A weak notion of the idea that all universes exist is the many worlds interpretation of quantum mechanics. This is basically regular QM minus wave function collapse. Everett showed that, if you look at it right, a universe which does not have wave function collapse could actually be said to look to its inhabitants as though it did have collapse.

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This has the advantage that the universe becomes deterministic, and there is no new information or randomness which must appear as the universe evolves. Wei Dai proposed measuring the complexity of a universe model by the size of the program it would take to run the universe. My feeling is that this should also count the size of the initial conditions, and the size of any randomness which must be generated during the course of the run. (I find it disturbing to imagine an algorithmic pseudo-random number generator being used to generate what appears as true randomness in the universe.) With this kind of measure, a QM universe minus wave function collapse will require a much smaller program than one which incorporates collapse, since the latter will require randomness to determine how each collapse occurs. Recent astronomical measurements suggest that the universe will expand forever. In simple Friedmann models this corresponds to a universe which is open and infinite in spatial extent. There are some parallels between an open universe with wave function collapse and one without. If the universe does have wave function collapse (i.e. many worlds is not true) you could still find spatially distant regions of the universe which were arbitrarily close to identical. There would be an infinite number of copies of each such region. You could then identify all such identical regions as one entity, and as this entity evolves it will split into sub-parts where different events occur. This is very similar to what happens within the MW model. What I'm not sure about then is whether the infinite universe with wave function collapse can also be simulated with a small program, like a universe without collapse. Can you avoid the need for randomness by some trick where you don't try to specify the universe as a literal 4-dimensional manifold, but use some other level of description? Just as, when we're simulating the MW universe we don't try to identify the individual universes (there is ambiguity about how to split them), perhaps we can avoid specifying where everything happens in the infinite universe. This needs more thought... Hal