Dear CMR,
Interleaving.
----- Original Message -----
From: "CMR" <jackogreen.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Wednesday, January 21, 2004 1:07 AM
Subject: Re: Is the universe computable?
>
> > Think of it this way, what is the cardinality of the equivalence
class
> > of representations R of, say, a 1972 Jaguar XKE, varying over *all
> > possible languages* and *symbol systems*?
> > I think it is at least equal to the Reals.
> > Is this correct? If R has more than one member, how can we coherently
> > argue that "information is physical" in the material monist sense?
> >
> [CMR]
> Assuming you mean R is countably infinite(?), then a solution would be a
> finite universe of underlying discrete structure, ala Fredkin, I imagine.
>
[SPK]
If Fredkin is proposing a Cellular Automata based model that would be
the case, but CA based models have a problem of their own: how to show that
the global synchrony of the shift function can obtain. It is puzzleling to
me why it is hard to find a discussion of this in the literature.
> >[SPK]
> > What if the "informing" and "constraining" (?) is done, inter alia,
> > by the systems that "use up" the universal resources?
> >
> > What if, instead of thinking in terms of a priori existing
solutions,
> > ala Platonia, if we entertain the idea that the *solutions are being
> > computation in an ongoing way* and that what we experience is just one
(of
> > many)stream(s) of this computation. Such a computation would require
> > potentially infinite "physical resources"...
> > Would it be to much to assume that all we need to assume is that the
> > "resources" (for Qcomputations, these are Hilbert space dimensions) are
> > all that we have to assume exists a priori?
> > Does not Quantum Mechanics already have such build in?
> [CMR]
> Yes, this would indeed follow. But what of a view of QM itself emerging
form
> qubits?
> as, for instance, expressed in the so-called Bekenstein bound: the entropy
> of any region
> of space cannot exceed a fixed constant times the surface area of the
> region.
[SPK]
Maybe I am mistaken but does not QM enter into the very definition of a
qubit?
As the to idea of Bekenstein's bound, that is, IMHO, more of a problem
than a solution and leads in the wrong direction. It has been shown
(
http://tph.tuwien.ac.at/~svozil/publ/embed.htm) that it is impossible to
completely "embed" the logical equivalent of a QM system (with Hilbert space
dimensions greater than 2) into the logical equivalent of a classical
system.
I take this to explicitly rule out considerations that space-time can be
treated as just a Minkowskian (or, more generally, one would consider the
Poincare' group) space and expect to be able to treat it as the background
or "support" for the necessary machinery of a QM system.
>[CMR]
> This suggests
> that the complete state space of any spatially finite quantum system is
> finite, so
> that it would contain only a finite number of independent qubits.
>
[SPK]
Again, that does not work because we can not take space-time (ala GR) to
be "big enough" to allow us to fit QM into it. On the other hand, it has
been shown that a QM system, considered as a quantum computational system,
can simulate, with arbitrary accurasy, any classical system, given
sufficient "Hilbert space" dimensions - which play the role of "physical
resources" for QM systems.
See:
http://arxiv.org/abs/quant-ph/0204157
This leads me to the idea that maybe space-time itself is something that
is secondary. It and all of its contents (including our physical bodies)
might just be a simulation being generated in some sufficiently large
Hilbert space. This idea, of course, requires us to give Hilbert space (and
L^2 spaces in general?) the same ontological status that we usually only
confer to space-time. ;-)
Kindest regards,
Stephen
Received on Wed Jan 21 2004 - 12:01:31 PST