Is Quantum Mechanics Deterministic or Non-deterministic?

Juan Pablo Jorge, Federico Holik

In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.

Peter Mittelstaedt

Stefan Bastel

This paper introduces a non-deterministic model of time as a three-dimensional structure comprising past, present, and future. The present is described as a superposition of all causal futures, with weights evolving deterministically, while the collapse into a single future remains non-deterministic. This model naturally resolves the EPR paradox by introducing a shared present for entangled particles, eliminating the need for non-locality or hidden variables. The framework is consistent with quantum mechanics, thermodynamics, and relativity.

Brigitte Falkenburg, Friedel Weinert

Mohamed Saladin El Naschie

Your Name

A deterministic framework for quantum mechanics is constructed utilizing the split octonionic algebra Osplit. Heisenberg’s uncertainty principle is derived as an algebraic identity from the trivalent associator on the manifold, restricting microscopic state functions to minimal left ideals. The current formulation ensures that quantum uncertainty remains a purely deterministic topological effect, governed by the intrinsic discrete volume constraints of the underlying division algebra. The present framework maps quantum observables directly into a completely deterministic geometric flow, defining the mass quantum as a stable topological soliton on the non-associative worldsheet.