trillion trillion years. But its growth is unbounded. Physicists frequently confuse unbounded growth with actual infinity.

To make this point clear, suppose I have a circle in the plane of radius t, where t is time measured in seconds. The radius and area of the circle are finite at times t = 1, t = one zillion, t = googolplex to the googolplex, and finite for any time t that you can name. What is true is that the area of the circle is unbounded as t gets arbitrarily large. But it's never infinite. It is always finite.

So like I say, when the first physics postdoc applies for a grant to count the points in a region of spacetime to see if the Continuum hypothesis is true, then I'll believe that physicists understand the meaning of mathematical infinity and take it seriously. 

Until then, I don't think physicists understand the meaning of the word that they so casually throw around. And they don't even take their own ideas about infinity seriously, else they'd be more precise.

 

Edited July 3, 2023 by wtf

[Genady]

Evidence that physicists DO know the difference between infinite and very big, but finite is that they understand very well the difference between instantaneous action in Newtonian physics and very fast, but finite one in relativity.

[studiot]

1 hour ago, Genady said:

Evidence that physicists DO know the difference between infinite and very big, but finite is that they understand very well the difference between instantaneous action in Newtonian physics and very fast, but finite one in relativity.

 

8 hours ago, Genady said:

Just a technicality, but I think the question is not "infinite vs finite" but rather "bounded vs unbounded".

So would you like to explain this further ?

[Genady]

11 minutes ago, studiot said:

 

So would you like to explain this further ?

Yes.

Firstly, I assume that the OP question refers to the spatial extent of the universe. Then, an infinite universe would be the one with infinitely many positions in it. An unbounded universe would be the one that for any number D there are positions with distance between them being greater than D.

I think that the OP talks about the latter rather than the former.

[studiot]

17 minutes ago, Genady said:

Yes.

Firstly, I assume that the OP question refers to the spatial extent of the universe. Then, an infinite universe would be the one with infinitely many positions in it. An unbounded universe would be the one that for any number D there are positions with distance between them being greater than D.

I think that the OP talks about the latter rather than the former.

 

1) So you are saying there are only countably many positions in this first universe ?

2) Surely this depends upon how you define 'distance'. How does that work in a universe where distance is defined as the length of the peano curve between two points ?

[Genady]

55 minutes ago, studiot said:

 

1) So you are saying there are only countably many positions in this first universe ?

2) Surely this depends upon how you define 'distance'. How does that work in a universe where distance is defined as the length of the peano curve between two points ?

Re 1. No, I'm not saying this.

Re 2. I take a spatial part of the spacetime metric.

[MigL]

Regardless of how Mathematicians try to spin the question of the continuum vs granular universe, the fact remains that light, and therefore information, travels at the same speed in a vacuum in either condition.
This transfer of information is what determines the 'sphere of causality', otherwise known as the observable universe.
And Physics tells us that, aside from a long, long time ago, when the whole universe had to have been in causal contact in order to acheive thermal equilibrium ( and isotropy/homogeneity ), anything currently outside our observable universe cannot have any effect on us because it is no longer in causal contact.
IOW, the extent of the universe, either finite or infinite, outside the observable is of no actual significance.

But it could make for light conversation at your next dinner party.

[Endy0816]

1 hour ago, MigL said:

Regardless of how Mathematicians try to spin the question of the continuum vs granular universe, the fact remains that light, and therefore information, travels at the same speed in a vacuum in either condition.
This transfer of information is what determines the 'sphere of causality', otherwise known as the observable universe.
And Physics tells us that, aside from a long, long time ago, when the whole universe had to have been in causal contact in order to acheive thermal equilibrium ( and isotropy/homogeneity ), anything currently outside our observable universe cannot have any effect on us because it is no longer in causal contact.
IOW, the extent of the universe, either finite or infinite, outside the observable is of no actual significance.

But it could make for light conversation at your next dinner party.

 

Could be philosophical implications if there's repeating volumes of the observable universe or lack thereof.

