Journal of Modern Physics, 2015, 6, 18201832 Published Online October 2015 in SciRes. http://www.scirp.org/journal/jmp http://dx.doi.org/10.4236/jmp.2015.613186 How to cite this paper: Chung, D.Y. (2015) The Theory of Everything as the Reversibility Theory. Journal of Modern Physics, 6, 18201832. http://dx.doi.org/10.4236/jmp.2015.613186 The Theory of Everything as the Reversibility Theory DingYu Chung Utica, MI, USA Email: dy_chung@yahoo.com Received 31 August 2015; accepted 19 October 2015; published 23 October 2015 Copyright © 2015 by author and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract In the posited reversibility theory, 1) all physical laws and phenomena are permanently reversi ble, 2) all physical laws are derived from the reversible Mthe ory (extension of string theory) in the reversible multiverse, and 3) temporary irreversibl e entropy increase is allowed through re versibility breaking, symmetry breaking, and low entropy be ginning . Dealing with all physical laws and phenomena, the reversibility theory is the theory of everything, including thermody namic, cosmology, the composition (baryonic matter, dark matter, and dark energy) in the un iverse, the periodic table of all elementary particles, the galaxy evolution, superconductivity, and black hole. In the reversible Mtheory, spacetime dimension number oscillates between 11D (spacetime dimension) and 10D and between 10D and 4D. The reversible Mtheory includes 11D membrane, 10D string, and variable D particl e. Spacetime dimension number between 10 and 4 decreases with decreasing speed of light, decreasing vacuum energy, and increasing rest mass. In our dual universe of positivenegative energy universe, the reversible oscillation between 10D with and 4D in the negative energy universe without kinetic energy is the reversible cyclic frac tionalizatio ncondensation for the reversible cyclic expansioncontraction of the universe. With out kinetic energy, the individual particles have no individual momenta for entropy increase. The negative energy universe is the locally reversible universe for dark energy. In the positive energy universe where we live, the absorption of the interuniversal void forced the direct transformation from 10D to 4D as the inflation followed by the Big Bang, and created kinetic energy that provided individual momenta for individual particles to produce irreversible entropy increase, resulting in the reversibility breaking of the reversible oscillation. The positive energy universe is the locally irreversible universe. The dual universe as a whole is reversible guided by the reversible negative energy universe. As a result, the irreversible positive energy universe with the irreversible entro py increase is temporary, and will disappear. Keywords The Theory of Ever ythin g, Reversibility Theory, Entropy, The rmody namic, Cyclic Universe,
D.Y. Chung Multiverse, Interuniversal Void, MT heory, Cosmology, String Theory 1. Introduction In the s econd law of t her mod ynamic s, the entro py (a measure of the disorder of a system) of an isolated system can increase, but not decrease. In other words, the entropy of a closed system will never decrease into the future. There are two mysteries about this irreversible entropy increase as described in “From Eternity to Here: The Quest for the Ultimate Theory of Time” by Sean Carroll [1]. Firstly, this irreversible entropy increase of a ma croscopic collection of particles is different from all microscopic reversible processes where for every allowed process there exists a timereversed process that is also allowed. Secondly, the universe started with the very low entropy state as the inflationBig Bang in a very small space, not with the high entropy state near equilibrium state in a large space. Such low entropy beginning is a mystery. In this paper, the mysteries of the irreversible entropy increase are explained by the posited reversibility theory. In the posited reversibility theory, 1) all physical laws and phenomena are permanently reversible, 2) all physical laws are derived from the reversible Mtheory(extensio n of string theor y) in the reversible multiverse, and 3) temporary irreversibility of entropy increase is allowed through reversibility breaking, symmetry break ing, and low entropy beginning as described in the previous papers [2] [3]. Dealing with all physical laws and phenomena, the reversibility theory is the theory of everything, including 1) thermodynamic in this paper, 2) cosmology [2][4], 3) the composition (baryonic matter, dark matter, and dark energy) in the universe [5] [6], 4) the period ic table of elementary particles [7][9] for all elementary particles (quarks, leptons, gauge bosons, the Higgs boson, and the kneesanklestoe in cosmic rays), 5) the galaxy evolution [10] [11], 6) superconductivity [12], and 7) black hole [13] [14]. The theoretical results are in good agreement with the observations, and the calculated values