The Case of the Disappearing (and Re-Appearing) Particle

Abstract

A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and post-selections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. The particle (when looked for using a projective measurement) seems to disappear from the first box where it would have been previously found with certainty, appearing instead within the third box, to which no tunneling is possible, and later re-appearing within the second. It turns out that local measurement (i.e. opening one of the boxes) fails to indicate the particle’s presence, but subtler measurements performed on the two boxes together reveal the particle’s nonlocal modular momentum spatially separated from its mass. Another advance of this setting is that, unlike other predictions of the TSVF that rely on weak and/or counterfactual measurements, the present one uses actual projective measurements. This outcome is then corroborated by adding weak measurements and the Aharonov-Bohm effect. The results strengthen the recently suggested time-symmetric Heisenberg ontology based on nonlocal deterministic operators. They can be also tested using the newly developed quantum router.

Interaction-Free Effects Between Distant Atoms

“…For example, an analysis performed using the TSVF approach within quantum mechanics suggested that the born/unborn photon has unique physical properties [57,58]. Moreover, recent experiments [59,60] and thought experiments [61][62][63] employ strong rather than weak measurements for analyzing new phenomena. A subsequent work [18], based on Davies et al [57,58], examines through the analysis of weak values the evolution between two strong "no-emission" measure-ments: the wave-function is first weakly radiated and then weakly "drawn back" to its still-excited atom.…”

Pre- and post-selection paradoxes in quantum walks

“…The TSVF led to intriguing PPS paradoxes [28], such as the 3-box paradox [15], superluminal velocities [29], quantum Cheshire cat [30], quantum pigeonhole effect [31], or disappearing and reappearing particles [32], just to name a few. These paradoxes gave rise to a number of controversies and their true 'paradoxical' nature is still debated [16][17][18][19][20][21].…”

“…However, we are going to show a PPS paradox for which the particle can be at two or three different cycles at the same time and can hop between them. This resembles the paradox of a disappearing and reappearing particle [32]. Let us pre-select the state of the system in a uniform superposition pre pre 0 1 18 1 2 3 1 2 3 1 2 3 1 18 1 2 3 1 2 3 1 2 3 .…”

Negation of photon loss provided by negative weak value

“…Weak values have been applied to many quantum paradoxes so far [21][22][23][24][25][26][27][28][29][30]; an appearance of the negative weak value −1 often plays an important role.…”