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.
Charge-Parity-Time (CPT) symmetry is widely regarded as a fundamental property of physical laws that govern the evolution of our universe. It is a common belief that a CPT transformation turns our universe into its “mirror image” and vice versa. It has the implication that a “mirror-image” of our universe―with all objects having their positions reflected by an arbitrary plane (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (corresponding to a charge inversion)―would evolve under exactly our physical laws. In order to preserve CPT symmetry, every violation of the combined symmetry of two of its components (such as CP) must have a corresponding violation in the third component (such as T); in fact, mathematically, these are the same thing. Thus, violations in T symmetry are often referred to as CP-violations. CP-violation is the violation of the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C symmetry) and when its spatial coordinates are inverted (“mirror” or P symmetry). The discovery of parity non-conservation or P-violation [
It can be argued that, without a formal geometrical and logical basis for equilibrium-based bipolar coexistence, CPT symmetry as a truth-based model is an incomplete or even flawed theory. For instance, we know that once antimatter and matter existed in near perfect unitary counterbalance but antimatter vanished without a trace on a cosmic scale. This remains one of the greatest mysteries of the universe. On the other hand, newly discovered particle-antiparticle oscillation [
Questions of Group 1. Why “mirror-image”? Isn’t our universe in a dynamic equilibrium of bipolar coexistence of particle-antiparticles and negative-positive energies? Is there a unification of energy and information? What is the logic of CPT symmetry? What is the geometry of CPT symmetry? What is the cause of CPT symmetry? What is the role of CP-violation in quantum coherence and decoherence or collapse? Is there a logical unification of CPT symmetry and CP violation? Without bipolar dynamic equilibrium can any truth-based model be complete?
In a classical world, emergence is the process of coming into view or becoming exposed after being concealed. Generally speaking, it is the process of coming into being important or prominent. While natural and social emergence is observed everywhere in the classical world, emergence at the quantum level remains a mystery undefined logically and mathematically. Up to this day, we do not have a generally accepted view on how quantum superposition and entanglement emerges, how matter and antimatter emerges, and how spacetime emerges after the Big Bang. Even worse, after decades intensive research, we still don’t know how some important quantum phenomena can disappear. Besides, the supposedly spacetime disappearance into a black hole, as a bottleneck of quantum mechanics and quantum computing, quantum decoherence and collapse theories associated with measurements, has been without a major theoretical breakthrough for decades. If quantum coherence is an emergence, could quantum decoherence or collapse be submergence? If so, how can we define quantum emergence and submergence as opposite processes in logical and mathematical terms?
The difficulty with the collapse approach is that, given an initial state with a certain symmetry, one cannot end up with a state that fails to have the symmetry in question. The problem is that Shrödingier’s equation is fully deterministic and the only place where determinism is lost in the context of quantum theory is at the point where one addresses the connection with the measurements. Thus, researchers of dynamical collapse theories seek to modify quantum theory by assuming a fundamental departure from Shrödingier’s deterministic wave function. Roger Penrose has been a strong advocate for such a departure [
Different from quantum collapse, quantum decoherence in quantum mechanics is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition while a total superposition of the global or universal wave function is assumed remain intact (and remains coherent at the global level). Since quantum computers are expected to rely heavily on the undisturbed evolution of quantum coherence, decoherence becomes a bottleneck for the practical realization of quantum computers which require that coherent states be preserved and that decoherence be managed, in order to actually perform quantum computation. Research on decoherence has gained momentum in recent decades since it is proposed in 1970 [
While no major theoretical breakthrough has been reported in this research area, in July 2011, researchers from University of British Columbia, Canada, and University of California, Santa Barbara, were able to reduce environmental decoherence rate “to levels far below the threshold necessary for quantum information process- ing” by applying high magnetic fields in their experiment [
Question of Group 2. Can quantum emergence and submergence be a unifying theory of coherence and decoherence? Can a quantum cellular automaton be bipolar equilibrium-based? Can the cause of coherence and decoherence be geometrically and logically revealed? Can CP-violation be the cause?
While it seems that there is no good option capable of addressing the issue at hand within the existing range of interpretational approaches to quantum theory, new interpretations of quantum mechanics have been reported. A cellular automaton interpretation (CAI) is proposed and strongly advocated by Gerard ‘t Hooft [
Notably, ‘t Hooft avoided the quantum coherence and decoherence problem in his CAI interpretation of quantum mechanics. He stated: “Some authors do suspect that gravity is a new elementary source of ‘quantum decoherence’, but such phrases are hardly convincing. …Anyway, decoherence [
While the CAI interpretation by ‘t Hooft can be deemed a truth-based realist approach to quantum mechanics, an equilibrium-based bipolar quantum cellular automata (BQCA) theory is presented in [
Questions of Group 3. Could a cellular automaton interpretation of quantum mechanics provide a fundamental departure from the established theories and observations? How does the new interpretation relate quantum superposition and entanglement to agents in quantum and classical worlds? Can quantum emergence and submergence unify quantum coherence, decoherence and collapse theories under a generalized theory of CPT symmetry? Can local BQCAs form a globally coherent BQCA? Can the nature of coherence and decoherence be revealed by multiagent BQCA emergence and submergence?
Background independence is a desirable property in the quest for quantum gravity. Lee Smolin is best known for advocating background independence in his quest for loop quantum gravity [
The crux of the problem is that there is no precise definition for background independence. We need a minimum set of necessary and sufficient conditions for complete background independence. Without such a set of conditions, a unique logical foundation for quantum gravity cannot be developed. For instance, until this day, a popular definition of a background independent geometry requires the unnecessary condition of being coordinate-free but does not require the imperative condition of supporting both reductionism and emergence. This definition failed to realize that some coordinate can be completely background independent. Without any such coordinate, it would be impossible to have background independent logical reasoning on quantum emergence and submergence. The unnecessary and insufficient conditions have inhibited the development of a truly background independent geometry and a new formal logical foundation for quantum gravity. As a result, the quest for quantum gravity has so far failed to find a definitive battleground and quantum superposition and entanglement still find no formal logical definition in Hilbert space. Now we post the 4th set of key questions:
Questions of Group 4. What is complete background independence? Could quantum superposition and entanglement be logically characterized as background independent quantum emergence? Could quantum decoherence and dynamic collapse be characterized as quantum submergence? Could quantum decoherence and collapse be fundamentally CP-violation under a generalized CPT symmetry? Can a background independent geometry have a coordinate? Can a quantum world be unified with a classical world within a background independent geometry?
In a search for answers to the four groups of questions, this work presents G-CPT symmetry―a fundamentally different interpretation of quantum mechanics (Note: The notion “G-CPT symmetry” is first coined in [
This work is organized in six sections. Section 2 presents a background review and analysis of the basic development of the theory with scientific support. Section 3 presents G-CPT symmetry as an equilibrium-based quantum cellular generalization of CPT symmetry―a unifying paradigm of quantum emergence and submergence for causal analysis of quantum coherence and decoherence or collapse. Section 4 presents a many-world model of quantum emergence and submergence. Section 6 presents a discussion and makes a number of predictions based on the theory. Section 5 draws a few conclusions.
