[time 470] QUANTUM-D: Noncomputable dynamics for quantum theory

Stephen P. King (stephenk1@home.com)
Fri, 23 Jul 1999 09:51:39 -0400

Dear Matti,

        This is a very good intro to the computation question as I think of it!

QUANTUM-D: Noncomputable dynamics for quantum theory

Noncomputable dynamics for quantum theory

Date: Fri, 2 Jan 1998 00:57:05 -0800 (PST)
From: Mitchell Porter <mitch@thehub.com.au>
To: quantum-d@teleport.com
Subject: Noncomputable dynamics for quantum theory

Part of Roger Penrose's hypothesis regarding the form
of a final theory is that its dynamics should be
noncomputable. Recall that this simply means that no
Turing machine could reproduce this dynamics in the
output of a calculation. Mathematics already offers
examples of noncomputable sequences whose first few
elements we know, but only because we have hit upon
methods that suffice to identify those particular

When looking for noncomputability in physics, Penrose
suggests that quantum gravity with topology change 
might be noncomputable, since four-manifolds are 
not classifiable, and four-manifolds would interpolate
between the spacelike hypersurfaces at either end
of a sum over histories. This would give us 
noncomputable amplitudes, and so noncomputable
transition probabilities. 

This might be suitable for a noncomputable stochastic
theory, but I wonder if we could go further and have
a deterministic noncomputable theory. In this regard
I find Chaitin's number interesting. Chaitin's number
is the halting probability for a Turing machine,
given certain weightings on initial conditions.
Not only is Chaitin's number noncomputable, it is a
random real, which means that it is statistically
indistinguishable from a random series.

Could the apparent randomness of quantum behavior,
rather than resulting from real (albeit structured)
randomness, be the result of a pseudorandom,
deterministic noncomputable dynamic?


on Chaitin's number

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