from cosmology, the composition in the universe, and the periodic table of elementary par ticles are in good agreement with the observed values. This paper deals with ther modynamic of the reversibil ity theory. In the reversible Mtheory [6], spacetime dimension number oscillates between 11D (spacetime di mension) and 10D and between 10D and 4D without the conventional compactization of string. The reversible Mtheory includes 11D membrane, 10D string, and variable D particle from 4D to 11D. Spacetime dimension number between 10 and 4 decreases with decreasing speed of light, decreasing vacuum energy, and increasing rest mass. 4D has zero vacuum energy. The reversibility theory posits that the multiverse is reversible, so all uni verses in the multiverse are reversible cyclic universes which have the inexhaustible resources of spacetime to expand. In the reversible multiverse, one of the most important exclusions is the exclusion of the collision of expanding universes which cannot be reversed. The exclusion of the collision of expanding universes leads to the formation of the “interuniversal voids” that is functioned as the permanently gap among universes to keep universes apart. To p reve nt the c oll isio n, t he interuniversal void detaches the incoming massener gy i n the inter uni ver sal void to keep expanding universes apart without collision. When our observable universe absorbed the interuniversal void, the absorbed interuniversal void with the property of the detachment of massenergy was transformed into the reverse Higgs field (the massless particle generating field) that detached adjacent massenergy in the un iverse, resulting in the conversion of rest mass (massive particles) into kinetic energy (massless particles) start ing the Big Bang. The abso rption o f the i nteruni versal void with zero vacuum ene rgy a lso started the inflatio n by converting the 10D universe with high vac uum energy universe into the 4D universe with zero vacuum e nergy universe. The inflati on followed b y the Bi g Bang occurred in our obs ervable universe [3]. A zerosum energy dual universe of positive energy universe and negative energy universe can be created in the i nte ru ni ve r sal vo i d, and t he ne w d ual un ive r se is a ga in s ur ro und ed by the int erun ive rs a l vo id . Und er s ym me tr y, the ne w positive a nd negat ive ener gy univer ses unde rgo mut ual anni hilatio n to rever se to the interuni versal void immediately. Under symmetry breaking as in our dual universe, t he new positive energy universe absorbs the interuniversal void, while the new negative energy does not. In our dual universe, the reversible oscillation between 10D with and 4D in the negative energy universe without kinetic energy is the reversible cyclic frac tionalizationcondensation for the cyclic expansioncontraction of the universe. Without kinetic energy, the in dividual particle s have no individ ual momenta for entrop y increase. As a result, the ne gative energy u niverse i s the locally reversible universe ass dark energy. In the positive energy universe where we live, the absorption of
D.Y. Chung the interuniversal void forced the direct transformation from 10D to 4D as the inflation followed by the Big Bang, and created kinetic energy that provided individual momenta for individual particles to produce irreversi ble entropy increase in a macroscopic collection of particles, resulting in the reversibility breaking of the re versible oscillation between 10D and 4D. As a result, the positive energy universe is the locally irreversible un iverse. Guided by the reversible negative energy universe the dual universe as a whole is reversible involving the reversible absorptiondesorption of the interuniversal void. Consequently, the irreversible positive energy universe with the irreversible entropy increase is temporary, and will disappear. The explanation of the first mystery of the irreversible entropy increase is that all physical laws are perma nently rever s ible, and t he te m p orary reversible entropy increase derived from the absorption of the interuniversal void will disappear. The explanation of the second mystery of the irreversible entropy increase is that to have exactly reversible absorptiondesorption of the interuniversal void for the reversible dual universe, the absorp tion and desorption have to be uniform. The space of the universe, such as the 10D universe, where the absorp tiondesorption occurs has to be small enough for the uniform absorptiondesorption. A small space results in a low entropy beginning such as the inflatio nBig Bang for the beginnin g of the irreversi ble entropy increase. The pur po se o f the pa per is to exp lai n the re versi bil it y theo ry a s the the or y of e ver ythi ng i ncl udi ng al l p hysi cal laws and phenomena [2][14] derived from the reversible Mtheory in the reversible multiverse described previously [2] [3] and irreversible entropy increase described in this paper. Section 2 describes the reversible Mtheory based on spacetime number oscillation. Section 3 explains the reversible multiverse. The reversible cyclic dual universe with irreversibility breaking and symmetry breaking, and low entropy beginning is ex plained in Section 4. Section 5 explains temporary irreversible entropy increase. 