Related papers: Ideal quantum clocks and operator time

Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics the equation describing change of the state of quantum system with respect to energy is introduced. The operator of time appears to be the generator…

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…

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…

In order to study the "problem of time", Rovelli proposed a model of a two harmonic oscillator system where one of the oscillators can be thought of as a 'clock' for the other oscillator. In this paper we examine a model where the…

In single Hilbert space, Pauli's well-known theorem implies that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian signifies that the time operator and the Hamiltonian possess completely continuous…

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…

A formalism for quantizing time reparametrization invariant dynamics is considered and applied to systems which contain an `almost ideal clock.' Previously, this formalism was successfully applied to the Bianchi models and, while it…

We replace the usual Hamiltonian constraint of quantum gravity H|psi>=0 by a weaker one <psi|H|psi>=0. This allows |psi> to satisfy the time-dependent functional Schrodinger equation. In general, only the phase of the wave function appears…

The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born's rule do not apply backward in time. Here, we resolve this problem within a rigorous operational…

We study the quantum properties of an oscillator in proper time. This proper time oscillator is a particle model with mass that is on shell. Its internal time can be treated as a self-adjoint operator. The displaced time and displaced time…

Time remains one of the least well understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable…

Applying ideas from monadic dynamics to the well-established framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use strongly complementary structures to give…

The operational formulations of quantum theory are drastically time oriented. However, to the best of our knowledge, microscopic physics is time-symmetric. We address this tension by showing that the asymmetry of the operational…

Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schr\"odinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s).…

We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…

The problem of time operator in quantum mechanics is revisited. The unsharp measurement model for quantum time based on the dynamical system-clock interaction, is studied. Our analysis shows that the problem of the quantum time operator…

We introduce a self-adjoint operator that indicates the direction of time within the framework of standard quantum mechanics. That is, as a function of time its expectation value decreases monotonically for any initial state. This operator…

In thermodynamics, quantum coherences - superpositions between energy eigenstates - behave in distinctly nonclassical ways. Recently mathematical frameworks have emerged to account for these features and have provided a range of novel…

I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays…

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…