I never understood why this is implied. An infinite universe doesn’t have to be infinitely variable. The number 1.1111… is infinite, but 2 never appears.
So much for Boltzmann Brains then. Note this is a thought experiment that has always made me extremely stabby-for one thing a B. Computer would appear to be much more viable (if still ridiculously improbable), but to have ALL of the necessary component atoms of the required elements present in some gas cloud somewhere, THEN to have them somehow come together in a purely random and arbitrary way (vs. a chemical much less evolutionary way) has always seemed massively ridiculous to me. Far far more likely that the duplicate brain/processor/mind would be formed organically in a favorable environment (as in a planet) over uncountable generations (incl. the meat-heads in question eventually building artificial brains) than in some chaotic void somewhere.
But the oft quoted argument is about an infinite universe.
True, this is a bit orthoganal to questions of whether the real universe is infinite in some way.
I’m not saying a specific spot is expanding faster than light. I’m saying that the entire universe everywhere is expanding faster than light. Therefore, if there is a boundary – an admittedly huge “if” – the spacetime at the boundary is also expanding faster than light just like everywhere else in the universe is.
Oh, I just remembered a semi-related question I had for the group:
Is there any infinity we are aware of anywhere in the universe, or is the only infinity the universe itself?
Yea, just because something goes on for infinity does not guarantee everything and anything must occur. See Infinite monkey theorem.
And all you need for the argument is the fact that infinity (any infinity, no need for Cantor) is greater than any finite number.
Define “aware of”. If spacetime is Euclidean on small scales, then the number of points in a line an inch long is infinite.
Physical things, not mathematical constructs. Is the universe itself the only infinite thing in existence?
Confusion here is quite understandable: after all, intuitively, what could be bigger than infinity?
The idea of qualitatively different types of infinity was indeed very controversial when Cantor first proposed it, though it is an accepted part of pure math nowadays.
A simple example is a proof that there are infinitely more real numbers than integers, even though the integers can keep on counting for ever. Look up Cantor’s diagonal argument in Wikipedia or other sources.
Depends what you mean by existence. Does a mathematical idea ‘exist’?
I do not think the universe works like that. We have 118 elements in the universe.
We see a finite number of each element in the observable universe. Combined, there are thought to be 10^80 atoms in the universe. Each atom is discrete. None are 1.1111…
Even if we assume any atom is as likely to connect with any other atom (which they don’t) there is a finite number of arrangements of those 10^80 atoms. After that things will start to repeat. If we have infinite time the repeats have to happen.
Or, if infinite space, there are infinite “you” out there because those 118 elements in the 10^80 atoms can only be put together so many ways and in an infinite sequence it is likely the “you” sequence repeats.
ETA: For any sci-fi writers here it might be a neat hook to make your hero a person who the universe only spins out once. That particular hero sequence will never, ever repeat. They are “special” somehow. How that matters is for you, the writer, to figure out.
I don’t think this does necessarily follow. It’s like if I roll a fair die an infinite number of times, I might expect to roll a 6 (indeed roll a 6 infinite times). However, there are infinite infinite sets with no sixes at all, e.g. { 1, 1, 1, 1, … } or { 1, 2, 1, 2, …}. Of course the probability of any of these sets appearing is zero, but the probability of any infinite set is zero. So we have to use language like “almost-certainly”.
And in terms of Poincare, it might be that the universe just “winds down” in finite time and nothing happens after that. It’s not my view, mind; I think that since entropy is probabilistic a “wound-down” universe will spontaneously become low-entropy in finite time, I’m just saying we don’t know that the universe will continue to evolve infinitely.
I have sometimes wondered whether the real number system is actually the right type of mathematics to describe the physical world.
L. E. J. Brouwer had some thoughts about this.
We’re getting into the philosophy of the foundation of mathematics here, though… Platonism and all that…
In a way Arthur Clarke did this with Alvin in ‘The City and the Stars’.
I happen to have recently watched a veritasium video about Cantor’s diagonal argument a couple weeks ago that I thought explained it in a straightforward way. (Cued up to 4:29; jump there if it doesn’t take you.)
But if there were such a boundary in the world, then it wouldn’t be the case that it recedes faster than c from every point in the universe—the fact that there are points relative to every point in the universe that recede faster than c (the Hubble sphere) depends on spacetime (if flat) being infinite.
Various infinities crop up in quantum field theory. Most of those, we’re pretty sure are just due to the fact that such theories are only effective—i.e. not expected to be valid all the way to arbitrary high energies/short length scales. But technically, every quantum field has infinitely many degrees of freedom (but really, that’s just related to the fact that there are infinitely many points of spacetime in an arbitrarily small interval). A subtle case is the existence of randomness: no computer, performing a finite number of operations, can produce truly random numbers; but with an infinite number of steps, that becomes possible. So if you believe there is true randomness in physics—again, something our best current models tell us is the case—then there is something at least equivalent to such infinite machinery at work.
I do believe in true randomness, actually, which is another departure from the reddit consensus. Interestingly, it appears that quantum computers have recently managed to generate true random numbers. From last March:
Is there an infinity involved in this machine? That’s not an attempted gotcha; I genuinely do not know.
My larger question about whether or not there are any infinities in nature is about concrete things. Is there anything that generates infinite heat, or has infinite mass, or is infinitely dense (a singularity?), etc… Stuff like that. The universe being infinite (if flat) is all of a sudden a macroscopic classical object with infinite spatial dimensions. I’m just wondering if an infinite universe stands alone as the only infinite classical macroscopic thing that exists. That wouldn’t necessarily be a deal-breaker for me, but I would consider it to be a curiosity.
I think the explanation I’m looking for is probably here, but I can’t quite wrap my head around “the Hubble sphere depends on spacetime (if flat) being infinite.” This seems like of restating of the premise that if the universe is flat it must be infinite. There’s a leap in logic going on that I do not understand.
As an aside, like many Wikipedia pages on physics, it’s a little too dry for me to be able to properly follow. And then one of the external links led me to this, which I’m having even more trouble with:
“Equivalent to” would need to do a lot of work here.
We have no reason to believe everything the universe is doing is the result of a computation and therefore no reason to believe there are a non-finite number of steps (or indeed any steps) behind random data.
Exactly. This is a metaphor that I think has arisen from recent developments in our technology.
There is a saying: if your only tool is a hammer, everything starts to look like a nail.
Likewise, if your habitual tool is a computer, everything starts to look like an algorithm?
I think the “problem” (so to speak) in our understanding and perception is that if true randomness underlies quantum effects and underpins all of physics and our reality then why do we see order? Where does the “flip” or change happen from random to the order we all experience?
ETA: I suspect a solid answer to this would get that person a Nobel Prize.