Would definitely have to work back to the start and then forward again though.

 

 

 

Edited July 4, 2023 by Endy0816

[Genady]

9 hours ago, Endy0816 said:

if there's repeating volumes of the observable universe

How is it possible considering that observable universe does not have a constant size but rather changes with time?

And considering that our observable universe differs from the one of a galaxy which is 10 bln ly from us.

[Endy0816]

13 hours ago, Genady said:

How is it possible considering that observable universe does not have a constant size but rather changes with time?

And considering that our observable universe differs from the one of a galaxy which is 10 bln ly from us.

It would change likewise.

Be a case of a low probability event becoming a certainty with enough attempts.

There could well be a physical law that prevents this from occuring too.

[Genady]

10 minutes ago, Endy0816 said:

It would change likewise.

Be a case of a low probability event becoming a certainty with enough attempts.

There could well be a physical law that prevents this from occuring too.

If a galaxy becomes not observable because of the universe expansion and disappears from the observable universe, where does it go?

PS. Perhaps I misunderstood the idea of "repeating volumes of the observable universe". In this case, just ignore my question.

[Endy0816]

8 hours ago, Genady said:

If a galaxy becomes not observable because of the universe expansion and disappears from the observable universe, where does it go?

PS. Perhaps I misunderstood the idea of "repeating volumes of the observable universe". In this case, just ignore my question.

Nowhere really. Light is just unable to reach us.

Imagine Universe as a jar filled with marbles, with each marble representing some observer's observable universe.

Depending on the size of the jar and number of possible marbles, one might reasonably expect to find two perfectly identical marbles.

[MigL]

1 hour ago, Endy0816 said:

one might reasonably expect to find two perfectly identical marbles.

Two identical observable universes would need to have all their constituent quantum particles in identical states.
Unfortunately, observable universes overlap.
If you live 20 km away from me, your observable universe extends 20 km further, in that same direction, than mine does.

Observable universes are not separate and distinct 'marbles'; they are a mathematical construct, based on the speed of light and expansion rate, centered on the observer.

[Genady]

2 hours ago, Endy0816 said:

Depending on the size of the jar and number of possible marbles, one might reasonably expect to find two perfectly identical marbles.

No, if there are uncountably many possibilities.

[Endy0816]

58 minutes ago, MigL said:

Two identical observable universes would need to have all their constituent quantum particles in identical states.
Unfortunately, observable universes overlap.
If you live 20 km away from me, your observable universe extends 20 km further, in that same direction, than mine does.

Observable universes are not separate and distinct 'marbles'; they are a mathematical construct, based on the speed of light and expansion rate, centered on the observer.

Only overlap to a degree. We have past light/information reaching us, but the distance has continued to grow.

27 minutes ago, Genady said:

No, if there are uncountably many possibilities.

If the Universe is also infinite?

..and no I don't know the truth of the matter is either. My gut tells me it isn't possible, but that's hardly scientific.

Edited July 5, 2023 by Endy0816

[Genady]

1 minute ago, Endy0816 said:

If Universe is also infinite?

Yes, the expectation is still 0.

[MigL]

2 hours ago, Endy0816 said:

Only overlap to a degree. We have past light/information reaching us, but the distance has continued to grow.

Your  ( and mine ) observable universe, and everything in it that can causally affect us, extend for billions of light years.
Yet in the example I posed ( you and I live 20 km apart )our observable universes differ by 20 km.

That seems to be a very LARGE degree of overlap, wouldn't you say ?

[deema78]

I'm sorry but the question is absurd. Why does there HAVE to be a reason for existence? I get it. We all want it. But i'm not sure that 'the answer' actually exists. To have an answer would mean there is a god. You would say no, of course. There is either a design or there is not. Period. Chaos or practice

[Genady]

4 minutes ago, deema78 said:

I'm sorry but the question is absurd. Why does there HAVE to be a reason for existence?

I'm sorry, but where is "a reason for existence" mentioned in the OP?