Newsgroups: sci.physics.particle,sci.physics,alt.consciousness,comp.ai.philosophy
From: price@price.demon.co.uk (Michael Clive Price)
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Subject: Re: Information Theory and QM
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Date: Mon, 31 Oct 1994 00:00:00 +0000
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Ralf Engeldinger writes:
> The square of the modulus of the wavefunction is the probability
> density. But this is not very helpful for conceptional purposes.
> Nonrelativistic QM (and esp. the probability interpretation just
> mentioned) is not a fundamental theory. It is only a low energy limit
> of relativistic quantum field theory. This theory is mathematically
> much more difficult but conceptionally it can do without all the
> interpretations and all the ideology (Copenhagen, Bohm, wavefunction
> collapse, etc.).

There is the same need for an interpretation in QFT as there is in
non-rel' QM:
****************
Q14  Is many-worlds a relativistic theory?
     -------------------------------------
     What about quantum field theory?
     --------------------------------
     What about quantum gravity?
     ---------------------------

It is trivial to relativise many-worlds, at least to the level of
special relativity.  All relativistic theories of physics are quantum
theories with linear wave equations.  There are three or more stages to
developing a fully relativised quantum field theory:

First quantisation: the wavefunction of an N particle system is a
complex field which evolves in 3N dimensions as the solution to either
the many-particle Schrodinger, Dirac or Klein-Gordon equation or some
other wave equation.  External forces applied to the particles are
represented or modelled via a potential, which appears in the wave
equation as a classical, background field.

Second quantisation: AKA (relativistic) quantum field theory, which
handles the creation and destruction of particles by quantising the
classical fields and potentials as well as the particles.  Each particle
corresponds to a field, in QFT, and becomes an operator.  Eg the
electromagnetic field's particle is the photon.  The wavefunction of a
collection of particles/fields exists in a Fock space, where the number
of dimensions varies from component to component, corresponding to the
indeterminacy in the particle number.  Many-worlds has no problems
incorporating QFT, since a theory (QFT) is not altered by a metatheory
(many-worlds), which makes statements *about* the theory.

Third quantisation: AKA quantum gravity.  The gravitational metric is
quantised, along with (perhaps) the topology of the space-time manifold. 
The role of time plays a less central role, as might be expected, but
the first and second quantisation models are as applicable as ever for
modelling low-energy events.  The physics of this is incomplete,
including some thorny, unresolved conceptual issues, with a number of
proposals (strings, supersymmetry, supergravity...) for ways forward,
but the extension required by many-worlds is quite trivial since the
mathematics would be unchanged.

One of the original motivations of Everett's scheme was to provide a
system for quantising the gravitational field to yield a quantum
cosmology, permitting a complete, self-contained description of the
universe.  Indeed many-words actually *requires* that gravity be
quantised, in contrast to other interpretations which are silent about
the role of gravity.  (See "Why *quantum* gravity?")
****************

Michael Price                        price@price.demon.co.uk
