Measurement of Time-of-Arrival in Quantum Mechanics

It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta t_A \sim 1/E_k$, where $E_k$ is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.Comment: References added. To appear in Phys. Rev.

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

Real clocks and the Zeno effect

Real clocks are not perfect. This must have an effect in our predictions for the behaviour of a quantum system, an effect for which we present a unified description encompassing several previous proposals. We study the relevance of clock errors in the Zeno effect, and find that generically no Zeno effect can be present (in such a way that there is no contradiction with currently available experimental data). We further observe that, within the class of stochasticities in time addressed here, there is no modification in emission lineshapes.Comment: 12 a4 pages, no figure

Populism: A Brief Biography

Within the past ten years the vocabulary of political sociology has been augmented by the addition of the world ’populism’. Its general acceptance has yet to be achieved; but in past five years its use has spread enormously. The purpose of the paper is to provide a brief \u27biography\u27 of the concept of \u27populism\u27, examining the changing way in which the word has come to be used in its lifetime. It is argued that the confusion which has attended the growth in its use is not merely a semantic problem, arising from the inability of various writers to define their terms, but an important indicator of the nature of the phenomena. The major difficulty is seen as lying in the lack of an acceptable general theoretical framework within which to handle the political development of peasant societies. The notion of such societies as \u27part societies’, widespread in current anthropology, is examined as a possible starting point for such a general framework

Rural-urban differences and the break-up of Yugoslavia

There has been widespread debate over the possible causes of the break-up of the former Yugoslav federation : but relatively little attention has been paid to the importance of rural-urban differences in this process. The central claim of the article is that the economic, political and social exclusion which some specific segments of the Yugoslav rural population came to experience in relation to the urban-centred “system” can be regarded as having played an important contributory part in the genesis and course of the struggles surrounding the disintegration of Yugoslavia. This broad hypothesis is explored through brief discussions of two case-studies, the Serb krajina in Croatia, and “Herceg-Bosna”. While expressly rejecting single-factor explanations of change, the author argues that in looking for explanations of the phenomenon of secessionism in these cases we need to take into consideration the profound state of economic depression into which these areas had fallen

Ambiguities of arrival-time distributions in quantum theory

We consider the definition that might be given to the time at which a particle arrives at a given place, both in standard quantum theory and also in Bohmian mechanics. We discuss an ambiguity that arises in the standard theory in three, but not in one, spatial dimension.Comment: LaTex, 12 pages, no figure

A microfabricated ion trap with integrated microwave circuitry

We describe the design, fabrication and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions' motional degrees of freedom, the key to multiqubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled 43Ca+ ion.Comment: 4 pages, 5 figure

Time-of-arrival in quantum mechanics

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev.

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.

Temporal Ordering in Quantum Mechanics

We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one particle (in higher dimensions). In quantum mechanics, we find that diffraction effects introduce a minimum inaccuracy to which the temporal order-of-arrival can be determined unambiguously. The minimum inaccuracy of the measurement is given by dt=1/E where E is the total kinetic energy of the two particles. Similar restrictions apply to the case of coincidence measurements. We show that these limitations are much weaker than limitations on measuring the time-of-arrival of a particle to a fixed location.Comment: New section added, arguing that order-of-arrival can be measured more accurately than time-of-arrival. To appear in Journal of Physics