Related papers: Doubly Quantum Mechanics
The classical and continuum limit of a quantum gravitational setting could lead, at mesoscopic regimes, to a very different notion of geometry w.r.t. the pseudo-Riemannian one of special and general relativity. A possible way to…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
We consider Hilbert's problem of the axioms of Physics at a qualitative or conceptual level. This issue is more pressing than ever as we seek to understand how both General Relativity and quantum theory could emerge from some deeper theory…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
A underlying dynamical structure for both relativity and quantum theory-``superrelativity'' has been proposed in order to overcome the well known incompatibility between these theories. The relationship between curvature of spacetime…
The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures…
Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition 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…
We prove that Riemannian metrics in General Relativity in the \emph{`normal-coordinates'} gauge are in one-to-one correspondence with curvature 2-forms. We discuss how this can be used as a change of variables in the operator formalism to…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
$SU(\infty)$-QGR is a quantum approach to Universe and gravity. Its main assumption is infinite mutually commuting observables in the Universe, leading to representation of $SU(\infty)$ by its Hilbert spaces and those of its subsystems. The…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…