Is Infinity Real?

Dr Adequate writes:

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Think of time as being like space, and imagine viewing it sub specie aeternitatis --- a God's-eye view if you will. From that point of view, wouldn't it look even odder if it just started at some point?

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No, not really. If there were an infinite past, then processes that would reach equilibrium after an infinite amount of time (or even a sufficiently large amount of time) would have done just that. Since they haven't, then there must not be an infinite past.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

Wow...nice point. Very nice.To adhere to the alternative would imply that equilibrium NEVER happens, things are in a constant chaotic systematic unpredictability. Something like the constant shaking of an Anti-Einstein's Godly dice on every particle pair creation with all of the subsequent Heisenbergian Chaos. Disney's mouse traps and ping pong balls indeed!Yes.
Let us put away these foolish things and look forward to the inexorable heat-death of the Universe in an adult manner.

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- xongsmith, 5.7d

Perhaps you could list these processes so that we can check the veracity of your claim?

Sure, there's nothing odd about the entropic arrow of time (well, there is, but not in this context) - a slope on a hill has a direction of steepest descent defined at each point, but that still does not suggest that anything is "moving" - there is still no dynamics. The Universe is still a static four dimensional object, just with a low entropy end and a high entropy end.Penrose's latest ideas suggest an eternally expanding, repeatedly "Big Banging" Universe, where the heat-death approaching end-state actually creates the conditions for the next generation Big Bang... a bit like the old cyclical universe but without any big crunch.Rrhain's mistake is to assume that there are processes that can reach a real equilibrium - in a suitably expanding eternal universe, there are not. Think of our earlier discussion about the lack of thermal equilibrium/maximul entropy in a universe with accelerating exapansion.Edited by cavediver, : No reason given.

cavediver responds to me:

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If there were an infinite past, then processes that would reach equilibrium after an infinite amount of time (or even a sufficiently large amount of time) would have done just that. Since they haven't, then there must not be an infinite past.

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Perhaps you could list these processes so that we can check the veracity of your claim?

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The heat death of the universe, for one.Now, one might suppose that there is a way for the universe to "restart" itself, cycles of Big Bangs and such. But that would require a significant change in the Second Law regarding the nature of energy. Is it possible to have an infinitely recurring process whereby enough energy to populate the entire universe is generated? We have yet to find any perfect system anywhere else...why should the universe be an exception?At any rate, this is an interesting concept. It would mean that while the observable universe in its current state "started" at a finite point in the past, there is an unobservable universe. This, of course, raises the question: If it is unobservable, does it even exist? If we thought that string theory had a hard time due to the inability to run an experiment that tested it, how much more difficult would it be to run tests on a universe that by its very definition is incapable of being observed? The mathematics may be very beautiful (and I say that as a mathematician who does think that inifnity really exists), but unless we can find some way to demonstrate it, it will be nothing but a pretty framework with no substance.Now, I certainly like the idea. There is something personally disconcerting about a "one-shot" system on the scale of the universe. I don't have the common "logical" problem that comes up of, "If the universe is infinite, how did we get to 'now'?" To my mind, every stretch upon an infinite process is just as real as any other and we can exist anywhere along it, so why not where we are? There's nothing special about where we are, we just are.But again, until we can find some way of examining such a construct, it is nothing but a pretty picture we've painted for ourselves. Might be true, might not be.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

Ah, but we don't get heat death with a past-infinite cosmology, only with past-finite cosmologies: so for example, classic FRW open and flat space-times are past-finite (they have a Big Bang) and they have heat death; but de-Sitter, which is past-infinite, does not. The exponential expansion driven by the Cosmological Constant ensures that there is no state of thermal equilibrium, hence no heat death. The Universe simply gets colder and colder. Sure, in a spatially infinite universe. I'm not sure about "perfect system" but this is in danger of the fallacy of composition - which is relevant in this topic given the tired old argument of "there's nothing in the Universe that is infinite, therefor the Universe cannot be infinite." Exactly Which is why we are all about the evidence... Try here...Edited by cavediver, : No reason given.

