This following is pure/idle/random speculation, and rather old from my personal point of view.
Many years ago ran across the "grandfather paradox" in science fiction. The stories always seemed to revolve around an effectively immutable past. At the time, this struck me as wrong - given time-travel (a rather big given) the past cannot be immutable. At the same time I expected each individual's memory of their own personal past to remain unchanged. Starting from the (apparent) paradox, this lead to a sort of thought-experiment.
Assume an infinite universe. In an infinite universe, all combinations of atom, molecules, planets, galaxies ... must occur. Nature seems to tend to elegance, so identical combinations should (perhaps) exist once, and this continuum of combinations must be somehow adjacent, along a dimension of sorts. Identical combinations collapse to a singular instance - something like a standing wave. This means every possible world exists in a continuum along some dimension. Every possible past and every possible future exist in this continuum. Many possible pasts (an infinite number - or nearly so) could lead to a single future. A single past could - based on a single quantum fluctuation - could lead to more than one future (though in most cases not).
Assuming this model, the "grandfather paradox" cannot exist. By traveling into and changing the past puts you onto a one of the infinite different paths to the future. You cannot change the past from which you came, but you can change another (though "change" is the wrong word).
Well fine - this was an entertaining bit of speculation derived from reading science fiction as a teenager in the 1970's. Did not expect this to have any measurable impact on "reality". Did not expect this to be in any way measurable.
But what if it was measurable? What could we measure if this were in any way an accurate model?
Before I thought the model was absurdly unmeasurable - after all we could have two world-paths differing only by the single random quantum fluctuation of a single atom - the combinations might in some sense finite, but still for all practical purpose infinite. Many pasts might collapse to a single future, and random quantum fluctuation light-years away will almost never impact the combined weave of probabilities that make up any one present. Assuming the tendency to elegance in the universe - perhaps our present in the sum of many (a nearly infinite number) of pasts that computed to the same present.
What if this were measurable?
As we look further out into the universe, we are looking out to regions that have no impact on our present or future. Might we expect to see all possible pasts - the further out we look - that compute to our single (as we perceive) future? Would the universe look "fuzzy" the further we look? Would we see all possible pasts? Could we measure when parts of our present came from a differing pasts?
Could this collapse of combinations reach into the macroscopic levels? Could you and I remember the past differently, as we are from different threads of experience through the weave of possibilities? As long as our differing memory has no effect on the future, could these threads of experience cross between differing "realities"?
Oddly enough, starting with the premise of an infinite universe, and adding the apparent elegance of nature, you end up with a weave of near-infinite (though finite) set of possible pasts leading to a near-infinite (though finite) set of futures. Is it possible this is measurable, as we peer further out into the universe?