It is pointed out that some already-known inequalities (Bell's inequalities) and some new ones presented here can be used to test experimentally the validity of a general conception of the foundations of microphysics. This conception mainly consists in considering sets of propositions (having the structure of lattices but possibly of non-Boolean ones) and in assuming that when a proposition is true on a system $S$ this constitutes an intrinsic property of $S$ , which can be neither imparted to $S$ nor withdrawn from $S$ as long as $S$ is "isolated." It is shown that if experiments of the type of those used to test Bell's inequalities turn out to corroborate the quantum-mechanical predictions, such a result could be used in order to invalidate directly the general conception just described. This is done without reference to the general principles of quantum mechanics. More generally, our derivation does not depend for its validity on assuming the truth of any particular physical theory abstracted by induction from experimental knowledge.It is pointed out that some already-known inequalities (Bell's inequalities) and some new ones presented here can be used to test experimentally the validity of a general conception of the foundations of microphysics. This conception mainly consists in considering sets of propositions (having the structure of lattices but possibly of non-Boolean ones) and in assuming that when a proposition is true on a system $S$ this constitutes an intrinsic property of $S$, which can be neither imparted to $S$ nor withdrawn from $S$ as long as $S$ is "isolated." It is shown that if experiments of the type of those used to test Bell's inequalities turn out to corroborate the quantum-mechanical predictions, such a result could be used in order to invalidate directly the general conception just described. This is done without reference to the general principles of quantum mechanics. More generally, our derivation does not depend for its validity on assuming the truth of any particular physical theory abstracted by induction from experimental knowledge.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsMar 15, 197548 citations

Unification of Energy Concepts in Generalized Phase Space Theories

Libo Jiang, Daniel R. Terno, Oscar Dahlsten

We consider how to describe Hamiltonian mechanics in generalized probabilistic theories with the states represented as quasiprobability distributions. We give general operational definitions of energy-related concepts. We define generalized energy eigenstates as the purest stationary states. Planck's constant plays two different roles in the framework: the phase space volume taken up by a pure state and a dynamical factor. The Hamiltonian is a linear combination of generalized energy eigenstates. This allows for a generalized Liouville time-evolution equation that applies to quantum and classical Hamiltonian mechanics and more. The approach enables a unification of quantum and classical energy concepts and a route to discussing energy in a wider set of theories.We consider how to describe Hamiltonian mechanics in generalized probabilistic theories with the states represented as quasiprobability distributions. We give general operational definitions of energy-related concepts. We define generalized energy eigenstates as the purest stationary states. Planck's constant plays two different roles in the framework: the phase space volume taken up by a pure state and a dynamical factor. The Hamiltonian is a linear combination of generalized energy eigenstates. This allows for a generalized Liouville time-evolution equation that applies to quantum and classical Hamiltonian mechanics and more. The approach enables a unification of quantum and classical energy concepts and a route to discussing energy in a wider set of theories.

arXiv:2403.01398Physical Review LettersMar 21, 20247 citations

Basic Concepts

Karl Blum

Springer series on atomic, optical, and plasma physicsOct 4, 20110 citations

Two Approaches to Measurability Concept and Quantum Theory

Alexander Shalyt-Margolin

In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture; analogs of Fourier transformations from the momentum representation to the coordinate one and vice versa are constructed. It is shown how to produce a measurable analog of the Heisenberg picture. At the end of this paper the obtained results are used to substantiate another (more general) definition of the measurability concept that is not based on the Heisenberg Uncertainty Principle and its generalization, as it has been in the previous works of the author, and may be equally suitable for both non-relativistic and relativistic cases.In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture; analogs of Fourier transformations from the momentum representation to the coordinate one and vice versa are constructed. It is shown how to produce a measurable analog of the Heisenberg picture. At the end of this paper the obtained results are used to substantiate another (more general) definition of the measurability concept that is not based on the Heisenberg Uncertainty Principle and its generalization, as it has been in the previous works of the author, and may be equally suitable for both non-relativistic and relativistic cases.

arXiv:1709.03875Sep 5, 20170 citations

Basic Concepts

Alexandre M. Zagoskin

Graduate texts in contemporary physicsJan 1, 19980 citations

S

this constitutes an intrinsic property of

S

, which can be neither imparted to

S

nor withdrawn from

S

as long as

S

is "isolated." It is shown that if experiments of the type of those used to test Bell's inequalities turn out to corroborate the quantum-mechanical predictions, such a result could be used in order to invalidate directly the general conception just described. This is done without reference to the general principles of quantum mechanics. More generally, our derivation does not depend for its validity on assuming the truth of any particular physical theory abstracted by induction from experimental knowledge.