2. The Reversible MTheory In the posited reversibility theory, all physical laws and phenomena are permanently reversible, and all physical laws are derived from the reversible Mtheoryas d escri bed pr evi o usly [6]. Mtheory requires the presences of 10D (sp ace time dimension) and 11D for stri ng and membr ane, respect ively, in contrast to the observed 4 D. In conven tional Mtheory with fixed spacetime dimension number, the explanation of the hidden extra space dimensions is the compactization of the extra space dimensions, so spacetime appears to be 4D. In the reversible Mtheory, di mension number oscillates between 11D and 10D and between 10D and 4D dimension by dimension reversibly. There is no compactization. The objects in the reversible Mtheory includes 11D membrane (211) as membrane (denoted as 2 for 2 space dimensions) in 11D, 10D string (1 10) as string (denoted as 1 for 1 space dimension) in 10D, and variable D particle (04−11) as particle (denoted as 0 for 0 space dimension) in 4D to 11D. Spacetime dimension number varies with varying speed of light, vacuum energy, and rest mass. Varying speed of light has been proposed to explain the horizon problem of cosmology [15]. J. D. Barrow [16] proposes that the time dependent speed of light varies as some power of the expansion scale factor a in suc h way that , (1) where c0 > 0 and n are constants. The increase of speed of light is continuous. In this paper, varying dimension number (VDN) relates to quantized varying speed of light (QVSL), where the speed of light is i nvariant in a constant spa cetime dimension number, and the speed of light varies with va ryin g s pac etime dimension number from 4 to 10. (2) where c is the obse rved spe ed of li ght in t he 4 D s pac etime, CD is the quantized varying spe ed of li ght in s pa ce time dimension number, D, from 4 to 10, and α is the fine structure constant for electromagnetism. In Mtheory, the string requires 10D, while the observed spacetime is 4D, so D is from 4 to 10. (10D and 11D are equal in the speed of light.) Each dimensional spacetime has a specific speed of light. (Since from the beginning of our observable un iverse, the spacetime dimension has always b een fo ur, there is no ob servab le varying sp eed of l ight in o ur observa ble universe.) The s p eed of ligh t in creases with th e in creasi n g spacetim e dim en sion num ber D. In special relativity, modified by Equation (2) is expressed as (3a)
D.Y. Chung . (3b) Equation (3a) means that a particle in the D dimensional sp acetime can have the superluminal speed c/αD4, whic h is hi gher than the obse rved s peed of light c, and has the rest mass M0. Equation (3b) means that the same par ticle in the 4D spacetime with the ob ser ved sp eed o f li ght a cquire s M0/α2(d−4) as the rest mass, where d = D. D from 4 to 10 in Equation (3a) is the spacetime dimensio n nu mber de fini ng the va r ying sp ee d of light. I n E qua tion (3b), d from 4 to 10 is “mass dimension number” defining varying mass. For example, for D = 10, Equation (3a) shows a superluminal p article in elevendime nsional spacetime, whi le Eq uatio n (3 b) sho ws that t he sp eed of light of t he same particle is t he observed speed of light with the 4D spacetime, and the mas s dimen sion is ele ven. I n other words, 10D spacetime can transform into 4D spacetime with 10d mass dimension. 10D4d in Equation (3a) becomes 4D10d in Equation (3b) through QVSL. QVSL in terms of varying spacetime dimension number, D, brings about varying mass in terms of varying mass dimension number, d. Mass dimension is also proposed in the Wesson’s SpaceTi meMatter (STM) th e ory as th e matter dim en si on to account f or th e ex t ra space dimensi ons [17]. The QVSL transformation transforms both spacetime dimension number and mass dimension number. In the QVSL transformation, the decrease in the speed of light leads to the decrease in spacetime dimensio n number and the increas e of mass in t erms of in creas in g mass dimension number from 4 to 1 0, (4a) (4b) () () QVSL D,dD, dnn →± (4c) where D is the spacetime dimension number from 4 to 10 and d is the mass dimension number from 4 to 10. For example, in the QVSL transformation, a particle with 10D4d is transformed to a particle with 4D10d. In terms of rest mass, 10D spacetim e h as 4d with th e lowest rest mass , an d 4D sp acetim e h as 10d w ith the hig h est rest m ass. Rest mass decreases with increasing spacetime dimension number. The decrease in rest mass means the in crease in vacuum energy (Evacuum = E – M0,Dc2), so vacuum energy increases with increasing spacetime