Organization: Penn State University
Date: Mon, 23 Nov 1992 08:19:42 EST
From: <MRG3@psuvm.psu.edu>
Newsgroups: sci.physics,alt.sci.physics.new-theories
Subject: Re: Is orthogonality of kets same as distinguishability of paths?

nnget
In article <By2xKH.J5G@well.sf.ca.us>, sarfatti@well.sf.ca.us (Jack Sarfatti)
says:
>
>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
emai>unitary evolution between preparations and detections.

>
The ket formulation, or the more general density operator formulation, deals
with all of the state preparation/evolution/separate measurements on
correlated subsystems/etc issues just fine.  In fact, the bulk of the
literature (if not all) on FTL communication through quantum entanglement
uses a vector formulation.

For an introduction, see von Neumann's rather dusty volume "Mathematical
Foundations of Quantum Mechanics", which discusses in detail how to
deal with state preparation etc.

>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.

Then why does all the literature successfully use a ket formulation to
discuss such questions?
It is not sufficient to claim it is unsuccessful just because it does not
give the same answers as Sarffatti Physics.

>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.

It is certainly not clear why one should consider "quantum connection
machines" as needing higher order corrections, nor has the nature of those
corrections been specified.  Therfore, Sarffatti Physics must be interpreted as
a speculative variant of standard quantum mechanics.

>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?

-it is incorrect to add incoherently in the middle of a path, as it seems
you may have done.  (at least your prose suggests this)
-the answer to your question is yes, for quantum mechanics as it is now
understood.  I cannot speak for future refinements of QM, but those
refinements are not contained in our present understanding (standard QM).

>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?

Orthogonality may be interpreted as a mathematical statment.  However,
you should remember that two kets may be linearly independent and not be
orthogonal.  They are distinguishable in that they may produce different
statistics for an ensemble, but there is NO measurement in standard
QM which will allow you to determine which one was the "actual" state.
-mike gallis