🚀 go-pugleaf

In article <92097.101806U53644@uicvm.uic.edu> U53644@uicvm.uic.edu writes:
>Please pardon me if this is a silly question (I'm a Math/Elec.Eng. grad, not
>physics), but can one tell that a wave function has collapsed at a certain
>distant point before light from that point would have arrived? If not, then
>does the simultaneous collapse of that wave function everywhere transmit
>information at faster than light speeds? If not, what's the paradox?

You can't use this to transmit information. Suppose I have two
particles with spin 1/2 produced by the decay of a spin-zero state.
They are separated by a light-day. If I measure s_x of one particle, I
know immediately what s_x of the other particle is (i.e., the
wavefunction has collapsed). If someone else measures s_x of the other
particle a second after I measure mine, she must measure the value I
predict based on my measurement (i.e., if we use the same coordinate
system and I measure +1/2 then she must measure -1/2).  However, this
person can't know that I've already measured my particle.  The
information that I've measured my particle can only reach her if I
send a message saying, ``Hey you, I've measured s_x,'' and this
message propagates at the speed of light. The only thing that happens
instantly is that the particle is instantly in an eigenstate of s_x.
However, you can't observe the state of the particle without disturbing
it, so there's no way to tell when the superposition of + and - states
collapses into an eigenstate. Thus, there's no way to communicate
using wavefunction collapse.

Some people are working on using the values of meaured spin (actually,
the polarization of photons) to communicate without anyone being able
to eavesdrop (see Bennett et al., Phys. Rev. Lett. Vol 68, p. 557
(1992) for example). However, the information propagates at the speed
of light. They merely use the fact that s_x and s_y don't commute to
provide security. There's nothing about the wavefunction collapse in
there.

What makes people uncomfortable about the wavefunction collapse is the
same thing that made people uncomfortable about electricity and gravity
before the advent of quantum field theory. They don't like the idea of
action at a distance. The principal objection Newton had to address with
his theory that gravity was responsible for the orbits of heavenly bodies
was that no one liked to think that one body could influence another
when there was no physical connection between the two.

We have resolved this discomfort by explaining such forces in terms of
the exchange of bosons (gravitation comes from hypothetical gravitons,
electromagnetism from photons, the nuclear binding force from pions,
the strong force from gluons, and the weak force from W and Z bosons).
(BTW, I am a simple experimentalist in atomic physics and some more
schooled than me in field theory may pull out the flamethrowers about
this simplification, pointing out, for instance that pions are not
fundamental in the same way as the other particles. This will not be
relevant to the point I am making here).  However, we still get
uncomfotable with the idea of action at a distance in
quantum-mechanical measurement.

There's another, related, problem: Schrodinger's cat. Put a cat in a
box with an ``infernal machine.''  The machine contains a single atom
of a radioactive isotope and a detector that can detect this decay.
When the detector fires, the machine breaks a vial of cyanide gas,
which kills the cat.

The paradox is, when exactly one half-life has passed, the cat's
wavefunction is 50% alive and 50% dead. If I look into the box
(perform a measurement) and find the cat dead, did I kill it by
looking (collapsing the wave function)? If I wait until the
probability that the nucleus has decayed is 99.9999% and look in the
box, if the cat is miraculously still alive, have I brought it back
from the dead?  These conclusions violate our common sense about
things and it makes people uncomfortable to feel that belief in
quantum mechanics would require them to say that looking can kill (or
revive) the cat.

There's a very good book on the subject, called ``Speakable and
Unspeakable in Quantum Mechanics'' by John Bell (of Bell's theorem)
published by Cambridge University Press (1987).  Also, see Bell's
article ``Against Measurement'' and Peierls's response ``In Defence of
Measurement'' in Physics World Aug. 1990, p.33 and Jan. 1991, p. 19,
respectively.

---Jon
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Jonathan M. Gilligan		Time and Frequency Division
<jongill@lilac.bldrdoc.gov>	National Institute of Standards and Technology
				Boulder, Colorado, USA