Infinite Time Vs. Finite Matter and Energy Okay, so I'm hoping someone with much more physics knowledge than me can shed some light on an odd discussion that I had with my brother some years ago. I've heard similar ideas, but nothing quite like what we came up with.
I'll try to make this as understandable as possible. If there is only a finite amount of matter and energy in the universe (although a massive and mind boggling amount) but time is infinite... does that present the possibility that all things are (in an even more massively mind boggling length of time) destined to repeat exactly over and over? Like this exact moment or all of our exact lives and experiences? I'm not asking this with any spiritual or religious undertones. I'm not at all religious and don't believe in such magical, nonsense. I'm asking this from a purely physics and time basis.
The best example we could come up with is this... the lottery seems almost impossible to win because the odds are so staggering. But if the odds are one in ten billion to win, and you hold all the possible numbers (the infinity of time vs finite number of matter) it's inevitable that you will win. Correct?  So, if time is infinite (so it's holding all the numbers) is it not inevitable that eventually everything will have to repeat due to a limited amount of options? No matter how many quadrillion of quadrillion aeons need to pass for things to find themselves in the same orientations and states electrically, all options would have to be cycled through and eventually exhausted. And once that happens some repetition of some kind has to start because all the possible combinations would have existed already?
 A: The phenomenon you are referring to is Poincaré recurrence. The idea is that if a closed system has only a finite number of possible states then it must eventually return to a state that is has been in before.
However the universe is not a closed system with a finite number of states and the recurrence theorem does not apply to it. For example the average density of the universe is decreasing with time. The observable universe will never return to a state just like its state right now because its density will never again be as high as it is right now. So the answer is that no the universe will not eventually repeat.
There are a couple of complications that I suppose we ought to mention. I have assumed that the universe will expand forever, but there have been suggestions it could eventually recollapse and my even oscillate in some cyclical fashion. However the physics behind these theories is so speculative that it's hard to say anything concrete about them.
It's also suggested that if the universe is infinite there will be repetitions in space (rather than time). For example if you travel far enough you'll find another copy of yourself. Again, while these ideas are fun the physics behind them is not convincing enough for most of us to take them seriously.