Niels Bohr was the first to bring YinYang into quantum theory for his wave-particle duality principle. When Bohr was awarded the Order of the Elephant by the Danish government, he designed his own coat of arms (
It is observed, however, that particle and wave are not direct opposites. While Bohr recognized wave-particle complementarity, he stopped short of identifying the essence of YinYang bipolar coexistence and bipolar complementarity (
Theoretically, if bipolar dynamic equilibrium of negative-positive energies and/or input-output information is the most fundamental form of equilibrium, any multidimensional model in spacetime geometry is less fundamental. A YinYang bipolar complementarity principle is, therefore, imperative for a bipolar equilibrium-based logical interpretation of the quantum world.
YinYang bipolar complementarity principle claims that action-reaction, particle-antiparticle, input-output, negative-positive energies, or the Yin and the Yang of Nature in general constitute the direct opposites (
According to the bipolar complementarity principle, man-woman, space-time, particle-wave, truth-falsity, mind-matter, and imaginary-real complementarities are not exactly bipolar opposites, not bipolar interactive and, thus, less fundamental. For instance, while particle-wave and space-time do not form symmetries and do not interact with each other as bipolar opposites, they can be posited the result of particle-antiparticle bipolar interaction. It is suggested that this could be the reason why Bohr asserted that a causal description of a quantum
process cannot be attained and quantum mechanics has to content itself with wave-particle complementary descriptions [
Quantum superposition plays a key role in quantum coherence. In his textbook, Paul Dirac [
Despite the theoretical significance, Dirac’s examples suggest a very simple and inexpensive experiment to demonstrate quantum superposition of polarized photons. Such an experiment is usually performed in high school physics labs. The experiment tells us:
1) Light gets through polarizers (filters) A and B if both are aligned vertically (or horizontally) (
2) If polarizer A remains in vertical polarization and polarizer B is rotated 90˚ to horizontal polarization, no light gets through (
3) Light partially gets through the intersection of polarizer C with polarizer A and polarizer B if C is turned along the diagonal 45˚ and slipped between A (in the rear) and B (in front) (
According to Dirac, with complex number coefficients that represent “probability amplitudes”, the diagonally polarized photon can be represented as a superposition of vertical v and horizontal h states with bra-ket notation in Hilbert space (
Einstein and Schrödinger later attacked the idea of superposition by arguing that it would apply to macroscopic objects like a cat being alive and dead. This quantum phenomenon has been referred to as Schrödinger’s Cat paradox. On the other hand, the quantum mechanical interpretation of entanglement is questioned by the EPR paper [
Schrödinger’s Cat has remained a paradox for many decades. An equilibrium-based bipolar quantum geometry (BQG) is proposed based on the YinYang bipolar complementarity principle for resolving the paradox [
Definition 1. A bipolar dynamic equilibrium is a process of bipolar interaction and state change among bipolar equilibrium, non-equilibrium, and eternal equilibrium states of any action-reaction pair or any collection of such pairs.
Definition 2. A bipolar quantum agent (BQA) is a bipolar dynamic equilibrium. A global bipolar dynamic equilibrium may subsume local ones and a non-elementary BQA may consist of elementary BQAs (Adapted from [
Definition 3. A BQA is said equilibrium-based if it adapts to an equilibrium state under a closed world condition or without external disturbance.
Postulate 1. If an elementary particle or BQA is in a non-equilibrium negative state that can be characterized with the bipolar value (−1,0), its antiparticle must be a BQA in another non-equilibrium state that can be characterized with the bipolar value (0,+1) and the two in a pair without annihilation must be a BQA in an equilibrium state which can be characterized with the bipolar value (−1,+1). The non-existence or annihilation of the particle-antiparticle pair can be characterized with an eternal equilibrium state with the bipolar value (0,0).
Postulate 2. If an elementary particle is its own antiparticle, the BQA must have distinct states that can be characterized as negative (−1,0), positive (0,+1), bipolar equilibrium (−1,+1) and eternal equilibrium (0,0), respectively.
Postulate 3. A BQA as a bipolar dynamic equilibrium can emerge from the Yin and Yang of Nature or from other elementary BQAs and can submerge back to the Yin and Yang or other elementary BQAs.
Definition 4. Bipolar quantum geometry (BQG) has three shape-free and quadrant-irrelevant dimensions: the Yin and the Yang dimensions are the two reciprocal and interdependent bipolar opposites from which a third dimension―bipolar dynamic equilibrium as a bipolar quantum superposition of the Yin and Yang dimensions- can emerge and submerge.
Definition 5. A geometry with complete background independence must satisfy the minimum set of conditions: 1) it is shape-free, quadrant irrelevant and spacetime transcendent; 2) it supports reductionism, emergence and submergence; 3) it is ubiquitous.
It is proven that BQG satisfies the conditions of complete background independence [
BQA and BQG provide an ontological and geometrical basis for an equilibrium-based mathematical abstraction for both reductionism and emergence. The equilibrium-based mathematical abstraction have led to bipolar dynamic logic (BDL), bipolar dynamic fuzzy logic (BDFL) and bipolar quantum linear algebra (BQLA) [
deemed a real-valued extension of BDL on one hand or a bipolar dynamic generalization of fuzzy logic (FL) [
§ BL is truth-based without physical semantics and BDL is equilibrium-based with both logical and physical semantics. BDL generalizes BL from the truth-based domain or Boolean lattice L = {0,1} to the equilibrium-based domain or quantum lattice B1 = {−1,0} 0,+1}. BL is not a causal logic. BDL is a formal causal logic (see Appendix).
§ BDFL is a bipolar dynamic generalization of FL from the truth-based domain or fuzzy lattice LF = [0,1] to the equilibrium-based domain or quantum lattice
§ BQLA is a bipolar dynamic generalization of linear algebra (LA) from the truth-based domain or lattice L∞ = [−∞,+∞] to the equilibrium-based domain or quantum lattice
§ Without bipolarity BL, FL and LA are inadequate for the direct representation of a BQA with equilibrium and non-equilibrium states.
§ Without a shred of dynamics, truth-values cannot form a causal set like B1, BF and B∞.
§ BDL, BDFL and BQLA subsume BL, FL and LA because any being or truth in spacetime must exist in a bipolar dynamic equilibrium of input-output information or negative-positive energies.
§ BL, FL and LA can be used together with BDL, BDFL and BQLA as long as equilibrium or non-equilibrium conditions are not violated.
