Related papers: Quantum measurements of time
The measurement process in quantum mechanics is usually described by the von Neumann projection postulate, which forms a basic constituent of the laws of quantum mechanics. Since this postulate requires the outside observer of the system,…
New prescription to treat position and time equally in quantum mechanics is presented. Using this prescription, we could successfully derive some interesting formulae such as time-of-arrival for a free particle and quantum tunneling…
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
The self adjoint operator of time in non-relativistic quantum mechanics is found within the approach where the ordinary Hamiltonian is not taken to be conjugate to time. The operator version of the reexpressed Liouville equation with the…
The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent…
In the arrival time problem in quantum mechanics, a standard formula that frequently emerges as the probability for crossing the origin during a given time interval is the current integrated over that time interval. This is semiclassically…
A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially…
We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
We present a new method to measure the work $w$ performed on a driven quantum system and to sample its probability distribution $P(w)$. The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be…
In quantum mechanical experiments one distinguishes between the state of an experimental system and an observable measured in it. Heuristically, the distinction between states and observables is also suggested in scattering theory or when…
We calculate the time of arrival probability distribution of a quantum particle using the Bohmian formalism. The pilot-wave is given by the wave function of the one dimensional vacuum squeezed state but written in the Schr\"odinger…
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through…
We investigate a detector scheme designed to measure the arrival of a particle at $x=0$ during a finite time interval. The detector consists of a two state system which undergoes a transition from one state to the other when the particle…
We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a…
A question of the time the system spends in the specified state, when the final state of the system is given, is raised. The model of weak measurements is used to obtain the expression for the time. The conditions for determination of such…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do…
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…