Related papers: Von Neumann's No Hidden Variable Theorem
For a hidden variable theory to be indistinguishable from quantum theory for finite precision measurements, it is enough that its predictions agree for some measurement within the range of precision. Meyer has recently pointed out that the…
Measurement Independence is an assumption used in foundational arguments since the EPR thought experiment in 1935, and assumed in a majority of hidden variable models of QM. In this thesis we review the crucial role of this assumption in…
Bell's theorem implies that any completion of quantum mechanics which uses hidden variables (that is, preexisting values of all observables) must be nonlocal in the Einstein sense. This customarily indicates that knowledge of the hidden…
In this paper we find a simple rule to reproduce the algebra of quantum observables using only the commutators and operators which appear in the Koopman-von Neumann (KvN) formulation of classical mechanics. The usual Hilbert space of…
State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
We have recently showed that it is possible to deal with collections of indistinguishable elementary particles (in the context of quantum mechanics) in a set-theoretical framework by using hidden variables, in a sense. In the present paper…
The role of gauge invariance is reconsidered by "deriving it without assuming it" within an autonomous approach to interactions of Standard Model particles. In this approach, the renormalizable interactions are purely constrained by quantum…
In order to overcome ambiguity problem on identification of mathematical objects in noncommutative theory with physical observables, quantum mechanical system coupled to the NC U(1) gauge field in the noncommutative space is reformulated by…
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 review the well-known Hellmann Feynman Theorem (HFT), originally developed for Hermitian systems to facilitate the calculation of forces among the molecules. Our work extends this foundational theorem to the domain of non-Hermitian…
Hidden variables theories for quantum mechanics are usually assumed to satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an…
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process…
The problem of a correct description of the physical phenomena of the Heisenberg uncertainty relation is solved by using a variable hidden in Newtonian mehcanics.
We develop, as the first of a six-paper series, an operator-algebraic framework relating non-relativistic quantum mechanics and special relativity. Three structural facts organize the framework. (i)~The photon sector of free QED is a…
The structure of representations describing systems of free particles in the theory with the invariance group SO(1,4) is investigated. The property of the particles to be free means as usual that the representation describing a…
Non-Hermitian but ${\cal PT}-$symmetric quantum system of an $N-$plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H(\gamma,v,c)$ is picked up, in its special exceptional-point limit $c \to 0$ and $\gamma \to v$, as…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to…