BDL leads to a number of simplifications. Quantum superposition in Dirac’s bra-ket notation (Equation (1)) can be simplified to Equation (2a) in bipolar logical form. Quantum entanglement can be logically defined by Equation (2b). The simplification makes it possible to avoid complex number coefficients. Since BQG is background independent, vertical (v) and horizontal (h) as two direct opposites in a bipolar dynamic equilibrium each can be negative or positive, respectively. Without bipolarity, however, Dirac’s quantum superposition principle does not account for bipolar complementarity, does not support emergence and submergence through bipolar interaction, and stopped short of evolving to a logical definition for quantum superposition and entanglement. BQG and BDL, on the other hand, provides a geometrical and logical basis for both quantum superposition and quantum entanglement.
Bipolar Logical Definition of Generic Quantum Superposition:
Bipolar Logical Definition of Generic Quantum Entanglement:
A key element of BDL is bipolar universal modus ponens (BUMP)―a bipolar dynamic generalization of modus ponens (MP) which states that,
In Equation (2c),
space p is therefore more specific. BUMP reads: If
It is shown in [
1) Let vertical polarizers A and B be both in state (0,+1) or let two horizontal polarizers be both in state (−1,0), logically, we have
2) Let vertical polarizer A be in state (0, +1) and horizontal polarizer B in state (−1, 0),
3) Let diagonal polarizer C (45˚) be in bipolar equilibrium state (−1,+1), the question is how a single photon can logically get through A, C and B if C is slipped between A and B.
Is there a bipolar conjunctive operator in BDL that allows a single photon to get through the three polarizers in Case (c)? The problem can be formulated as: What is the unknown operator *such that
1)
2)
If the Boolean operator & takes effect in the place of *, light can only get through the diagonal polarizer C but cannot get through B as we have:
BDL does, however, have another conjunctive &- such that
The results in Equations (3a)-(3d) are supported with well-known experimental results for the quantum superposition principle [
While Dirac tells us that “diagonally polarized photon can be represented as a superposition of vertical and horizontal states, with complex number coefficients that represent probability amplitudes,” the nature of superposition has never been logically clarified. It is shown in [
mysterious without a unique logical system for equilibrium-based bipolar dynamic reasoning. Thus, the analytical power of the quantum mechanical interpretation of superposition is compromised by the complex number coefficients.
For instance, the probability for a vertically prepared photon to pass the diagonal polarizer C as a square of a
complex number coefficient is
brium-based bipolar logic or probability value (−1/4, +1/4). Evidently, we have
general, the bipolar probability amplitude of a bipolar variable
Furthermore, it is clear from
The comparison further confirms that YinYang bipolar complementarity is the most fundamental complementarity which may lead to the emergence and submergence of a bipolar quantum superposition. On the other hand, the real and imaginary dimensions of complex numbers are not most fundamental because they do not support background independent bipolar interaction and emergence.
According to the bipolar complementarity principle, space-time and particle-wave complementarities are less fundamental concepts subject to bipolar complementarity and bipolar dynamic equilibrium. Thus, the 3-D information of particle-wave in Hilbert space are ever changing phenomenon because spacetime is ever changing due to bipolar dynamic equilibrium. We need a point of departure from spacetime relativity and particle-wave duality. While BDL is such a point of logical departure, BQLA extends BDL to a point of mathematical departure from bra-ket notations in Hilbert space. The result is a multidimensional bipolar equilibrium-based unification of energy and information for symmetry and regulation of multiple BQAs in the background independent ubiquitous BQG.
Given bipolar quantum agent
§ The Yin or negative energy/information of e:
§ The absolute Yin energy/information of e:
§ The Yang or positive energy/information of e:
§ The absolute Yang energy/information of e:
§ Equilibrium state of e:
§ Non-equilibrium state of e:
§ Eternal equilibrium state of e:
§ Bipolar energy/information of e:
§ Imbalance of e:
§ Balance of e:
§ Harmony of e:
§ Bipolar superposition in scalar form:
§ Bipolar superposition in vector form:
§ Superposition magnitude:
§ Equilibrium-Based Unification of energy/information:
The unification of energy/information provides a necessary condition for an equilibrium-based energy/infor- mation conservational generalization of CPT symmetry. Elementary energy/information measures can be extended to system energy/information measures with BQLA for bipolar regulation. Each row, column, or a whole bipolar matrix can have negative, positive and bipolar energy/information with absolute total and balance. While BDL is logical but not fully mathematical, BQLA leads to an algebraic unification of bipolar energy/informa- tion that in turn leads to formal algebraic definitions of equilibrium and harmony―a unifying concept for both the classical and quantum worlds.
Bipolar Algebraic Addition:
Bipolar Algebraic Multiplication:
Linear multiplication or division:
Bipolar Conjunctive Multiplication:
Bipolar Disjunctive Multiplication:
With Equation (5a)-(5b), system level bipolar quantum superposition of multiple BQAs can be mathematically characterized with bipolar matrix addition and multiplication using BQLA similarly as in LA. We prove in what follows that quantum superposition with bipolar addition and multiplication makes it possible to have a fundamental departure from Dirac’s Bra-ket superposition in Hilbert space for systematic analysis of multiple BQA superposition.
Theorem 1. With background independence, bipolar addition is essentially bipolar quantum superposition of two BQAs into one in BQG.
Proof. Given BQAs A = (x, y) and B = (u, v), following Equation (4m) and Equation (5) we have:
Since A and B are both bipolar vectors in BQG, Hilbert space vector addition is converted to scalar addition in Equation (6) as illustrated in
Theorem 2. With background independence, bipolar multiplication can, under certain condition, be used to characterize equilibrium-based BQA composition into a new BQA through bipolar interaction and superposition in BQG.
Proof. While composite BQA is discussed later, at the most abstract level a BQA is simply a bipolar dynamic equilibrium per Definition 2. Given two BQAs A and B, let A = (x,y) and B = (u,v), a new BQA C can be formed where
Theorem 3. With background independence, bipolar multiplication converts vector multiplication from Hilbert space to algebraic computation in BQG with the preservation of vector magnitude and without the preservation of background dependent information.
Proof. It follows from that
Theorem 4. With background independence, bipolar matrix multiplication can, under certain condition, be used for characterizing the composition of a set of BQAs into another set of BQAs through bipolar interaction and quantum superposition in BQG.
Proof. Given the square bipolar matrix
the column bipolar matrix
formed where
Thus, the multiplication of a row BQA matrix and a column BQA matrix results in a new BQA―an ensemble or composite of component BQAs in a superposition. The result of each such row by column multiplication results in a newly composed BQA. An n × n bipolar square matrix multiplied by an n × 1 bipolar column matrix results in n new column matrix of BQAs which can be deemed a set of BQAs or a single composite BQA.
All agents are input/output (I/O) systems that can be classified as linear or nonlinear. If we apply input x to a dynamic system and obtain output y, scaling input x may give a scaled y such as the input ax leads to ay, where a is a scalar. When this property is true, we say that the I/O system is a linear system. Otherwise, it is nonlinear.
