From: jbaez@riesz.mit.edu (John C. Baez)
Newsgroups: sci.physics
Subject: Re: Uncertainty Principle [T.Bollinger => LONG]
Date: 5 Sep 92 17:03:29 GMT
Organization: MIT Department of Mathematics, Cambridge, MA

In article <1992Sep5.071519.16554@asl.dl.nec.com> terry@aslws01.asl.dl.nec.com (Terry Bollinger) writes:

>THE "DISTURBED PARTICLE" INTERPRETATION OF QUANTUM UNCERTAINTY

>Historically, some of the earlier books on QM certainly tended to describe
>it that way, especially when folks with an essentially classical background
>were trying to come to grips with it.  But it has problems, and does in fact
>tend to "overtrivialize" the profoundly bizarre underlying principles that
>are involved in QM.  E.g., Dr. Richard Feynman found such views misleading
>and somewhat offensive, and in his writings he argues against relying too
>heavily on such analogies.  

I have often wondered about the fact that the Gedankenexperimenten used
to argue for the uncertainty principle in the first place are based on
what seems like classical reasoning TOGETHER with the assumption E =
hbar nu relating the energy and frequency of a photon, or p =
hbar/lambda relating the momentum and wavelength.  These arguments tend
to work along the lines that to see something you have to hit it with
photons, and to see it accurately you have to use photons of short
wavelength hence lots of energy and momentum, which disturb what you're
trying to see.  What do these arguments really prove, if anything?  Of
course, historically they they were used to arrive at the current
framework of quantum mechanics and one can feel free to forget them once
you buy this framework.  But it still is interesting to ponder how these
arguments manage to convince people of the necessity of the uncertainty
principle.   Certainly you can't prove by pure logic that the world must
be quantum mechanical rather than classical!  These arguments seem to be
using the properties of photons to "sneak quantum mechanics in the back
door".   Perhaps they are showing that a world with light described
quantum-mechanically and other particles described classically is
inconsistent or otherwise incoherent?  It would be nice if someone could
extract the rigorous core, if any, out of these hand-wavy arguments.

>In Vol. III of his Lectures he goes to some
>lengths to point out that in Stern-Gerlaugh the separation of the base
>states does *not* "disturb" the particles in the sense of irreversibly
>preventing the original composite state from being recovered.  You can
>"rebuild" the state simply by recombining the base state paths -- something
>that makes no sense at all from a strict disturb-the-states perspective.

If you look at my explanation of your angular momentum puzzle - 
which seems essentially the same as Mcirvin's - you will see that it
relies on the fact that measuring one component of the angular momentum
of a particle really does affect other components of the angular
momentum of the particle.  (I made this precise in my previous post.
Basically, all I mean is that if you measure J_x of an electron, then
J_y, then J_x, you needn't get the same answer for J_x both times; in my
previous post I said how to reconcile this with conservation of angular
momentum.)  So unless this is full of baloney, there DOES seem to be
something to the "disturb-the-particle" view of uncertainty - although
it doesn't tell the whole story.

It's rather murky to me right now.

>THE FOURIER TRANSFORM INTERPRETATION OF QUANTUM UNCERTAINTY
>
>One of the most beautiful and readable discussions I've seen on this subject
>is by Dr. Roger Penrose in his popular book "The Emperor's New Mind."  On
>pages 243-250 of the paperback edition you will find two sections entitled
>"The quantum state of a particle" and "The uncertainty principle."  What
>you will read is a fascinating discussion of the remarkable symmetry that
>lies between particles as they are described in "ordinary" space of three
>dimensions, and "momentum" space in which they are positions according to
>their momentum values instead of their ordinary-space locations.

>In Dr. Penrose's discussion, the wavefunction that describes a particle
>has the appearance of a corkscrew in both of these spaces.  

To the mathematically literate a formula for the wavefunction might
clarify these mysterious corkscrews a lot.  The lay audience could
easily be forgiven for thinking that quantum corkscrews are just as
screwy as space potatos.  I am trying to think of a function from the
real numbers to the complex numbers whose graph looks like a corkscrew,
AS DOES that of its Fourier transform.  I guess a Gaussian times a
complex exponential does the trick:

exp(ikx - (x-a)^2/c^2)

will be a Gaussian bump of width c centered at a times a complex
exponential (a "corkscrew") of frequency k.  The Fourier transform of
such a function will be another of the same general form (times some
constant).   These functions are especially nice when studying position
and momentum operators, Fourier transforms and such; a real workout on
their mathematical structure can be found in Folland's book Harmonic
Analysis on Phase Space.

>The resulting relationships are like some sort of pair of clubs with a long-
>term unresolved dispute about joint membership.  Join one of the clubs 100%
>(make your corkscrew so short that you have an EXACT location in either
>ordinary space or momentum space), and you are 100% LOST from the other
>club.  Your location in it becomes scattered literally over the entire
>universe, so that at any one location you're probability of being "found"
>by a detector becomes flat-out zero.  A distressing state of affairs!

I sorta like it myself.  For many beautiful theorems quantifying exactly
how a wavefunction that is concentrated in position space has to be
spread out in momentum space, check out Folland's book.  Gaussians are
the functions that come the closest to being members of both clubs.


>HIDDEN VARIABLES, PILOT WAVES, AND THE DANGERS OF PHILOSOPHICAL EXTREMES

>BTW, it's my guess that part of the reason of the reason why Dr. David Bohm,
>author of a superb text on QM and a neo-hidden-variable "pilot wave" in his
>interpretation of QM, unexpectely went New-Agey on everbody. 

A rather odd sentence, that, but I get your drift.  :-)  Another victim
of the lure of quantum quackery (in my humble opinion) is Josephson, the
Nobelist of "Josephson junction" fame - whose circuits use sneaky
quantum tricks closely related to the Bohm-Aharanov effect.  Check out
his letter to the editor in the August (?) "Physics Today" in which he
defends Jahn's research on telekinesis!