Abstract:
A prespacetime model of elementary particles, four forces and consciousness has been formulated, which illustrates how the self-referential hierarchical spin structure of the prespacetime provides a foundation for creating, sustaining and causing evolution of elementary particles through matrixing processes embedded in said prespacetime. The prespacetime model reveals the creation, sustenance and evolution of fermions, bosons and spinless entities each comprised of an external wave function or external object and an internal wave function or internal object located respectively in an external world and internal world of a dual-world universe. The prespacetime model provides a unified causal structure for weak interaction, strong interaction, electromagnetic interaction, gravitational interaction, quantum entanglement, consciousness and brain function. The prespacetime model provides a unique tool for teaching, demonstration, rendering, and experimentation related to subatomic and atomic structures and interactions, quantum entanglement generation, gravitational mechanisms in cosmology, structures and mechanisms of consciousness, and brain functions.

Description:
[0001]    This application is a continuation application of U.S. patent application Ser. No. 12/964,558 filed on Dec. 9, 2010, which claims priority from U.S. provisional application Ser. No. 61/288,333 filed Dec. 20, 2009, which applications are fully incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The invention herein relates to modeling creation, sustenance and evolution of elementary particles through self-referential hierarchical spin structures of prespacetime. In particular, working model for creating, sustaining and causing evolution of fermions, bosons and spinless particles are described as teaching tools. Further, working model for weak interaction, strong interaction, electromagnetic interaction, gravitational interaction, quantum entanglement, consciousness, brain function are also described as teaching tools. 
       BACKGROUND OF THE INVENTION 
       [0003]    Many experiments have shown that quantum entanglement is physically real (see Aspect, A., Dalibard, J., &amp; Roger, G. Experimental test of Bell&#39;s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804-1807 (1982)). It is ubiquitous in the microscopic world and manifests itself macroscopically under some circumstances (see Ghosh, S., Rosenbaum, T. F., Aeppli, G. &amp; Coppersmith, S. N. Entangled quantum state of magnetic dipoles. Nature 425, 48-51 (2003)). However, the essence and implications of quantum entanglement are still hotly debated. For example, it is commonly believed that quantum entanglement alone cannot be used to transmit binary or classical information. Further, despite of the fact that all interactions in biological systems at molecular and sub-molecular levels are quantum interactions in nature, it is commonly believed that quantum effects do not play any roles in biological functions such as brain functions due to quantum decoherence (see Tegmark, M. The importance of quantum decoherence in brain processes. Phys. Rev., 61E: 4194 (2000)). 
         [0004]    Yet, I have recently discovered non-local effects of chemical substances on biological systems such as a human brain produced through quantum entanglement (Hu, H. P., &amp; Wu, M. X. Photon induced non-local effect of general anesthetics on the brain. NeuroQuantology 4, 17-31 (2006), Hu, H. P., &amp; Wu, M. X. Non-local effects of chemical substances on the brain produced through quantum entanglement. Progress in Physics v3, 20-26 (2006)). I have also discovered evidence of non-local chemical, thermal and gravitational effects produced through quantum entanglement (Hu, H. P., &amp; Wu, M. X. Evidence of non-local physical, chemical and biological effects supports quantum brain. NeuroQuantology 4, 291-306 (2006); Hu, H. P., &amp; Wu, M. X. Evidence of non-local chemical, thermal and gravitational effects. Progress in Physics v2, 17-21 (2007)). 
         [0005]    My invention and discovery were made against such background. No model has previously been known which can model the creation, sustenance and evolution of fermions, bosons and spinless particles through the self-referential hierarchical spin structures of the prespacetime. Further, No model has previously been known which can model in a unified manner weak interaction, strong interaction, electromagnetic interaction, gravitational interaction, quantum entanglement, consciousness, and brain function through the self-referential hierarchical spin structures of the prespacetime. 
       SUMMARY OF THE INVENTION 
       [0006]    I have now invented the prespacetime model for modeling in the unified manner the creation, sustenance and evolution of fermions, bosons and spinless particles and the weak, strong, electromagnetic and gravitational interactions, quantum entanglement, consciousness, and brain function through the self-referential hierarchical spin structures of the prespacetime. 
         [0007]    The subject invention is originated from my research on self-reference, nature of spin, consciousness, brain functions and nature of quantum entanglement. I have theorized that spin is a primordial self-referential process driving quantum mechanics, spacetime dynamics and consciousness (Hu, H. P. &amp; Wu, M. X. Spin as primordial self-referential process driving quantum mechanics, spacetime dynamics and consciousness. NeuroQuantology, 2, 41-49 (2004); also see Cogprints ID2827 (2003)). I have also theorized that spin is a mind-pixel and the nuclear and/or electronic spins inside brain play important roles in certain aspects of brain functions such as perception (Hu, H. P., &amp; Wu, M. X. Spin-mediated consciousness theory. Medical Hypotheses 63, 633-646 (2004); also see arXiv e-print quant-ph/0208068v1 (2002)). 
         [0008]    Further, I have discovered the non-local effects of chemical substances on biological systems such as a human brain produced through quantum entanglement (Hu, H. P., &amp; Wu, M. X. Photon induced non-local effect of general anesthetics on the brain. NeuroQuantology 4, 17-31 (2006), Hu, H. P., &amp; Wu, M. X. Non-local effects of chemical substances on the brain produced through quantum entanglement. Progress in Physics v3, 20-26 (2006)). I have also discovered the evidence of non-local chemical, thermal and gravitational effects produced through quantum entanglement (Hu, H. P., &amp; Wu, M. X. Evidence of non-local physical, chemical and biological effects supports quantum brain. NeuroQuantology 4, 291-306 (2006); Hu, H. P., &amp; Wu, M. X. Evidence of non-local chemical, thermal and gravitational effects. Progress in Physics v2, 17-21 (2007)). 
         [0009]    The subject invention is based on my realization that in the beginning there was prespacetime alone (e 0 =1) materially empty but wants to express itself. So, it began to imagine through primordial self-referential spin  1 =e 0 =e iM-iM =e iM e −iM =e −iM /e −iM =e iM /e iM  . . . such that it created an external object to be observed and an internal object as observed, separated them into an external world and an internal world, cause them to interact through a self-referential Matrix and thus gave birth to a universe which it has since sustained and made to evolve. 
         [0010]    The prespacetime is comprised of a body mathematically represented by Euler number e and a mind represented by imaginary unit i above e. The body and mind of the prespacetime is ground of all existence, can form external and internal wave functions as external and internal objects (with each pair forms an elementary entity or particle) and interaction fields between elementary entities which accompany the imaginations of the prespacetime. The body and mind can be self-acted on by the self-referential Matrix L M  of the prespacetime. The prespacetime has imagining power i to project external and internal objects by projecting, for example, external and internal phase ±M=+±(Et−p·x)/ above the body e. The universe so created is a dual-world comprising of the external world to be observed and internal world as observed under each relativistic frame x μ =(t, x). In one view, the internal world (which by convention may have either negative or positive energy) is the negation/image of the external world (which by convention may also have either positive or negative energy). According to the present model, an absolute frame of reference exists and the said frame is the body e of the prespacetime. Therefore, if the prespacetime stops imagining, the universe would disappear into materially nothingness e i0 =e 0 =1. 
         [0011]    In the present model, there exists an accounting principle for the dual-world which is conservation of zero. By way of an example, the total energy of the external object and its counterpart, the internal object, is zero. Also in this dual-world, self-gravity is the non-local self-interaction (wave mixing) between the external object in the external world and its negation/image in the internal world, that is, the negation appears to its external counterpart as a black hole visa versa. Gravity is the non-local interaction (quantum entanglement) between a first entity and a second entity or the external object of one entity or particle with the internal world as a whole. 
         [0012]    According to the prespacetime model: (1) two spinors of a Dirac electron or positron are respectively the external and internal objects of the electron or positron; (2) electric and magnetic fields of a linear photon are respectively the external and internal objects of the photon which are always self-entangled; (3) a proton is likely a spatially confined positron with the confinement through an imaginary momentum, that is, downward self-reference; and (4) a neutron is comprised of an unspinized proton and a bound and spinized electron. 
         [0013]    In the prespacetime model, consciousness in a broad embodiment is simply the prespacetime having both transcendental and immanent properties. The transcendental aspect of the consciousness is the origin of primordial self-referential spin including the self-referential Matrix and the consciousness projects the external and internal worlds through the said self-referential spin and, in turn, the immanent aspect of the consciousness observes the external world as the observed internal world through the said self-referential spin. A biological consciousness such as a human consciousness is a limited and particular version of this dual-aspect consciousness such that a human has limited free will and limited observation which is mostly classical at macroscopic levels but quantum at microscopic levels. 
