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Journal of Modern Physics, 2012, 3, 1261-1271 http://dx.doi.org/10.4236/jmp.2012.329163 Published Online September 2012 (http://www.SciRP.org/journal/jmp) YinYang Bipolar Atom—An Eastern Road toward Quantum Gravity* Wen-Ran Zhang Department of Computer Science, Georgia Southern University, Statesboro, USA Email: wrzhang@georgiasouthern.edu Received June 19, 2012; revised July 22, 2012; accepted July 31, 2012 ABSTRACT Based on bipolar dynamic logic and bipolar quantum linear algebra, a causal theory of YinYang bipolar atom is intro- duced in a completely background independent geometry that transcends spacetime. The causal theory leads to an equi- librium-based super symmetrical quantum cosmology of negative-positive energies. It is contended that the new theory has opened an Eastern road toward quantum gravity with bipolar logical unifications of particle and wave, matter and antimatter, relativity and quantum entanglement. Information recovery after a black hole is discussed. It is shown that not only can the new theory be applied in physical worlds but also in logical, mental, social and biological worlds. Fal- sifiability of the theory is discussed. Keywords: YinYang Bipolar Atom; Bipolar Geometry; Quantum Cellular Automata; Matter and Antimatter; Information Recovery after a Black Hole; Real World Quantum Gravity 1. Introduction Stephen Hawking’s black hole theory originally suggested that the universe would ultimately disappear in a black hole without information preservation. This suggestion was criticized for violating the 2nd law of thermodyna- mics. To remedy the inconsistency, Hawking proposed black body evaporation [2] and then particle emission [3]. After then he held his position for three decades. In 2004, he finally conceded a bet and agreed that black hole emis- sion does in fact preserve information. But so far it is unclear how to recover the information from the evapo- ration or particle emission and how the universe will evolve after a black hole. This uncertainty makes quan- tum theory incomplete and nihilism unavoidable. For ins- tance, M-theory predicts that a great many universes were created out of nothing [4, p. 5]. Equilibrium is a well-known scientific concept that subsumes symmetry or broken symmetry. Since equilib- rium is central in the 2nd law of thermodynamics—the paramount law of existence, energy, life, and information where bipolar equilibrium is a generic form, YinYang bipolar equilibrium-based approach to physics and sci- ence provides a fundamental super symmetrical alterna- tive for scientific unification. (Note: Equilibrium subsumes equilibrium, non-equilibrium and quasi-equilibrium be- cause local non-equilibriums can form global equilibrium or quasi-equilibrium.) Atom as a basic unit of matter should follow equilib- rium or non-equilibrium conditions. It consists of a dense, central nucleus surrounded by a cloud of negatively char- ged electrons. The nucleus contains a mix of positively charged protons and electrically neutral neutrons (except in the case of hydrogen-1). The electrons of an atom are bound to the nucleus by the electromagnetic force. Like- wise, a group of atoms can remain bound to each other, forming a molecule. In the case of antimatter atom, the cloud is formed with positively charged positrons and the atomic nucleus is negatively charged. Molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. A cova- lent bond is a form of chemical bonding that is charac- terized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces be- tween atoms when they share electrons is known as co- valent bonding. An atom containing an equal number of protons and electrons is electrically neutral. Otherwise, it has a posi- tive or negative charge. A positively or negatively charged atom is known as an ion. An atom is classified according to the number of protons and neutrons in its nucleus: the number of protons determines the chemical element and the number of neutrons determines the isotope of the element. Figure 1 shows some examples. Legendary Danish physicist Niels Bohr, a father figure of quantum mechanics, brought YinYang into quantum theory for his particle-wave complementarity principle. *The idea has been partially presented in Ref. [1]. C opyright © 2012 SciRes. JMP W.