Related papers: Quantum and classical effects in a light-clock fal…
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…
Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the…
We explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at…
Based on the consideration of naturalness and physical facts in Einstein's theories of relativity, a nontrivial spacetime physical picture, which has a slight difference from the standard one, is introduced by making a further distinction…
t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of…
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…
Semi-classical gravity attempts to define a hybrid theory in which a classical gravitational field is coupled to a unitarily evolving quantum state. Although semi-classical gravity is inconsistent with observation, a viable theory of this…
We study gravitational back-reaction within the Page-Wootters formulation of quantum mechanics by treating time as a quantum degree of freedom. Our model introduces a distinction between global coordinate time, represented as a relational…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The statistical state of any (classical or quantum) system with non-trivial time evolution can be interpreted as the pointer of a clock. The quality of such a clock is given by the statistical distinguishability of its states at different…
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a ``clock''. Conditional probabilities are…
A quantum clock working as a control device is examined. The quality of the control process is characterized by the magnitude of deviation of perturbed state from unperturbed state of the controlled system. Uncertainty relations that relate…
The notions of time in the theories of Newton and Einstein are reviewed so that the difficulty which impedes the unification of quantum mechanics (QM) and general relativity (GR) is clarified. It is seen that GR by itself contains an…
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A…
General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the…
The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…
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…
An extension of standard quantum mechanics is proposed in which the Newtonian time appearing as a parameter in the unitary evolution operator is replaced with the time shown by a `quantum clock'. Such a clock is defined by the following…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
In this continuation paper, we apply the general relativistic quantum theory for one particle systems, derived in paper II of this series, to a simple problem: the quantum Schwartzchild problem, where one particle of mass {\it m% }…