Similarly, a logic is said a linear logic if it satisfies the distributive law such as
Logical linearity and physical nonlinearity can be deemed a duality. It is unclear, however, how to unify logical linearity and physical nonlinearity for nonlinear dynamic logical reasoning of quantum superposition. Is there a dynamic logic that is logically linear but physically nonlinear?
BDL, BDFL and BQLA [
A further examination, however, reveals that, due to equilibrium-based bipolar dynamic interaction, BDL presents a unification of logical and physical systems. Since all beings must exist in certain bipolar dynamic equilibrium of input-output (I/O) or negative-positive energies/information, the bipolar operators can characterize different bipolar dynamic interactions and can change an equilibrium state to a non-equilibrium state with nonlinear bipolar dynamic behaviors. For instance, a(input, output) or a(−pole, +pole) is a linear scaling if a is a scalar; (−1,0) &-( −1,+1) = (0,+1) is logically linear but physically non-linear because a bipolar variable is not a scalar and a bipolar operator does not scale. Thus, logically, the binary operators of BDL are linear or bilinear that provide a basis for the soundness of the logic; physically it has nonlinear dynamics embedded and is inherently nonlinear. This is fundamentally different from truth-based linear or bilinear systems which do not assume equilibrium-based physical semantics.
It may be further argued that linearity, by definition, refers to the mathematical property but not physical property of a system such as linear logic (cf. [
With the logical basis, BQLA borrows the forms of classical linear algebra but performs nonlinear bipolar dynamic operations in bipolar dynamic equilibrium domains. As a nonlinear bipolar dynamic generalization of LA, BQLA is to BDL as LA is to BL or BQLA is to LA as BDL is to BL. With the unification of logical linearity and physical non-linearity, an information conservational unification of CPT symmetry and CP violation under bipolar dynamic equilibrium is made possible.
The concepts of bipolar elementary energy and information laid a basis for modeling bipolar quantum superposition of multiple BQAs as a multidimensional dynamic equilibrium with BQLA.
Electron and positron form a typical bipolar particle-antiparticle pair. It is believed that matter and antimatter once existed in near perfect counterbalance immediately after the big bang but antimatter vanished without a trace on a cosmic scale-one of the greatest mysteries of the universe. Today, antimatter does not exist normally, at least on Earth, but we know that it is real because positron has been discovered [
Since an electron carries one unit of negative charge (−1), a negative charge is generally deemed an electron. On the other hand, a positron carries one unit of positive charge (+1) but a positive charge is not deemed a positron. This conceptual imbalance can trace its origin to Dirac’s prediction of positron [
Now, it is well-known that, in positron emission or beta plus decay (β+ decay), a proton is converted to a neutron while releasing a positron (β+) and an electron neutrino. On the other hand, in beta minus decay (β− decay), a neutron turns into a proton and the nucleus emits an electron (β−) and an antineutrino. To certain extent, positron emission justifies proton being an island of positron as Dirac originally suggested. The problem is that proton consists of quarks [
asymmetry. According to Richard Feynman, the “encryption” or hidden positron idea was suggested by John Wheeler in 1940 (cf. [
In any case, matter and antimatter atoms are formed with particles and antiparticles in certain combinations. The quarks of a proton do carry a total of one positive charge and a proton does emit a positron in β+ decay. In terms of negative-positive energy/information conservation, the hidden positron hypothesis is logically a valid theory. The theory has led to an equilibrium-based axiomatization of physics with BDL and BQLA in BQG [
Postulate 4. An antiparticle can be logically encrypted and physically concealed or insulated within a particle and vice versa.
Postulate 5. A positron is logically encrypted and physically concealed within a proton to prevent it from annihilation with an electron; an electron is logically encrypted and physically concealed within an antiproton to prevent it from annihilation with a positron.
Based on the above postulate, we have
Definition 6 (Matter and Antimatter Emergence and Submergence). A matter or antimatter atom is logically a set of electron-positron pairs or BQAs insulated from annihilation and regulated by the nucleus of the atom. When N electron-positron pair(s) as component BQAs
Theorem 5. Matter or antimatter emergence can be characterized as a multidimensional quantum superposition with a bipolar quantum cellular automaton interpretation of quantum mechanics.
Proof. Given N electron-positron pair(s) insulated from annihilation as component BQAs
BQCA in BQLA:
BQCA Power Law:
In Equation (7), M(t) is an N by N bipolar quantum logic gate matrix that characterizes the nucleus bipolar regulatory energy/information at time t; E is an N by 1 bipolar matrix characterizing the bipolar energy/information of a column matrix of N BQAs such as the electron-positron pairs of an atom at time t. Equation 7(a) is based on Equation (5a)-(5b). It defines system level quantum superposition with BQLA matrix multiplication; Equation 7(b) defines a bipolar quantum power law. Time is introduced into the equations (Note: Although BQG is background independent, it subsumes spacetime, time and/or space can be added as needed).
Thus, a BQCA characterizes a multidimensional bipolar dynamic equilibrium emerged from bipolar quantum superposition without annihilation due to the concealment (See Postulates 4 and 5).
of wave and particle [
With BQCA, a quantum agent can be regulated to maintain energy/information conservation. When the absolute total energy of each row
While the condition that the absolute total energy and/or information of each row
Definition 7. Given a regulatory bipolar matrix M(t) defined on BF such that
Theorem 6. The law of energy/information conservation/preservation, degeneration and regeneration:
1) An energy/information conservational bipolar quantum logic gate matrix exhibits holistic energy/informa- tion conservation regulatory functionality at the system level. That is, if ∀j,
2) An energy/information regeneration bipolar quantum logic gate matrix exhibits holistic energy/informa- tion regeneration regulatory functionality at the system level. That is, if ∀j,
3) An energy/information regeneration bipolar quantum logic gate matrix exhibits holistic energy/informa- tion degeneration regulatory functionality at the system level. That is, if ∀j,
Proof. 1) If ∀i,j,
It can be further postulated that energy/information degeneration or regeneration increases or decreases energy/information of the environment, respectively. Thus, bipolar energy/information conservation (Equations 8a-8b) can be deemed a global dynamic equilibrium process with local non-equilibrium states. It can be further posited a necessary condition for quantum coherence. Under this condition, local CP-violation can lead to harmonic oscillations among a set of BQAs. This can be posited another condition for coherence. Global energy/information conservation with local CP-violation is illustrated as follows:
Column energies of
Global energy/information conservation of
Figures 9(a)-(d) show examples of bipolar energy/information conservation, regeneration, degeneration and oscillation, respectively, with particle-wave unification. Each bipolar wave form is also a BQA = (x,y) or a bipolar subatomic particle.
Theorem 7. Quantum decoherence and collapse can be logically unified under quantumsubmergence of a multidimensional quantum superposition with a bipolar quantum cellular automaton interpretation of quantum mechanics.
