Thanks, that explains why I had no idea what you meant by deterministic. It’s not a meaning for the term that I would have guessed. I obviously wasn’t assuming that the universe is deterministic in that sense.
It does open up more questions, and so is interesting. Let us use the function notation D2(x) to refer to the deterministically single allowed timeline of semiverse 2 given that semiverse 1 has timeline x, and similarly for D1. Such a universe is only possible if D1 and D2 satisfy certain conditions, in particular that there exists at least one pair (x,y) such that D2(x) = y and D1(y) = x.
We can eliminate the case where D1 or D2 are constant, since those correspond to causally isolated or one-way semiverses and are therefore boring.
For almost all other function pairs, almost all timelines x in one semiverse have no corresponding timeline y since in general D1(D2(x)) != x. This places drastic limitations either on what single semiverse timelines are allowed in ways that are utterly foreign to conventional causality or even continuity, or on what sorts of functions D1 and D2 are allowed. Almost all ordinary deterministic laws of physics will fail this condition.
So for this notion of determinism to be sustained, we have to consider universes in which even within a single semiverse with no flipping, the laws of physics are utterly different from our own.
That’s a good way of framing it! There’s some discussion in acedemia on this topic under Novikov self-consistency principle (not quite the same, since it’s only in one universe, but pretty similiar, and I wouldn’t be surprised if results carry over).
Note that I do actually break this rule in my protocol which involves flipping a coin to decide whether to build a relationship. However this can be fixed by flipping an “equilibrium coin”. Effectively this is a device which has exactly two self consistent equilibria. For example you might have a device where either an item wont be switched at all, or it will be switched at exactly the right time to cause itself to switch in the first place. Flipping counts as heads, not flipping as tails.
Thanks, that explains why I had no idea what you meant by deterministic. It’s not a meaning for the term that I would have guessed. I obviously wasn’t assuming that the universe is deterministic in that sense.
It does open up more questions, and so is interesting. Let us use the function notation D2(x) to refer to the deterministically single allowed timeline of semiverse 2 given that semiverse 1 has timeline x, and similarly for D1. Such a universe is only possible if D1 and D2 satisfy certain conditions, in particular that there exists at least one pair (x,y) such that D2(x) = y and D1(y) = x.
We can eliminate the case where D1 or D2 are constant, since those correspond to causally isolated or one-way semiverses and are therefore boring.
For almost all other function pairs, almost all timelines x in one semiverse have no corresponding timeline y since in general D1(D2(x)) != x. This places drastic limitations either on what single semiverse timelines are allowed in ways that are utterly foreign to conventional causality or even continuity, or on what sorts of functions D1 and D2 are allowed. Almost all ordinary deterministic laws of physics will fail this condition.
So for this notion of determinism to be sustained, we have to consider universes in which even within a single semiverse with no flipping, the laws of physics are utterly different from our own.
That’s a good way of framing it! There’s some discussion in acedemia on this topic under Novikov self-consistency principle (not quite the same, since it’s only in one universe, but pretty similiar, and I wouldn’t be surprised if results carry over).
Note that I do actually break this rule in my protocol which involves flipping a coin to decide whether to build a relationship. However this can be fixed by flipping an “equilibrium coin”. Effectively this is a device which has exactly two self consistent equilibria. For example you might have a device where either an item wont be switched at all, or it will be switched at exactly the right time to cause itself to switch in the first place. Flipping counts as heads, not flipping as tails.