Related papers: Projection evolution and quantum spacetime
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time $t$. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended…
It is unclear whether an observable notion of time exists in quantum gravity even in principle because spacetime itself fluctuates. We propose a form of observable time in perturbative quantum gravity. First, we define an elapsed proper…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
We present a method, which we shall call the probabilistic evolutionary process, based on the probabilistic nature of quantum theory to offer a possible solution to the problem of time in quantum cosmology. It offers an alternative for…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
The understanding of time and dynamics can be elucidated by examining the concept of entanglement in quantum theory. This particular perspective on time is referred to as the timeless approach, which posits that the universe exists in a…
We introduce a framework for non-linear time evolution in quantum mechanics as a natural non-linear generalization of the Schrodinger equation. Within our framework, we derive simple toy models of dynamical geometry on finite graphs. Along…
The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We prove that, under suitable assumptions, operationally motivated data completely determine a space-time in which the quantum systems can be interpreted as evolving. At the same time, the dynamics of the quantum system is also determined.…
We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.
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…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
The existence of a minimum measurable length scale was suggested by various theories of quantum gravity, string theory and black hole physics. Motivated by this, we examine a quantum theory exhibiting a minimum measurable time scale. We use…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…