From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Is orthogonality of kets same as distinguishability of paths?
Organization: Whole Earth 'Lectronic Link
Date: Sat, 21 Nov 1992 18:48:16 GMT


The real issue in my debate with Ramsay, Gallis et-al over whether or not
standard quantum mechanics permits quantum connection communication
involves several basic ambiguities in quantum mechanics.

1. What is the proper relation of Dirac ket formalism to more intuitive
Feynman histories picture?

The Dirac ket is based on a "single time" Hamiltonian picture. In contrast
the Feynman history is a multi-time Lagrangian picture that includes the
non-unitary preparation and non-unitary detection in addition to the
unitary evolution between preparations and detections.

For correlated systems the Feynman picture is better because, for example,
for a photon pair, the two photons need not be detected at "the same time"
or even at a space-like separation which would be simultaneous in a
specific frame only.

It is not clear that the Feynman picture really is equivalent to the Dirac
ket or Hilbert space picture. In fact Isham's Lectures on Quantum Gravity
suggest that Feynman's is more fundamental and that Hilbert space emerges
as a kind of low energy approximation.

2. How do we determine when to add amplitudes coherently or incoherently.
The real debate is whether I can add the relevant pair amplitudes
coherently or not because the quantum connection signal is a nonlocal
"fringe" modulation effect. Even if the amplitudes can be added coherently,
will a sum over all possibilities at the transmitter always wash out the
signal at the receiver as Stapp claims is always the case?

3. What are the physical conditions for two kets to be orthogonal? Is
orthogonality a form of distinguishability? That is, how is the
orthogonality of single-time kets related to the distinguishability of the
nonlocal Feynman path amplitudes of which the kets are a spacelike slice?

In particular, are the kets for photon passing one slit or another
orthogonal if the two paths are indistinguishable, by virtue of the
experimental design, or, rather, are they parallel, becoming perpendicular
only when the experimental design is changed (i.e., the Heisenberg
microscope is switched on)? That is, the boundary conditions determine the
structure of the Hilbert space and the observable whose eigenstates are
measured. Thus, if the Feynman paths are indistinguishable the design does
not allow a determination of the eigenstates of the operator that tell us
which slit the photon passes. If the kets are really snapshots of the paths
should the kets be orthogonal in that case?

4. But I have shown that a quantum connection signal may be possible in
either case, kets parallel or perpendicular. When they are perpendicular
the issue is one of phase noise dispersion. Also we are only at this level
talking of the mean signals. I still maintain that even if the mean signals
vanish, as in the case of using a transmitter beam splitter with mean
unitary phase shift of p1/2 - the zero-point fluctuations in that phase
shift can be manipulated via Casimir effect, for example, so that the
fluctuations at the transmitter beam splitter will modulate the
fluctuations in photocurrents at the receiver counters - I predict. To do
this may require sophisticated small signal analysis - but I bet it can be
and will be done one day.
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