204:, the first state vector evolves from the electron leaving its source, the second state vector evolves backwards from the final location of the electron on the detection screen, and the combination of forwards and backwards evolving state vectors determines what occurs when the electron passes the slits.
59:
is not complete; rather, both forwards and backwards evolving quantum states are required to describe a quantum state: a first state vector that evolves from the initial conditions towards the future, and a second state vector that evolves backwards in time from future boundary conditions. Past and
211:. It can be employed in particular for analyzing pre- and post-selected quantum systems. Building on the notion of two-state, Reznik and Aharonov constructed a time-symmetric formulation of quantum mechanics that encompasses probabilistic observables as well as nonprobabilistic weak observables.
80:, can be obtained formally by separating out the initial conditions (or, conversely, the final conditions) by performing sequences of coherence-destroying operations, thereby cancelling out the influence of the two state vectors.
234:
In TSVF, causality is time-symmetric; that is, the usual chain of causality is not simply reversed. Rather, TSVF combines causality both from the past (forward causation) and the future (backwards causation, or
136:
195:
167:
975:
Aharonov, Yakir; Albert, David Z.; Vaidman, Lev (1988-04-04). "How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100".
265:
in 1986, although Ruth
Kastner has argued that the two interpretations (Transactional and Two-State Vector) have important differences as well. It shares the property of
219:
In view of the TSVF approach, and in order to allow information to be obtained about quantum systems that are both pre- and post-selected, Yakir
Aharonov,
44:
310:
270:
55:
in 1955, who named it the Double
Inferential state-Vector Formalism (DIVF). Watanabe proposed that information given by forwards evolving
839:
643:
447:
60:
future measurements, taken together, provide complete information about a quantum system. Watanabe's work was later rediscovered by
755:
315:
463:
Aharonov, Yakir; Bergmann, Peter G.; Lebowitz, Joel L. (1964-06-22). "Time
Symmetry in the Quantum Process of Measurement".
207:
The two-state vector formalism provides a time-symmetric description of quantum mechanics, and is constructed such as to be
258:
93:
246:, TSVF yields the same predictions as standard quantum mechanics. Lev Vaidman emphasizes that TSVF fits very well with
243:
1079:
251:
305:
208:
35:
relation in which the present is caused by quantum states of the past and of the future taken in combination.
254:, with the difference that initial and final conditions single out one branch of wavefunctions (our world).
43:
The two-state vector formalism is one example of a time-symmetric interpretation of quantum mechanics (see
278:
266:
201:
51:
in 1921, and later by several other scientists. The two-state vector formalism was first developed by
984:
947:
880:
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699:
676:
553:
472:
391:
348:
172:
144:
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Aharonov, Y; Vaidman, L (1991-05-21). "Complete description of a quantum system at a given time".
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417:
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834:, Volume 1, Lecture Notes in Physics, vol. 734, pp. 399–447, 2nd ed., Springer, 2008,
337:"Das Kausalproblem der Quantentheorie als eine Grundfrage der modernen Naturforschung ĂĽberhaupt"
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522:
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443:
28:
382:
Watanabe, Satosi (1955). "Symmetry of physical laws. Part III. Prediction and retrodiction".
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561:
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Reznik, B.; Aharonov, Y. (1995-10-01). "Time-symmetric formulation of quantum mechanics".
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52:
48:
16:
Description of quantum mechanics in which the present depends on both the past and future
988:
951:
884:
791:
768:
Heaney, Michael B. (2013). "A symmetrical interpretation of the Klein-Gordon equation".
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557:
476:
395:
352:
740:
The
Retrocausal Nature of Quantum Measurement Revealed by Partial and Weak Measurements
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236:
65:
61:
959:
892:
744:
Quantum
Retrocausation: Theory and Experiment (13–14 June 2011, San Diego, California)
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638:, Volume 1, Lecture Notes in Physics 734, pp. 399–447, 2nd ed., Springer, 2008,
421:
69:
56:
908:
589:
521:, Handbook of the Philosophy of Science, North-Holland, Elsevier, pp. 275–416,
368:
247:
220:
77:
72:
in 1964, who later renamed it the Two-State Vector
Formalism (TSVF). Conventional
281:
and with the time-symmetric theories of
Kenneth B. Wharton and Michael B. Heaney
996:
514:
224:
47:). Time-symmetric interpretations of quantum mechanics were first suggested by
1048:
1021:
1020:
Aharonov, Yakir; Cohen, Eliahu; Gruss, Eyal; Landsberger, Tomer (2014-07-26).
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843:
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About position measurements which do not show the
Bohmian particle position
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548:
412:
360:
828:
The Two-State Vector
Formalism of Quantum Mechanics: an Updated Review
812:
751:
689:
664:
632:
The Two-State Vector Formalism of Quantum Mechanics: an Updated Review
830:. In: Juan Gonzalo Muga, Rafael Sala Mayato, Íñigo Egusquiza (eds.):
634:. In: Juan Gonzalo Muga, Rafael Sala Mayato, Íñigo Egusquiza (eds.):
854:
336:
928:
A Suggestion for a Teleological Interpretation of Quantum Mechanics
1038:
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442:, Quantum Mechanical Studies for A. M. Shimony, Volume Two, 1997,
663:
Aharonov, Yakir; Cohen, Eliahu; Landsberger, Tomer (2017-03-12).
