Re: Cardinality of the MW

From: <hal.domain.name.hidden>
Date: Mon, 12 Jul 1999 11:44:26 -0700

Christopher Maloney, <dude.domain.name.hidden>, writes:
> Does anyone know what the cardinality of the branches in
> the traditional MWI is? By traditional, I mean that from
> the Schrodinger's Equation. It seems plausible to me
> that it's 2^c, by an intuitive reasoning similar to the
> above. I think it depends on whether the universe is
> finite or infinite in the number of particles it holds.

This does sound correct for the traditional MWI, but I think most
researchers today would expect it to be less.

In the original Schrodinger Equation, you can measure a particle's
position and find it to be a real number x. As a real number this has
cardinality c. However in more modern theories taking into account
gravity, there is an expectation that distance is quantized at around
the Planck length, where the structure of spacetime breaks down into a
churning froth of energy. In that case we would be able to measure only
a finite number of positions, and likewise for other quantum measurements.

This would mean that the cardinality of the branches of the MWI universe
would be c.

We also get this result in the everything model where Turing machine
programs generate all possible universes. The number of possible TM
programs is c (if we allow them to be of unlimited length).

On the whole I think c is the most likely candidate for the number of
possible universes.

Note that there is some dispute in the mathematical world over how big
c is. Some suggest that it is a rather small infinite cardinal, possibly
aleph-one, meaning the second smallest one (just above aleph-zero,
which is the cardinality of the integers). Others suggest that it may
be larger, possibly much larger, bigger than aleph-(aleph-zero).

Hal
Received on Mon Jul 12 1999 - 11:49:50 PDT