I thought something very much the same (in my stumbling provisional way)several years ago when I first read about the expansion of space.I thought that once there is sufficient lack of energy and matter around the time of heat death the force of expansion would get to a critical point and there was another big bang.But my thinking was space got too thin and ripped (or something like that) so I can't really imagine it works like that: seemed to make sense to me at the time, though.ABE: I've just read some of your link and it seems to say that low variance of temperature regions from supermassive black holes in the past aeon are detectable.Does this mean information can 'cross over' the big bang point from one aeon to the next?Edited by Larni, : Crossing over aeons.Edited by Larni, : Formatting

Talk:Hilbert's paradox of the Grand Hotel - Wikipedia

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Suppose a new guest arrives and wishes to be accommodated in the hotel. Because the hotel has infinitely many rooms, we can move the guest occupying room 1 to room 2, the guest occupying room 2 to room 3 and so on, and fit the newcomer into room 1. By repeating this procedure, it is possible to make room for any finite number of new guests." This ignores a significant point; in this case, the process of switching guests to new rooms is infinite, so although the new guest is settled in room 1, the infinite hallway between the rooms always contains a person switching rooms with the next guest in the line. This means, though each room has a new occupant, the number of occupied rooms is exactly the same, for eternity. Whereas before, there was an infinite number of occupied rooms and no one in the hallway, now there is the same infinite number of occupied rooms and one person in the hallway- the hallway will never be empty,

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I agree. Infinity is a concept. Infinity is not a thing.

The idea that anything has infinite rooms is a premis. This idea is used to form a mental construct. Just because someone decides to say that there is a hotel with infinte rooms does not mean such a thing exists. The whole thing proves nothing. The point is does infinity exist. Does time exist? Are infinity or time physical things? Answer that and you will have the whole thing solved.

What if they all move at the same time?

No-one said it did.

I think john6zx was 'having a stab' at figuring out what it was granpa was trying to say.
Even the text highlighting is from the wikitalk page and not put in to highlight granpa's point.
I also question the partial quoting from that page that cut off this part:

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Besides, there is truly no such thing as an infinite number of anything, because no matter how many rooms and guests there are, that number is not infinity. You can't have an infinite number of occupied rooms, even conceptually- the concept simply doesn't allow it. The fact that mathematicians accept this so called paradox seems to make it clear that they really don't fully understand the character of infinity.

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I am having trouble seeing how granpa's response actually relates to the OP's question.
But at a push, I would agree with john6zx's interpretation [guess] of granpa's meaning.What is your understanding of how granpa's post addresses the question: "Is eternity real?"?

You could also ask "Is Reality infinite?" See cavediver for more.But then you could also ask "Is Reality real?"I got a chance to read this book, "The Illusion of Reality", which actually went into how we creatures sort of come up with ad hoc shortcuts to pave in rest of the work of sensing things. For example, you look at a piece of graph paper and, even taking in the well-known blindspot effect, even way out at the peripheral, your brain is saying "okay...i get it...its turtles all the way down from here - next?" so as to be able to move your head & process things fast enough to leap out of the way of a leopard and live to have children.It's sort of like a compression algorithm.

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- xongsmith, 5.7d

cavediver responds to me:

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but de-Sitter, which is past-infinite, does not.

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But a de Sitter universe has no matter. While it certainly seems like we are becoming a de Sitter-style universe due to the expansion of the universe and the dominance of the cosmological constant, we aren't there now.But that said, if the universe were infinitely old, why haven't we achieved de Sitter status yet? The universe is expanding...and accelerating at that. Unless we are going to suggest some process that kicks out instantons....

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Sure, in a spatially infinite universe.

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So what happened to the First Law? Everything's gotta be somewhere. If there's an infinite amount of energy to be had, where is it?

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I'm not sure about "perfect system"

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Classic Second Law. There is no perfect system. All processes bleed energy that can never be recovered. So unless there is an infinite amount of energy, this process of kick-starting universes over and over again will eventually fail.

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but this is in danger of the fallacy of composition - which is relevant in this topic given the tired old argument of "there's nothing in the Universe that is infinite, therefor the Universe cannot be infinite."

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Except I've already stated that I do think that infinity does exist.

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Which is why we are all about the evidence...

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It certainly is an interesting time to be a cosmologist.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.