438:, in: Robert Sonné Cohen, Michael Horne, John J. Stachel (eds.):
1022:"Measurement and collapse within the two-state vector formalism"
665:"The Two-Time Interpretation and Macroscopic Time-Reversibility"
861:
Vaidman, Lev (2007-03-07). "Backward evolving quantum states".
721:
Ruth E. Kastner, talk presented at Cambridge 2014 Conference,
1032:(1–2). Springer Science and Business Media LLC: 133–146.
257:
The two-state vector formalism has similarities with the
614:, Kluwer Academic Publishers, 1996, pp. 141–154,
175:
147:
96:
471:(6B). American Physical Society (APS): B1410–B1416.
440:
Potentiality, Entanglement and Passion-At-A-Distance
983:(14). American Physical Society (APS): 1351–1354.
934:(submitted 14 June 2000, version of 4 August 2000)
863:Journal of Physics A: Mathematical and Theoretical
723:Free Will and Retrocausality in the Quantum World,
612:Bohmian mechanics and quantum theory: an appraisal
189:
161:
131:{\displaystyle \langle \Phi |\ \ \ |\Psi \rangle }
130:
650:(submitted 21 May 2001, version of 10 June 2007)
542:(4). American Physical Society (APS): 2538–2550.
846:(submitted 21 May 2001, version of 10 June 2007)
169:evolves backwards from the future and the state
940:Journal of Physics A: Mathematical and General
8:
1026:Quantum Studies: Mathematics and Foundations
917:Two-time interpretation of quantum mechanics
436:Protective measurements of two-state vectors
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842:, DOI 10.1007/978-3-540-73473-4_13,
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45:Interpretations of quantum mechanics
507:Non-relativistic quantum mechanics
181:
151:
122:
100:
14:
946:(10). IOP Publishing: 2315–2328.
869:(12). IOP Publishing: 3275–3284.
261:of quantum mechanics proposed by
316:Positive operator valued measure
197:evolves forwards from the past.
915:Yakir Aharonov, Eyal Y. Gruss:
311:Wheeler–Feynman absorber theory
271:Wheeler–Feynman absorber theory
851:The Two-State Vector Formalism
602:Yakir Aharonov, Lev Vaidmann:
190:{\displaystyle |\Psi \rangle }
177:
162:{\displaystyle \langle \Phi |}
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826:Yakir Aharonov, Lev Vaidman:
630:Yakir Aharonov, Lev Vaidman:
434:Yakir Aharonov, Lev Vaidman:
259:transactional interpretation
997:10.1103/physrevlett.60.1351
960:10.1088/0305-4470/24/10/018
893:10.1088/1751-8113/40/12/s23
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252:many-worlds interpretation
21:two-state vector formalism
1049:10.1007/s40509-014-0011-9
832:Time in Quantum Mechanics
800:10.1007/s10701-013-9713-9
636:Time in Quantum Mechanics
485:10.1103/physrev.134.b1410
404:10.1103/RevModPhys.27.179
384:Reviews of Modern Physics
335:Schottky, Walter (1921).
306:Delayed choice experiment
932:arXiv:quant-ph/0006070v2
923:(submitted 28 July 2005)
921:arXiv:quant-ph/0507269v1
857:(submitted 10 June 2007)
844:arXiv:quant-ph/0105101v2
742:, AIP Conf. Proc. 1408:
648:arXiv:quant-ph/0105101v2
566:10.1103/physreva.52.2538
227:developed the theory of
977:Physical Review Letters
209:time-reversal invariant
770:Foundations of Physics
279:John Archibald Wheeler
244:de Broglie–Bohm theory
215:Relation to other work
202:double-slit experiment
200:In the example of the
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163:
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27:) is a description of
519:Philosophy of Physics
192:
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133:
746:, pp. 120-131,
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989:1988PhRvL..60.1351A
952:1991JPhA...24.2315A
885:2007JPhA...40.3275V
792:2013FoPh...43..733H
736:Avshalom C. Elitzur
681:2017Entrp..19..111A
558:1995PhRvA..52.2538R
477:1964PhRv..134.1410A
396:1955RvMP...27..179W
353:1921NW......9..492S
341:Naturwissenschaften
87:is represented by:
876:quant-ph/0606208v1
523:Footnote on p. 327
511:Jeremy Butterfield
361:10.1007/bf01494985
187:
159:
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1080:Quantum mechanics
855:arXiv:0706.1347v1
752:10.1063/1.3663720
690:10.3390/e19030111
536:Physical Review A
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242:Similarly as the
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413:10945/47584
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225:Lev Vaidman
1069:Categories
675:(3): 111.
322:References
74:prediction
1075:Causality
1058:2196-5609
1039:1406.6382
1005:0031-9007
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901:1751-8113
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422:122168419
269:with the
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152:Φ
149:⟨
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98:⟨
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285:See also
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33:causal
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452:p. 2
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277:and
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83:The
68:and
25:TSVF
19:The
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