A few random thoughts:

Not only can't you erase information, in the MWI I believe you can't
create it either.  The constancy of information is another way of
expressing the QM principle of unitarity.

I think it's also tied to time symmetry.  Universes with time symmetry
would be unable to create or destroy information.  The MWI is time
symmetric (that is, the Schrodinger equation is time symmetric).

Wolfram investigated a variety of CA systems, some of which happened to
be time symmetric.  Generally I think those were more likely to create
very regular patterns, while it was the time-asymmetric ones that were
more likely to be chaotic and show interesting patterns.

One advantage of being unable to destroy information is that it
automatically makes learning and memory possible.  These capabilities are
probably necessary for the evolution of intelligence.  It's not clear
though that complete inability to destroy information is necessary for
memory to work though.

Perhaps if we favor simple universes, there is basically a choice between
complete information preservation vs universes where it is not preserved
well at all once you move above the Planck scale (e.g. information might
be 0.999% preserved per Planck time step, which is not at all for our

The idea of a universe where there are a few obscure loopholes that break
the laws of physics is possible in this model, but somewhat unlikely.
And there is no guarantee that the loopholes would be easy to find.

Hal Finney

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