🚀 go-pugleaf

In article <336@mtnmath.UUCP>, paul@mtnmath.UUCP (Paul Budnik) writes...
>In article <3NOV199213105174@csa2.lbl.gov>, sichase@csa2.lbl.gov (SCOTT I CHASE) writes:
>> 
>> The wavefunction of an electron describes it's position distribution in 
>> a particular electromagnetic potential, not its shape.  The shape of an 
>> electron would be determined by the wavefunctions of its constituents, 
>> if they were found to exist.  If you don't understand this, I recommend 
>> Liboff's _Quantum Mechanics_ as a good place to freshen up on the 
>> interpretation of the wave function.  
> 
>I understand that the constituents of the proton determine its shape
>as defined by cross section and that the electron does not seem to have
>any constituents and thus has a point like cross section.

Good.  We agree on the phenomenology.

>I suspect that all the standard interpretations of the wave function
>are wrong. 

I'm not sure that an interpretation can be right or wrong.  All 
"fair" interpretations (those supported  by the mathematics) are
correct in exactly the same sense that QM is correct - there is no 
experimental evidence which contradicts the specific quanititative
predications that can be made from them.   On the working assumption that
QM itself is ultimately correct (possibly not a good assumption, but
never mind) then there is no scientific way to distinguish among
interpretations.  Hence, all are equivilent.

>That there is more than one interpretation is one
>indication that this is true. 

This is certainly a false statement.  There is almost always more than
one way to interpret the equations of physics, with each way giving you
a somewhat different insight into what the equations are telling you.
Let's take an example from an entirely different field.  You can write
down the differential equations that describe fluid flow - an expression
for the velocity potential of a fluid, along with boundary conditions. 
If the fluid is incompressible, you get a simple equation, Laplace's
equation: Del^2 psi = 0.  What does this mean?  Well, you can interpret
it in two completely different but equivalent ways:

	(1) The fluid flows such that, subject to the boundardy conditions,
the total kinetic energy of the fluid is minimized.
	(2) Every element of fluid has momentum and is subject to forces
from neighboring elements.  Each element moves according to Newton's Law
for the infinitesmal mass of the element.

As you may know, you arrive at the first interpretation from deriving
the equation of motion by application of Hamilton's principle, while you
arrive at the second by old fashion study of force vectors.

Is there a way to judge between the two interpretations?  No.  They both
lead to the same equation for psi, so make identical testable predications.
They are both only as correct as the equation of motion is valid.

The difference between this example and QM is that QM strikes in a more
fundamental way at the meaning of reality, which you expect naively, to
have an unambigous nature.  But the nature of reality, so far as it 
can be understood through physics, is determined by the equations of 
the theory.  All interpretations, however distinct or discordant they 
seem to you, are equivalent.  If one is wrong then all are wrong.  Your
attempt to distinguish among them is doomed to failure.  The best that
you can hope to do is to demonstrate that one or another of the interpretations
does not in fact follow from the principles of QM, and therefore is
not a valid interpretation.

>I object to teaching and discussing interpretations of the wave function 
>as if they were established fact instead of the philosophical speculation 
>that they are.

They are not philosophical speculations.  They are interpretations of the
equations.  That is how it is taught.

>For the same reason I object to the statement that the wave function does 
>not define a shape. 

Well, now we're back to square one.  You do not understand the meaning of the
wavefunction, if you can continue to make this statement.  Any book on
QM will illustrate how you can describe point-like particles by a wave 
function, which has nothing to do with its shape, or lack thereof.

>If the wave function is an objective physical phenomena
>it does define a shape albeit a highly mallable one. This is an open
>question subject to experimental test. To treat it otherwise is a mistake.

You keep saying this, but you do not tell us what experimental test you
have in mind.  How do you plan to determine the shape of an electron by
measuring its wave fuction?  

-Scott
--------------------
Scott I. Chase			"It is not a simple life to be a single cell,
SICHASE@CSA2.LBL.GOV		 although I have no right to say so, having
				 been a single cell so long ago myself that I 
				 have no memory at all of that stage of my 
				 life." - Lewis Thomas