-R. ZHANG 1262 (a) (b) (c) (d) Figure 1. (a) Matter hydrogen atom; (b) Proton of a hydro- gen surrounded by an electron cloud; (c) Matter helium atom with a nucleus (two protons and two neutrons) and two electrons; (d) Tiny nucleus of a helium atom is sur- rounded by electron cloud (Creative Commons: by User: Yzmo). When he was awarded the Order of the Elephant by the Danish government in 1947, he designed his own coat of arms which featured in the center a YinYang logo (or Taiji symbol) with the Latin motto “contraria sunt com- plementa” or “opposites are complementary”. While quantum mechanics recognized particle-wave complementarity it stopped short of identifying the es- sence of YinYang bipolar coexistence. Without bipola- rity any complementarity is less fundamental due to the missing “opposites”. On the other hand, if bipolar equi- librium is the most fundamental form of equilibrium, any multidimensional model such as string, superstring or M-theory cannot be most fundamental. In brief, action- reaction forces, particle-antiparticle pairs, negative-posi- tive energies, input and output, or the Yin and Yang in general are the most fundamental opposites of nature, but man and woman, space and time, particle and wave, truth and falsity are not exactly bipolar opposites. This could be the reason why Bohr believed that a causal description of a quantum process cannot be attained and we have to content ourselves with particle-wave complementary des- criptions [5]. It may also be the reason why modern phy- sics so far failed to find a definitive battleground for quantum gravity. Einstein pointed out: “For the time being we have to admit that we do not possess any general theoretical ba- sis for physics which can be regarded as its logical foundation.” “Physics constitutes a logical system of thought which is in a state of evolution, whose basis (principles) cannot be distilled, as it were, from experi- ence by an inductive method, but can only be arrived at by free invention.” In the above light, a causal theory of YinYang bipolar atom is introduced in this paper based on bipolar dy- namic logic and bipolar quantum linear algebra [6-8]. The theory provides a springboard to an equilibrium-ba- sed logical unification of particle and wave, matter and antimatter, relativity and quantum theory, strings and rea- lity as well as big bang and black hole. Information reco- very after a black hole is discussed. The logical, phy- sical, mental, biological and social implications of this work are formalized into a Q5 paradigm of quantum gra- vities [8]. This paper is organized into six sections. Following this introduction, a background review of the mathema- tical basis of this work is presented in Section 2. Yin- Yang bipolar atom is presented in Section 3. Bipolar quantum cellular automata are introduced in Section 4. Section 5 presents the theory of YinYang bipolar quan- tum gravity. Section 6 draws a few conclusions as well as philosophical distinctions. 2. YinYang Bipolar Dynamic Logic and Quantum Linear Algebra 2.1. YinYang Bipolar Quantum Lattice and Bipolar Dynamic Logic (BDL) Aristotle’s causality principle became controversial in the 18th century after David Hume challenged it from an em- pirical perspective. Hume argued that causation is irredu- cible to pure regularity. YinYang bipolar dynamic logic (BDL) [6,8-10] has changed this situation in a funda- mental way. BDL is defined on a bipolar quantum lattice B1 = {–1, 0} {0, +1} = {(0,0), (0,1), (–1,0), (–1,1)} in YinYang bipolar geometry as shown in Figure 2. The four values of B1 form a bipolar set [8] which stand res- pectively for eternal equilibrium (0,0), non-equilibrium (–1,0), non-equilibrium (0,+1); equilibrium or harmony (–1,+1). Equation (1)-(12) in Table 1 provide the basic operations of BDL. The laws in Table 2 hold on BDL. Most interestingly, BUMP makes equilibrium-based bipo- lar quantum causality logically definable. An axiomatization of BDL (Table 3) has been proven sound and complete [8]. A key element in the axioma- tization is bipolar universal modus ponens (BUMP) (Ta- ble 4) which is a bipolar tautology, a non-linear bipolar dynamic generalization of classical modus ponens and a logical representation of bipolar quantum entanglement. Thus, BDL generalizes Boolean logic to a quantum logic where and – are “balancers”; and are intuitive “oscillators”; – and – are counter-intuitive “oscilla- tors”; & and &– are “minimizers.” The linear, cross-pole, bipolar fusion, oscillation, interaction and entanglement properties are depicted in Figure 3. Bipolar relations and equilibrium relations are defined in [6,8,11,12]. 