Proof. Based on Equation (8), when
Definition 8. A BQA in the logical form (x,y) is said a primitive BQA. A BQA in the BQCA matrix form
Definition 9. Given two BQAs A1 and A2, primitive or composite, we say A1 and A2 are in a 2-party quantum entanglement, denoted A1W A2, if
It should be noted that, for any bipolar agent A we have
Theorem 8. Without bipolar coexistence of negative-positive energies/information, bipolar interaction and energy/information conservation would be impossible with CP-violation.
Proof. First, without bipolar coexistence of negative-positive energies/information, bipolar interaction and CP-violation cannot be fully represented. Secondly, without such bipolar coexistence, the absolute total energy/information equality
While truth has been deemed the essence of being since Aristotle, without bipolarity truth-based logic and linear algebra are incapable of bipolar causal interaction, self-organization, and dynamic regulation for bipolar emergence and submergence due to bipolar cancelation. For instance,
The above examples clearly show that, without bipolar regulation, bipolar equilibrium-based emergence and submergence is impossible. Of course, we can attempt to use a positive regulation matrix. But a positive matrix does not show bipolar interaction and balancing cause-effect relation toward a bipolar dynamic equilibrium, non- equilibrium or oscillating state. For instance,
From the above, it is clear that (−,+) bipolarity is a key for bipolar causality, bipolar quantum superposition and bipolar quantum entanglement. It provides a holistic, unitary, and analytical framework for the complex interaction and regulation of quantum agents. While quantum mechanics heavily relies on probability and do not lend itself as an analytical system, the analytical nature of the bipolar equilibrium-based approach provides a geometrical and logical basis of quantum mechanics, quantum gravity, quantum emergence and submergence for the analysis of coherence, decoherence and/or collapse.
Theorem 8 shows that, different from other alternative interpretations of quantum mechanics, BQCA as a point of departure from quantum mechanics is a fundamental one. The tradeoff is the less fundamental 3-D space which emerges from bipolar interaction in a forever changing state, the gain is the most fundamental equilibrium-based background-independent bipolar complementarity for logically definable causality of local and non-local quantum agent emergence and submergence toward an equilibrium-based computing paradigm of quantum agents and quantum intelligence [
Theorem 9. Any natural agent can be characterized as a BQA or BQCA and any BQA or BQCA can be characterized as either a vector or point in BQG.
Proof. It follows from that any being in the universe including the universe itself can be characterized as a bipolar dynamic equilibrium of negative-positive energies. Andgiven any BQA or BQCA variable A, we have
While BDL provides a basis for generic quantum superposition and entanglement, BQLA and BQCA provides a computational basis for multiagent quantum superposition and entanglement. In this section we present an axiomatic formulation of G-CPT symmetry of multiple BQAs for quantum emergence and submergence.
Definition 10. 1) G-CPT Symmetry is an equilibrium-based generalization of CPT symmetry where electromagnetic particle-antiparticle and gravitational action-reaction bipolarities are unified into a dynamic equilibrium of bipolar coexistence. 2) Under G-CPT symmetry, any unregulated or asymmetrical movement of an object constitutes a G-CP-violation or G-T-violation.
For instance, the apparatus movement in an asymmetrical quantum measurement can be deemed unregulated. Natural and symmetrical movements of celestial objects, on the other hand, can be deemed regulated by G-CPT symmetry. Thus, Definition 10 prompted the entry of G-CP-violation into causal analysis of quantum decoherence and collapse.
Theorem 10. (2-party entanglement emergence and submergence). Given BQAs
1) Keeping
2) Keeping both M1(t) and M2(t) energy/information conservational at all times, formally,
Proof. To have
It should be remarked that Theorem 10 provides some necessary conditions for quantum coherence that may not be sufficient. For instance,
Theorem 11 (Information preservation principle). Quantum emergence and submergence entails the preservation of global G-CPT symmetry with or without local G-CP-violation.
Proof. It follows from that without global G-CPT symmetry there would be no bipolar dynamic equilibrium, no bipolar quantum agents (BQAs), no Yin and no Yang.
Theorem 12 (Information no-preservation principle). Quantum emergence and submergence cannot preserve background dependent information such as space and time.
Proof. It follows from that bipolar dynamic equilibrium entails G-CP-violation or equivalently G-T-violation which causes spacetime fluctuation.
Theorem 13 (Indeterminacy principle). If quantum coherence and decoherence or collapse are fundamentally quantum emergence and submergence under G-CPT symmetry, there would be no deterministic solution to the “measurement problem” in spacetime geometry; a relativistic and analytical approach to the problem in a background-independent geometry would be unavoidable.
Proof. It follows from Theorems 11 and 12.
Theorem 14. Since BQLA addition and multiplication operations can preserve G-CPT symmetry, G-CPT symmetry can be preserved in the emergence and submergence of a multiagent BQCA consisting of local or non-local background-independent BQAs with or without G-CP-violation using BQLA within BQG.
Proof. It follows from the proofs of Theorems 1 - 13.
Theorem 15 (Collective adaptation to global equilibrium under G-CPT Symmetry). Given
Proof. It follows from that Condition (1) enables the energy of each element of E(t) be transmitted and distributed to E(t+1) in 100% with or without G-CP-violation; Condition (2) prevents the energy of E from bipolar oscillation toward a globally isotropic quantum world. Thus, the rebalancing process will continue indefinitely based on Equation (7a)-(7b) even after a dynamic bipolar equilibrium or symmetry is reached.
Based on Theorem 15, it can be concluded that, without bipolarity, there would be no G-CPT symmetry because: a) without bipolarity, there would be no charge parity and bipolar energy/information conservation as for Condition (1); b) without bipolarity, Condition (2) in Theorem 15 cannot be met.
With the discovery of CP-violation, CPT (Charge-Parity-Time) symmetry is now believed a fundamental law in physics (cf. [
Theorem 16 (Unification of CPT Symmetry and CP Violation). All symmetries in the universe are direct or indirect results of G-CPT symmetry. All violations of symmetry are direct or indirect results of G-CP-violation under the dynamic equilibrium of a global G-CPT symmetry..
Proof. Since weak and strong nuclear forces can be unified with electromagnetic force per Nobel Prizes in physics for 1979 and 2008 [
While bipolar quantum superposition and entanglement makes quantum emergence and submergence possible, with energy/information preservation the emergence and submergence makes it possible for different quantum worlds to come and go with G-CPT symmetry. For instance, a big bang leads to the emergence of a world and a black hole leads to the submergence of a world. Naturally, G-CPT symmetry subsumes an equilibrium-based many world model of quantum coherence and decoherence or collapse. The new approach is distinguished from other many-world or multiverse models by 1) its ubiquitous background-independent geometrical basis, 2) its bipolar dynamic logical basis and 3) its equilibrium-based unification of the many worlds into a single universe for geometrical, logical and causal analysis of quantum coherence and decoherence or collapse.
