Juergen Schmidhuber writes:
> I welcome feedback on a little web page on Zuse's 1967 thesis
> (which states that the universe is being computed on a cellular automaton):
>
> http://www.idsia.ch/~juergen/digitalphysics.html

That's very interesting; I was not aware of Zuse.  Unfortunately I
don't know German so I can't read his paper.

Regarding the question of the compatibility of CA models with relativity
and QM, Wolfram looks into this in some detail.  He essentially abandons
a simple CA model in favor of a more complex network of interacting
nodes, which has some features similar to the Lorentz transformation of
relativity.  Then to address the EPR style long-distance correlations of
QM, he proposes that while the network is mostly local, it has occasional
nodes which get stretched apart and are connected to distant nodes.
These are rare but allow for the type of information flow necessary to
reproduce long-distance QM correlations.  All in all it is a pretty ad
hoc and unconvincing model.

I tried to read the t'Hooft paper referenced here but it was over my
head.  It also struck me though as not really addressing the discrepancy
between long-distance correlations and local CA models.  It seems very
much an open and difficult question to me to show how a local CA model
can reproduce relativity and QM.

One issue which CA models tend to ignore is the MWI.  Most CA models
are built as hidden variable theories which define a single universe.
Some multiverse models have that structure as well.  But it seems to me
that this is an entirely unnecessary restriction.  If a CA can model
a universe, it can model a multiverse, and likewise with any other
computing model like TMs.

The MWI is fully deterministic, which may make it a more attractive
target for modelling with a deterministic computational theory than
attempting to reproduce the statistical phenomena of QM, essentially
via hidden variables.  Any hidden variable theory, CA based or not,
has two strikes against it from the beginning due to the the many well
known difficulties of Bell inequalities and EPR correlations.

Regarding entropy, it is pointed out that entropy does not grow in a
CA model.  Wolfram discusses this as well.  While entropy technically
does not grow, you can get phenomena that look very much like entropy
growth in a CA model.  Eventually you will get a Poincare recurrence
if the universe is finite.  But if you start in a sufficiently simple
state, there are many CA models which will mimic entropy growth into a
more complex state.  And this may be close enough to explain our universe.

Alternatively, of course the MWI as a deterministic theory also does
not have entropy growth.  As mentioned above, computational models of
our universe might well do better to aim towards an MWI world.

As far as the claim that we already know the algorithm that runs our
universe, and it is the UD: I think this is amusing but ultimately
misleading.  It's true that a dovetailer which runs all programs will
indeed run our own universe's program (assuming it has one), but I think
it is a misuse of terminology to say that the UD is the algorithm that
is running our universe.  I would reserve that phrase to refer to the
specific program that generates our universe and no others.  It will be a
tremendous accomplishment of physics and philosophy when that program is
discovered, but it is misleading to give the impression that we already
know what it is.

I think a better terminology here would be something like, we don't
need to know the specific program that describes our universe in order
to imagine how to program a computer that would in fact generate our
experiences, at least in theory.  And then go on and explain about
running all programs at once, etc.

Hal Finney

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