I’m not referring to counter factual worlds from science fiction movies or even the many worlds hypothesis of Hugh Everett (although that is the most plausible resolution of the quantum measurement problem we have). What I’m talking about is the possibility of an uncountable number of overlapping macroscopic existences on top of a single microscopic substrate.
As I discussed previously, from any given set, finite or infinite, we can always construct a set with more elements. For example, if I have a list of objects, I can always take combinations of objects and combinations of combinations and so forth to make as many meta-objects as I like. This is how we can infer the existence of real numbers just starting from the integers and as I’ll argue, how we can have multiple universes overlapping on the same substrate.
Consider the entire time history of a universe, or a simulated universe if you would prefer something concrete. That universe can always be discretized into a set of bits, either finite or countably infinite. Hence, a representation of a universe is a string of bits. Now, let’s say we have macroscopic objects in this universe, such as galaxies, stars, planets, rocks and perhaps even life forms (however you want to define them). These macroscopic objects will be described by some subset of bits, either finite or infinite. The world we know and love, which consists of people and pets and dreams and everything else, can be coded in terms of bits. However, there are many, many possible combinations of bits that we don’t consider, either because we can’t experience them or simply don’t care about them. And, these other combinations of bits could be the foundations of completely self-contained worlds. In other words, running in direct parallel on the same bit stuff as us, could be countless numbers of other universes.
Let’s be even more concrete. Suppose, we take a universal Turing machine. Then we know that by simply taking all possible input bit strings, we can generate every possible computation. We thus have an algorithm to generate every possible computable universe. However, the computations are not unique in two ways. One is that two inputs could possibly generate the same output, and the other is that a single universe could be discretized in multiple ways. Although we could generate all universes, there does not exist an algorithm to tell us what kind of universe we have. We don’t even know at what scale we should look at to see if any interesting structure arises. It could be at the scale of 10 bits, a billion bits, or bits. There is also no reason that there could not be interesting structure or even “universes” at multiple scales or even overlapping universes at the same scale. In fact there could be an infinite number of emergent parallel universes arising from the same simulation. Just like in a picture where there is figure and ground, there could be a universe in the figure world and a separate, although correlated one, in the background world. So at this very moment, there could be multiple other universes with their own histories and own laws of physics sharing the same bits as you.