Quantum Process Algebra with Priorities

Laszlo Tisza

The perennial aspect of the Newtonian foundation of mathematical physics is that the concept of ``motion,'' that is, ``kinematics,'' is to serve as the interface between mathematics and physics. Kinematics subdivides into the theory of orbital translation and that of undulation and spinning. Newtonian mechanics is based on giving to translational kinematics a priority over the other modes, since planetary revolution can be represented as translation modified by gravitation. The so-called breakdown of classical physics stems from giving the translational priority a canonical status and extending it to the constituents of matter. We claim that in this case the priority is to be reversed. The main content of this paper is to establish the algebraic model for an indivisible, undulating entity that we call a ``wave simplex.'' It is used as the point of departure for a non-Newtonian quantum dynamics in which physical and algebraic concepts are in close correspondence. The postulates of the classical phenomenological theories and those of the canonical theories based on translational priority are established as theorems under the proper limiting conditions, and forces are constructed rather than postulated. While the formal structure of two-level quantum mechanics is established as well, exception is taken to treating spin as a property of a point particle. It is considered self-evident that a spinning object is orientable, a property accounted for in terms of a unitary triplet. This is the point of departure for an intrinsic particle dynamics. A main result is the integration of classical and quantum physics, thus closing the gap created by the heuristic method of canonical quantization.

Viktoras Rimsha, Laimontas Rimsha

In this paper we propose a unified conceptual framework in which quantum probability, quantum logic, and classical probability theory are understood as different structural levels of a single theoretical hierarchy. Starting from a statistical interpretation of quantum interference, previously developed by the authors, we argue that quantum probability is not an alternative to classical Kolmogorov probability, but a more general structure. Classical probability theory emerges as a limiting case corresponding to the disappearance of interference and the effective decomposition of the whole into independent elements. Within this framework, the Birkhoff–von Neumann quantum logic appears as a natural logical expression of quantum probability rather than as an abstract algebraic construction detached from physical meaning. The priority of the whole over its parts plays a central role in both quantum probability and quantum logic, while classical logic and probability arise when this priority becomes trivial. We emphasize that the proposed interpretation does not reject existing quantum formalism, but reinterprets its logical and probabilistic foundations. This approach may have implications for the conceptual understanding of quantum algorithms and quantum information processing.

Yong Wang

Martin Lützel

This deposit serves as a priority record and proof-of-concept for a novel, discrete framework of quantum decoherence and error correction based on the d0 topological graph model. It documents the fundamental departure from classical continuous-time decoherence models (e−t) toward a strictly discrete, structurally quantized decay process. The uploaded material establishes intellectual priority for the algorithmic mapping of topological graph updates (Pachner moves) to quantum logic gates, demonstrating that decoherence is not a function of continuous time, but a countable geometric process of environmental entanglement.

Dick J. Hoekzema