You have a credit account for each person in the company.
If you have credit with your boss, and unknown to your boss’ boss, everything’s fine.
If you have credit with your boss’ boss, but your boss doesn’t, something’s not fine.
There's a theorem "Poincaré recurrence theorem" which says if a system is finite, given infinite time, it will return to a state arbitrarily close to its initial state.
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.
My apologies, but I believe that this theorem applies to a subset of possible systems with certain properties which are called "conservative systems," not any arbitrary system.
The objection hasn't been made in your SE question, so I assume I am missing something, but why does 'if a system is finite' apply to the universe? The 'given infinite time' would need to be a 'faster' infinite than universal expansion?
The food on your plate is finite, but if you're served more faster (no slower) than you eat it, then you won't empty the plate even given infinite time.
The observable universe would have to be a conservative system for Poincaré recurrence to apply to it. I don't think that's possible; isn't it leaking matter that looks like it won't come back?
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?
Assume that the volume of the visible universe grows, and then consider a ball that just circles on larger and larger circles. Clearly, the ball does not need to get back arbitrarily close to where it started.
