Related papers: When does "Time" become "Observable" ?
In the usual formulation of quantum theory, time is a global classical evolution parameter, not a local quantum observable. On the other hand, both canonical quantum gravity (which lacks fundamental time-evolution parameter) and the…
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a…
We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity…
Quantum coherence is a fundamental resource that quantum technologies exploit to achieve performance beyond that of classical devices. A necessary prerequisite to achieve this advantage is the ability of measurement devices to detect…
We have previously shown (arXiv:1912.00033) that three approaches to relational quantum dynamics -- relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations -- are equivalent. Here we show that this `trinity'…
Time has been an elusive concept to grasp. Although we do not yet understand it properly, there has been advances made in regards to how we can explain it. One such advance is the Page-Wootters mechanism. In this mechanism time is seen as…
A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation…
Effective quantum cosmology is formulated with a realistic global internal time given by the electric vector potential. New possibilities for the quantum behavior of space-time are found, and the high-density regime is shown to be very…
This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the…
We discuss the corrections to the orbital period of a particle in a constant magnetic field, driven by the model of noncommutative geometry recently associated to a quantum clock. The effects are extremely small, but in principle…
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
The role played by Time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a Time Operator. As we shall discuss,…
Two systems for a charged particle are studied, the first one when it is under the effect of a constant electric field, and the second one when it is under the effect of a constant electromagnetic field. For both systems, it is possible to…
Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
Time plays a fundamental role in our ability to make sense of the physical laws in the world around us. The nature of time has puzzled people -- from the ancient Greeks to the present day -- resulting in a long running debate between…
The aim of the article is to argue that the interpretations of quantum mechanics and of probability are much closer than usually thought. Indeed, a detailed analysis of the concept of probability (within the standard frequency theory of R.…