A 1-world BQG (1W-BQG) as a 2-dimensional space of YinYang bipolar complementarity is pivotal in hosting BDL, BQLA, and BQCA for BQA formation and multiagent BQA interaction in a dynamic equilibrium or non- equilibrium. While all agents in the universe can be deemed BQAs, how agents in the classical world interact with those in the quantum world is a mystery. For instance, the cause of decoherence and/or collapse by a measurement apparatus―a visiting BQA from the classical world-is geometrically and logically an unknown. We thus have the question: Can the background independent BQG be used to model BQA interactions between a classical and a quantum world?
Theorem 17. If BQAs in both the classical and the quantum worlds are all characterized as a bipolar dynamic equilibrium in bipolar scalar forms of (x,y) and (u,v),
Proof. It follows from that,
To illustrate we show in
While BQG has been proven adequate for hosting BDL, BQLA, and BQCA for BQA formation and multiagent BQA interaction in dynamic equilibrium or non-equilibrium, the conversion of agents from the classical world to the quantum world is practically impossible in many cases. For instance, a quantum disturbance can be caused by
a measurement apparatus―a visitor agent from the classical world, but it is a stranger in the quantum world. One possibility is to go back to 2-D and then n-D Hilbert space. But it would be problematic because the condition for complete background independence will be violated. Without the condition quantum agent emergence and submergence would be impossible. Another possibility is to define the remaining 2-D space beyond the BQG as a classical world. The 2-world arrangement allows multiagent BQCA formation in the quantum world and bipolar interaction between the two different worlds. Each world follows a different mathematical abstraction: one is equilibrium-based and background independent; another is truth-based and background dependent. Since any being or truth has to stay in certain bipolar dynamic equilibrium, the two worlds are unified under bipolar dynamic equilibrium
Definition 11. A 2-World BQG (2W-BQG) consists of two 2-D regions: 1) a bipolar equilibrium-based quantum world which forms the original BQG with a Yin dimension, a Yang dimension and a bipolar equilibrium dimension; 2) a truth-based classical word that includes all the remaining 2-D space beyond the quantum world.
Definition 12. A BQA within a quantum worldis called a normal BQA. A BQA within a classical worldis called an abnormal BQA. A BQA on the border line between the two worlds belongs to both worlds.
Theorem 18. Within the 2-world model, the superposition of two normal BQAs is always another normal BQA. The superposition of two abnormal BQAs can be normal or abnormal. The superposition of a normal BQA and an abnormal BQA can be normal or abnormal.
Proof. It follows from that,
1) Given two normal BQAs A = (x,y) and B = (u,v), the superposition
2) Given a normal BQA A = (x,y) and an abnormal BQA B = (u,v), the superposition
Given two abnormal BQAs A = (x,y) and B = (u,v), the superposition
Theorem 19. Logically definable bipolar quantum entanglement is only valid among normal BQAs. An abnormal BQA in the classical world can be logically converted into a normal one for logically definable bipolar quantum entanglement.
Proof. It follows from that an agent in the classical world cannot be specified as a bipolar variable (x,y) such that "(x,y) Î B1, BF or B¥ until the agent is converted to a normal BQA. On the other hand, any agent is a BQA because any agent must be a collection of particles, antiparticles, or negative-positive energies which are inherently bipolar.
Recall that, BQG is for bipolar interaction and bipolar dynamic equilibrium analysis. It is quadrant irrelevant. Superposition results from bipolar interaction which transcends spacetime and thus can be represented with scalar values. From the above theorem, it is clear that 2W-BQG may play an important role in the analysis of bipolar quantum disturbance, decoherence and collapse. It makes it possible to integrate BQAs from different worlds and to picture quantum disturbances caused by visiting abnormal BQAs. Most interestingly, the observation that the superposition of two abnormal BQAs may be normal provides an important lead for research and development of symmetrical quantum measurement technologies for zero-disturbance or reduced level of decoherence of quantum entanglement.
While Shrödingier’s equation is fully deterministic and the only place where determinism is lost in the context of quantum mechanics is at the point of a measurement, G-CP-violation under G-CPT symmetry presents a fundamental departure from Shrödingier’s deterministic wave function through the incorporation of gravitation into G-CP-violation under G-CPT symmetry―a quantum gravity theory with logically definable causality.
Theorem 20. Submergence of a quantum entanglement can be caused by G-CP-violation under G-CPT symmetry.
Proof. If any gravitational or electromagnetic disturbance associated with a quantum measurement causes additional local G-CP-violation of a two-party entanglement, the conditions for coherence in Theorem 15 can be violated to result in submergence of the entanglement while global G-CPT symmetry is preserved. Thus, the theorem follows from the two conditions of Theorem 15 and last theorem.
Quantum emergence and submergence theory leads to a unification of coherence, decoherence and collapse theories.
With the emergence-submergence theory, the “measurement problem” becomes a logically comprehensible problem.
1) Quantum superposition can be logically and mathematically characterized as an emergence of YinYang bipolar equilibrium of two BQAs A = (x,0) and B = (0,y) of a 2W-BQG and we have,
Based on Equation (8a), the emergence can be logically defined as an energy/information conservational operation with a bipolar quantum logic gate matrix.
The nature of quantum decoherence and collapse can be logically and mathematically characterized as quantum submergence (ß) or the loss of a 2-party bipolar equilibrium without losing the two BQAs, where
The separation of (x,y) can also be defined as the reverse of Equation (11b) with energy/information conservation.
In Equation (11d),
2) Quantum decoherence can also be logically and mathematically characterized as the loss of the bipolar equilibrium of a nonlocal 2-party BQA entanglement due to disturbance that caused the submergence or returning of the two BQAs to a world as separate agents. If we use the submergence or decoherence operator ß as the reverse of a superposition or entanglement (W), a submergence of a bipolar entanglement can be logically described as a causal relation as proven in Theorem 15 with different cases. Formally, given
Case 1:
Case 2:
The 2-world model can be extended to a three world BQG (3W-BQG) model as shown in
While the 3W-BQG shows the advantage of bipolar equivalence, it lacks bipolar symmetry. This deficiency can be remedied with a 4-world model.
Definition 13. A 4-World BQG (4W-BQG) has two symmetrical quantum worlds and two symmetrical classical worlds. The two quantum worlds are two symmetrical BQGs jointed at (0,0) and the joint creates the two symmetrical classical worlds at the same time, one is a positive world and the other a negative one (see
The 4-world model might be seen as merely a 2-D Cartesian coordinate or analytical geometry with four quadrants, but it is not. First the coordinate is not an X-Y coordinate but a YinYang bipolar coordinate. The quantum worlds are bipolar equilibrium-based and background-independent, that means the four worlds can be rotated or flipped as needed as long as the symmetries are preserved. Thus, the 4-world model is essentially different from
analytical geometry, one hosts equilibrium-based BDL, BQLA, BQAs and BQCAs; another hosts truth-based BL, LA, classical world agents and truth-based cellular automatons which can be background dependent.
In the 4-world model, local quantum superposition and entanglement can be positioned in one quantum world; non-local quantum superposition and entanglement can cross two symmetrical quantum worlds. One classical world provides a region for positive disturbances and another for negative disturbance.
