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science = determinism? (Schrodinger: algorithm or phenomena?)

Shmuel (Seymour J.) Metz nospam at nsf.gov.invalid
Tue Nov 30 15:10:00 EST 1999

Maynard Handley wrote:

> (1) There are no particles, only fields. There is an EM field, an electron
> field etc.

But "particle" is an extraordinarily useful fiction, and the working
physicist blithely talks about particles as though they really existed,
except when he is doing work that requires making the distinct. Even QFT
is normally done by using creation (of "particles") and annihilation (of
"particles") operators. Of course, those "particles" are not a good
match for a layman's intuition ;-)

> (2) In a model of NON-INTERACTING fields, the "amount" of field (VERY
> roughly, it's amplitude, more carefully its energy) can only change by
> discrete amounts. This is in contrast to a classical field where the
> amount of energy can change by any amount no matter how small.

No way! Quantization of the Hamiltonian is characteristic of bounded
systems, and the Hamiltonian of a free field has a continuos spectrum.
See Principles of Quantum Mechanics by PAM Dirac for a dated but very
readable treatment.

> (4) What really makes a field theory a quantum field theory (and gives you
> the behavior above) is that the entity one cares about, the state, the
> element of one's Hilbert space, is now a superposition of all the possible
> classical field configurations weighted with some complex number.
> (Appreciating this also makes it clear the link between QFT and
> statistical mechanics where one likewise deals with configurations of all
> possible classical fields weighted in some fashion, only this time by
> Exp[-kT].)

You can't map classical field configurations into QM, since that would
require simultaneous measurements of non commuting observables. I
suspect that you are thinking of path integrals, but that is another
kettle of fish entirely.

> However in all of this, particles never appear. The interactions that are
> claimed as particle interactions (eg photoelectric effect, compton effect)
> are still field-field interactions (electron field interacting with EM
> field) with all that entails with respect to being spread over space and
> time.

Actually, those are examples of observables whose spectra are discrete
when the system is confined. And, again, "particle" is a useful
shorthand when discussing them.

> What is causing the localization is NOT that the entities involved
> are particles, but that whatever it is that causes collapse of the wave
> function (which as I have said before looks to be gravity) favors a
> particular basis for Hilbert space which is based on localized fields.

Begging the question of whether the collapse of the wave function is
real or just another useful fiction. It is just as easy to do QM without

> Yes this stuff is hard and abstract. To understand it well, one needs to
> start by learning a lot of somewhat recondite mathematics,

Unless you're doing string theory, the required Mathematics is fairly
basic; Linear Algebra, Functional Analysis, a little Group Theory and a
bit of Fiber Bundles. The real problem is that most physicists are
incredibly sloppy about their Mathematics, and sometimes it's decades
before things are redone on a sound basis. That only reason that it
works is that they are able to use their physical intuition to avoid
some of the booby traps.

> a bunch of
> mumbo-jumbo mystic incantations, "wave-particle duality, virtual
> particles, uncertainty principle", much like say the atomic theory of
> Democritus.

Well, the Jeremy Rifkins of the world may sling those terms around
without understanding them, but they are really pretty clear. For
instance, the Heisenberg Uncetainty Principle is just a measure of the
degree to which P and Q do not Commute and "virtual particles" are a
convenient shorthand for computations.


Shmuel (Seymour J.) Metz
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