An EPR experiment is studied where each particle undergoes a few weak measurements along some pre-set spin orientations, whose outcomes are individually recorded. Then the particle undergoes a strong measurement along a spin orientation freely chosen at the last moment. Bell-inequality violation is expected between the two final strong measurements within each EPR pair. At the same time, agreement is expected between these measurements and the earlier weak ones within the pair. A contradiction thereby ensues: i) Bell's theorem forbids spin values to exist prior to the choice of the spin-orientation to be measured; ii) A weak measurement cannot determine the outcome of a successive strong one; and iii) Indeed no disentanglement is inflicted by the weak measurements; yet iv) The weak measurements’ outcomes agree with those of the strong ones. The most reasonable resolution seems to be that of the Two-State-Vector Formalism, namely, that the experimenter’s choice has been encrypted within the weak measurement's outcomes, even before the experimenter themselves knows what their choice will be. Causal loops are avoided by this anticipation remaining encrypted until the final outcomes enable to decipher it.
An EPR experiment is studied where each particle undergoes a few weak measurements along some pre-set spin orientations, whose outcomes are individually recorded. Then the particle undergoes a strong measurement along a spin orientation freely chosen at the last moment. Bell-inequality violation is expected between the two final strong measurements within each EPR pair. At the same time, agreement is expected between these measurements and the earlier weak ones within the pair. A contradiction thereby ensues: i) Bell's theorem forbids spin values to exist prior to the choice of the spin-orientation to be measured; ii) A weak measurement cannot determine the outcome of a successive strong one; and iii) Indeed no disentanglement is inflicted by the weak measurements; yet iv) The weak measurements’ outcomes agree with those of the strong ones. The most reasonable resolution seems to be that of the Two-State-Vector Formalism, namely, that the experimenter’s choice has been encrypted within the weak measurement's outcomes, even before the experimenter themselves knows what their choice will be. Causal loops are avoided by this anticipation remaining encrypted until the final outcomes enable to decipher it.
Quantum weak measurement is presented as shedding new light on the retrocausality question. It is shown to leave a system almost unaffected while gathering information about it. Next, an EPR experiment is studied where each particle undergoes a few weak measurements along some pre-set spin orientations. These weak outcomes are individually recorded. Then the particle undergoes a strong measurement along a spin orientation freely chosen at the last moment. Bell-inequality violation is expected between the two final strong measurements within each EPR pair. At the same time, agreement is expected between these strong measurements and the earlier weak ones performed on that pair. A contradiction thereby ensues: i) Bell’s theorem forbids spin values to exist prior to the choice of the spin-orientation to be measured; ii) A weak measurement cannot determine the outcome of a successive strong one; and iii) Indeed no disentanglement is inflicted by the weak measurements; yet iv) The weak measurements’ outcomes agree with those of the strong ones, suggesting the existence of pre-determined values. The most reasonable resolution seems to be that of the Two-State-Vector Formalism, namely, that the experimenter’s choice has been encrypted within the weak measurement’s outcomes, even before the experimenter themselves knows what their choice will be. Causal loops are avoided by this anticipation remaining encrypted until the final outcomes enable to decipher it.
In this thesis, the article “Can a Future Choice Affect a Past Measurement’s\nOutcome?” is used as a starting point to explore the peculiar\ncorrelations between subsequent weak (i.e. non-projective) and\nstrong measurements in a variation of the EPR-Bell experiment. Bell’s\ntheorem states that particles may not possess predetermined values.\nHowever, as the outcomes of the subsequent weak and strong measurements\ndo statistically agree, an apparent contridiction arises. The\nauthors claim that the correlations between the results are best explained\nusing the time-symmetric two-state vector formalism, stating\nthat the experimenter’s future choice has been encrypted in the weak\nmeasurement’s outcomes.\nAlternative explanations are analyzed and a numerical simulation was\nmade to invigorate the notion of a so called weak-bias. Meaning that\nthe weak measurements sufficiently influence the particles’ states to\naccount for the statistical agreement.