dimen sion number. The vacuum energy of 4D particle is zero. 11D membr ane and 10 D string are eq ual in the spee d of light, res t mass , and v acu um energy . Since the speed of light for > 4D particle is greater than the speed of light for 4D particle, the observation of > 4D superluminal particles by 4D particles violates casualty. Thus, > 4D par ticles are hidden particles with respect to 4D particles. Particles with different spacetime dimensions are trans parent and oblivious to one another, and separate from one another if possible. In the reversible Mtheory, there are two different reversible oscillations: the oscillation between 11D and 10D and the oscillatio n between 10D and 4D. The reversible osc illation between 11D membra ne and 10D string is de scribed in Sec tion 4.The trans for mation d ur ing the o scillat ion be tween 10D part icle and 4 D i nvol ves t he stepwise t wo step tr ansfor matio n: the QV SL tr ansfor mation a nd the var ying sup er symmetr y trans formation fr o m 10D4d to 4D4d. The QVSL transformation involves the transformation of spacetime dimension, D whose mass increases with decreasing D for the decrease in vacuum energy. The varying supersymmetry transformation involves the transformatio n of the mass dimension nu mber , d whose mass de crease s with decr ea sing d for the frac tionali zatio n of particle, as follows. ( )()() ( )() QVSL varying supe r symmetry stepwise twostep varying transformation 1 D,dD1,d1 2 D,dD,d1 ← →± ←→ ± (5) The repetitive stepw is e tw os te p tran s formati on be twe e n 10D4d a n d 4D4 d as follows. 10D4d 9D5d9D4d 8D5d4D5d4D4d↔↔↔↔↔↔ (6) In this t wostep tra nsfor mation, the tra nsfor mation fro m 10D4 d to 9D5 d involves the QV SL trans for mation as in Equation (4c). Calculated from Equation (4b), the mass of 9D5d is 1/ α 2 ≈ 1372 times of the mass of 10D4d. The transformation of 9D5d to 9D4d involves the varying supersymmetry transformation. In the normal super symmetry transformation, the repeated application of the fermionboson transformation carries over a boson (or fermion) fro m one point to the same boson (or fermion) at another point at the same mass. In the “varying su
D.Y. Chung persymmetry transformation”, the repeated application of the fermionboson transformation carries over a boson from one point to the boson at another point at different mass dimension number in the same spacetime number. The repeated varying supersymmetry transformation carries over a boson Bd into a fermio n Fd and a fermion F d to a boson Bd−1, wh ich can be exp ressed as f o ll ows (7a) (7b) where Md,B and Md, F are the masses for a boson and a fermion, respectively, d is the mass dimension number, and α d,B or α d,F is the fine structure constant that is the ratio between the masses of a boson and its fermionic partner. Assuming α ’s are the same, it can be ex pres sed as . (7c) The mass of 9D4d is α 2 ≈ (1/137)2 times of t he mas s o f 9D 5 d t hro ugh t he varyin g s up e rs ym met r y tra n s forma tion. The transformation from a higher mass dimensional particle to the adjacent lower mass dimensional particle is the fractionalization of the higher dimensional particle to the many lower dimensional particles in such way that the number of lower dimensional particles becomes (7d) The fractionalization also applies to D for 10D4d to 9D4d, so (7e) Since the supersymmetry transformation involves translation, this stepwise varying supersymmetry transfor mation leads to a translational fractionalization, resulting in the cosmic expansion. Afterward, the QVSL trans formation transforms 9D4d into 8D5d with a higher mass. Th e t wostep transfor mation rep eats until 4D4d, and then reverses stepwise back to 10D4d for the cosmic contraction. The oscillatio n between 10D and 4D results in the reversible cyclic fractionalization contraction for the reversible cyclic expansioncontraction of the universe. There is no kinetic energy in the universe where the oscillation between 10D and 4D occurs. In the Boltzmann formula of thermodynamic, the absolute entropy S of an ideal gas to the q uantity W, whic h is the n umber of the arrangements of particles corresponding to a given macroscopic collection of particles: (8) where kB is the Boltzmann’s constant. The Boltzmann formula shows the relationship between entrop y and the number of ways the atoms or molecules of a ther modynamic system can be arranged. The various atoms or mo lecules have different positions and momenta for irreversible entropy increase, because the increase in the num ber of different arrangements of particles in a macroscopic collection of particles requires the movements of in dividual particle s in a macroscopic collection of particles. (There is no entropy increase in a single microscopic particle.) Individual momenta from kinetic energy are required for irreversible entropy increase in a macroscopic collection of pa rticles. In other words, kinetic energy transforms a