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From: sarfatti@ix.netcom.com (Jack Sarfatti)
Subject: Vaidman's 1987 Ph.D. Dissertation
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Date: Fri, 28 Oct 1994 16:36:59 GMT
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Sarfatti's Notes on Lev Vaidman's 1987 Ph.D. dissertation "The 
Problem of the Interpretation of Relativistic Quantum Theories".

1964 Aharonov, Bergman & Lebowitz (ABL) showed probabilities for 
results of measurement at time t from pre- and post-selected wave 
functions in a time symmetric way.  

Vaidman claims a new interpretation of QM: the state of a quantum 
system at time t is described by a pair of vectors instead of by a 
single one.  The first vector is selected by the last complete set 
of measurements before time t, the other is selected by the first 
complete set of measurements performed after t.

He and Aharonov also introduce a new class of "multiple-time" 
measurements. For two times they prepare and test situations defined 
by the pair of vectors described above.

"... in the description of the quantum system by the generalized 
multiple-time state where we consider information coming from both 
directions of time." p.50

* Sarfatti note: The "OR" really new physics called for by Roger 
Penrose in Shadows of the Mind probably requires these generalized 
multiple time states for the proper description of coherent mental 
states of the brain.

Results:

(i) A new measurement procedure for nondemolition verification of 
nonlocal states.  For example, the EPRB entangled state of two spin-
1/2 particles.

(ii) EPR correlations between states at different times of the same 
particle! 

* Sarfatti note: I had same idea independently.  This is important 
for time travel gedankenexperiments around closed timelike curves.

Vaidman writes "When such correlations are established, the system 
has novel properties... the result of the measurement of any of the 
three Cartesian components of the spin of a single spin-1/2 particle 
at a single time can be inferred with certainty from the results of 
two other measurements, one of which is carried out before, and the 
other after, the time in question."

* Sarfatti note: This is very important.  The standard text book 
explanation of the Heisenberg uncertainty principle is for only one 
state vector evolving from the past to the present.  That is not 
contradicted.  Additional information evolving from the future to 
the present makes exact knowledge of the simultaneous values of 
noncommuting observables in the present possible -- at least at the 
future time!  That is, we apparently can retrodict the exact 
simultaneous past values of noncommuting observables using both pre- 
and post-selected data.

iii) "Weak measurements": an ensemble of N spin 1/2 particles pre-
selected to have Sx = +1/2 and post-selected to have Sy = +1/2, will 
be found at intermediate time with total angular momentum at 45 
degrees to x-y axes = N/sqrt2 which is sqrt2 larger than N/2.  "The 
weak value of the component of spin (along the 45 degree direction) 
of any one particle of the above ensemble is ... bigger by a factor 
sqrt2 than any eigenvalue."  An actual experiment is suggested.  

* Sarfatti note: Aharonov later used this basic idea for a "quantum 
time machine" for travel back in time to before the machine was 
made! In contrast to the limitation on time travel through 
hypothetical traversable wormholes.

iv) Strong relativistic causality (i.e. no locally measureable 
influences outside the light cone) severely restricts the form of 
entangled multiparticle states and the types of local interactions 
between the measuring apparatus and the observed system.

This enables a covariant account of histories of quantum systems 
that have been measured any number of times.  "A covariant 
description for such histories is not possible in the existing 
formalism, since it cannot give a covariant account for the collapse 
which occurs after each interaction with an external measuring 
device."

*Sarfatti note: Does this demolish the Gell-Mann/Hartle approach?

".. the nonlocal state of the system which consists of two separate 
parts is measurable if, and only if, it has the following form:

|1,2> = (1/sqrtN) sum i = 1 to N of |i>1 |i>2

If it has unequal weights: "Therefore, local actions in one part can 
change the probability of results of local measurements in part two 
.." p.25

* Sarfatti note: In the Aspect experimental test of Bell's 
inequality N = 2.  This is compatible with strong causality because 
it is not possible to use this state for communication outside the 
light cone even though spacelike correlations are measured that 
violate the locality condition of Bell's inequality.  Even if the 
weights were unequal, Eberhard's theorem shows that faster-than-
light communication is still not possible for the standard von-
Neumann collapse measurements of "the first kind" made on an esemble 
of pairs.  However, Vaidman in his thesis, and Pitowski (later on  
with new kinds of nondemolition measurements made on single pairs) 
show how such communication outside the light cone is in principle 
possible.  This is an empirical problem of fact that tests our 
common sense notions of cause and effect.