In the EPR experiment, each measurement addresses the question "What spin value has this particle along this orientation?" The outcome then proves that the spin value has been affected by the distant experimenter's choice of spin orientation. We propose a new setting where the question is reversed: "What is the orientation along which this particle has this spin value?" It turns out that the orientation is similarly subject to nonlocal effects. To enable the reversal, each particle's interaction with a beam-splitter at t1 leaves its spin orientation superposed. Then at t2, the experimenter selects an "up" or "down" spin value for this yet-undefined orientation. Only after the two particles undergo this procedure, the two measurements are completed, each particle having its spin value along a definite orientation. By Bell's theorem, it is now the "choice" of orientation that must be nonlocally transmitted between the particles upon completing the measurement. This choice, however, has preceded the experimenter's selection. This seems to lend support for the time-symmetric interpretations of QM, where retrocausality plays a significant role. We conclude with a brief comparison between these interpretations and their traditional alternatives, Copenhagen, Bohmian mechanics and the Many Worlds Interpretation.
Entanglement and nonlocality are studied in the framework of pre-/postselected ensembles with the aid of weak measurements and the two-state-vector formalism. In addition to the EPR–Bohm experiment, we revisit the Hardy and Cheshire Cat experiments, whose entangled pre- or postselected states give rise to curious phenomena. We then turn to even more peculiar phenomenon suggesting “emerging correlations” between independent preand postselected ensembles of particles. This can be viewed as a quantum violation of the classical “pigeonhole principle.” Introduction It is seldom acknowledged that seven years before the celebrated Bell paper [1], Bohm and Aharonov [2] published an analysis of the EPR paradox [3]. They suggested an experimental setup, based on Compton scattering, for testing nonlocal correlations between the polarizations of two annihilation photons. In 1964, Bell proposed his general inequality, thereby excluding local realism. During the same time, Aharonov et al. constructed the foundations of a time-symmetric formalism of quantum mechanics [4]. While Bell's proof utilizes entanglement to demonstrate nonlocal correlations,wewill describe inwhat follows the emergence of nonlocal correlations between product states. For this purpose, however, we shall invoke weak measurements of pre- and postselected ensembles. In classical mechanics, initial conditions of position and velocity for every particle fully determine the time evolution of the system. Therefore, trying to impose an additional final condition would lead either to redundancy or to inconsistency with the initial conditions. This is radically different in quantum mechanics. Because of the uncertainty principle, an initial state vector does not fully determine, in general, the outcome of a future measurement. However, adding a final (backward-evolving) state vector results in a more complete description of the quantum system in between these two boundary conditions, which has a bearing on the determination of measurement outcomes. The basis for this time-symmetric formulation of quantum mechanics was laid down by Aharonov, Bergman, and Lebowitz (ABL), who derived a symmetric probability rule concerning measurements performed on systems, while taking into account the final state of the system, in addition to the usual initial state [4].
We analyze an idealized experiment in which weak which-path measurements do not prevent consecutive weak interference measurements, and then again the which-path information is recovered by strong measurements. We also show how the same effect can be obtained even by all strong and weak measurements being carried out on a single particle. The simplified setting enables critically assessing competing interpretations of the results. The most natural one turns out to be that of the Two-State-Vector Formalism, according to which the quantum two-state between an earlier and a later measurement is equally determined by both of them.
Abstract. For unit vectors a, b, entanglement requires that spin measurements satisfy those just given for a≠b. Bell’s hidden variable quantum mechanical local particle with a=b cannot provide the values for a≠b and, hence, the values for an entangled particle system. The perception that any hidden variable quantum mechanical description of an entangled system of particles is non-local depends on Bell’s inappropriate definition of locality, which excludes entanglement for a distant particle, and the condition that a=b, which does not give the values for a≠b as required to give the quantum mechanical expectation values, when entanglement occurs for systems that are close, not distant, and ignores that entanglement is a local phenomenon. Expecting the condition a=b and a local particle analysis with no distant entangled particle to give the quantum mechanical result is absurd. Any disentanglement of once entangled particles moving apart sets the spin measurements at those given for a≠b if a≠b and those given for a=b if a=b. Any subsequent measurement of the set values agrees with those for a≠b if a≠b and those given for a=b if a=b just as if the particles are entangled still. In examples where Bell’s inequality is supposedly violated, the conditions for which the inequality is true are not met. There is no contradiction.