The geometry of generalized quantum logics

Federico Holik

We discuss the relationship between logic, geometry and probability theory under the light of a novel approach to quantum probabilities which generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories.

Krystyna Bugajska, Slawomir Bugajski

Peter D. Finch

Federico Holik

We discuss the relationship between logic, geometry and probability theory under the light of a novel approach to quantum probabilities which generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories.

Wawrzyniec Guz

Wen-Ran Zhang

Without the geometry of light and logic of photon, observer-observability forms a paradox in modern science, truth-equilibrium finds no unification, and mind-light-matter unity is unreachable in spacetime. Subsequently, quantum mechanics has been shrouded with mysteries preventing itself from reaching definable causality for a general purpose analytical quantum computing paradigm. Ground-0 Axioms are introduced as an equilibrium-based, dynamic, bipolar set-theoretic unification of the first principles of science and the second law of thermodynamics. Related literatures are critically reviewed to justify the self-evident nature of Ground-0 Axioms. A historical misinterpretation by the founding fathers of quantum mechanics is identified and corrected. That disproves spacetime geometries (including but not limited to Euclidean and Hilbert spaces) as the geometries of light and truth-based logics (including but not limited to bra-ket quantum logic) as the logics of photon. Backed with logically definable causality and Dirac 3-polarizer experiment, bipolar quantum geometry (BQG) and bipolar dynamic logic (BDL) are identified as the geometry of light and the logic of photon, respectively, and wave-particle complementarity is shown less fundamental than bipolar complementarity. As a result, Ground-0 Axioms lead to a geometrical and logical illumination of the quantum and classical worlds as well as the physical and mental worlds. With logical resolutions to the EPR and Schrödinger's cat paradoxes, an analytical quantum computing paradigm named quantum intelligence (QI) is introduced. It is shown that QI makes mind-light-matter unity and quantum-digital compatibility logically reachable for quantum-neuro-fuzzy AI-machinery with groundbreaking applications. It is contended that Ground-0 Axioms open a new era of science and philosophy-the era of mind-light-matter unity in which human-level white-box AI&QI is logically prompted to join Einstein's grand unification to foster major scientific advances.