2.2. Bipolar Quantum Linear Algebra (BQLA) The bipolar lattice B1 = {–1,0} {0,1} and bipolar fuzzy lattice BF = [–1,0] [0,1] can be naturally extended to the infinite bipolar lattice B = [–,0] [0,+]. While B1 and BF are bounded complemented unit square crisp/fuzzy lattices, respectively, B is unbounded. (x,y),(u,v) B , Equations (13) and (14) define two major operations. Tensor Bipolar Multiplication: (x,y) (u,v) (xv+yu, xu+yv); (13) Copyright © 2012 SciRes. JMP W.-R. ZHANG 1263 Figure 2. Hasse diagrams of B1 in YinYang bipolar geome- try. Figure 3. YinYang bipolar relativity: (a) Linear interaction; (b) Cross-pole non-linear interaction; (d) Oscillation; (e) Two entangled bipolar inte ractive variables. Table 1. YinYang Bipolar Dynamic Logic (BDL). (Note: The use |x| through this paper is for explicit bipolarity only). Bipolar Partial Ordering: (x,y) (u,v), iff |x| |u| and y v; (1) Compl e men t: (x,y)(-1,1)-(x,y)(x,y)(-1-x,1-y); (2) Implication : (x,y)(u,v)(x u,y v)( x u), y v); (3) Negation: (x,y) ( y, x); (4) Bipolar least upper bound (blub): blub((x,y),(u,v))(x,y)(u,v)(-(|x| |u|),y v); (5) Bipolar greate st lower b ound (b glb): bglb((x,y),(u,v)) (x,y)(u,v) (-(|x| |u|),y v)); (6) -blub: blub ((x,y),(u,v)) (x,y)(u,v) (–(y v),(|x| |u|)); (7) -bglb: bglb ((x,y),(u,v)) (x,y)(u,v) (– (y v), (|x| |u|))); (8) Cross-pole greatest lower bound (cglb): cglb((x,y),(u,v))(x,y)(u,v)(-(|x| v| |y| u|),(|x| u| |y| v|)); (9) Cross-pole least upper bound (cglb): club((x,y),(u,v))(x,y)(u,v)(-1,1)–( (x,y)(u,v)); (10) -cglb: cglb ((x,y),(u,v)) (x,y)-(u,v) ((x,y)(u,v)); (11) -club: club ((x,y),(u,v))(x,y)-(u,v) ((x,y) (u,v)). (12) Tab le 2. Bipolar laws. Excluded Middle (x,y) (x,y) (-1,1); (x,y)(x,y) (-1,1); No Contradiction ((x,y)&(x,y))(-1,1); (( x,y)&( x,y))(-1,1); Linear Bipolar DeMorgan’s Laws ((a,b)(c,d)) (a,b)(c,d); ((a,b)(c,d)) (a,b)& (c,d); ((a,b) (c,d)) (a,b) (c,d); ((a,b) (c,d)) (a,b)& (c,d); Non-Linear Bipolar DeMorgan’s Laws ((a,b) (c,d)) (a,b) (c,d); ((a,b) (c,d)) ((a,b) (c,d); ((a,b)- (c,d)) (a,b)- (c,d); ((a,b)- (c,d)) (a,b)- (c,d) Table 3. Bipolar axiomatization Bipolar Linear Axioms: BA1: (-,+)((-,+)(-,+)); BA2: ((-,+)((-,+)(-,+))) ((( -,+)(-,+))((-,+)(-,+))); BA3: ((-,+)(-,+))(((-,+)(-,+)) (-,+)); BA4: (a) (-,+)&(-,+)(-,+); (b) (-,+)&(-,+)(-,+); BA5: (-,+)((-,+)((-,+)&(-,+))); Non-Linear Bipolar Universal Modus Ponens (BUMP) BR1: IF ((-,+)(-,+)), [((-,+)(-,+))&((-,+)(-,+))], THEN [(-,+)(-,+)]; Bipolar Predicate Axioms and Rules of Inference BA6: x,(-(x),+(x))(-(t),+(t)); BA7: x,((-,+)(-,+))((-,+)x,(-,+); BR2-Generalization: (-,+)x,(-(x),+(x)) Table 4. Bipolar Universal Modus Ponens (BU M P ) . =(-,+), =(-,+), =(-,+), and =(-,+) B1, [( ) & ()] () ()]. Two-fold universal instantiation: 1) Operator instantiation: as a universal operator can be bound to &, , &, , , , , . ( ) is designated bipolar true or (-1,+1); ((-,+)(-,+)) is undesignated. 2) Variable instantiation: x, (-,+)(x) (-,+)(x); (-,+)(A); (-,+)(A). Bipolar Addition: (x,y) + (u,v) (x+u, y+v) (14) In Equation (13), is a cross-pole multiplication op- erator with the infused non-linear bipolar tensor seman- tics of --=+, -+=+-=1, and ++=+; + in Equation (14) is a linear bipolar addition or fusion operator. With the two basic operations, classical linear algebra is naturally ex- tended to BQLA with bipolar fusion, diffusion, interac- tion, oscillation, and quantum entanglement properties. These properties enable physical or biological agents to interact through bipolar fields such as atom-atom, cell- cell, heart-heart, heart-brain, brain-brain, organ-organ, and