With infinite time will order spontaneously emerge from heat death?
Was Epicurus right?
While the theorem itself is well proven, I can't find a physicist who can say one way or another whether this applies to our universe.
https://physics.stackexchange.com/questions/200722/poincaré-...
(Obviously IANAPhysicist.)
I don't understand all the properties a system must have so the Poincaré recurrence theorem applies, but as long as we don't know whether the (entire) universe is finite, that's sufficient to show that Poincaré recurrence may be impossible. In that situation, we can either find information that makes it impossible for sure, or otherwise we know that we don't know.
‘Nothing else can affect us‘ doesn't contradict that, because ‘us‘ would cease to exist at the Poincaré recurrence time (if not earlier).
N.B. I'm just pointing out some basic things, while having no clue how much merit the idea has in the first place, even if the universe has finite state space and infinite time. (I mean just the idea of trying to apply the Poincaré recurrence theorem to the whole universe, not Penrose's work.) AFAICT the proof only says that almost every state recurs infinitely often. So if you picked some state at random as your starting state, it's essentially guaranteed that it will recur, but when it comes to applying this to the universe, isn't it presumptuous to regard the big bang as such a state?
Feynman put it way better than me though. It was in the Messenger Lectures series if you’re curious. 6 wonderful and accessible videos; his audience was primarily laypeople, not scientists. Quite enjoyable.
Basically when all particles are moving at speed of light, time becomes meaningless and you can consider space to be infinitely small. I.e. identical conditions to Big Bang
The theory is more that with "infinite" expansion, the universe becomes so spread out as to in spot become emptier than the vacuum energy, and a new universe spontaneously erupts in that low energy locale. In a very small nutshell.
The relevant part is at the end. Essentially, given enough time, quantum effects will result in an entire new universe spontaneously popping into existence. That time is ~10^(10^(10^56)).[0]
But, the number of ways that all particles in the universe can be arranged is only ~10^(10^115). That number is much smaller than the time to just go 'pop, new universe'. So, the much larger number also becomes about the time it takes to just have a new universe identical to our current one just go 'pop, new universe'.
The other entries in that article are just as joyously mind-bending. I really really love that page!
https://en.wikipedia.org/wiki/Timeline_of_the_far_future
[0] Side note: The time for a 'Boltzmann Brain' (a consciousness that just floats in the infinite void thinking away, somehow) to spontaneously appear is only ~10^(10^50).
EDIT: Changed Fat to Far
Also, I forgot to mention that all these timelines are in years.
But then I thought about it and about any human unit of time really doesn't change the numbers much at all. Heck, even measured as units of 'age-of-the-current-universe', the extra 0s just fade into the rounding errors very quickly.
To be clear here, that is stating that however you measure time pretty much has no meaning at these scales.
As the Wikipedia page[0] puts it:
> Although listed in years for convenience, the numbers beyond this point are so vast that their digits would remain unchanged regardless of which conventional units they were listed in, be they nanoseconds or star lifespans.
0: https://en.wikipedia.org/wiki/Timeline_of_the_far_future#cit...
The answer may be yes or no in any particular axiomatization (model) of the physical laws, but depends strongly on the choice of model. Unlike a normal situation, when we talk about very-low-probability effects we are subject to any influence of "quantum gravity" and other "new/unknown physics" that may have a finger, however light, on the scale.
In the Standard Model I think the answer is yes, but we are already aware of some deficiencies (neutrino transitions).
Does this hold true for a 1/infinity chance event?
Or (not sure if this is analogous) if you choose infinitely many real numbers ~ unif(0, 1), is it guaranteed you will hit every number in that interval at least once? I'm not even sure the question is well-defined to be honest (at least not without making assumptions about infinities that we have no way to show hold true for this universe), but if it is, is the answer yes? It's not obvious to me.
For illustration, you are almost guaranteed to not win the lottery, but when you play again and again, then after something like 14 million times playing (for the German Lotto) you will win, and again after something like 28 million times playing, and so on, so you expect to often over long enough timescales, and you can start to impose additional constrains, for example winning with consecutive numbers, or the first few primes. And after a long enough timescale you start to win again with these additional constrains.
https://www.amazon.com/dp/0593171721/ref=cm_sw_r_sms_awdb_bt...
For example a complete brain capable of imagining it’s in a universe could spontaneously occur... (Boltzmann brain) but the catch is that there needs to be enough usable energy for it to function. So even if order suddenly occurs, heat death means an eventual limit to complexity.
Ultimately something needs to happen to cause a sudden reverse into very low entropy, ie another Big Bang or something of the like.
We’re talking like 10^50 years here before heat death ends thought so... the universe has some time still.
When someone comments on the craziness of theories about before the big bang (and therefore the cause to which it was an effect), it is always worth remembering that the big bang itself was considered crazy by many initially.
The name even came from a dismissive description (with massive vocal air-quotes around "big bang") that just stuck as it is actually a good description (at least by dint of being catchy).
Crazy does not necessarily mean something is incorrect.
We call them crazy to keep our selves from going off the deep end and talking about ufos, the foundations of mathematics or the genetic differences between races.
That said, as far as I know it falls into the body of theories that struggle to make falsifiable predictions, and of the limited such predictions it has made nobody has found data that validates them in a statistically significant way yet.