However, flat/negative curvature plus the size of the universe being infinite and the cosmological principle, which basically states that the universe lacks a preferred direction and location would imply the conclusion, as it would mean our collection of atoms isn’t special at all, and this goes for any finite portion of the universe.
As a basic counterexample, just consider a fully empty infinite universe. It is in equilibrium (and does not violate any known laws of physics), it has an infinite size, and it adheres to the cosmological principle (because every single region is just as empty as any other region). And yet, it quite obviously does not contain every possible configuration of atoms that the laws of physics would allow...[1]
Or a universe that just has copies of the same non-empty local structure, repeated in an evenly-spaced grid. From the perspective of any of the local structures, the universe looks the same in every direction. But the collection of possible states is confined to be finite by the repeated tiling pattern.
As a basic counterexample, just consider a fully empty infinite universe. It is in equilibrium (and does not violate any known laws of physics)
Your premise violates quantum mechanic, actually. Such an universe’s amplitude distribution is delta function (fully empty with probability 1, any other state with probability 0), which does not have second derivative so its future evolution is undefined.
Actually, collections of atoms (let’s call them structures) can be special.
For instance, there are structures which tend to produce copies of themselves; with some changes (one sign flip), one can obtain structure which tends to destroy its instances. They have approximately same complexity so their rate of randomly arising is equal; however, over time count of former structures increases while count of latter decreases. So we shouldn’t expect all atom collections to appear with equal probability even in full universe.
However, flat/negative curvature plus the size of the universe being infinite and the cosmological principle, which basically states that the universe lacks a preferred direction and location would imply the conclusion, as it would mean our collection of atoms isn’t special at all, and this goes for any finite portion of the universe.
No, I don’t think that alone would do it, either.
As a basic counterexample, just consider a fully empty infinite universe. It is in equilibrium (and does not violate any known laws of physics), it has an infinite size, and it adheres to the cosmological principle (because every single region is just as empty as any other region). And yet, it quite obviously does not contain every possible configuration of atoms that the laws of physics would allow...[1]
Or a universe that just has copies of the same non-empty local structure, repeated in an evenly-spaced grid. From the perspective of any of the local structures, the universe looks the same in every direction. But the collection of possible states is confined to be finite by the repeated tiling pattern.
Unless we use a definition of “possible” that just collapses into tautology due to macro-scale determinism...
Your premise violates quantum mechanic, actually. Such an universe’s amplitude distribution is delta function (fully empty with probability 1, any other state with probability 0), which does not have second derivative so its future evolution is undefined.
Ah, oops.
Actually, collections of atoms (let’s call them structures) can be special.
For instance, there are structures which tend to produce copies of themselves; with some changes (one sign flip), one can obtain structure which tends to destroy its instances. They have approximately same complexity so their rate of randomly arising is equal; however, over time count of former structures increases while count of latter decreases. So we shouldn’t expect all atom collections to appear with equal probability even in full universe.