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.

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...


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