Related papers: Quantum mechanics over sets
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality', 'superposition', 'interference', 'entanglement' and 'emergence'. The aim of QMod is…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung's hydrodynamic formulation of QM and Louis de Broglie's and David Bohm's pilot wave models. The aims of the approach are as follows: 1) to…
The connection is established between two theories that have developed independently with the aim to describe quantum mechanics as a stochastic process, namely stochastic quantum mechanics (sqm) and stochastic electrodynamics (sed).…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
This paper calls attention to the current state of the probability (P) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper notices how fundamental issues raised in quantum…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
Quantum machine learning (QML) is a computational paradigm that seeks to apply quantum-mechanical resources to solve learning problems. As such, the goal of this framework is to leverage quantum processors to tackle optimization,…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
Quantum Mechanics, the physical theory describing the microworld, represents one of science's greatest triumphs. It lies at the root of all modern digital technologies and offers unparalleled correspondence between prediction and…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…