genome-genome bio-electromagnetic quantum fields as well as biochemical pathways. Thus, the bipolar pro- perties are suitable for equilibrium-based bipolar dy- namic modeling with quantum aspects where one kind of equilibrium or non-equilibrium can have causal effect to another. Given an input bipolar row vector matrix E = [ei] = [( ii ,ee ,mm )] B , I = 1, 2, ..., k, and a bipolar connectivity matrix M = [mij] = [( ij ij ,vv 1 ,; k )], i = 1, 2, ..., k and j = 1, 2,..., n, we have V = E M = [Vj] = [(ii )]. While E is the input vector to a dynamic system characterized with the connectivity matrix M, V is the result row vector with n bipolar elements following Equation (15). j jjjj ij i VEM VvvVem (15) Equation (15) has the same form as in classical linear Copyright © 2012 SciRes. JMP W.-R. ZHANG 1264 algebra except for: 1) ej and mij are bipolar elements; 2) the multiplication operator is defined in Equation (13) on bipolar variables with bipolar (quantum) entanglement; and 3) the Σ operator is based on bipolar addition de- fined on bipolar variables in Equation (14). BQLA provides a new mathematical tool for modeling YinYang-n-elements with explicit bipolar equilibrium, quasi- or non-equilibrium representation for energy and stability analysis. Energies in a row matrix can be con- sidered as physical or biological energies of any agents such as quantum or cosmological negative and positive energies, repression and activation energies of regulator proteins. Energies embedded in a connectivity matrix can be deemed organizational energies that bind the agents together. The following laws hold for any physical or biological systems [7,8,13]. YinYang Bipolar Elementary Energy. Given a bipo- lar element , ,eee 1) ε−(e) = e– is the Yin or negative energy of e; 2) ε+(e) = e+ is the Yang or positive energy of e; 3) ε(e) = (ε−(e), ε+(e)) = (e–, e+) is the YinYang bipolar energy measure of e; 4) The absolute total |ε|(e) = |ε−|(e) + |ε+|(e) is the to- tal energy of e; 5) εimb(e)=|ε+|(e) |ε−|(e) is the imbalance of e; 6) EnergyBalance(e) = (|ε|(e)−|εimb(e)|)/2.0 = min(|e−|, e+); 7) Harmony(e) = Balance(e) = (|ε|(e) − |εimb(e)|)/|ε|(e). YinYang Bipolar System Energy. Given an k n bipolar matrix M = [mij] = (M−,M+) = ( j j ,m j j m ), where M− is the Yin half with all the negative elements and M+ is the Yang half with all the positive elements, 1) is the negative or Yin energy of M; 11 M kn ij 11 kn ij ij ij m 11 kn ij ij ij m 2) is the positive or Yang energy of M; 11 M kn ij 3) the polarized total, denoted ε(M) = (ε−(M), ε+(M)) is the YinYang bipolar energy of M of M; 4) the absolute total, denoted |ε|(M) = |ε−|(M) + |ε+|(M), world of matter and antimatter for the first time. Since action and reaction or negative and positive en- ergies can be electromagnetic or gravitational in nature, YinYang bipolar atom can serve as a basis for real world quantum gravity. If we treat the centrifugal and centripe- tal forces of a planet similarly as that of an electron (or positron) rotating around its nucleus, gravity can be a superposition on quantum interaction. In either case, sin- ce nothing can escape bipolar equilibrium or non-equi- librium, renormalization is made possible in equilibrium- based terms using BQLA and BQCA. The YinYang negative-positive energies also provide a possible unification for the many universes in M-theory. It can be argued that the multiverses have to follow the same equilibrium or non-equilibrium conditions of the 2nd law of thermodynamics and become one universe. Other- wise, the two energies can’t form the regulating force of the multiverses. Thus, the different laws followed by dif- ferent universes as described in The Grand Design have to be unified under the same 2nd law of thermodynamics. Different from other approaches to quantum gravity, the equilibrium-based approach is rooted in the real world. Due to YinYang bipolarity in mental health, bioinformat- ics, life and social sciences [6-13,17-23], physical and logical quantum gravity can be naturally extended to mental, biological and social quantum gravities [8]. Thus, it is contended that the new approach has opened an East- ern road toward quantum gravity. 