Related papers: Non-inertial quantum clock frames lead to non-Herm…
Starting with the modified Dirac equations for free massive particles with the $\gamma_5$-extension of the physical mass $m\rightarrow m_1 + \gamma_5 m_2$, we consider equations of relativistic quantum mechanics in the presence of an…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
A cyclic nature of quantum mechanical clock is discussed as ``quantization of time." Quantum mechanical clock is seen to be equivalent to the relativistic classical clock.
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…
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
We summarize our investigation of the extent to which the choice of internal clock influences the dynamics in quantum models of gravity. Firstly, at the classical level, we define an extension to the Hamilton-Jacobi theory of contact…
It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
Understanding different aspects of time is at the core of many areas in theoretical physics. Minimal models of continuous stochastic and quantum clocks have been proposed to explore fundamental limitations on the performance of timekeeping…
A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and…
We study the non-unitary relation between quantum gravitational models defined using different internal times. We show that despite the non-unitarity, it is possible to provide a prescription for making unambiguous, though restricted,…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a…
We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of…
The problem of time evolution in quantum cosmology is studied in the context of a dust-filled, spatially flat Friedmann-Robertson-Walker universe. In this model, two versions of the commonly-adopted notion of internal time can be…
Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
In this article, we discussed certain properties of non-Hermitian $\CP$-symmetry Hamiltonian, and it is shown that a consistent physical theory of quantum mechanics can be built on a ${\cal C} \CP$-symmetry Hamiltonian. In particular, we…