macroscopic collection of particles from one way o f the ar rangeme nt of pa rticles (order) into many ways of the arrangements of particles (disorder), and the process from order to disorder is irreversible in anisolated macroscopic collection of moving particles. There is no ki netic e nerg y in the unive rse wher e the o scill ation b etwe en 10D and 4D occurs. Witho ut kinet ic ene rgy, i n dividual particles do not have independent individual momenta, and without individual momenta for individual particles, the oscillation does not have entropy increase in a macroscopic collection of particles. The pr esence of ki netic e nerg y in our obser vab le uni verse i mplie s that the o rigin o f kine ti c energ y is o utside of the universe where the oscillation occurs. As shown la ter, t he origin o f kinetic ener gy is in the interuni versal void outside of the universe where the oscillation occurs. As shown later, the reversibility breaking of the re versible oscillation is through the creation of kinetic energy derived from the absorption of the interuniversal void by the universe. As in our universe, the absorption of the interuniversal void forced the direct transforma tion from 10D4d to 4D10d as the inflation followed by the Big Bang, and created kinetic energy that provided individual momenta for individual particles to produce irreversible entropy increase in a macroscopic collection of particles, resulting in the reversibility breaking of the reversible oscillation between 10D and 4D. As shown later, the inflationBig Bang generated baryonic matter, dark matter, and kinetic energy as follows.
D.Y. Chung ( )() the inflationthe Big Bang 10D4dthe interuniversal void4D10d baryonic matter 4D4ddark matter 4D5d,4D6d,4D7d,4D8d,4D9dkinetic energy +→ → ++ (9) 3. The Reversible Multiverse The multiverse has been studied extensively. For example, Brian Greene [18] described the nine types of the multiverse which produce complicated collections of universes. The reversibility t heor y posits a simple ver sion of the multiver se. The posited si mple multiverse is the reversible multiverse that excludes any permanently irre versible physical laws and phenomena. In the reversible multiverse, the allowed universes have to b e reversible cyclic universes with permanently reversible physical laws and phenomena, resulting in only limited types of allowed universes. Temporary irreversible universes are allowed. The collision of expanding universes which have the inexhaustible resource of spacetime to expand is permanently irreversible due to the impossibility to reverse the c ollisi on of exp andi ng unive rses. T o preve nt the c ollision o f exp anding uni verses, every universe is surrounded by the interuniversal void that is functioned as the permanent gap among universes. The interuni versal void has zero energy, zero spacetime, and zero vac uum energy, whil e univer se has non zero energy, the inexhaustible resource of spacetime to expand, and zero or/and nonzero vacuum energy. T o maintai n the p er manent gap among universes, the interuniversal void detaches the incoming massenergy in the interuniversal void, so massenergy stays permanently within universes only. Surrounded by the interuniversal void as the permanent gap among universes, an expanding universe with the inexhaustible resource of spacetime expands without colliding with other universes. The detachment of the incoming massenergy i n the interuniversal void prevents the collision of expanding universes. As a result, the the properties of the interuniversal void include the detachment of massenergy in addition to zero energy, zero spacetime, and zero vacuum energy. On the other hand, the properties of universe include the attachment of massener gy in ad ditio n to nonzero energy, the inexhaustible resource of spacetime to expand, and zero or/and nonzero vacuum energy. The detachment and the attach ment of massenergy are equivalent to the repulsion and the attraction of massenergy, respectively. In other words, the interuniversal void repulses (detaches) massenergy, while universe attracts (attaches) mass energy. A zerosum energy dual universe of positive energy universe and negative energy universe can be created in the zeroenerg y inte runi versal void , and the new d ual univer se is a gain s urro unded b y the interu niver sal vo id to avoid t he c ol lis io n o f uni ver se s . U nde r symme try, t he ne w po si tive ene r g y uni ve rs e a nd t h e ne w ne gative e ner g y univer se u ndergo mutua l anni hilatio n to revers e to the inter univer sal vo id i mmediat ely. U nder symmetry break ing with the asymmetric al absorp tion of the interuniversal vo id, our dual uni verse has l ast ed a lo ng ti me wit hout reversing immediately to the interuniversal void as described later. The precise definition of the reversibility in the reversible multiverse is the reversibility between universes and the interuniversal void. All universes are created in the interuniversal void, and all universes have to be able to reverse back to the interuniversal void. The parameters involved in the formation of the same type of universes can be different. Reversible symmetry breaking and tempor a ry irrever sib ility are allo wed. A dual universe can be created in the interuniversal void, and equally, the “intrauniversal void” can also be created in a universe by the absorption of the interuniversal void. The intrauniversal void can be reversed to the inter universal void by the desorpti on of the intr auniver s al void . 