Different from other models, within the 4-world model, the superposition of any two BQAs can be normal or abnormal unless both of them are within the same world. Sincenothing “cancels” gravity because it is only attractive unless a symmetrical gravitational source is created, the 4-world model is interesting due to its symmetrical property for bipolar quantum entanglement and its potential for developing symmetrical measurement technologies such that the gravitational effects of two symmetrical measurement apparatus can be cancelled.
Theorem 21. Decoherence of a bipolar quantum entanglement can, theoretically, be minimized or prevented by applying symmetrical measurement.
Proof. It follows from that symmetrical measurement from all sides of an entanglement at the same time causes symmetrical disturbances that cancel each other and logically maintain the coherence of the bipolar quantum entanglement.
From the early sections, we see that
1) The 1W-BQG shows the advantage of complete background independence;
2) The 2W-BQG shows the advantage of quantum word and classical world interaction;
3) The 3W-BQG shows the advantage of non-local quantum equivalence;
4) The 4W-BQG shows the advantage of quantum symmetry.
While the four world models show some different properties, the ubiquitous nature of YinYang bipolarity makes BQG ubiquitous―a property of background independence. Thus, BQG can be anywhere. That means, the 1W-, 2W-, 3W- and 4W-BQG models can be combined in any configuration for different applications. This leads to a many world model of BQG. This is not further discussed in this work.
Einstein asserted [
In light of the above, BQG and BDL has been proposed as an equilibrium-based geometrical and logical foundation for quantum mechanics and quantum gravity with an equilibrium-based interpretation of energy/information, quantum superposition and entanglement. Although it is questionable whether the equilibrium- based geometrical and logical system is what Einstein sought for physics in the last century, BQG has been proven completely background independent and BDL has been proven a bipolar dynamic generalization of Boolean logic (BL). BDL does satisfy the simplicity criterion set forth by Einstein and has passed a major falsifiability test with a logical exposition of the longstanding puzzle of Dirac 3-polarizer experiment.
While background independent geometry has been advocated by Lee Smolin in the quest for quantum gravity [
Now, BDL and BQLA have led to an equilibrium-based bipolar quantum cellular automaton (BQCA) interpretation of quantum mechanics and quantum gravity. Not only has BQCA logically unified matter and antimatter atoms, it also has led to a cellular model for quantum emergence and submergence. While alternative interpretations of quantum mechanics all have led, in practice, to exactly the same answers and predictions regarding the observations, fundamentally different from others the equilibrium-based interpretation claims thatspace- time, particle-wave and imaginary-real are not most fundamental complementarities and therefore quantum mechanics in Hilbert space cannot be most fundamental, albeit practically useful.
It is observed that missing in the Hamiltonian, Schrödinger’s wave function, Hilbert space, Dirac bra-ket notation, complex numbers, qubits, and quantum logic gates is the common property of bipolar complementarity. While Schrödinger’s wave function is deterministic and does not account for bipolar coexistence, BDL and BQLA provide explicit bipolar representation. While alternative interpretations of quantum mechanics so far failed to deviate themselves from quantum mechanics in a fundamental way, bipolar quantum superposition and entanglement present a fundamental departure from the established theories. A key property of this departure is the background independent bipolar property of BQG that makes BDL and BQLA transcendent over spacetime and particle-wave. With this transcendence, quantum decoherence or collapse can be interpreted as quantum submergence of a superposition―a reverse process of quantum emergence with logically definable causality for an analytical paradigm.
Quantum entanglement or quantum non-locality as an unresolved illogical paradox has generated enormous amount of confusion. It was once called “spooky action at a distance” by Einstein. The background-independent multiagent BQCA approach provides an equilibrium-based causal logic interpretation to the paradox and lead to the following predictions (adapted from [
Prediction 1. Quantum entanglement can be classified as local or non-local and strong or weak. A local entanglement is a strong one with a nucleus as a local regulatory center; a non-local entanglement is a weak one without a local regulatory center. Any local entanglement as a local dynamic equilibrium must exists in a global entanglement or equilibrium.
Prediction 2. Matter or antimatter atom is logically a set of n-party locally entangled electron-positron pairs through a bipolar quantum logic gate characterizing the nucleus―an organizational or regulatory center of the atom under G-CPT symmetry.
Prediction 3. A composite quantum agent with two or more non-local quantum agents can be deemed an n-party non-local entanglement.
Prediction 4. Any composite quantum agent in the universe including the universe itself is a combination of local and non-local quantum entanglements.
Prediction 5. Every composite BQA in the universe including the universe itself is a BQCA.
The unification of quantum locality and non-locality provides a basis for quantum biology, mind-body unification and quantum intelligence. Evidently, a background independent geometry with spacetime transcendence is essential for logically definable quantum causality as well as local and non-local quantum entanglements.
A letter from Einstein to R. A. Thornton dated Dec. 7, 1944 wrote [cf. [
Could most scientists of this generation be suffering from the lack of that kind of independence from prejudices? G-CPT symmetry leads to the following predictions (adapted from [
Prediction 6. Quantum superposition and entanglement is fundamentally a bipolar dynamic equilibrium or harmony that can emerge from the bipolar interaction of Nature’s Yin and Yang and submerge to the Yin and Yang with global energy/information conservation.
Prediction 7. Any valid and fundamental departure from quantum mechanics must be able to 1) provide a logical definition of quantum entanglement, 2) provide a logical unification of energy and information, and 3) provide a logical exposition of Dirac 3-polarizer experiment. Otherwise, it is either invalid or non-fundamental.
Prediction 8. Quantum coherence is fundamentally the emergence of a local BQCA of n-party (2 < n <¥) quantum superposition or entanglement (coupled) into a global BQCA of ¥-party superposition and/or entanglement. Quantum decoherence or collapse is fundamentally quantum submergence of a local BQCA decoupled from a global BQCA back to the classical world.
Prediction 9. Quantum uncertainty in general is due to 1) the less fundamental nature of Bohr’s particle-wave complementarity compared with YinYang bipolar complementarity, 2) the less fundamental nature of spacetime or Hilbert space compared with YinYang bipolar quantum geometry, 3) the less fundamental nature of quantum superposition compared with bipolar quantum superposition, 4) the less fundamental nature of CPT symmetry compared with G-CPT symmetry, and 5) the less fundamental nature of truth compared with bipolar dynamic equilibrium.
Prediction 10. The fact that different interpretations of quantum mechanics all lead, in practice, to exactly the same answers and predictions regarding the observations is due to the lack of holistic observations of YinYang bipolar coexistence in dynamic equilibrium which is required for resolving the problem of decoherence and/or collapse associated with “the measurement” problem.