         [0014]    Key to the present model is: (1) occurrence of a primordial phase distinction through imagination i of the prespacetime, (2) matrixing of the prespacetime into the external and internal wave functions respectively as the external and internal objects of a first entity or particle in the dual world or interaction fields for interacting with a second entity or particles, and (3) governance of the external and internal wave functions by the self-acting and self-referential Matrix which accompanies the imagination i of the prespacetime so as to enforce the accounting principle of conservation of zero in the dual world. 
         [0015]    The prespacetime model provides for interactions of the external and internal worlds through quantum entanglement since I have experimentally demonstrated that gravity is the manifestation of quantum entanglement (Hu, H. P., &amp; Wu, M. X. Evidence of non-local physical, chemical and biological effects supports quantum brain. Neuro-Quantology 4, 291-306 (2006); Hu, H. P., &amp; Wu, M. X. Evidence of non-local chemical, thermal and gravitational effects. Progress in Physics v2, 17-21 (2007)). 
         [0016]    The prespacetime model provides for interactions within the external world through classical and relativistic physical laws with light speed c as the speed limit of the external interactions and influences of the internal world on the external objects in the external world through as gravity macroscopically and quantum effects microscopically. Thus, according to the prespacetime model, the interactions within the external world and/or the internal world are local interactions and conform to special theory of relativity, but the interactions across the dual world are non-local interactions, that is, quantum entanglement or gravity. 
         [0017]    Therefore, according to the present model, the meaning of the special theory of relativity is that the speed limit c is only applicable in each of the dual world but not interactions between the dual-world. Indeed, the reason that no external object can move faster than the speed of light and it gets heavier and heavier as its speed approach the speed of light is due to its increased quantum entanglement with the internal world through its counterpart the internal object. 
         [0018]    My prespacetime model may be more completely understood by reference to the following detailed description considered in connection with the accompanying drawings. However, it should be understood that the drawings are designed for purposes of illustration only and not as a definition of the limits of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]      FIG. 1  is a schematic view of the primordial phase distinction according to the prespacetime model producing an external and internal phase distinction in the prespacetime. 
           [0020]      FIG. 2  is a schematic view of a matrix equation according to the prespacetime model illustrating a relationship among the external object, the internal object and the self-acting and self-referential Matrix Rule. 
           [0021]      FIG. 3  is another schematic view of the matrix equation according to the prespacetime model illustrating self-interaction between the external and internal object of an entity/particle through the Matrix Rule. 
           [0022]      FIG. 4  is a schematic view of interactions and relationships of a first entity or particle and a second entity or particle in the dual-world according to the prespacetime model. 
           [0023]      FIG. 5  is a schematic view of interactions and relationships of a first entity and a second biological entity such as a human brain in the dual-world according to the prespacetime model. 
           [0024]      FIG. 6  is a schematic and mathematical view of self-referential hierarchical spin processes for creating elementary entities/particles according to the prespacetime model. 
           [0025]      FIG. 7  to  FIG. 17  is schematic and mathematical views of metamorphous self-referential spin processes generating different forms of the Matrix Rule according to the prespacetime model. 
           [0026]      FIG. 18  to  FIG. 34  is schematic and mathematical views of metamorphous self-referential hierarchical spin processes for creating, sustaining and causing evolution of elementary entities/particles according to the prespacetime model. 
           [0027]      FIG. 35  to  FIG. 38  is schematic and mathematical views of the metamorphous self-referential hierarchical spin processes for creating, sustaining and causing evolution of composite entities/particles such as a neutron and a proton according to the prespacetime model. 
           [0028]      FIG. 39  and  FIG. 42  are schematic and mathematical views of metamorphous determinant views (equations) of the elementary entities/particles according to the prespacetime model. 
           [0029]      FIG. 43  is schematic and mathematical views of meanings of a Schrodinger equation and a quantum potential according to the prespacetime model. 
           [0030]      FIG. 44  is schematic and mathematical views of a third state of matter according to the prespacetime model. 
           [0031]      FIG. 45  to  FIG. 48  is schematic and mathematical views of the weak interactions according to the prespacetime model. 
           [0032]      FIG. 49  to  FIG. 52  is schematic and mathematical views of the electromagnetic interactions and different forms of Maxwell equations according to the prespacetime model. 
           [0033]      FIG. 53  to  FIG. 56  is schematic and mathematical views of the strong interactions and spatial self-confinement processes according to the prespacetime model. 
           [0034]      FIG. 57  to  FIG. 61  is schematic and mathematical views of different forms of the quantum entanglement (self-gravity) and the gravitational interactions between a first entity or particle and a second entity or particle according to the prespacetime model. 
           [0035]      FIG. 62  and  FIG. 63  are schematic and mathematical views of electromagnetic interactions involving nuclear and/or electronic spin in the brain associated with consciousness and brain function according to the prespacetime model. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0036]    The detailed description of the prespacetime model is organized into 10 sections. 
       I. Overall Scheme of the Prespacetime Model 
       [0037]      FIG. 1  to  FIG. 5  illustrates an overall scheme of the prespacetime model including: (1) occurrence of a primordial phase distinction through imagination i of the prespacetime, (2) matrixing of the prespacetime into the external and internal wave functions respectively as the external and internal objects of a first entity or particle in the dual world or interaction fields for interacting with a second entity or particles, (3) governance of the external and internal wave functions by the self-acting and self-referential Matrix Rule which accompanies the imagination i of the prespacetime so as to enforce the accounting principle of conservation of zero in the dual world, (4) relationships of a first entity and a second entity between themselves and with the external and internal world of the dual-world, and (5) relationships of a first entity and a second biological entity which is a brain and relationships of the said first entity and the brain with the external and internal world of the dual-world. 
         [0038]    Considering first  FIG. 1 , the prespacetime model includes the occurrence of the primordial phase distinction in the mind of the prespacetime comprised of +M and −M through the imagination i of the prespacetime above the body of the prespacetime which can also be expressed as e 0 =e iM-iM =e iM e −iM =e −iM /e −iM =e iM /e iM . In one particular embodiment, ±M=±(Et−p·r)/=±p μ x μ /. 
         [0039]    The primordial phase distinction is accompanied by matrixing of the prespacetime into the external and internal wave functions respectively as the external and internal objects of a first entity or particle in the dual world or interaction fields for interacting with a second entity or particles. 
         [0040]    Considering  FIG. 2 , the prespacetime model includes the external and internal objects, the governance of the external and internal objects by the self-acting and self-referential Matrix to enforce the accounting principle of conservation of zero in the dual world. 
         [0041]    Considering  FIG. 3 , the prespacetime model includes the self-interaction between the external and internal object of an entity or particle through the Matrix Rule. 
         [0042]    Considering  FIG. 4 , the prespacetime model includes the relationships of a first entity and a second entity between themselves and with the external and internal world of the dual-world. 
         [0043]    Considering  FIG. 5 , the prespacetime model includes the relationships of a first entity and a second biological entity such as a brain and relationships of the said first entity and the brain with the external and internal world of the dual-world. 
         [0044]    Therefore, as illustrated in  FIG. 1  through  FIG. 5 , the prespacetime is comprised of a body mathematically represented by Euler number e and a mind represented by imaginary unit i above e. The body and mind of the prespacetime is grounds of all existence, can form external and internal wave functions as external and internal objects (with each pair forms an elementary entity or particle) and interaction fields between elementary entities which accompany the imaginations of the prespacetime. The body and mind can be self-acted on by the self-referential Matrix Rule L M  of the prespacetime. The prespacetime has imagining power i to project external and internal objects by projecting, for example, external and internal phase ±M=±(Et−p·x)/ above the body e. 
         [0045]    The universe so created is a dual-world comprising of the external world to be observed and internal world as observed under each relativistic frame x μ =(t, x). In one view, the internal world (which by convention may have either negative or positive energy) is the negation/image of the external world (which by convention may also have either positive or negative energy). According to the present model, an absolute frame of reference exists and the said frame is the body e of the prespacetime. Therefore, if the prespacetime stops imagining, the universe would disappear into materially nothingness e i0 =e 0 =1. 
         [0046]    The prespacetime model provides for interactions of the external and internal worlds through quantum entanglement since I have experimentally demonstrated that gravity is the manifestation of quantum entanglement (Hu, H. P., &amp; Wu, M. X. Evidence of non-local physical, chemical and biological effects supports quantum brain. Neuro-Quantology 4, 291-306 (2006); Hu, H. P., &amp; Wu, M. X. Evidence of non-local chemical, thermal and gravitational effects. Progress in Physics v2, 17-21 (2007)). 
         [0047]    The prespacetime model provides for interactions within the external world through classical and relativistic physical laws with light speed c as the speed limit of the external interactions and influences of the internal world on the external objects in the external world through as gravity macroscopically and quantum effects microscopically. Thus, according to the prespacetime model, the interactions within the external world and/or the internal world are local interactions and conform to special theory of relativity, but the interactions across the dual world are non-local interactions, that is, quantum entanglement or gravity. 
