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"The Two-State Vector Formalism:
an Updated Review
Yakir Aharonov1,2 and Lev Vaidman1
1 School of Physics and Astronomy
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel-Aviv 69978, Israel
2 Department of Physics and Department of Computational and Data Sciences
College of Science, George Mason University, Fairfax, VA 22030

Abstract. In this paper we present the two-state vector formalism of quantum mechanics.
It is a time-symmetrized approach to standard quantum theory particularly
helpful for the analysis of experiments performed on pre- and post-selected ensembles.
Several peculiar effects which naturally arise in this approach are considered. In particular,
the concept of “weak measurements” (standard measurements with weakening of
the interaction) is discussed in depth revealing a very unusual but consistent picture.
Also, a design of a gedanken experiment which implements a kind of quantum “time
machine” is described. The issue of time-symmetry in the context of the two-state
vector formalism is clarified."

From my message to Fred Alan Wolfon June 10, 2010
Thanks Fred for the papers, I ordered Aharonov's Quantum Guide for the Perplexed

Yes, what I am doing is fixing the Penrose-Rindler qubit 2-spinor formulation of the gravitational Einstein-Cartan tetrad theory to be consistent with the Aharonov-Vaidman -> Hoyle-Narlikar --> Cramer approach that all derives from Wheeler-Feynman classical EM 1940

Note both basis spin vectors --> 2 real null tetrads are in the forward light cone in Penrose-Rindler theory - also they use rectangular Cartesian basis that needs to be orthogonally transformed to the local spherical wave basis

l'^a = (1/2)^1/2(t^a + R^a)   advanced spherical wave (destiny star wave) real null tetrad

n^a = (1/2)^1/2(t^a - R^a)   retarded spherical wave (history wave) real null tetrad

also the IT rectangular Cartesian tetrads including t^a are precisely the entangled Bell pair states of quantum information theory in terms of the 2-spinor quBITs.

IT FROM BIT (John Archibald Wheeler)

For the orthonormal base triads of Cartan's mobile frames.

eR  = isin@cos& + jsin@sin& + kcos@

~ (1/2)^1/2[sin@cos& (|A+>|A'-> + |A->|A'+>) + sin@sin&(|A+>|A'-> - |A->|A'+>) + cos@(|A+>|A'+> - |A->|A'->)]

e@ = icos@cos& + jcos@sin& - ksin@

~ (1/2)^1/2[cos@cos& (|A+>|A'-> + |A->|A'+>) + cos@sin&(|A+>|A'-> - |A->|A'+>) + sin@(|A+>|A'+> - |A->|A'->)]

e& = -isin& + jcos&

~ (1/2)^1/2[-sin& (|A+>|A'-> + |A->|A'+>) + cos&(|A+>|A'-> - |A->|A'+>)

These are spacelike vectors outside the light cone.

et is a timelike vector inside the light cone.

~ (1/2)^1/2(|A+>|A'+> + |A->|A'->)]

Category: Science