Prediction 11. A valid and fundamental departure from Schrödinger’s deterministic wave function entails a bipolar dynamic equilibrium-based quantum gravity unification of particle-antiparticle bipolarity and gravitational action-reaction bipolarity. Without such a unification, a valid interpretation of quantum mechanics cannot be a fundamental departure from Shrödingier’s deterministic wave function.
Prediction 12. A fundamental departure from the crossroad of theoretical physics entails a new philosophy, a new logic, a new geometry, a new set theory, and a new mathematical abstraction for background independent causal reasoning. Any other departure from the crossroad is simply “what goes around comes around.”
Prediction 13. All logical, physical, social, biological and mental regeneration and degeneration are fundamentally quantum emergence and submergence, respectively, and all worlds are bipolar quantum entangled under G-CPT symmetry. Thus, a valid quantum gravity theory must be a unifying theory of logical, physical, social, biological, and mental quantum gravity with information conservation.
Quantum emergence and submergence under G-CPT symmetry provides a theoretical basis for the unification of big bang and black hole theories with information conservation.
Prediction 14. Big bang is a process of quantum emergence from a quantum world to a classical world; black hole is a process of quantum submergence from a classical world to a quantum world.
Prediction 15. No world can be completely separated from other worlds; all classical and quantum worlds must be unified under the global dynamic equilibrium of G-CPT symmetry.
Prediction 16. A possible solution to quantum decoherence or collapse associated with the “measurement problem” is to develop bipolar symmetrical quantum registers and bipolar symmetrical measurement technologies that can reduce or prevent quantum submergence.
It should be remarked that, the fact that researchers were able to reduce environmental decoherence rate “to levels far below the threshold necessary for quantum information processing” by applying high magnetic fields in their experiment [
Prediction 17. A fundamental departure from quantum mechanics is more likely to appear in a less established journal than in an established one due to the strong establishment of classical logical thinking in established scientific fields and their lack of the kind of independence from prejudices from which most scientists of this generation are suffering.
Prediction 18. Truth-based logic is human logic; equilibrium-based logic is God (or Nature) logic. Mankind has been using human logic for thousands of years in seeking truths from the universe. Now, it is time for mankind to seek and accept God logic as a guiding light for scientific and technological endeavors.
Fundamentally different from established quantum mechanical and quantum gravity theories, the new theory is backed by a completely background independent holistic formal logical, geometrical, and algebraic system. This distinction has been shown essential for modeling the quantum world as a multiagent environment with logically definable quantum causality for causal analysis of quantum coherence, decoherence and collapse under G-CPT symmetry with or without G-CP-violation.
While this work has been focused on logically definable causal analysis, it can be further developed from a logical foundation to a physical one with future research efforts. The potential is backed with a number of vindications including:
1) While mainstream science is based on truth and singularity in which time starts with big bang and ends with black hole, dynamic equilibrium is based on bipolarity of input-output or negative-positive energies. However, the theory of truth and singularity is not a contradiction but a vindication of bipolarity because the bipolar property of nature’s basic forces and particles are the only properties that can survive a big bang as well as a black hole due to particle-antiparticle emission [
2) The new interpretation is based on an equilibrium-based logical extension of Niels Bohr’s particle-wave interpretation of YinYang duality to electromagnetic particle-antiparticle and gravitational action-reaction bipolar complementarity. Bipolar complementarity has led to the unification of energy and information.
3) Bipolar complementarity has resulted in BDL―a sound and formal generalization of Boolean logic from bivalent truth domain to bipolar equilibrium-domain. With the first logical exposition of Dirac 3-polarizer experiment, BDL has been vindicated as a valid causal logic that leads to the unification of mind, light and matter [
4) Without YinYang bipolarity, logically definable causality would be impossible [
5) BDL has led to BQLA―a bipolar quantum linear algebra that has been shown preserving quantum superposition amplitude and enables energy-information conservation, regeneration and degeneration of a BQCA for global regulation.
6) BDL and BQLA have made it possible to define both local and non-local bipolar quantum superposition and entanglement as multiagent BQCAs for unified logical analysis of quantum emergence, submergence, decoherence and collapse.
7) The background independent property of BQG has led to the unification of classical and quantum worlds into a many-world model.
8) Multiagent BQCAs have led to a geometrical and logical quantum gravity theory where electromagnetic and gravitational disturbance can be accounted for as G-CP-violations under G-CPT symmetry.
Finally, G-CPT symmetry has led to a number of philosophical, logical and technical predictions. Unlike string theory where strings or monopoles are imaginable but untestable, dipoles and bipolarity as a basis for the new theory are observable everywhere. Thus, G-CPT symmetry exhibits the necessary falsifiability for a scientific theory and the predictions are expected to be testable in the future. After all, as an equilibrium-based logical theory G-CPT symmetry will, hopefully, lead to analytical and physical solutions to the quantum disturbance problem associated with the “measurement problem” and serve as a point of fundamental departure from the crossroad of theoretical physics but not as “what goes around comes around” .
This paper was reviewed and accepted for publication by Journal of Modern Physics (JMP). It was transferred to JQIS on the author’s request. The author acknowledges the JMP anonymous reviewers for their helpful comments and suggestions.
Wen-Ran Zhang, (2016) G-CPT Symmetry of Quantum Emergence and Submergence—An Information Conservational Multiagent Cellular Automata Unification of CPT Symmetry and CP Violation for Equilibrium-Based Many-World Causal Analysis of Quantum Coherence and Decoherence. Journal of Quantum Information Science,06,62-97. doi: 10.4236/jqis.2016.62008
(Adapted from [
Appendix 1: Figures A1-A4 show a world of bipolar sets, bipolar lattices, and bipolar interactions.
An equilibrium-based axiomatization is shown in
Bipolar Partial Ordering: |
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Excluded Middle | |
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No contradiction | |
Distributive Laws | |
Bipolar DeMorgan’s Laws | |
Bipolar Interactive DeMorgan’s Laws |
§ Bipolar conjunction: e.g.
§ Bipolar fusion, disjunction or quantum superposition: e.g.
§ Bipolar annihilation, minimization, or conjunction: e.g.
§ Bipolar interaction and oscillation: e.g.
§ Bipolar fission: e.g. fission
Unipolar Axioms (UAs): UA1: | Bipolar Axioms (BAs): BA1: |
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Inference Rule-Modus Ponens (MP): UR1: | Bipolar Universal Modus Ponens (BUMP) (* can be bound to any binary bipary bipolar operator) BR1: IF |
Predicate axioms and rules UA6: | Bipolar Predicate axioms and Rules of inference BA6: |
As a causal set, a bipolar relational matrix R is characterized with bipolar logical values such as (0,0) for no relation, (−1,0) or (−0.8,0) for conflict relation, (0,+1) or (0,+0.7) for coalition, and (−1,+1) or (−0.9,+0.9) for harmonic relation, respectively, with different crisp or fuzzy strengths. The Å-Ä bipolar transitive closure of R is the smallest bipolar transitive relation containing R (Zhang & Zhang, 2004) denoted by  and
It has been proven that, let