Related papers: The Time-Energy Principle in Algebraic Geometry
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators,…
We construct the quantum mechanical model of the COW experiment assuming that the underlying space time has a granular structure, described by a canonical noncommutative algebra of coordinates $x^{\mu}$. The time-space sector of the algebra…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate…
Light experiences dielectric matter as an effective gravitational field and matter experiences light as a form of gravity as well. Light and matter waves see each other as dual space-time metrics, thus establishing a unique model in field…
The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the…
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric…
It is often said that time vanishes in quantum gravity. One general approach to quantum gravity accepts this fundamental timelessness but seeks to derive time's emergence at a non-fundamental level. To better assess such approaches, I…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
We analyze the nature of space-time nonlocality in string theory. After giving a brief overview on the conjecture of the space-time uncertainty principle, a (semi-classical) reformulation of string quantum mechanics, in which the dynamics…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
Some properties of the $q$-Fourier-sine transform are studied and $q$-analogues of the Heisenberg uncertainty principle is derived for the $q$-Fourier-cosine transform studied in \cite{FB} and for the $q$-Fourier-sine transform.
The concepts of space, time, and matter are of central importance in any theory of the gravitational field. Here I discuss the role that these concepts might play in quantum theories of gravity. To be concrete, I will focus on the most…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the…
We consider the cluster of problems raised by the relation between the notion of time, gravitational theory, quantum theory and thermodynamics; in particular, we address the problem of relating the "timelessness" of the hypothetical…