Abstract
Since its publication, Aharonov and Vaidman’s three-box paradox has undergone three major advances: i). A non-counterfactual scheme by the same authors in 2003 with strong rather than weak measurements for verifying the particle’s subtle presence in two boxes. ii) A realization of the latter by Okamoto and Takeuchi in 2016. iii) A dynamic version by Aharonov et al. in 2017, with disappearance and reappearance of the particle. We now combine these advances together. Using photonic quantum routers the particle acts like a quantum “shutter.” It is initially split between Boxes A, B and C, the latter located far away from the former two. The shutter particle’s whereabouts can then be followed by a probe photon, split in both space and time and reflected by the shutter in its varying locations. Measuring the former is expected to reveal the following time-evolution: The shutter particle was, with certainty, in boxes A+C at t1, then only in C at t2, and finally in B+C at t3. Another branch of the split probe photon can show that boxes A+B were empty at t2. A Bell-like theorem applied to this experiment challenges any alternative interpretation that avoids disappearance-reappearance in favor of local hidden variables.
Highlights
Such is the familiar state revealed by the double-slit experiment, featuring in every introductory text on QM, to which Feynman1 has referred as presenting the theory’s core mystery
We submit that the same credibility assigned to the above states [1], [2] goes, for the same reasons, to even more intriguing phenomena recently derived from quantum theory
These can be summarized in equations [4], [6] below, already implicit in [1], [2] and presented in what follows with their own Bell-Hardy type proofs
Summary
Such is the familiar state revealed by the double-slit experiment, featuring in every introductory text on QM, to which Feynman has referred as presenting the theory’s core mystery. Which, in everyday language, reads: The particle traverses in some sense both paths 1 and 2, assuming a definite path only under position measurement taken during its passage. Upon position measurement, this inevitably invokes the notorious measurement problem and the contentious “collapse.” Understandably, attempts were made to show that this superposition reflects only our subjective ignorance, while the particle itself goes on one definite side. Which, in everyday language, reads: Each particle’s spin (like the particle’s position in Eq 1) is both ↓ and ↑ along every direction, yet maximally correlated with the other, becoming definite in a certain direction for both particles only under measurement performed on either one of them
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