Related papers: Time as a Dynamical Variable
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that…
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…
The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with…
I propose a general geometric framework in which to discuss the existence of time observables. This frameworks allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist…
Time reversal symmetry occupies a distinctive role in quantum mechanics, fundamentally requiring an anti-unitary operator to ensure a physically consistent representation. As such, the time reversal operator combines a unitary…
The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated…
We define the action operator in the consistent histories formalism, as the quantum analogue of the classical action functional, for the simple harmonic oscillator case. The action operator is shown to be the generator of time…
Attempts to treat time on an equivalent footing with space in quantum mechanics have been apparently dominated by `timeless' approaches, such as the one of Page and Wootters, which allow meaningful discussion of a `time operator'. However,…
Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…
The Hamiltonian formulation with action-angle variables is very useful when considering the motion of particles undergoing a self-force reaction due to gravitational wave emission. Using the proper time as a parameter along the trajectory…
$\mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{PT}$-symmetric systems, with a number of $\mathcal{PT}$-symmetry related applications. This…
We study a quantum theory with complex time parameter and non-Hermitian Hamiltonian structure. In this theory, the real part of the complex time is equal to `usual' physical time, whereas the imaginary one is proportional to inverse…
A time operator is a Hermitian operator that is canonically conjugate to a given Hamiltonian. For a particle in 1-dimension, a Hamiltonian conjugate operator in position representation can be obtained by solving a hyperbolic second-order…
The question of how to interpret and compute arrival-time distributions in quantum mechanics remains unsettled, reflecting the longstanding tension between treating time as a quantum observable or as a classical parameter. Most previous…
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…
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…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…