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We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian…
It is argued that the conclusions obtained by Renninger (Zeitschrift fur Physik 136, 251 (1953)), by means of an interferometer thought experiment, have important implications for a number of still ongoing discussions about quantum…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
We propose a modification of Maxwell's macroscopic fundamental set of equations in vacuum in order to clarify Faraday's law of induction. Using this procedure, the Lorentz force is no longer separate from Maxwell's equations. The Lorentz…
The idea of atoms is old but X-rays provided the first probe into the physical atom. Photographs of X-ray scattering from crystals -Laue spots- were the first visual proof for the physical existence of atoms arranged in a perfect geometric…
Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly…
It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show…
As we approach the centennial anniversary of modern quantum mechanics this paper revisits the foundational debates through a new poll within the research community. Inspired by the survey by Schlosshauer, Kofler, and Zeilinger at the…
The last Nobel Prize of the Millenium in Physics has been awarded jointly to Professor Gerardus 't Hooft of the University of Utrecht in Holland and his thesis advisor Professor Emeritus Martinus J.G. Veltman of Holland. According to the…
An approach to quantum mechanics is developed which makes the Heisenberg cut between the deterministic microscopic quantum world and the partly deterministic, partly stochastic macroscopic world explicit. The microscopic system evolves…
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the…
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
In a recent note David Mermin attributed the idea that wave function collapse is a physical process to a misunderstanding of probability and the role it plays in quantum mechanics. There are, however, further misconceptions at play, some of…
In 1963, Eugene Paul Wigner was awarded the Nobel Prize in Physics for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry…
Quantum mechanics has lacked a widely recognized interpretation since its birth. Many of these are still under consideration because interpretations are tough or impossible to disprove experimentally. We show how to distinguish…
We trace the evolution of quantization conditions from Planck's introduction of a new fundamental constant (h) in his treatment of blackbody radiation in 1900 to Heisenberg's interpretation of the commutation relations of modern quantum…