5.2. Falsifiability Falsifiability is a must for any viable physical theory. It is of course correct that bipolar quantum entanglement needs experimental verification. However, 1) bipolar atom finds its equivalent representation in classical atom theory (Figure 5); 2) bipolar quantum entanglement or BUMP is physical and logical; 3) unlike the predicted but unverified existence of monopoles in string theory, di- poles are everywhere. Thus, we have: Postulate 1: Bipolar quantum entanglement is the most fundamental entanglement in quantum gravity. Postulate 2: YinYang bipolarity is the most funda- mental property of the universe. The two postulates are actually logically provable axi- oms. For Postulate 1, if a bipolar element (Figures 4 and 5) characterizes the energy superposition of gravitational and quantum action-reaction, an atom would be a set of bipolar elements. As the total must be equal to the sum, without bipolar entanglement there would be no atom level entanglement. Postulate 2 follows Postulate 1. Postulate 3: YinYang bipolar atom is a bipolar set of quantum entangled particle and antiparticle pairs. Postulate 4: Gravity is fundamentally large or small scale bipolar quantum entanglement. Postulate 5: The speed of gravity is limited by the speed of quantum entanglement and not by that of light. According to Einstein, “Evolution is proceeding in the direction of increasing simplicity of the logical basis (principles).” “We must always be ready to change these notions—that is to say, the axiomatic basis of phys- ics—in order to do justice to perceived facts in the most perfect way logically.” While string and superstring theories up to 11 or more dimensions failed the simplic- ity measure, YinYang bipolar atom and bipolar quantum entanglement are simple and logically comprehendible with definable causality in BUMP. The bipolar quantum interpretation coincides with MIT Professor Seth Lloyd’s startling thesis that the universe is itself a quantum com- puter [24]. According to Lloyd, the universe is all about quantum information processing. Once we understand the laws of physics completely, we will be able to use small-scale quantum computing to understand the uni- verse completely as well. Could YinYang bipolar quan- tum entanglement or BUMP be such a basic law? 6. Conclusions Based on YinYang bipolar dynamic logic and bipolar quantum linear algebra, a logically definable causal the- ory of YinYang bipolar atom has been introduced. The causal theory has led to an equilibrium-based super sym- metrical quantum cosmology of negative-positive ener- gies. It is contended that the new theory has opened an Eastern road toward quantum gravity with bipolar logical unifications of matter-antimatter, particle-wave, strings and reality, big bang and black hole, quantum entangle- ment and relativity. It has been shown that not only can the theory be applied in physical worlds but also provides a Q5 paradigm of physical, logical, mental, biological and social quantum gravities. Furthermore, it provides a logically consistent cyclic process model of the universe with information recovery after a black hole. The strength of the equilibrium-based approach is its interpretation and unification aspects. The strength comes from the background-independent property of YinYang bipolar geometry that transcends spacetime. The strength would also be a weakness should YinYang be exclusive of spacetime geometry. Fortunately, the new geometry is not exclusive but inclusive. It promotes equilibrium, har- mony and complementarity by hosting, regulating or in- Copyright © 2012 SciRes. JMP W.-R. ZHANG 1270 tegrating background-dependent models as emerging pa- rameters for more challenging scientific explorations and unifications. This work is limited to qualitative simulation, interpre- tation and unification. A major research topic is bipolar quantization and space emergence. The negativepositive energies of an electron-positron pair under certain condi- tion provides a candidate bipolar unit for quantization with space emergence as a result of particle-antiparticle interaction. 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