http://philsci-archive.pitt.edu/arch...d-preprint.pdf

Open or Closed?
Dirac, Heisenberg, and the relation
between classical and quantum mechanics

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Among these [outstanding problems
apart from renormalisation] he [Dirac]
lists the following:

One of the problems is . . . accounting
for the number 137. Other problems are
how to introduce the fundamental length
to physics in some natural way, how to
explain the ratios of the masses of the
elementary particles and how to explain
their other properties. I believe separate
ideas will be needed to solve these
distinct problems and that they will be
solved one at a time through successive
stages in the future evolution of physics.

At this point I find myself in disagreement
with most physicists. They are inclined to
think one master idea will be discovered
that will solve all these problems together.
(Dirac 1963, p. 50)

Clearly Heisenberg would be counted among
those who believed these various problems
needed to be solved all at once. One of
Dirac’s more surprising approaches to
solving these problems involved
reintroducing an aether.

Once again, he took the key to solving
a quantum problem to lie in the
development of a more adequate classical
theory. In 1951 he had developed yet
another classical electrodynamics, one
that required postulating a velocity field
defined at all points of space-time.

Dirac interpreted this velocity as the
velocity of the aether relative to the
Earth. He argued that such an aether could
be rendered consistent with relativity
theory as long as one subjected the aether
velocity to the quantum uncertainty
relations. In this way Dirac was able to
recover the Lorentz invariance of his theory.

When, in 1952, Leopold Infeld pointed out
that one could accept all of the conclusions
of Dirac’s new electrodynamics without
postulating an aether, Dirac responded as
follows:

“Infeld has shown how the field equations
of my new electrodynamics can be written
so as not to require an aether. This is not
sufficient to make a complete dynamical
theory. It is necessary to set up an action
principle and to get a Hamiltonian formulation
of the equations suitable for quantization
purposes, and for this the aether velocity is
required” (Dirac 1952).

For Dirac, the Poisson bracket correspondence
that he had discovered in 1925 provided an
important link between classical and quantum
mechanics. One can only take an advantage of
this correspondence if one has a Hamiltonian
version of the classical theory. Thus in his
search for a new QED, his strategy was to
develop an appropriate Hamiltonian version
of classical electrodynamics, which could
then be quantized.

If this meant reintroducing an aether and
absolute simultaneity, then he was willing
to do this. This reinforces the fact that,
for Dirac, even the most accepted and well-
established parts of theories were open to
future revision.

When confronted with these same difficulties
of QED, Heisenberg, by contrast,attempted to
solve all of these problems at once by
restricting himself to observables only
—the same trick that had worked for him in
1925. This approach led Heisenberg to abandon
quantum field theory in favor of the S-matrix
program.

For Dirac, on the otherhand, agreement with
experiments was not the final test of a theory.
Regarding renormalization theory he writes,

“Just because the results happen to be in agreement
with observation does not prove that one’s
theory is correct” (Dirac 1987, p. 196).

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--
Pete Brown
Falls Creek
OZ
www.mountainman.com.au

QUOTE for the Day:

"I think it is safe to say that no one
understands Quantum Mechanics.
(Richard Feynman)