Related papers: Space of events and the time observable
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
We introduce observables associated with the space-time position of a quantum point defined by the intersection of two light pulses. The time observable is canonically conjugated to the energy. Conformal symmetry of massless quantum fields…
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…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
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…
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…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the…
We define a new dynamical variable, the relative existence e, in terms of space and time. Taking it as a generalized positional coordinate, we show that for conservative systems the canonically conjugated momentum is identified as the…
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality.…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
The Hamiltonian constraint system is the canonical formulation of a physical system with a Hamiltonian constrained to vanish. In terms of the canonical variables, we define what we call reference observable, with respect to which other…
We consider the quantum mechanical behavior of a driven particle in an infinite 1D potential well. We show that the time dependent perturbation series is induced by the delicate non-trivial properties of the momentum operator in this case,…