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Say the universe its infinite. How does that infinity compare to the infinity of microstates available to an arbitrary volume? Lets say it's a larger ordering, though I invite any experienced theorists to weigh in. Then might we encounter at least an infinity of microstates for any given finite volume?

But what of the microstates of the externality of the volumes in question, it is of a larger infinity. So couldn't we conclude that every pair of internal microstate, and volumetric complement actually exists.

Imagine that. Douglas Adams' conception of the whale popping into existence above the surface of a planet must be reality. But do we really admit that such discontinuities exist in time as well as space? Can any finite macrostate be followed by any other?

closed as off-topic by Conifold, Jishin Noben, Frank Hubeny, Mark Andrews, Eliran Mar 14 at 5:31

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  • One might want to think of "infinity" as being unbounded in a certain sense. Perhaps unbounded in size or in the number of objects in a volume of fixed size. – Frank Hubeny Mar 13 at 1:18
  • This seems like a question about statistical physics but with details missing. Universe is infinite in what sense? An infinite universe can be empty and have no microstates whatsoever. What sorts of microstates are considered? What does "larger ordering" or "larger infinity" mean? How does one get from this to a whale "popping up"? Physics SE seems like a better place to ask, perhaps they can also fill in the details. – Conifold Mar 13 at 6:50
  • Are you asking if countable and uncountable infinity are the same thing? I'd love to know that. Because if they are, free will almost certainly doesn't exist. Because the infinity between seconds demonstrably exists, therefore the infinity between now and the future exists. That is, if all infinity is equal, and there is infinity between seconds the the future must already exist. – Richard Mar 13 at 21:36
  • I've heard that an infinite universe violates some foundation of thermal dynamics and is typically used to form the modern traditional View that the universe is finite. I don't know the details of it, or take a stance one way or the other myself, just think it might be related? – marshal craft Mar 14 at 10:40
  • You are misunderstanding the point of thermodynamics. Of course you can find an infinite configuration approaches for a specific system. But the point is to select one and assess the behavior of the system within such requisite. For example, you can calculate the entropy of a set of dices related to the sum of the individual values. But you can do it also with the multiplication. Or sum square. Or square sum. Etc. Just choose one and work within such approach. – RodolfoAP Mar 16 at 17:47