         [0048]    Therefore, according to the present model, the meaning of the special theory of relativity is that the speed limit c is only applicable in each of the dual world but not interactions between the dual-world. Indeed, the reason that no external object can move faster than the speed of light and it gets heavier and heavier as its speed approach the speed of light is due to its increased quantum entanglement with the internal world through its counterpart the internal object. 
       II. Genesis in a Nutshell 
       [0049]    In the present model, the prespacetime is omnipotent, omnipresent and omniscient. The prespacetime creates, sustains and causes evolution of primordial entities or elementary particles within the prespacetime itself by self-referential hierarchical spin as shown in mathematical expression  210  of  FIG. 6 . in which e is Euler number representing the body (ether)) of the prespacetime, h above e represents the head of the prepsacetime, i is imaginary unit representing imagination of the prespacetime, ±M is content of imagination i, L 1 =1 is Rule of One before matrixization, L e  is external rule, L i  is internal rule, L M,e  is external matrix rule, and L M,i  is internal matrix rule, L M  is self-referential Matrix Rule comprised of the external and internal matrix rule which governs elementary entities and conserves zero, A e e −iM =ψ e  is external wave function (external object), A i e −iM =ψ i  is internal wave function (internal object) and ψ is the complete wave function (object/entity in the dual-world as a whole). 
         [0050]    Alternatively, the prespacetime creates, sustains and causes evolution of primordial entities within the prespacetime itself by the self-referential hierarchical spin as shown in mathematical expression  220  of  FIG. 6  in which L 0  is Rule of Zero as defined by fundamental relationship  301  of  FIG. 7 , Det means determinant and M E , M m  and M p  are respectively matrices with ±E, ±m and ±|p| as elements and E 2 , −m 2  and −p 2  as determinants. 
         [0051]    The prespacetime spins as 1=e i0 =e iM-iM =e iM e −iM =e −iM /e −iM =e iM /e iM  before matrixization. The prespacetime also spins through the self-acting and self-referential Matrix Rule L M  after matrixization which acts on the external object and internal object to cause them to interact with each other as further described below. 
         [0052]    The Matrix Rule L M  of the prespacetime is derived from the fundamental relationship  301  of  FIG. 7  through self-reference within this relationship  301  which accompanies imagination i in the head of the prespacetime. For simplicity, light speed c is set to 1 (c=1) in  301  and, indeed, both the light speed c and Planck Constant  will be set to 1 (c==1) through out this application unless it is indicated otherwise. The fundamental relationship  301  of  FIG. 7  was discovered by Einstein. 
         [0053]    In the presence of an interacting field such as an electromagnetic potential A μ =(φ, A) of a first electrically charged entity or particle, the fundamental relationship  301  of  FIG. 7  becomes mathematical expression  302  of  FIG. 7  for a second electrically charged entity or particle with an electric charge e. 
       III. Metamorphous Forms of the Matrix Rule 
       [0054]    As one embodiment of the self-reference within the fundamental relationship  301  of  FIG. 7 , a first form of the Matrix Rule as shown in  306  of  FIG. 7  is derived through a first step shown in mathematical expression  303  in which |p| is defined by  304 , and a second step of matrixing left-land side of the last expression in  303  such that mathematical expression  305  holds in order to satisfy the fundamental expression  301  resulting in the first form  306 . 
         [0055]    As a second embodiment of the self-reference within the fundamental relationship  301  of  FIG. 7 , the first form  306  of  FIG. 7  can also be derived by the steps of a self-reference as in  307  of  FIG. 8  and a matrixing as in  308  of  FIG. 8  in which determinant sign Det is removed. 
         [0056]    After a fermionic form of spinization as defined in  309  of  FIG. 8  where σ=(σ 1 , σ 2 , σ 3 ) are Pauli matrices as defined in  310  of  FIG. 8 , the first form of the Matrix Rule as shown in  306  of  FIG. 7  transforms into a second form of the Matrix Rule as shown in  311  of  FIG. 8  in which α=(α 1 , α 2 , α 3 ) and β are Dirac matrices and H as defined in  312  is the Dirac Hamiltonian. The second form of the Matrix Rule  311  governs fermions in Dirac form such as Dirac electron and positron. On the other hand, the first form of the Matrix Rule  306  governs a third state of matter, that is, an unspinized (spinless) entity/particle with the electric charge e and a mass m such as a meson or a meson-like particle. A bosonic form of spinization shall be illustrated later. 
         [0057]    Defining a determinant view shown  313  of  FIG. 8 , a relationship shown in  314  can be derived. Therefore, in the determinant view, the fundamental relationship  301  is also satisfied. Indeed, a conventional determinant shown in  315  is also obtained. 
         [0058]    One kind of metamorphosis of mathematical expressions  303 ,  306 ,  307 ,  308 ,  311 ,  313  and  314  respectively is as  316 ,  317 ,  318 ,  319 ,  320 ,  321  and  322  of  FIG. 9. 317  is a unspinized form of the Matrix Rule in Weyl (chiral) form and is connected to  306  by a transform defined in  324  in which H is Hadamard matrix defined in  323  of  FIG. 10. 320  is a spinized form of the Matrix Rule in Weyl (chiral) form and is connected to  311  by a transform defined in  325  in which H is 4×4 Hadamard matrix. 
         [0059]    A second kind of metamorphosis of mathematical expressions  303 ,  306 ,  307 ,  308 ,  311 ,  313  and  314  respectively is as  326 ,  327 ,  328 ,  329 ,  330 ,  331  and  332 . Indeed, Q as defined in  333  is a quaternion and Q′ as defined in  334  is the conjugate of Q, Thus,  332  can be now rewritten as  335 .  327  is a unspinized form of the Matrix Rule in a third form and is connected to  306  by a transform defined in  337  in which HS is a matrix defined in  336 .  330  is a spinized form of the Matrix Rule in a third form and is connected to  311  by a transform defined in  338  in which HS is a 4×4 form of the matrix  336 . 
         [0060]    Yet a third kind of metamorphosis of mathematical expressions  303 ,  306  and  311  respectively is as  339 ,  340  and  341  of  FIG. 12 . 
         [0061]    When m=0, mathematical expression  343 ,  343 ,  344  and  345  is respectively derived from  303 ,  306 ,  307  and  308 .  343  governs massless particle with unobservable spin (spinless) in Dirac form. After a fermionic spinization  346 , the unspinized form  343  of the Matrix Rule becomes a spinized form  347  of the Matrix Rule which governs a massless fermion in Dirac form. After a bosonic spinization  348 , the unspinized form  343  of the Matrix Rule  343  becomes a spinized form  349  of the Matrix Rule which governs a massless boson in Dirac form. 
         [0062]    In the spinized form  349 , S=(S 1 , S 2 , S 3 ) as defined in  350  are spin operators for spin  1  particle. If a second form of the determinant view is defined by  351 , a result shown in  352  is derived. To satisfy the fundamental relationship  301  in the form  351  of the determinant view, the last term in  352  acting on the external and internal wave functions respectively needs to produce null result (zero) in a source-free zone as discussed later. 
         [0063]    Also when m=0, mathematical expression  353 ,  354  and  355  is respectively derived from  317 ,  319  and  320 .  354  governs massless particle with unobservable spin (spinless) in Weyl form. After the fermionic spinization  346 , the unspinized form  354  of the Matrix Rule becomes a spinized form  355  of the Matrix Rule which governs a massless fermion in Weyl form. After the bosonic spinization  348 , the unspinized form  354  of the Matrix Rule becomes a spinized form  356  of the Matrix Rule which governs a massless boson in Weyl form. 
         [0064]    If a third form of the determinant view is defined by  357 , a result shown in  358  is derived. To satisfy the fundamental relationship  301  in the form  357  of the determinant view, the last term in  358  acting on the external and internal wave functions respectively needs to produce null result (zero) in the source-free zone as discussed later. 
         [0065]    When E=0, 359 results from the fundamental relation  301 . Thus if timeless forms of Matrix Rule are allowed in the prespacetime,  360  and  361  is respectively derived from  306  and  317 . Both  360  and  361  further degenerate when m=0. Further, when |p|=0,  362  results from the fundamental relation  301 . Thus if spaceless forms of Matrix Rule are allowed in the prespacetime,  363  and  364  is respectively derived from  306  and  317 . The significance of the forms of Matrix Rule in this Paragraph shall be made clear later. At this moment, it is suggested that the timeless forms of Matrix Rule govern the external and internal wave functions (self-fields) which play roles of timeless gravitons, that is, they mediate time-independent interactions through space (momentum) quantum entanglement. On the other hand, the spaceless forms of Matrix rules govern the external and internal wave functions (self-fields) which play roles of spaceless gravitons, that is, they mediate space (distance) independent interactions through proper time (mass) entanglement. 