4. Reversibility Breaking Symmetry Breaking, and the Reversible Cyclic Dual Universe The reversibility theory posits that temporarily irreversible entropy increase is allowed through symmetry breaking, reversibility breaking, and low entropy beginning. One example is the evolution of our universe. In our uni verse, the symmetr y bre aking is the as ymmetrical absorp tion of the interuniver sal void b y the dual posi tivenega tive e nerg y uni verse. The positive energy universe absorbed the interuniversal void, while the negative univer se did not. As sho wn lat er, the absorp tion o f the inter univer sal void brea ks the reve rsib ilit y in the re versi ble Mtheory. As a result, the po si tive e ner g y uni ve rse becomes the locally irreversible universe, while the nega tive energy universe without absorbing the interuniversal void is the locally reversible universe. Because the multiverse is permanently reversible, the locally irreversible positive energy universe is te mporall y irreversible. The reversible negative energy universe that guides the reversible process allows the dual universe as a whole to be reversible. Our dual universe is the globally reversible cyclic dual universe as shown in Equation (10) and
D.Y. Chung Figure 1 for t he evo lution of our universe. symmetrybreakingreversibility breaking the dual positive energynegative energy universe the locally irreversible positive energy universethe locally reversible negative energy universe t → + →he globally reversible cyclic dual universe (10) As described previously [2][4], the reversible cyclic universe starts in the zeroenergy inte runi ver sal vo id , which produces the dual universe of the positive en ergy 11D membrane universe and the negative energy 11D membrane universe as in Figure 1. In some dual 11D membrane universes, the 11D positive energy membrane universe and the ne gative energ y 11D me mbra ne unive rse co alesce to under go annihi latio n and to retur n to the int erunive rsal void as in Figure 1. O n the othe r hand, in some d ual 11 D membr ane uni verse s like o ur dual univers e unde r the reversible oscillati on between 11D and 10D, the positive energy 11D membrane universe and th e negative energy 11D m embrane univ erse are tran sformed int o the posit ive energy 10D s tring unive rse and the negative energy 10D string universe as in Figure 1. The positive energy 11D membrane universe is transformed into the positive energy 10D string univers e as in Eq uations ( 11a) and (11b) . ( ) ( ) from11Dmembrane to10D string 11 10 theclose stringvibration 1010 1010 The1 MembraneTransformation 21inthe11DAdSspacestep1 2(1)101inthe11DAdS spacestep2 e RS g → → = (11a) ( ) ( ) theclosestringand the openstring vibrations 11 10 221 e sg←→ (11b) where 211 is membrane (denoted as 2) in 11D, s is the prestrong fo rce , 110 is string (denoted as 1) in 10D, 010 is particle (denoted as 0) in 10D, AdS is antide Sitter, and ge is the e xte rna l gr avito n. As shown in Equation (11a), one of the possible membrane transformations from the 11D membrane to the 10D string is the RS1 membrane transformation [19] [20] which i nvol ves t wo step s. 1) T he extra spatial dimen sion of the 11D membrane in the transformation from the 11D membrane to the 10D string becomes the spatial dimension transverse to the string brane in the bulk 11D antide Sitter space [19]. This transformation is derived fr o m th e transfor mation from membra ne to string. In the transformation fro m the two dimensio nal membra ne to the onedimensional string, the extra spatial dimension of the twodimensional membrane on the xy plane be comes the xaxi s tran sver se to the oned imens io nal str ing o n the yaxis i n the twodimensional xy space. 2) For the RS1 membrane transformation, two string branes are combined into the combined string brane. The external 10D particles generated by the close string vibration of the combined string brane are the 10D external gravitons which for m the exter nal gravi ton brane as the Gravitybrane (Planck Plane) in the RS1 of the Ra ndallSundrum model [19] [20]. As in the RS1 of the RandallSundrum model, the two branes with equal massenergy in the 11D antide Sit te r sp ace a re t he str i ng bra ne wi th wea k gra vit y and t he e xte rna l gra vi ton brane wit h stro n g gra vit y. Figure 1 . The global ly reversible cyclic dual universe.
