Search

Using the relativistic arrival-time distribution of Kijowski it is argued that the peculiar form of the spatial nonlocality—but not the nonlocality itself—of the “standard” distribution is an artifact of the nonrelativistic approximation. Also spatially nonlocal is the related local momentum density based on the symmetrization p ˆ ( X ) = p ˆ 1 / 2 | X 〉 〈 X | p ˆ 1 / 2 .

The paradoxical properties of the N -box problem ( N ⩾ 3 ) are dispelled by the straightforward exercise of constructing, for an arbitrary pre-selected state with N nonzero orthogonal components, the corresponding (unique) post-selected state such that this pair leads to the same properties. A new and interesting N -box problem is presented.

The “main claim” of the Comment is “alleged paradoxes dissolve by taking seriously the standard interpretation of quantum mechanics”. In fact, the authors merely suggest possible loopholes which I argue are ineffective, not addressing the spatial nonlocality which, in retrospect, is the essence of the unusual properties under discussion.

The spatial nonlocality of the “standard” arrival-time distribution is analyzed theoretically for an arbitrary initial wave function and found to be of an unusual nature.

The “standard” approach to times of arrival advocated by Equsquiza, Muga and Baute associates arrivals from the left (right) with positive (negative) wavenumber components of the wave function at the instant of arrival. Elementary arguments and calculated results exhibiting paradoxical properties call into question this sign of k assignment of direction of arrival.

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.

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.

The most general classical expression defining the first passage time is given in terms of the absorption rate with perfectly absorbing boundary conditions. Its operational use in quantum mechanics is discussed. In particular, in the quantum case an incompatibility is found with certain classical properties of the perfectly absorbing conditions.

A modification of the Salecker-Wigner quantum clock leads to precisely the expected result for the mean dwell time. However, the mean transmission and reflection times that apparently emerge naturally from the theoretical analysis can have unphysical properties. A relativistic analysis using the Dirac equation supports this conclusion.

A simple derivation, using Bohm trajectories, is given of Dumont and Marchioro's expression for the distribution of arrival times of transmitted particles at a point on the far side of a 1D barrier. Calculated distributions are presented and the “quantum speed-up effect” discussed from the Bohm trajectory viewpoint.