If you take a single branch and run it backward, you'll find that it diverges into a multiverse of its own. If you take all the branches and run them backward, their branches will cohere instead of decohering, cancel out in most places, and miraculously produce only the larger, more coherent blobs of amplitude they started from. Sort of like watching an egg unscramble itself.

And at the beginning of the universe we have a set of states which just point time-backwards at each other, which is why we cannot go meaningfully more backwards in time.

Something like:
A1 goes with probability 1% to B1, 1% to C1, and 98% to A2.
B1 goes with probability 1% to A1, 1% to C1, and 98% to B2.
C1 goes with probability 1% to A1, 1% to B1, and 98% to C2.

So if you ask about the past of A2, you get A1, which is the part that makes intuitive sense for us. But trying to go deeper in the past just gives us that the past of A1 is B1 or C1, and the past of B1 is A1 or C1, etc. Except that the change does not clearly happen in one moment (A2 has a rather well-defined past, A1 does not), but more gradually.

In the Game of Life, a single live cell with no neighbours will become a dead cell in the next step. Therefore, any possible present state that has at least one past state has an infinite number of one-step-back states (which differ from the one state merely in having one or more neighbourless cells at random locations, far enough from anything else to have no effect).

Some of these one-step-back states may end up having evolved from simpler starting tilesets than the one with no vanishing cells.

But does it really matter? If both states are possible, why not just say "my past contains ambiguity?"

With quantum mechanics, even though the "future" itself (as a unified wavefunction) evolves forward as a whole, the bit-that-makes-up-this-pseudofactor-of-me has multiple possible outcomes. We live with future ambiguity just fine, and quantum mechanics forces us to say "both experienced futures must be dealt with probabilistically". Even though the mechanism is different, what's wrong with treating the "past" as containing the same level of branching as the future?

EDIT: From a purely global, causal perspective, I understand the desire to be able to say, "both X and Y can directly cause Z, but in point of fact, this time it was Y." But you're inside, so you don't get to operate as a thing that can distinguish between X and Y, and this isn't necessarily an "orbital teapot" level of implausibility. If configuration Y is 10^4 more likely as a 'starting' configuration than configuration X according to your understanding of how starting configurations are chosen, then sure - go ahead and assert that it was (or may-as-well-have-been) configuration Y that was your "actual" past - but if the configuration probabilities are more like 70%/30%, or if your confidence that you understand how starting configurations are chosen is low enough, then it may be better to just swallow the ambiguity.

EDIT2: Coming from a completely different angle, why assert that one or the other "happened", rather than looking at it as a kind of path-integral? It's a celular automaton, instead of a quantum wave-function, which means that you're summing discrete paths instead of integrating infinitesimals, but it seems (at first glance) that the reasoning is equally applicable.

no, actually, I take that back, you might be able to get there via simplicity. I.e. if there's only one past that would have evolved from a simply-tiled start state for the automaton.

The simplest start state might actually be a program that simulates the evolution of every possible starting state in parallel. If time and space are unbounded and an entity is more complex than the shortest such program then it is more likely that the entity is the result of the program and not the result of evolving from another random state.

(Which is why I specified a different set of laws of physics.)

In that particular case, "never happened" has some weird ontological baggage. If a simulated consciousness is still conscious, then isn't its simulated past still a past?

Perhaps "didn't happen" in the sense that its future reality will not conform to its memory-informed expectations, but it seems like, if those memories form a coherent 'past', then in a simulationist sense that past did happen, even if it wasn't simulated with perfect fidelity.

Assuming that "you" are a point in consciousness phase-space, and not a "smear". If "you-ness" is a locus of similar-but-slightly-different potential states, then "mostly right" is going to be good enough.

And, given that every morning when you wake up, you're different-but-still-you, I'd say that there's strong evidence that "you-ness" is a locus of similar-but-slightly-different potential states, rather than a singular point.

This means, incidentally, that it may be possible to resurrect people without a physical copy of their brains at all, if enough people who remember them well enough when the technology becomes available.

Of course, since it's a smear, the question becomes "where do you want to draw the line between Bob and not-Bob?" - since whatever you create will believe it's Bob, and will act the way everyone alive remembers that Bob acted, and the "original" isn't around to argue (assuming you believe in concepts like "original" to begin with, but if you do, you have some weirder paradoxes to deal with).

Which is why it's better for there to be more people signed up, but not actually being frozen yet. The more money they get while the later you get frozen, the better the odds. If immortality is something you want, this still seems like the best gamble.