         [0066]    The above various forms of the self-acting and self-referential Matrix Rule are derived from one-tier matrixization (self-reference) and two-tier matrixization (self-reference) based on the fundamental relationship  301 . The first-tier matrixization makes distinctions in time (energy), proper time (mass) and undifferentiated space (total momentum) which involve scalar unit  1  and imaginary unit (spin) i. Then the second-tier matrixization makes distinction in three-dimensional space (three-dimensional momentum) based on spin σ, s or other spin structure if it exists. 
         [0067]    If partial distinction within the first-tier self-referential matrixization is allowed in the prespacetime, additional forms of Matrix Rule shown as  365  to  373  of  FIG. 16  are derived, for example. 
         [0068]    If a spatial self-confinement of an elementary entity/particle through imaginary momentum p i  (downward self-reference) such that m 2 &gt;E 2  is allowed in the prespacetime, a new fundamental relationship  374  or  375  of  FIG. 17  is derived from the fundamental relationship  301  of  FIG. 7 . Therefore, allowing the imaginary momentum (downward self-reference) in the prespacement for the elementary entity, new Dirac-like forms of Matrix Rule shown in  376  and  377  and new Weyl-like forms of Matrix Rule shown in  378  and  379  are derived. Bosonic versions of  377  and  379  are obtained by replacing σ with s. 
         [0069]    It is likely that the above additional forms of self-referential Matrix Rule  365  to  373  and  376  to  379  govern different particles in the particle zoo as discussed later. 
       VI. Genesis of Elementary Entities/Particles 
       [0070]    In one embodiment, a free plane-wave fermion such as an electron in Dirac form is created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  401 ,  402  and  403  of  FIG. 18 . A different expression of  403  is shown in  404 . After substitutions  405  and  406  such that actions of each element in the Matrix Rule on the external and internal wave functions can be explicitly shown, yet a third expression of  403  is derived as shown in  407 . Equation  403  also has a free spherical wave solution in the form shown in  408 . 
         [0071]    In another embodiment, the free plane-wave fermion such as the electron in Dirac form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  409 ,  410 ,  411  and  412  of  FIG. 19 . 
         [0072]    In a 3 rd  embodiment, a free plane-wave antifermion such as a positron in Dirac form is created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  413 ,  414  and  415  of  FIG. 20 . 
         [0073]    In a 4 th  embodiment, the free plane-wave antifermion such as the positron in Dirac form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  416 ,  417  and  418  of  FIG. 20 . 
         [0074]    In a 5 th  embodiment, a free plane-wave fermion such as an electron in Weyl (chiral) form is created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  419 ,  420  and  421  of  FIG. 21 . A different expression of  421  is shown in  422 . After substitutions  405  and  406  such that actions of each element in the Matrix Rule on the external and internal wave functions can be explicitly shown, yet a third expression of  421  is derived as shown in  423 . Equation  421  also has a free spherical wave solution. 
         [0075]    In a 6 th  embodiment, the free plane-wave fermion such as the electron in Weyl (chiral) form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  424 ,  425  and  426  of  FIG. 22 . 
         [0076]    In a 7 th  embodiment, a free plane-wave fermion such as an electron in a 3 rd  form is created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  427 ,  428 ,  430  and  429  of  FIG. 23 . A different expression of  429  is shown in  431 . After substitutions  405  and  406  such that actions of each element in the Matrix Rule on the external and internal wave functions can be explicitly shown, yet a third expression of  429  is derived as shown in  432 . 
         [0077]    In a 8 th  embodiment, the free plane-wave fermion such as the electron in the third form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  433 ,  434 ,  435  and  436  of  FIG. 24 . 
         [0078]    In a 9 th  embodiment, a linear plane-wave photon is created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  437 ,  438  and  439  of  FIG. 25 . 
         [0079]    In a 10 th  embodiment, the linear plane-wave photon is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  440 ,  441  and  442  of  FIG. 26 . The linear plane-wave photon has a wave function as shown in  443 . After substitutions  444  and  445  such that actions of each element in the Matrix Rule on the external and internal wave functions can be explicitly shown, two of the Maxwell equations in a vacuum are derived as shown in  447  by utilizing a relation shown in  446 . These two equations together with equations (or source-free conditions) in  448  form a complete set of the Maxwell equations in the source-free zone. 
         [0080]    In a 11 th  embodiment, a free plane-wave massless neutrino in Dirac form is created, sustained and caused to evolve in the prespacetime by replacing the bosonic spinization shown in  439  or  442  with the fermionic spinization shown in  449 . 
         [0081]    In a 12 th  embodiment, a linear plane-wave antiphoton is created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  450 ,  451  and  452  of  FIG. 27 . The linear plane-wave antiphoton has a wave function as shown in  453 . 
         [0082]    In a 13 th  embodiment, a free plane-wave massless antineutrino in Dirac form is created, sustained and caused to evolve in the prespacetime by replacing the bosonic spinization shown in  452  with the fermionic spinization shown in  454 . 
         [0083]    In a 14 th  embodiment, chiral plane-wave photons are created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  455 ,  456  and  457  of  FIG. 28 . Thus, left-handed external wave function ψ e,l  is decoupled from right-handed internal wave function ψ i,r . A different expression of  457  is shown in  458 . After substitutions  444  and  445  such that actions of each element in the Matrix Rule on the external and internal wave functions can be explicitly shown, yet a third expression of  457  is derived as shown in  459  which is comprised of two equations with one governing the left-handed external photon wave function and another governing the right-handed internal photon wave function as shown in  461  and  462  respectively. Equation  459  has a decoupled left- and right-handed plane wave solutions shown in  460 . The Maxwell equations in  447  can be derived from either  461  or  462 . 
         [0084]    In a 15 th  embodiment, chiral plane-wave massless neutrinos are created, sustained and caused to evolve in the prespacetime by replacing the bosonic spinization shown in  457  with the fermionic spinization shown in  463 . A different expression of  463  is given in  464 . After substitutions  444  and  445  such that actions of each element in the Matrix Rule on the external and internal wave functions can be explicitly shown, yet a third expression of  463  is derived as shown in  465  which is comprised of two equations with one governing the left-handed external neutrino wave function and another governing the right-handed internal neutrino wave function. 
         [0085]    In a 16 th  embodiment, a timeless wave function (instantaneous graviton) of a mass m in Dirac form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  466  and  467  of  FIG. 29 . Detail of imaginary content M in expression  467  will be determined later in this application. 
         [0086]    In a 17 th  embodiment, the timeless wave function (instantaneous graviton) of a mass m in Dirac form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  468  and  469  of  FIG. 29 . 
         [0087]    In a 18 th  embodiment, a timeless wave function (instantaneous graviton) of a mass m in Weyl form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  470  and  471  of  FIG. 30 . Again, detail of imaginary content Min expression  471  will be determined later in this application. 
         [0088]    In a 19 th  embodiment, the timeless wave function (instantaneous graviton) of a mass m in Weyl form is created, sustained and caused to evolve in the prespacetime as shown mathematical expressions  472  and  473  of  FIG. 30 . 
         [0089]    In a 20 th  embodiment, a spaceless (distance independent) wave function (spaceless graviton) of a mass m in Dirac form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  474  and  475  of  FIG. 31 . 
         [0090]    In a 21 th  embodiment, a spaceless (distance independent) wave function (spaceless graviton) of a mass m in Weyl form is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  476  and  477  of  FIG. 31 . 
         [0091]    In a 22 th  embodiment, the spaceless (distance independent) wave function (spaceless graviton) of the mass m in Weyl form is created, sustained and caused to evolution in the prespacetime as in shown mathematical expressions  478  and  479  of  FIG. 31 . 
         [0092]    In a 23 rd  embodiment, a spatially self-confined entity such as a proton in Dirac form is created, sustained and caused to evolve in the prespacetime through imaginary momentum p i  (downward self-reference) such that m 2 &gt;E 2  as shown in mathematical expressions  480 ,  481  and  482  of  FIG. 32 . In the present model, equation  481  governs the spatial self-confinement of an unspinized proton in Dirac form through the imaginary momentum p i  and, on the other hand, equation  482  governs the spatial self-confinement of the spinized proton in Dirac form through the imaginary momentum p i . 
         [0093]    In a 24 th  embodiment, the spatially self-confined entity such as the proton in Dirac form is created, sustained and caused to evolve in the prespacetime through the imaginary momentum p i  (downward self-reference) such that m 2 &gt;E 2  as shown in mathematical expressions  483 ,  484 ,  485  and  486  of  FIG. 32 . 
         [0094]    Thus, according to the present model, an unspinized antiproton and a spinized antiproton in Dirac form are respectively governed by equation  487  and  488  of  FIG. 33 . 
