Is it ever physically possible for a broken egg to reassemble into an unbroken one?

[Jehanne]

There's no actual physical law against it but if we assume purely random interactions of the component egg fragments and their environment then the odds of this ever happening are so small as to be effectively impossible.

That said, purely random interactions of the components isn't a reasonable assumption and a proper examination of the probability space shows that the number of philosophers, physicists, and general contrarians involved in causality research virtually guarantees the unbreaking of an egg if it hasn't already happened.

And if the probability is 1 in a googolplex, we don't *expect* to see actual examples in the current age of the universe (very far from it). But the probability is still non-zero.

If every fundamental particle in the universe was doing addition every Plank's time, the total computed since the Big Bang would be less than 10^135. This is *far, far, far* less than a googolplex.

I'll go further. If every fundamental particle added a total of a googol every Plank time, the total since the Big Bang would still be smaller than 10^235, which is still far, far, far less than a googolplex.

What do you think of ultimate reality being akin to Cantor's infinities within infinities, perhaps, our time and space being countably infinite sets within a infinitude of other countably infinite sets, across both time and space?