Time-Symmetrized Quantum Theory

Vaidman, Lev

doi:10.1002/(sici)1521-3978(199811)46:6/8<729::aid-prop729>3.0.co;2-q

Cited by 15 publications

(17 citation statements)

References 40 publications

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“…There is a question about the meaning of the weak value that we get following the post-selection [23]. Could it be that the measurement depends on a post selected vector i.e.…”

Section: The Interpretation Of Post-selectionmentioning

confidence: 99%

Introduction to Weak Measurements and Weak Values

Tamir¹,

Cohen²

2013

Quanta

144

146

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“…There is a question about the meaning of the weak value that we get following the post-selection [23]. Could it be that the measurement depends on a post selected vector i.e.…”

Section: The Interpretation Of Post-selectionmentioning

confidence: 99%

Introduction to Weak Measurements and Weak Values

Tamir¹,

Cohen²

2013

Quanta

144

146

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“…In this case, of course, the reversal of time arrow is identical to the interchange of the measurements at t 1 and t 2 . If the free Hamiltonian is not zero, then an appropriate modification should be made [35].…”

Section: Time-symmetric Aspectsmentioning

confidence: 99%

The Two-State Vector Formalism of Quantum Mechanics

Aharonov

Vaidman

Time in Quantum Mechanics

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129

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We present the two-state vector formalism of quantum mechanics. It is a timesymmetrized 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. Descriptions of Quantum Systems The Quantum StateIn the standard quantum mechanics, a system at a given time t is described completely by a quantum state |Ψ , (13.1) defined by the results of measurements performed on the system in the past relative to the time t. (It might be that the system at time t is not described by a pure quantum state, but by a mixed state (density matrix). However, we can always assume that there is a composite system including this system which is in a pure state.) The status of a quantum state is controversial: there are many papers on reality of a quantum state and numerous interpretations of this "reality". However, it is non-controversial to say that the quantum state yields maximal information about how this system can affect other systems (in particular, measuring devices) interacting with it at time t. Of course, the results of all measurements in the past, or just the results of the last complete measurement, also have this information, but these results include other facts too, so the quantum state is the most concise information about how the quantum system can affect other systems at time t.

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“…Finkelstein [15] and Bigaj [16] have attempted to define time asymmetric counterfactuals to overcome this difficulty. But in my view, the time asymmetry of quantum counterfactuals is an unnecessary burden [17]. We can consider a time symmetric (or time neutral) definition of quantum counterfactuals.…”

Section: Consider the Following Definition [11]mentioning

confidence: 99%