Aduke.2109
net.misc
utzoo!decvax!harpo!duke!cjp
Mon May 3 22:52:35 1982
Re: utcsrgv.329: Of quantum, uncertainty, and bishops

Thanks to Don Chan for his comments on quantum mechanics.
I think I see where he slips up though.  His statement about
uncertainty is correct, but the formula needs modification.
(Delta x) * (delta v) <= (H bar) is true if delta x is the
uncertainty in location, and delta v is the uncertainty in
*momentum*, rather than velocity.  At non-relativistic speeds,
the mass is constant;  velocity is proportional to momentum.
But the velocity you can impart to a particle by observing it's position
to arbitrarily high precision is limited by the speed of light!
So let's assume that I have equipment which measures a particle's
position to super-high precision.  This is allowed by Uncertainty.
Its momentum after my observation can be correspondingly super-high.
But this is accounted for by the relativistic gain in mass of the
particle due to its high velocity.  In other words, its momentum
can be unbounded but its velocity is bounded by c.  And I can
know arbitrarily well that the particle was *here* when I observed
it, and not a light year away, and also know that it won't be
observable at that distant place for at least a year.

So much for Uncertainty: you can't know *everything* about a
particle, but you *can* know enough about it to say where it
is *not*.

Now for wave functions.  I refer to the Copenhagen Interpretation
of Quantum Mechanics for my argument (thanks Don).
The quantum mechanical interpretation of a particle as a wave
function makes no statement about reality, but merely describes
its statistical behavior.  In particular, no claim is made that
the particle so described *can* be simultaneously observed
at two light-year separated points;  it just describes the
probabilities of being observed at a point *independently of
any other knowledge about the particle*.  If you *know* something
about the particle, then the *a priori* description need not
reflect the reality of what you know, indeed it does not reflect
the restrictions on speed-of-light propagation.  Basically I'm
saying that if you know anything at all about the location of
a given particle, then its mathematical wave function is a lie
everywhere beyond a speed of light from that particle.

		Charles Poirier (duke!cjp)