R. Sala Mayato

Feynman-path analysis of Hardy's paradox : Measurements and the uncertainty principle

Abstract Hardys paradox is analysed within Feynmans formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways. Contradictions arise if conflicting statements are applied to the same statistical ensemble. Usefulness of “strange” weak values for resolving the paradox is disputed.

Path integrals, the ABL rule and the three-box paradox

Abstract The three-box problem is analysed in terms of virtual pathways, interference between which is destroyed by a number of intermediate measurements. The Aharonov–Bergmann–Lebowitz (ABL) rule is shown to be a particular case of Feynmans recipe for assigning probabilities to exclusive alternatives. The ‘paradoxical’ features of the three box case arise in an attempt to attribute, in contradiction to the uncertainty principle, properties pertaining to different ensembles produced by different intermediate measurements to the same particle. The effect can be mimicked by a classical system, provided an observation is made to perturb the system in a non-local manner.

On constructing the wave function of a quantum particle from its Wigner phase-space distribution function

Abstract For a Schrodinger wave function, the part of the phase that depends only on time disappears in the construction of the corresponding Wigner phase-space (quasi)distribution function. Despite this, it can be recovered from the Wigner function using the quantum Hamilton–Jacobi equation. This is demonstrated for three simple cases.

Superluminal systematic particle velocity in relativistic stochastic Bohmian mechanics

Abstract For a Dirac electron scattering from a typical metal-insulator-metal tunnel junction (i.e., incident kinetic energy and barrier height both five orders of magnitude less than mc 2 ) the stationary-state systematic particle velocity of stochastic Bohmian mechanics can be superluminal in the immediate vicinity of a quasinode of the wave function.

M-indeterminate distributions in quantum mechanics and the non-overlapping wave function paradox

Abstract We consider the non-overlapping wave function paradox of Aharanov et al., wherein the relative phase between two wave functions cannot be measured by the moments of position or momentum. We show that there is an unlimited number of other expectation values that depend on the phase. We further show that the Wigner distribution is M-indeterminate, that is, a distribution whose moments do not uniquely determine the distribution. We generalize to more than two non-overlapping functions. We consider arbitrary representations and show there is an unlimited number of M-indeterminate distributions. The dual case of non-overlapping momentum functions is also considered.

First-arrival-time distributions for a Dirac electron in 1 + 1 dimensions

For the special case of freely evolving Dirac electrons in ( 1 + 1) dimensions, Feynman checkerboard paths have previously been used to derive Wigners arrival-time distribution which includes all arrivals. Here, an attempt is made to use these paths to determine the corresponding distribution of first-arrival times. Simple analytic expressions are obtained for the relevant components of the first-arrival propagator. These are used to investigate the relative importance of the first-arrival contribution to the Wigner arrival-time distribution and of the contribution arising from interference between first and later (i.e., second, third, etc.) arrivals. It is found that a distribution of (intrinsic) first-arrival times for a Dirac electron cannot in general be consistently defined using checkerboard paths, not even approximately in the nonrelativistic regime.