D.Y. Chung The weak gravity in the string brane is the predecessor of the observed weak gravity generated during the Big Bang [2] [7]. The external graviton in the external graviton brane is the predecessor of a part of the observed dark energy [6]. The 10D string brane and the 10D external graviton brane correspond to the predecessors of the observed universe (without dark energy) and a part of observed dark energy, respectively [2] [6] [7]. The reverse transformation from 10D to 11D is the RS1 str ing trans formation. In Equation (11b), the 10D particles generated from the open string vibration are the 10D particles for the prestrong force (denoted as s) which is the same for all s trings withou t positive or negative sig n. This prestrong force is the prototype of the observed strong force generated during the Big Bang [2] [7]. The 10D particle for the prestrong force from the open string vibration can only be in the 10D string brane. 11D membrane, 10D string, a nd 10D ext ernal gr avito n is equal in the speed of light, massenergy, and vac uum e nergy. In the negative universe through symmetry, the 11D antimembrane (2−11) is transformed into 10D antistring (1−10) with external antigraviton ge and the prestrong force s as in Equation (12). (12) The dual univer se of the po sitive e nergy 10 D str ing univer se with n unit s o f (110)n and the negati ve energy 10 D string universe with n units of (1−10)n is as follows. ( ) ( ) () () 10 10 11 ee nn s ggs − (13) There are four equal regions: the positive energy 10D string universe, the external graviton, the external anti graviton, and the negative e nergy 10D antistri ng universe. Some dual 10D string universesreturn to the dual 11D membrane universes under the reversible oscillation betw een 11D an d 10D. Alternatively, under symmetry breaking as in the case of our universe, the positive energy 10D stri ng univers e absorbs the interuniversal void, while the negative energy 10D string universe does not absorb the interuniversal void as described previously [2]. (In our universe, the external graviton and the external an tigravitonin the four regions also do not absorb the interuniversal void, so the percentage the area that does not absorb the interuniversal void is 75%, three out of four regions, as the maximum percentage of dark energy de scribe d previou sly [6]). The interuniversal void has zero vacuum energy. The absorption of the interuniversal void by the positive energy 10D string universe forces the positive energy 10D universe with high vacuum energy to be transformed into the universe with zero vacuum energy that is the vacuum energy of the 4D universe. However, the transformation from 10D to 4D is not immediate, because the strings have to be 10D, and it cannot be trans formed into 4D, therefore, strings have to be transformed into particles that allow the change of its dimension number freely to accommodate the transformation from the 10D universe to the 4D universe driven by the ab sorption of the interuniversal void. As des c ri bed pr ev i ous ly [2], the transformation of strings into particles comes from the emergence of positive charge and negative charge that allows the mutual annihilation of positively charged 10D strings and negatively charged 10D antistrings in the 10D string universes to produce positively charged 10D particles and negativ ely precharged 10D antiparticles in the 10D particle un i v erses . The emergence of positive charge and negative charge provides the prototype of the observed electromagnetic force with char gegenerated during the Big Bang [2] [7]. The emergence of the asymmetrical dual un iverse provides the prototype of the observed asymmetrical weak forcegenerated during the Big Bang [2] [7]. The emergence of positive charge and negative charge and the emergence of the asymmetrical dual universe occur at the same time, so the elec tromagnetic force and the weak force are unified as the electroweak force [2] [7] in the Standard Model. The transfo rmati on fro m the 10 D4d po sitive e nerg y univer se wit h high va cuum e nerg y to the 4 D10d positi ve energy universe with zero vacu um energy is the inflation. A t zero vacuum energy, the absorbed interuniversal void is transfor med into “the 4D intrauniversal void” with zero vacuum energy and with spacetime inside of the un iverse as described previously [3]. (The absorption of the interuniversal void by the positive energy 10D univer seis in the latent stage before the 4D positive energy universe, and is in the active stage in the 4D positive energy universe.) Derived from the interuniversal void, the intrauniversal void has the same property of the detachment of mass energy as the interuniversal void described in Section 3. I ns ide of the universe, the intrauniversal voi d with the property of the detachment of massenergy detaches adjacent massenergy in the universe, resulting in the conversion o f rest mass (massive par ticles) into kinetic energy (massle ss particles), so the intrauniversal void is the reverse Higgs field generating massless particles starting the first step of the Big Bang in the universe with the inexhaustible resource of spacetime to expand. The Higgs field inside of the universe is desorbed to become the
