If the Big Bang actually happened, just prior to the bang would have been lowest state of entropy ever, as the entire universe existed in one single configuration.
They mean there was only one possible configuration of matter, like a die that could only ever roll to "1".
I like to think of entropy as "the universe prefers to have the greatest degrees of freedom available to it and there is a cost to reducing degrees of freedom". For example, to make a perfect crystal you have to cool to absolute zero (and even then there can be residual entropy!). Effectively, entropy = the logarithm of the number of ways a thing can be ordered.
If a thing can only be ordered in one way, then its entropy is minimized.
Well, there isn’t matter at that time — and your analogy to dice is exactly my point.
That instant could roll to anything from its current position (and according to many worlds, did) — the phase space of that object is huge, far beyond anything we normally see. That single object has all the complexity of every possible universe stacked into an infinitesimal region!
We’re in a colder universe than it was at that compacted moment, which I’m having trouble aligning with your explanation about crystals: we’re seeing the cooling towards absolute zero as a superheated droplet spreads out and freezes.
Defects forming in the crystallization of iron doesn’t imply the cold, defect laden iron has more entropy than the liquid drop it cooled from.
The classical way to think about entropy is a relationship between scales. There are a lot of ways for matter and energy to arrange as a “cloud of smoke.” There far fewer ways for matter and energy to arrange as you. You have lower entropy than a cloud of smoke.
Just before the Big Bang (again, if it occurred), there would have been a perfect 1:1 relationship. There was only one possible way to be, and everything was that way. Zero entropy.
It is basically a definition, not empirical. Entropy only increases; the universe has a definite and specific history; therefore the beginning of things must have been only possible exactly one way, the lowest-entropy way.
If this sounds weird and non-scientific, it is! Scientists don’t know if the Big Bang occurred. We have basically no evidence to support any theory of what things were like before inflation.
> At least, in the context of this universe. But that is the entire and only context available to us.
But we know things take “multiple paths” — why does that not apply to the original singularity diverging into multiple universes?
> Whereas all sorts of different clouds of smoke exist, some probably even right this second just here on Earth.
But only a particular cloud exists — the one that comes out of your fire. You go from one log as it exists to one cloud as it exists… one state to one state.
We normally explain that as “there’s more potential ways to be a cloud than potential ways to be a log”, but that brings us back to my question…
Why do the potential other smoke clouds count as entropy in the case of smoke clouds but not potential other universes in the case of universes?
The universe has a collective state now, so I’m not seeing how scaling changes that.