Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox

Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's theory of constraints. A parametrization invariant formulation is obtained by introducing time and energy operators for the relativistic particle and then treating the Klein-Gordon equation as a constraint. The standard, physical Hilbert space is recovered, via integration over proper time, from an augmented Hilbert space wherein time and energy are dynamical variables. It is shown that the Newton-Wigner position operator, being in this description a constant of motion, acts on states in the augmented space. States with strictly positive energy are non-local in time; consequently, position measurements receive contributions from states representing the particle's position at many times. Apparent superluminal propagation is explained by noting that, as the particle is potentially in the past (or future) of the assumed initial place and time of localization, it has time to propagate to distant regions without exceeding the speed of light. An inequality is proven showing the Hegerfeldt paradox to be completely accounted for by the hypotheses of subluminal propagation from a set of initial space-time points determined by the quantum time distribution arising from the positivity of the system's energy. Spatial localization can nevertheless occur through quantum interference between states representing the particle at different times. The non-locality of the same system to a moving observer is due to Lorentz rotation of spatial axes out of the interference minimum.Comment: This paper is identical to the version appearing in J. Math. Phys. 41; 6093 (Sept. 2000). The published version will be found at http://ojps.aip.org/jmp/. The paper (40 page PDF file) has been completely revised since the last posting to this archiv

Laser-induced forces between carbon nanotubes

Carbon nanotubes are the focus of intense research interest because of their unique properties and applications potential. We present a study based on quantum electrodynamics concerning the optical force between a pair of nanotubes under laser irradiance. To identify separate effects associated with the pair orientation and laser beam geometry, two different systems are analyzed, For each, an analytical expression for the laser-induced optical force is determined, and the corresponding magnitude is estimated. © 2005 Optical Society of America

Quantum times of arrival for multiparticle states

Using the concept of crossing state and the formalism of second quantization, we propose a prescription for computing the density of arrivals of particles for multiparticle states, both in the free and the interacting case. The densities thus computed are positive, covariant in time for time independent hamiltonians, normalized to the total number of arrivals, and related to the flux. We investigate the behaviour of this prescriptions for bosons and fermions, finding boson enhancement and fermion depletion of arrivals.Comment: 10 a4 pages, 5 inlined figure

Examining Neolithic Building and Activity Areas through Historic Cultural Heritage in Jordan: A Combined Ethnographic, Phytolith and Geochemical Investigation

The INEA project (Identifying activity areas in Neolithic sites through Ethnographic Analysis of phytoliths and geochemical residues, https://research.bournemouth. ac.uk/2014/07/inea-project-2/) develops and applies a method that combines the analysis of plant remains (silica phytoliths) and geochemical residues to inform on construction methods and the use of space in recently abandoned historical villages and Neolithic settlements. It is a collaborative project based at Bournemouth University, in partnership with the Council for British Research in the Levant

Macroscopically local correlations can violate information causality

Although quantum mechanics is a very successful theory, its foundations are still a subject of intense debate. One of the main problems is the fact that quantum mechanics is based on abstract mathematical axioms, rather than on physical principles. Quantum information theory has recently provided new ideas from which one could obtain physical axioms constraining the resulting statistics one can obtain in experiments. Information causality and macroscopic locality are two principles recently proposed to solve this problem. However none of them were proven to define the set of correlations one can observe. In this paper, we present an extension of information causality and study its consequences. It is shown that the two above-mentioned principles are inequivalent: if the correlations allowed by nature were the ones satisfying macroscopic locality, information causality would be violated. This gives more confidence in information causality as a physical principle defining the possible correlation allowed by nature.Comment: are welcome. 6 pages, 4 figs. This is the originally submitted version. The published version contains some bounds on quantum realizations of d2dd isotropic boxes (table 1), found by T. Vertesi, who kindly shared them with u

A measurement-based approach to quantum arrival times

For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

Heat Kernel for Spin-3/2 Rarita-Schwinger Field in General Covariant Gauge

The heat kernel for the spin-3/2 Rarita-Schwinger gauge field on an arbitrary Ricci flat space-time ($d>2$) is investigated in a family of covariant gauges with one gauge parameter $\alpha$. The $\alpha$-dependent term of the kernel is expressed by the spin-1/2 heat kernel. It is shown that the axial anomaly and the one-loop divegence of the action are $\alpha$-independent, and that the conformal anomaly has an $\alpha$-dependent total derivative term in $d=2m\geq6$ dimensions.Comment: 11 pages, latex, ITP-SB-94-3