Universality of quantum symplectic structure

TL;DR

This paper demonstrates that within the `supmech' framework, the interaction between systems requires either all systems to be classical or all to be quantum with a universal Planck-like constant, highlighting a fundamental symmetry structure.

Contribution

It establishes the universality of quantum symplectic structure in the `supmech' framework, unifying classical and quantum mechanics through a common algebraic symplectic structure.

Findings

Interaction consistent only if all algebras are classical or quantum

Quantum algebras characterized by a universal Planck constant

Supports a unified algebraic framework for mechanics

Abstract

Operating in the framework of `supmech' (a scheme of mechanics which aims at providing a concrete setting for the axiomatization of physics and probability theory as required in Hilbert's sixth problem; integrating noncommutative symplectic geometry and noncommutative probability in an algebraic setting, it associates, with every `experimentally accessible' system, a symplectic algebra and operates essentially as noncommutative Hamiltonian mechanics with some extra sophistication in the treatment of states) it is shown that interaction between systems can be consistently described only if either (i) all system algebras are commutative or (ii) all system algebras are noncommutative and have a quantum symplectic structure characterized by a UNIVERSAL Planck type real-valued constant of the dimension of action.