         [0095]    In a 25 th  embodiment, a spatially self-confined entity such as a proton in Weyl form is created, sustained and caused to evolve in the prespacetime through the imaginary momentum p i  (downward self-reference) such that m 2 &gt;E 2  as shown in mathematical expressions  489 ,  490  and  490   a  of  FIG. 33 . In the present model, equation  490  governs the spatial self-confinement of an unspinized proton in Weyl form through the imaginary momentum p i  and, on the other hand, equation  490   a  governs the spatial self-confinement of the spinized proton in Weyl form through the imaginary momentum p i . 
         [0096]    In a 26 th  embodiment, the spatially self-confined entity such as the proton in Weyl form is created, sustained and caused to evolve in the prespacetime through the imaginary momentum p i  (downward self-reference) such that m 2 &gt;E 2  as shown in mathematical expressions  491 ,  492 ,  493  and  494  of  FIG. 34 . 
         [0097]    Thus, according to the present model, an unspinized antiproton and a spinized antiproton in Weyl form are respectively governed by equation  495  and  496  of  FIG. 34 . 
       V. Examples of Genesis of Composite Entities/Particles 
       [0098]    In a first embodiment, a neutron comprised of an unspinized proton in Dirac form shown in  501  and a spinized electron in Dirac form shown in  502  is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  503  and  504  of  FIGS. 35 and 505  of  FIG. 36  in which  506 ,  507  and  508  indicate proton, electron and neutron respectively. Further, the unspinized proton has electric charge e, the spinized electron has charge −e;  509  and  510  are respectively electromagnetic potential acting on the unspinized proton and the tightly bound spinized electron; and  511  is a binding potential from the unspinized proton acting on the spinized electron causing tight binding as discussed later in this application. If  509  is negligible due to fast motion of the tightly bound spinized electron,  512  is derived from  505 . Experimental data on charge distribution and g-factor of the neutron support the neutron in the present model which is comprised of the unspinized proton and the tightly bound spinized electron. A Weyl form of  505  and  512  are respectively  513  and  514  of  FIG. 36 . 
         [0099]    In a second embodiment, hydrogen comprised of an spinized proton in Dirac form shown in  515  and a spinized electron in Dirac form shown in  516  is created, sustained and caused to evolve in the prespacetime as shown in mathematical expressions  517 ,  518  and  519  of  FIGS. 37. 520 ,  521  and  522  of  FIG. 38  indicate proton, electron and hydrogen in  FIG. 37  respectively. Further, the spinized proton has electric charge e, the spinized electron has charge −e; and  523  and  524  are respectively electromagnetic potential acting on the spinized proton and the spinized electron in  FIG. 37 . If  523  is negligible due to fast motion of the spinized electron in  FIG. 37 ,  525  is derived from  519 . A Weyl form of  519  and  525  are respectively  526  and  527  of  FIG. 38 . 
       VI. Metamorphous View 
       [0100]    The preceding disclosures make it clear that the prespacetime can have many different forms of primordial entities/particles and different manifestations of a single entity/particle as different wave functions and/or fields in different contexts. For example, the wave functions of an electron can take the Dirac, Weyl, quaternion or determinant form discussed below respectively in different contexts depending on questions asked and answers sought. However, a particular answer given is determined by free will of the prespacetime known as measurement problem in quantum mechanics and understood currently as a randomness of Nature. For another example, depending on a particular context, a manifestation of the entity/particle such as an electron can be a bi-spinor (ψ, ψ) T  in the spinized self-interaction or a bi-vector (E, iB) T  (or an electromagnetic potential) in an electromagnetic interaction. Further, these forms are self-contained through their respective forms of self-referential Matrix Rule. 
         [0101]    If a first question is how a free fermion is created, several embodiments have shown in the preceding sections according to the present model. If a second is how an entity participates in weak interaction, an answer is through fermionic spinization and unspization according to the present model as shown later in this application. If a third question is how an entity participates in the strong interaction, an answer is through an imaginary momentum (downward self-reference) according to the present model as shown later in this application. If a fourth question is how an entity participates in electromagnetic interaction, an answer is through bosonic spinization and unspization according to the present model as shown later in this application. If a fifth question is how an entity participates in gravitational interaction, an answer is through timeless, spaceless and/or massless external and internal wave functions according to the present model as shown later in this application. 
         [0102]    Further, the present model also makes it clear that the primordial self-referential spin in the prespacetime is hierarchical and is the cause of the primordial distinction for creating the elementary entities/particles in the dual world. Indeed, according to the present model and as shown in preceding sections, there are several levels of self-referential spin: (1) spin in the mind of the prespacetime for making the primordial external and internal phase distinctions of the external and internal wave functions; (2) spin of the body (ether) of the prespacetime for making the primordial external and internal wave functions which accompanies the primordial phase distinctions; (3) self-referential mixing of these wave functions through various forms of the Matrix Rule producing self-interaction, quantum entanglement or gravity; (4) unconfining spatial spin through fermionic or bosonic spinization (electromagnetic and weak interactions) for creating bosonic and fermionic entities; and (5) confining spatial spin (strong interactions) creating appearance of quarks through the imaginary momentum (downward self-reference). 
         [0103]    As shown in the preceding sections, in the determinant view, a particular form of the Matrix Rule transforms into a particular Klein-Gordon form. As one embodiment of the present model, the transformation is accompanied by external and internal wave functions of an entity/particle governed by the particular form of the Matrix Rule forming a special product state ψ e ψ i * with ψ i * containing hidden variables, a quantum potential or self-gravity as shown below, visa versa. In the present model, the Klein-Gordon form and the special product state together form a equation in the determinant form illustrated below. 
         [0104]    By way of an example, from  550  and  551  of  FIG. 39  which respectively described an unspinized free particle in Dirac and Weyl form, two sets of equations in the determinant form are respectively derived as shown in  552  and  553  of  FIG. 39 . Equation  550  has a plane-wave solution shown in  554  from which the special product state is derived and shown in  555 . φ e  and φ i  in  556  are respectively an external and internal phase in the determinant view. Variables in ψ* i,−  play roles of the hidden variables to ψ e,+  which would be annihilated, if ψ* i,−  is allowed to merged with ψ e,+ . Indeed, if relativistic mass in the external wave function ψ e,+  is treated as inertial mass, relativistic mass in the conjugate internal wave function ψ* i,−  plays role of gravitational mass. We will discuss quantum potential below. 
         [0105]    By way of another example, from  557  and  558  of  FIG. 40  which respectively described a spinized free particle in Dirac and Weyl form, two sets of equations in the determinant form are respectively derived as shown in  561  and  562  of  FIG. 40 . 
         [0106]    By way of a third example, in the presence of a electromagnetic potential  563 , equations  550  and  551  respectively transform into  564  and  565  of  FIG. 41  from which two sets of equations in the determinant form are respectively derived as shown in  566  and  567  of  FIG. 41 . In  567  α and β are respectively given  568  and  569  of  FIG. 41 . 
         [0107]    By way of a fourth example, in the presence of the electromagnetic potential  563 , equations  557  and  558  respectively transform into  570  and  571  of  FIG. 42  from which two sets of equations in the determinant form are respectively derived as shown in  572  and  573  of  FIG. 42 . In  570  and  571 , couplings of E and B with spin o are implicit or hidden. However, in the determinant view, the couplings are made explicit as shown in equations  572  and  573  respectively. In the present model, the couplings are due to self-referential Matrix Rule L M  which mixes the external and internal wave functions. 
         [0108]    Schrodinger Equation shown in  580  is a non-relativistic approximation of equation  552  or  553 . The wave function in  580  has a form shown in  581 . Thus, equation  580  can be written as two coupled equations shown in  582  or  583  which describes non-relativistic self-reference of the wave components ψ Re  and ψ lm  due to spin i. If ψ Re  is designate as an external object, ψ lm  is an internal object in relation to ψ Re . Therefore, Schrodinger Equation in  580  is the non-relativistic approximation of the equation  552  or  553  which is the determinant form of the unspinized particle  550  or  551  with self-referential Matrix Rule reduced to spin i in time operator. 
         [0109]    From the wave function  581  a quantum potential Q can be extracted. By way of an example, for a special product in  584  parameters of which are given in  585 , a quantum potential  586  is derived. Q in  586  originates from spin i in  587 . Q would negate non-relativistic kinetic energy of the external wave function if the external wave function and the conjugate internal wave function would merge. 
         [0110]    Further, Pauli Equation  588  is a non-relativistic approximation of equation  570  which is the determinant view of a fermion in an electromagnetic field in Dirac form.  588  contains non-relativistic self-reference due to both spin i and σ. 
         [0111]    Conventionally, a scalar (spinless) particle is presumed to be described by Klein-Gordon equation and is classified as a boson. However, in the present model, the Klein-Gordon equation is an equation in the determinant form of a fermion, boson or an unspinized entity in which the external and internal wave functions (objects) form a special product state ψ e ψ i * with ψ i * as origins of hidden variables, quantum potential and self-gravity. Further, in the present model, the unspinized entity is neither a boson nor a fermion but classified as a third state of matter described by the unspinized equation in Dirac or Weyl (chiral) form shown respectively in  591  and  592  of  FIG. 44 . Hadronized versions of  591  and  592  in which momentum becomes imaginary are respectively as shown in  593  and  594 . 
