Related papers: The time-energy uncertainty relation for quantum e…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
We give a short review of known exact inequalities that can be interpreted as "energy-time" and "frequency-time" uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequency-time uncertainty…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
Quantum mechanics sets limits on how fast quantum processes can run given some system energy through time-energy uncertainty relations, and they imply that time and energy are tradeoff against each other. Thus, we propose to measure the…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend…
Time plays a crucial role in the intuitive understanding of the world around us. Within quantum mechanics, however, time is not usually treated as an observable quantity; it enters merely as a parameter in the laws of motion of physical…
All energy measurements of a quantum system are prone to inaccuracies. In particular, if such measurements are carried over a finite period of time the accuracy of the result is affected by the length of that period. Here I show an upper…
Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem. Correspondingly, the status of the energy-time uncertainty relation is unsettled. In the first part of this work the…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
We introduce a general framework for defining context-dependent time distributions in quantum systems using projective measurements. The time-of-flow (TF) distribution, derived from population transfer rates into a measurement subspace,…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the…
The problem of time is a deep paradox in our physical description of the world. According to Aristotle's relational theory, time is a measure of change and does not exist on its own. In contrast, quantum mechanics, just like Newtonian…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…
Time-energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows to grasp peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam-Tamm…
In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a…