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Isham 4
"6.3 The Consistent Histories Interpretation
6.3.1 Preamble
... the problem of time can be regarded as a development of the condiitonal
probability interpretation ... decoherence is really a process that
develops in time ,,, a system that has decohered could in principle
recohere at some lter time .... gravity should be quantized with something
like a functional integral over spacetime geometries....one way of defining
a real-time functional integral is to start with the canonical Hilbert
space quantum theory and then define the integral as the limit of a time-
sliced approximation to some matrix element of a unitary evolution operator
... But this is no help in a situation in which the Hilbert space structure
is one of the things we are trying to discover. ... The rival euclidean
[i.e.,'imaginary time' of Hawking js] is not much help either ... p.96 ...

The consisten histories interpretation ... measurement is not a fundamental
category; instead the theory itslef prescribes when it is meaningful to say
that a measurement has taken place....

6.3.2 Consistent Histories in COnventional Quantum Theory
....Consider... the process of making a series of measurements separated in
time.  Each measurement ... a set of questions - the answer to which is
either yes or no - and each such question is represented by a hermitian
projection operator ... 'does the value of A lie in the given subset a?'..
The discussion of conditional probabilities can be extended ... (6.3.4)

the intention of the consistent histories interpretation is to sidestep
this ... completely by talking directly about the probability of a history
,,, this is a considerable generalization of the notion of history as used
in a standard path integral where it usually means a path in the
configuration space of the system ...

The desire to assign probabilities to histories is initially frustrated by
the fact that this is precisely what cannot be done in conventional quantum
theory.  All that is possible there is to give a probability amplitude for
a history, but then the passage to the probability itself introduces
interference terms between different histories.... The classic example is
the two-slit experiment. " p.98

[I am proposing that the quantum connection communicator is an analog for a
photon pair of the classic two-slit experiment for a single unconnected
photon.  The extraordinary and ordinary paths of the transmitter photon in
the pair, correspond to the unconnected photon passing one or the other of
the two slits.  One transmitter photon path has a half-wave plate so that
both paths enter the single counter (each path with certainty) in the same
linear polarization state.  The arrival of the twin receiver photon at one
of the two receiver counters is like the arrival of the unconnected photon
at either a point of screen of constructive interference or a complementary
point of destructive interference.  Just as the total probability and
energy at the screen is conserved on summing over all points, so the sum
over both receiver counters conserves local probability and energy.  The
same is true trivially at the single transmitter counter.  Thus, there is
no problem with local conservation of probability or energy in my model -
in this sense the superluminal and backward in time information
transmission is operationally 'unitary' in the physical sense - also the
mathematical.  The quantum connection signal, that is locally decodable at
the receiver without having to get data from the transmitter, is the analog
to the fringes observed on a screen behind the two slits for the
unconnected photon.  In the photon pair case the transmitter photon passes
the two slits, so to speak, and its receiver twin shows the 'fringes' on
the 'screen' (the two receiver counters).  The fringes are due to the
indistinguishability of the pair amplitudes in which the receiver photon
arrives at a fixed receiver counter while its twin transmitter photon takes
both indistinguishable alternative paths (extraordinary and ordinary)
before being measured at the one and only transmitter counter. Sarfatti]