         [0112]    In the present model, the third state of matter does not subject to statistical behavior of either bosons or fermions. Wave function of a fermion or a boson is respectively a bispinor and bi-vector but the wave function of the third state is a two-component complex scalar field. In the present model, the third state of matter is precursor of both fermionic and bosonic matters/fields before fermionic or bosonic spinization. Thus, in the present model, the third state of matter steps into roles played by Higgs field in the Standard Model which so far has not been found. Further, in the present model, mass is created by self-referential spin. 
       VII. Weak Interaction 
       [0113]    In the present model, weak interaction is an expressive process (emission or radiation) through fermionic spinization with or without intermediary bosonic spinization and associated reverse process (capture or absorption). There are two kinds of mechanisms at play in the present model. The first kind is direct fermionic spinization of an unspinized massive particle as shown  601  of  FIG. 45 , an example of which is shown in  602 , and the reverse process shown in  603 , an example of which is shown in  604 . Processes  601  and  603  only conserve spin in the dual world as a whole. If they hold in reality, neutrino may not be needed in the weak interaction as currently understood or assumed. 
         [0114]    Thus, according to the present model, beta decay of a neutron may involve the spinizing process  601  during which an unspinized proton or unspinized electron gains spin ½ and a bound spinized electron becomes free as shown in  605  and  606 . Process  605  seems to be in closer agreement with experimental data on g-factor and charge density of neutron. There is no exchange particle involved in process  605  or  606 . Further, in a neutron synthesis from proton and electron, if the said synthesis exists in Nature, the reverse process  603  occurs during which a spinized proton (or spinized electron) loses spin ½ and a free electron becomes tightly bound to the proton. 
         [0115]    In the present model, equation  607  which can also be written as  608  governs a free unspinized particle having mass m and electric charge e respectively, that is, the unspinized particle is pion-like particle or a pion particle. After fermionc spinization of  607  or  608  through  601 , a spinized equation  609  or  610  is derived. Giving a plane-wave solution  611  for the external wave function of  607  or  608 , a complete solution for  607  or  608  is derived as shown in  612  in which N is a normalization factor and in deriving which  613  for an energy eigenstate is utilized. 
         [0116]    After fermionic spinization of solution  612  as shown in  614 , two solutions  615  and  616  are obtained respectively for external spin up and down. In these two solutions, external spin ½ is balanced by internal spin components which may be deemed as an antineutrino such that total spin of the spinized entity in the dual world is conserved to zero. Therefore, in the present model, the external spin up or down is allowed to be created without need of a separate antineutrino in beta decay and any excessive energy ΔE and or momentum Δp are allowed to cancel each other as shown in  617 . 
         [0117]    The second kind involves intermediary bosonic spinization  618  or  620  of an unspinized massive particle, examples of which are respectively shown in  619 , and  621 - 622 , during which transitory states known as vector bosons W − , W +  and/or Z 0  appear and disappear. In the present model, only process  620  mediates the weak interaction since in process  618  vector bosons W − , W +  and/or Z 0  are just transitory states which do not decay into fermions. 
         [0118]    The bosonic spinized equation in  619  for free massive spin  1  particle can have a form shown in  623  or  624 . Calculating the determinant defined in  625  results in  626 . As shown in preceding sections, last term M T  in  626  makes the fundamental relationship  627  not to hold in the determinant view  625  unless action of M T  on the external and internal components of the wave function produces null result as shown in  628  and  629 . In the present model, violations of  628  and/or  629  are allowed to exist transitorily, equations  623  or  624  describe respectively free vector bosons W −  and W + , and combination of wave functions in equations  623  or  624  describe free vector boson Z 0 , and M T  is treated as a transitory mass (or mass operator). 
         [0119]    In contrast to process  605  or  606 , vector bosons W −  and W +  respectively mediate spinization of an unspinzed proton or unspinized electron respectively as shown in  630  and  631 . It is expected that the various forms of Matrix Rule shown herein and their further metamorphoses together with the various forms of wave functions that these forms of the Matrix Rule govern will be able to accommodate all known particles in the particle zoo. 
         [0120]    Importantly, according to the present model, there maybe no parity violations in weak interactions such as beta decay as the apparent parity violation in the experiment may simply be explained as a spin polarization effect in which the spin polarization influences the dynamics and directions of the emitted electron in an external magnetic field. Also, there is no need for Higgs field for generating mass since mass is generated by self-referential spin within the prespacetime. 
       VII. Electromagnetic Interaction 
       [0121]    In the present model, electromagnetic interaction is an expressive process (radiation or emission) through bosonic spinization of a massless and spinless entity and associated reverse process (absorption). There are two kinds of mechanisms at play. The first kind is direct bosonic spinization (spinizing radiation) shown in  650 , an example of which is shown in  651 , and the reverse process shown in  652 , an example of which is shown in  653 . So, in the present model, radiation and absorption of a photon during acceleration of a charge particle is bosonic spinizing and unspinizing process shown in  654  and  655  respectively. Processes  654  and  655  may also occur in nuclear decay and perhaps other processes. 
         [0122]    Giving a plane-wave solution  656  for the external wave function of equation  657  or  658 , a complete solution for  657  or  658  is derived as shown in  659  in which N is a normalization factor and in deriving which  660  for an energy eigenstate is utilized. After bosonic spinization of solution  659  as shown in  661 , three solutions  662 ,  663  and  664  are obtained for spinized photon equation  665  or  666 . 
         [0123]    The second kind of electromagnetic interactions is release (radiation) or binding (absorption) of a spinized photon without unspinization as shown in  667  and  668  respectively.  667  and  668  occur at openings of an optical cavity or waveguide and may also occur in atomic photon excitation and emission and perhaps other processes. 
         [0124]    After bosonic spinization shown in  669 , Maxwell equations in vacuum (c=1; ε 0 =1) can be written as  670 ,  671  or  672  of  FIG. 51 . Calculating determinant defined in  673  results in  674  the last term M T  of which makes fundamental relationship  675  not to hold in the determinant view  673  unless action of M T  on E and iB produce null result because  628  and  628  only hold in a source-free region. Thus, at a location of a massive charged particle such as an electron or proton, equations  628  and  628  are also violated by a photon, so the photon appears to have mass M T  at the charged location which may result in particle pairs being created on collision of the photon with a massive charged particle such as the proton. 
         [0125]    In the Maxwell equations, these violations are counter-balanced by adding a source shown in  628  to the said equations which then can be written as  676 ,  677  or  678 . The Maxwell equations with source are, in turn, coupled to Dirac Equation of a charged fermion such as an electron or proton forming a Dirac-Maxwell system as further discussed later in this application. 
         [0126]    Importantly, a fermionic spinization scheme  679  can also be use to describe the Maxwell equations as shown in  680  and  681  for the source-free vacuum and  683  and  684  for a zone containing source  682 . Therefore, in the fermionic spinization scheme  679 , the bi-vector wave function (E,iB) T  is replaced by a 4×4 tensor comprising of two bi-spinors generated by projecting the bi-vector (E,iB) T  to spin σ. 
         [0127]    Further, in the present model, electric field E of a linear photon is the external wave function (external object) and magnetic field B of the linear photon is the internal wave function (internal object). These two fields are always self-entangled and their entanglement is their self-gravity. Therefore, in the present model, the relation between E and B in a propagating electromagnetic wave is not that a change in E induces a change in B visa versa but the change in E are always accompanied by the change in B visa versa due to their entanglement (self-gravity). That is, the relationship between E and B are gravitational and instantaneous. 
       VIII. Strong Interaction 
       [0128]    While weak and electromagnetic interactions in the present model are expressive processes involving fermionic and bosonic spinizations of spinless entities (the third state of matter) and their respective reverse processes, strong interaction in the present model does not involve spinization rather, strong force is a confining process. In the present model, spinless entities in general are unstable and decay through fermionic or bosonic spinization. Thus, in order to achieve confinement of a nucleon or stability of the nucleus, the present model suggests that strong interaction involve imaginary momentum in a confinement zone as illustrated below. There are two types of strong interaction at play. One is self-confinement of a nucleon such as a proton and the other is interaction among nucleons such a proton and a neutron. 
         [0129]    In the Standard Model, proton is assumed to be a composite entity comprised of three quarks confined by massless gluons and the interaction among the nucleons is mediated by mesons comprised of pairs of a quark and an antiquark which in turn interact through gluons. However, since no free quark has been observed, there is good reason to consider other options. In the present model, a proton is treated as an elementary particle which accomplishes spatial self-confinement through imaginary momentum downward self-reference). 
