Fractal Geometry and Nonlinear Analysis in Medicine and Biology
YinYang bipolar quantum geometry and bipolar quantum superposition Part II – Toward an equilibrium-based analytical paradigm of quantum mechanics and quantum biology
In Part I of this paper, YinYang bipolar quantum agent (BQA), bipolar quantum geometry (BQG) and 2-dimensional generic bipolar quantum superposition are introduced with a geometrical and logical exposition of Dirac 3-polarizer experiment. While the exposition qualifies BQG as a geometry of light, it is shown in this paper that the logical exposition can be extended to an analytical paradigm of quantum mechanics and quantum biology. It is shown that BQG as the geometry of light is also the geometry of Nature with a logical unification of matter and antimatter atoms into a bipolar quantum cellular automaton (BQCA) through multidimensional YinYang bipolar quantum superposition using bipolar quantum linear algebra (BQLA). With the BQCA interpretation of quantum mechanics, it is shown that matter and antimatter self-organization and spacetime emergence is logically possible within BQG. A scalable BQCA model for biological repressionactivation and/or degeneration-regeneration is introduced. Bipolar cellular division and bipolar fractality are proposed. Background independent normal and abnormal bipolar fractal branching is proposed. A discussion on quantum gravity and mathematical abstraction is presented. A few challenges and predictions are posted. It is contended that this work leads to an analytical paradigm of quantum mechanics and quantum biology that may contribute to equilibrium-based analysis of quantum decoherence and collapse as associated with quantum measurement.
In Part I of this paper, YinYang bipolar quantum agent (BQA), bipolar quantum geometry (BQG) and 2-dimensional generic bipolar quantum superposition are introduced with a geometrical and logical exposition of Dirac 3-polarizer experiment. While the exposition qualifies BQG as a geometry of light, it is shown in this paper that the logical exposition can be extended to an analytical paradigm of quantum mechanics and quantum biology. It is shown that BQG as the geometry of light is also the geometry of Nature with a logical unification of matter and antimatter atoms into a bipolar quantum cellular automaton (BQCA) through multidimensional YinYang bipolar quantum superposition using bipolar quantum linear algebra (BQLA). With the BQCA interpretation of quantum mechanics, it is shown that matter and antimatter self-organization and spacetime emergence is logically possible within BQG. A scalable BQCA model for biological repressionactivation and/or degeneration-regeneration is introduced. Bipolar cellular division and bipolar fractality are proposed. Background independent normal and abnormal bipolar fractal branching is proposed. A discussion on quantum gravity and mathematical abstraction is presented. A few challenges and predictions are posted. It is contended that this work leads to an analytical paradigm of quantum mechanics and quantum biology that may contribute to equilibrium-based analysis of quantum decoherence and collapse as associated with quantum measurement.
An equilibrium-based YinYang bipolar dynamic Generalization of CPT (G-CPT) symmetry is introduced based on energy/information conservational quantum emergence-submergence. As a bottleneck of quantum computing, quantum decoherence or collapse has been plaguing quantum mechanics for decades. It is suggested that the crux of the problem can trace its origin back to the incompleteness of CPT symmetry due to the lack of holistic representation for equilibrium-based bipolar coexistence. In this work, the notion of quantum emergence-submergence is coined as two opposite processes with bipolar energy/information conservation. The new notion leads to G-CPT symmetry supported by a Bipolar Quantum Cellular Automata (BQCA) interpretation of quantum mechanics. It is shown that the new interpretation further leads to the unification of electromagnetic particle-antiparticle bipolarity and gravitational action-reaction bipolarity as well as CPT symmetry and CP violation into a philosophically, geometrically and logically different quantum gravity theory. On one hand, G-CPT symmetry enables a Bipolar Quantum Agent (BQA) to emerge as a bipolar quantum superposition or entanglement coupled to a globally coherent BQCA; on the other hand, G-CP violation supports a causal theory of BQA submergence or decoupling from the global coherence. In turn, BQAs can submerge from one world but emerge in another within YinYang bipolar quantum geometry. It is suggested that all logical, physical, social, biological and mental worlds are bipolar quantum entangled under G-CPT symmetry. It is contended that G-CPT symmetry constitutes an analytical paradigm of quantum mechanics and quantum gravity—a fundamental departure from “what goes around comes around”. The new paradigm leads to a number of predictions and challenges.
Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement; 2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality.
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.
YinYang bipolar relativity leads to an equilibrium-based logically complete quantum theory which is presented and discussed in this chapter. It is shown that bipolar quantum entanglement and bipolar quantum computing bring bipolar relativity deeper into microscopic worlds. The concepts of bipolar qubit and YinYang bipolar complementarity are proposed and compared with Niels Bohr’s particle-wave complementarity. Bipolar qubit box is compared with Schrödinger’s cat box. Since bipolar quantum entanglement is fundamentally different from classical quantum theory (which is referred to as unipolar quantum theory in this book), the new approach provides bipolar quantum computing with the unique features: (1) it forms a key for equilibrium-based quantum controllability and quantum-digital compatibility; (2) it makes bipolar quantum teleportation theoretically possible for the first time without conventional communication between Alice and Bob; (3) it enables bitwise encryption without a large prime number that points to a different research direction of cryptography aimed at making prime-number-based cryptography and quantum factoring algorithm both obsolete; (4) it shows potential to bring quantum computing and communication closer to deterministic reality; (5) it leads to a unifying Q5 paradigm aimed at revealing the ubiquitous effects of bipolar quantum entanglement with the sub theories of logical, physical, mental, social, and biological quantum gravities and quantum computing.
While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term “equilibraton” is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence.