Related papers: The quantum clock: a critical discussion on space-…
We critically discuss the measure of very short time intervals. By means of a Gedankenexperiment, we describe an ideal clock based on the occurrence of completely random events. Many previous thought experiments have suggested fundamental…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
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…
We discuss time measurement in quantum gravity. Using general relativity for large distances and the uncertainty principle we find a minimum time interval of the order of the Planck time, therefore the uncertainty in time measurment is…
The starting point of this work is the axiomatic existence of a smallest measurable interval, viz. the Planck time $t_P$, set by quantum fluctuations in the vacuum metric tensor. By the Relativity Principle, the same limit must then apply…
Quantum theory and relativity offer different conceptions of time. To explore the conflict between them, we study a quantum version of the light-clock commonly used to illustrate relativistic time dilation. This semiclassical model combines…
We show that the space-time uncertainty relation for the quantum clock can be derived from the maximum force principle.
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…
Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…
A quantum clock must satisfy two basic constraints. The first is a bound on the time resolution of the clock given by the difference between its maximum and minimum energy eigenvalues. The second follows from Holevo's bound on how much…
The recently introduced concept of an "ideal quantum clock" (IQC) is extended. Especially it is shown that the time operator of an IQC is canonically conjugated to the Hamiltonian of the IQC in a certain pre-Hilbert space. Further it is…
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories.…
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special…
The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
The paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since General Relativity does not have a privileged time variable…
A quantum clock working as a control device is examined. The quality of the control process is characterized by the magnitude of deviation of perturbed state from unperturbed state of the controlled system. Uncertainty relations that relate…
In Einstein's gedankenexperiment for measuring space and time, an ensemble of clocks moving through curved spacetime measures geometry by sending signals back and forth, as in the global positioning system (GPS). Combining well-known…
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…