         [0130]    Condition for producing spatial self-confinement of the nucleon and a nuclear potential known as the Yukawa potential will be derived first. Equation for a massive but spinless entity in Dirac Form is as shown in  701  of  FIG. 53  which can also be written as  702 . 
         [0131]    Taking the wave function  701  to have an energy eigenstate −E (that is, the external and internal wave functions respectively have energy eigenstate −E and +E in the determinant view), calculations in  703  and  704  can be carried out resulting in equation  705  which can also be written as  706 . Equation  705  or  706  has radial solution shown in  707  which allows calculation in  708  be carried out by using a relationship in  709 . Thus, a complete radial solution of equation  701  or  702  for the energy eigenstate −E in Dirac form is given in  710  where N is a normalization factor. 
         [0132]    When condition shown in  711  of  FIG. 54  occurs, that is, when momentum in relationship  712  is imaginary, a wave function shown in  713 , in which α and β are respectively given in  714  and  715 , is derived from the wave function shown in  710 . Now, considering a special case of a timeless, spinless but massive entity for which condition in  716  holds, that is, rest mass of the massive entity is all comprised of imaginary momentum p i , a wave function is  717  is derived. The internal and external wave functions in  717  respectively have a form of Yukawa potential and a negative imaginary projection of the Yukawa potential. 
         [0133]    In the present model, interior (confinement zone) of an unspinized nucleon is describable by a wave function similar to expressions  713  or  717  and the confinement is achieved through the imaginary momentum p i  (downward self-reference) Therefore, in the present model three colors of the strong force are comprised of three-dimensional imaginary momentum. Further, a deep implication of the present model is that in a Machian quantum universe timeless edge or outside of the universe is connected to or simply is the timeless confinement zone of the nucleons. 
         [0134]    Taking that the internal wave function ψ i  (which is self-coupled to the external wave function ψ e  through equation  701  or  702 ) also couples with external wave function X e  of a second entity/particle (which is also self-coupled to its internal wave function X i ) in a manner given in  718  in which −g 2  is a coupling constant, part of a nuclear potential of a nucleon has a form given in  719  which is in the form of Yukawa Potential. It is pointed out here that a person skilled in the art can write a suitable full Hamiltonian for two interacting nucleons based on what is disclosed in this application. 
         [0135]    Considering an unspinized and a spinized form of proton in the present model, the equation for the free unspinized proton is given in  720  in Dirac form and the equation for the free spinized proton is given in  721  in Dirac form. In both  720  and  721 , p i  represents the imaginary momentum. It is pointed out here that a proton with a spin is the commonly known form of proton and, in the present model, a proton without spin, the unspinized proton, is permitted to be a component of the neutron comprised of the unspinized proton and a spinized electron as illustrated in preceding sections. 
         [0136]    From the preceding derivations in this section, the wave function of the unspinized proton with external and internal energy eigenstate −E and +E respectively can be written as shown in  722  (by convention, electron has positive external energy +E and internal energy −E). In contrast, an unspinized antiproton with external and internal energy eigenstate +E and −E respectively can have a wave function shown in  723 . Therefore, according to the present model, nuclear spin of the neutron is solely due to a tightly bound spinized electron and a nuclear potential causing tight binding of the spinized electron in the neutron is permitted to have the form in  719 . Indeed, experimental data on charge distribution and g-factor of the neutron support the herein model. 
         [0137]    A wave function of the spinized proton described by  721  is derivable by spinizing the solution shown in  722  a step shown in  724  in which is total angular momentum number. Choosing j=½, two solutions as shown in  725  and  726 , in which α is given in  727 , are derived. In the case of a timeless proton, that is, when condition shown in  728  holds, two solutions as shown in  729  and  730  are derived from solutions  725  and  726  respectively. In the present model, the spinization of unspinized proton is permitted to cause loss of tight binding between the spinized electron and the unspinized proton. 
       IX. Gravitational Interaction (Quantum Entanglement) 
       [0138]    I have experimentally shown that gravity is instantaneous interaction mediated by quantum entanglement (Hu, H. P., &amp; Wu, M. X. Evidence of non-local physical, chemical and biological effects supports quantum brain. Neuro-Quantology 4, 291-306 (2006); Hu, H. P., &amp; Wu, M. X. Evidence of non-local chemical, thermal and gravitational effects. Progress in Physics v2, 17-21 (2007)). 
         [0139]    In the present model, gravity is simply quantum entanglement across the dual-world. There are two types of gravity at play. The first type is self-gravity (self-interaction) between an external object (an external wave function) and an internal object (an internal wave function) of an entity (a wave function) governed by the various forms of Matrix Rule described in this application. The second type is the quantum entanglement (instantaneous interaction) between two entities/particles or one entity/particle and the dual-world as a whole which may be either attractive or repulsive. As further illustrated below, a gravitational field (a graviton) is just the wave function of the entities or particles which expresses intensity distribution and dynamics of self-quantum-entanglement (nonlocality) of the entity/particle. Indeed, the strong interaction actually is strong quantum entanglement (strong gravity). 
         [0140]    Three particular forms of gravitational field are illustrated below. The first form is a timeless (zero energy) wave function comprised of a timeless external wave function and a timeless internal wave function which plays role of a timeless graviton, that is, the timeless wave function mediates time-independent interactions through space quantum entanglement. The second form is a spaceless wave function comprised of a spaceless external wave function and a spaceless internal wave function which plays role of a spaceless graviton, that is, the spacelss wave function mediates space (distance) independent interaction through proper time (mass) entanglement. The third form is a massless wave function comprised of a massless external wave function and a massless internal wave function which plays role of a massless graviton, that is, the massless wave function mediates mass (proper-time) independent interactions through massless energy entanglement. 
         [0141]    A typical wave function contains all three (timeless, spaceless and massless) forms of gravitational field. In addition, the typical wave function also contains gravitational field originated from fermionic and/or bosonic spinization. As illustrated below, in the present model a timeless quantum entanglement between two entities accounts for Newton gravity. A spaceless and/or massless quantum entanglement between two entities is permitted to account for dark matter and Casimir effect. Importantly, in the present model a gravitational field originated from fermionic and/or bosonic spinization is permitted to account at least partially for dark energy. 
         [0142]    When condition  750  occurs,  751 , which can be written as  752 , is derived from the fundamental relationship  301 . In the present model,  751  or  752  is a relationship governing a Machian quantum universe in which total energy is zero as shown in  750 . Classically, this may be seen as either rest mass m being comprised of imaginary momentum or the momentum being comprised of imaginary mass. A timeless form of the Matrix Rule in Dirac or Weyl form is respectively given in  753  and  754  which respectively govern equations in  755  and  756 . The equation  755  can be rewritten as  757  or  758  and the equation  756  can be rewritten as  759  or  760 . Considering couplings of external and internal wave functions from in another angle,  757  and  759  can be rewritten respectively as  761  and  762 . 
         [0143]    Equation  763 , which can be rewritten as  764 , is derived from  757  or  758  and has a radial solution in the form of Yukawa potential shown in  765 . Thus, in equation  755 , M=−imr, that is, the momentum is comprised of imaginary mass and, further,  765  is an external timeless wave function and has a form of Newton gravitational or Coulomb electric potential at large distance r→∞. Following steps shown in  766  and  767 , a complete radial solution for equation  755  is derived as shown in  768  in which N is a normalization factor. Indeed, a similar solution as shown in  769  can be derived for equation  756 . 
         [0144]    Considering the internal timeless wave function V D,i  (which is self-coupled to the external timeless wave function V D,e  shown in  757  or  758 ) also couples through timeless quantum entanglement with an external wave function ψ e  of another entity of a test mass m (which is also self-coupled to its own internal wave function ψ i ) as shown in  770 , for example, in which where iκ is a coupling constant and G=κ/4π is Newton Gravitational Constant, a Newtonian gravitational potential shown in  771  is derived for a large distance r→∞. It is pointed out here that a person skilled in the art can write a suitable full Hamiltonian for timeless gravitational interaction of two interacting entities based on what is disclosed in this application. 
         [0145]    When condition  772  occurs, equation  773  is derived from the fundamental relationship  301 . In the present model,  773  is a relationship governing a spaceless quantum universe in which total space is zero as shown in  773 . Classically, this may be seen as the rest mass m being comprised of time momentum (energy E). A spaceless form of the Matrix Rule in Dirac or Weyl form is respectively given in  774  and  775  which respectively govern equations in  776  and  777 . The equation  776  can be rewritten as  778  and has solutions  779  and  780 , and the equation  777  can be rewritten as  779  and has solutions  781  and  782 . 
