🚀 go-pugleaf

In article <1992Sep29.170356.13002@newshost.lanl.gov> jlg@cochiti.lanl.gov (Jim Giles) writes:
)In article <1992Sep28.202508.17001@lmpsbbs.comm.mot.com>, bhv@areaplg2.corp.mot.com (Bronis Vidugiris) writes:
)|> [...]
)|> But it is possible to distinguish between theories where wavefunctions
)|> are hypothetical entities that collapse 'at the speed of light' (aka 'in a
)|> lorentz invariant manner), and wavefunctions are hypothetical entities that
)|> collapse 'instantaneously' - or some of the other equivalent alternatives
)|> that may not involve collapse.
)
)It is not possible to distinguish between wavefunctions that are
)hypothetical entities and  wavefunctions which are real objects.
)Not empirically.  Therefore, their introduction violates Occam's
)razor.

I worded my post the way I did to <try to> sidestep this very issue!

) A wavefunction is easily determined to be a mathematical
)abstraction which computes probability distributions.  I'm happy
)that they remain only that.   `Collapse' cannot be determined to 
)happen at all!  Since the wavefunction computes *distributions*, 
)it applies to large numbers of events, not to individual ones.

However, there is a undesirable (IMO) feature of QM with the current
formalism, a problem that can be avoided if the formalism is modified
only very slightly (i.e. the formalism is modified so that the hypothetical
wavefunction collapses in a different manner).

This feature is the 'non-locality' of QM.

However, a more important question is whether reality exhibits these
non-local effects.  This hasn't been totally answered, but no prediction
of QM has been proven wrong - yet.  However, QM hasn't been totally proven
right, and the modification to it is very small.

Anyway, if you set up an experiment with a pair of photons in the 'singlet'
state (i.e. opposite spins) and measure the spin of  both photons along
an arbitrary axis with an angle from the vertical of theta1 (for detector1)
and theta2 (for detector2)

detector 1     <======     source           =======>    detector 2


you get the following result from QM

p(theta1,theta2) = p1(delta) = cos^2(theta2-theta1)

However, Bell has shown that any local realistic theory must follow
the relationship.

1-p2(2*delta) <= 1 - 2*p2(delta)

There are some similar inequalities with a formal proof in 'Bell's Therom:
Theoretical Tests and Implications' by Clauser and Shimony, which has (alas)
disappeared from my files.  There's a really simple proof of the inequality
in Quantum Reality by Nick Herbert which is much less formal.

Anyway, there *is* a way to distinguish between the two condtions I
was describing.  Local Realistic theories predict that you will have a
constraint on p1(delta).  A simple 'speed-of-light-collapse' theory predicts
that p1(delta) *will* change its value when the spins are measured in a
'timelike' manner (i.e within a lightcone) vs a 'spacelike' manner.