         [0146]    As illustrated below, most quantum entanglements mentioned in quantum mechanics are spaceless quantum entanglement (gravity) between two entities, dark matter may be manifestation of this non-Newtonian gravity, and Casimir effect may be due to this type of spaceless quantum entanglement or, at least, may have contribution from spaceless quantum entanglement. For simplicity, considering two mass m 1 +m p  and m 2  respectively located at space point  1  and  2 . Their respective spaceless wave functions can be written in Weyl form as shown in  783  and  784  which form a first product state V 1W+  V 2W− . After m p  leaves V 1W+  as an emitted particle and get absorbed by V 2W− , two more spaceless wave functions in Weyl form are formed as respectively shown in  785  and  786  which form a second product state V 1W−  V 2W+ . 
         [0147]    These two products then form a joint quantum state as shown in  787  in which m 1  and m 2  are quantum entangled due to interaction with and through m p . In the present model, this space (distance) independent quantum entanglement (non-Newtonian gravity) between two entities is permitted to be a cause of dark matter. It is further permitted to be a cause of or, at least, contribute to Casimir effect. 
         [0148]    When condition  788  occurs, equation  789  is derived from the fundamental relationship  301 . In the present model,  773  is a relationship governing a massless quantum universe in which total mass is zero as shown in  789 . Classically, this is seen as the total energy being comprised of space momentum. A massless form of the Matrix Rule in Dirac or Weyl form is respectively given in  790  and  791  which respectively govern equations in  792  and  793 . Equation  792  has solutions  796  and  797 , and equation  793  has solutions  798  and  799 . Equations  792  and  793  describe self-interaction of external and internal massless and spinless wave functions. Thus, quantum-entangled state of two massless and spinless entities similar to  787  for the two spaceless entities described above. In the present model, the mass-independent quantum entanglement (non-Newtonian gravity) between the two massless entities may contribute to dark matter. 
       X. Consciousness and Brain Function 
       [0149]    I have theorized that spin is a primordial self-referential process driving quantum mechanics, spacetime dynamics and consciousness (Hu, H. P. &amp; Wu, M. X. Spin as primordial self-referential process driving quantum mechanics, spacetime dynamics and consciousness. NeuroQuantology, 2, 41-49 (2004); also see Cogprints ID2827 (2003)). I have also theorized that spin is a mind-pixel and the nuclear and/or electronic spins inside brain play important roles in certain aspects of brain functions such as perception (Hu, H. P., &amp; Wu, M. X. Spin-mediated consciousness theory. Medical Hypotheses 63, 633-646 (2004); also see arXiv e-print quant-ph/0208068v1 (2002)). 
         [0150]    Further, I have discovered the non-local effects of chemical substances on biological systems such as a human brain produced through quantum entanglement (Hu, H. P., &amp; Wu, M. X. Photon induced non-local effect of general anesthetics on the brain. NeuroQuantology 4, 17-31 (2006), Hu, H. P., &amp; Wu, M. X. Non-local effects of chemical substances on the brain produced through quantum entanglement. Progress in Physics v3, 20-26 (2006)). I have also discovered the evidence of non-local chemical, thermal and gravitational effects produced through quantum entanglement (Hu, H. P., &amp; Wu, M. X. Evidence of non-local physical, chemical and biological effects supports quantum brain. NeuroQuantology 4, 291-306 (2006); Hu, H. P., &amp; Wu, M. X. Evidence of non-local chemical, thermal and gravitational effects. Progress in Physics v2, 17-21 (2007)). 
         [0151]    My experimental results referenced above indicate that consciousness is not located in a brain but associated with the prespacetime. Therefore, these results support consciousness (prespacetime) as the basis of reality. Indeed, in the present model, the reality is an interactive quantum reality centered on consciousness (prespacetime) and interaction between consciousness and reality is most fundamental self-reference. Further, consciousness (prespacetime) is both transcendent and immanent, that is, the transcendental aspect of consciousness produces and influences reality through self-referential spin as interactive output of consciousness and, in turn, reality produces and influences immanent aspect of consciousness as interactive input to consciousness also through self-referential spin. 
         [0152]    In the present model, biological consciousness such as human consciousness is a limited or individualized version of the above dual-aspect consciousness such that a human has limited free will and limited observation/experience which is mostly classical at macroscopic levels but quantum at microscopic levels. By way of an example, as a limited transcendental consciousness, a human has through free will a choice of what measurement to do in a quantum experiment but not the ability to control the result of measurement. So, the result appears to the human as random. On the other hand, at the macroscopic level, a human also has a choice through free will of what to do but the outcome, depending on context, is sometimes certain and at other times uncertain. Further, as a limited immanent consciousness, a human can only observe measurement result in a quantum experiment which the human conducts and experiences macroscopic environment surrounding the human as the classical world. 
         [0153]    The present model is also concerned with how human experience (as limited immanent consciousness) is produced through the brain and how human free will (as limited transcendental consciousness) may operate through the brain. As illustrated in  FIG. 5 , there are two kinds of interactions between an object (entity) outside the brain (body) and the brain (body). The first and commonly known kind is the direct physical and/or chemical interactions such as sensory input through the eyes. The second and less-known kind but experimentally proven to be true is the instantaneous interactions through quantum entanglement. The entire world outside the brain (body) is associated with the brain (body) through quantum entanglement thus influencing and/or generating not only the human&#39;s feelings, emotions and dreams but also the physical, chemical and physiological states of the human&#39;s brain and body. 
         [0154]    By way of an example, in the present model quantum entanglement shown in  FIG. 5  is permitted to participates in sensory experience such as vision in one embodiment as follows: (1) A light ray reflected and/or emitted from an object outside the brain enters the eye, gets absorbed, converted and amplified in the retina as propagating action potentials which travel to the central nervous system (CNS); (2) In the CNS, the action potentials drive and influence the mind pixels which according our theory is the nuclei such protons with net nuclear spins and/or electrons with unpaired spins; and (3) Either the driven or influenced dynamic patterns of the mind-pixels in the internal world form the experience of the object, or more likely our visual experience of the object is the direct experience of the object in the external world through quantum entanglement established by the physical interactions. In the latter case, there is no image of the outside world in the brain. Further, in the case that the object outside the brain is an image such as a photograph, there is also the possibility that the visual experience is not only the experience of the photograph as such through quantum entanglement but also experience of the object within the photograph through additional quantum entanglement. 
         [0155]    An action potential in a retina, a neural pathway or the CNS is driven by voltage-gated ion channels on neural membranes as embodied by Hodgkin-Huxley model shown in  801  of  FIG. 62  in which V m  is electric potential across the neural membranes, C m  is capacitance of the membranes, g i  is ith voltage-gated or constant-leak ion channel. An overall effect of the action potentials and other surrounding factors, especially magnetic dipoles carried by oxygen molecules due to their two unpaired electrons, is that inside neural membranes and proteins, there exist varying strong electric field E and fluctuating magnetic field B which are also govern by the Maxwell equation shown in  802  which is traditionally written as  803  in which classical (macroscopic) electric density and current inside the neural membranes are set to zero. 
         [0156]    Microscopically, electromagnetic field E and B and their electromagnetic potential A μ =(φ, A) which is connected to E and B through equation  804  interact with a proton of electric charge e and an unpaired electron of charge −e respectively as two sets of Dirac-Maxwell systems  805  and  806  for the proton and  807  and  808  for the electron in which β and α are Dirac matrices. In equations  805  and  807 , interactions (couplings) of E and/or B with the proton and electron&#39;s spin operator (σ) p  and (σ) e  respectively are hidden. These couplings are due to self-referential Matrix Rule which causes mixing of external and internal wave functions and can be made explicit in the determinant view as shown in  809  and  810  for the proton which is in Dirac and Weyl form respectively before the determinant view. A similar calculations as those in  809  and  810  can be carried out for the electron to show explicit couplings of (σ) e  with E and B. 
         [0157]    In the present model, a first effect of the couplings is that the action potentials through E and B (or A μ ) input information into mind-pixels which are nuclear or electronic spin in the brain. Also, in the present model, the said information is likely carried in temporal and spatial variations of E and B (frequencies and timing of neural electric spikes and their spatial distribution in the CNS). A second effect of the couplings in the present model is that the couplings allow transcendental aspect of consciousness through wave functions of the proton and/or electron to back-influence E and B (or A μ ) which in turn back-affect the action potentials through the Hodgkin-Huxley neural circuits shown in  801  in the CNS. 
         [0158]    Importantly, in the present model a human free-will as a macroscopic quality of limited transcendental consciousness is permitted to originate microscopically under particular high electric voltage environment inside the neural membranes. By way of an example, the present model permit the human free will as thought or imagination produces changes in the phase of external and internal wave functions through  811 , where ( ) e  and ( ) i  respectively indicate external and internal wave functions, which in turn back-affect E and B (or A μ ) in the high electric voltage neural membranes through the Dirac Maxwell systems illustrated shown in  805  and  806  for the proton and  807  and  808  for the electron. 
         [0159]    It will be evident from the above that there are other embodiments which are clearly within the scope and spirit of the present invention, although they were not expressly set forth above. Therefore, the above disclosure is exemplary only, and the actual scope of my invention is to be determined by the claims.