D.Y. Chung external Higgs field outside of the universe. In terms of the Higgs mechanism, the reverse Higgs field derived from the in terunive rsal v oid desorbs the lon gitu dinal com ponent (t he Hig gs fie ld) insi de of th e univ erse to becom e the external Higgs f ield outside of the universe, an d generated massless particles. The equation for the first step of the B ig Bang is a s Equation (14) interuniversal voidHiggs fieldreverse Higgs fieldexternal Higgs field+→ + (14) The se cond step of the Big Bang is t he exchange pr ocess between the partial ab sorption of the Higgs bosons (the mediating particles) from the external Higgs field and the partial desorption of the reverse Higgs field inside to be come the interuniversal void outside of the universe. Under s y m m etry breakin g , th e s e cond s tep is t h e p arti al rev ersa l of the first step. In terms of the Higgs mecha nism, t he absor bed Higgs b osons pro vide the l ongitudinal compone nts for massless particles to form massive particles, and desorbed the reverse Higgs field inside to become the interuni versa l void outside to co mplete the excha nge process. Photo n without ab sorbing the Higgs boson remains massl ess in the p artia l conver sion, a nd the unabso rbe d Higgs b oson beco mes the ob serve d Higgs bo son [8]. T he eq uat ion for the second step of the Big Bang is as Equation (15). partial reverse Higgs fieldHiggs boson from the external Higgs field Higgs fieldinteruniversal void + →+ (15) In summary, the twostep pr ocess d ur ing the B ig Bang inc lude d 1) the conversio n of rest mass (massive par ticles) into ki netic energy (massless particles) by the creation of the reverse Higgs field derived from the absorption of the interuniversal void outside of the universe and 2) the partial conversion of massless particles into partial massive particles by the pa rti al absorption of the Higgs bosons from the external Higgs field outside of the universe. creationofreverse Higgs field dereived fromtheabsorption ofinteruniveral void partial absorptionofHiggs bosons fromexternal Higgs field massive particlesmassless particles partial massive part → → icles (16) The absorp tion of the interunivers al void forced the direct transfor matio n from 10D 4d t o 4D10d a s the inflatio n followed by t he Big B ang, and created kinetic ener gy t hat provided i ndividual momenta for individual par ticles to prod uce irreve rsible en tropy inc rease in a macr oscopic co llection of particles, resulting in the reversibility break ing of the rever sible oscillation b etween 10D a nd 4D. The pos itive energy univer se becomes the loca lly irrever si ble universe. Without absorbing the interuniversal void, the coexisting negative energy universe follows the re versibility of the reversible Mtheory becomes the locally reversible universe that oscillates between 10D and 4D dim e n s i on by dimen s i on . The repetitive stepwise twostep transformation from 10 D4d to 4D10d as follows. 10D4d 9D5d 9D4d 8D5d4D5d4D4d hidden negative energy universe dark energy ↔↔↔↔↔↔ ←← (17) The negative energy universe universe consists of two periods: the hidden negative energy universe and the dar k ene r gy un ive r se. T he hid d en ne ga ti ve e nergy universe composes of the >4D particles . As mentioned befor e, particles with different spacetime dimensions are transparent and oblivious to one another, and separate from one ano ther if p o ssi bl e. T hus , > 4D particles are hidden and separated particles with respect to 4D particles in the pos itive e ner gy uni ver se (o ur o bser vab le uni verse ). T he hidd en negat ive ene rgy u niver se with D > 4 and the o b servable universe with D = 4 are the “parallel universes”. The 4D particles transformed from hidden >4D par ticles in the negative energy universe are observable dark energy for the positive energy universe, resulting in the accelerated expanding universe. Since the dark universe without kinetic energy, the presence of dark energy is not different from the presence of the cosmological constant. In terms of quintessence, such dark energy can be consi dered the tracking q uinte ssence [21] from the negati ve energ y universe with the sp ace time d i mensio n number as the tracker. Observ abl e da rk energ y emerged about 5 billion years ago (more precisely 4.71 ± 0.98 billion years ago at z = 0.46 ± 0.13 [22]. According to the calculation in the cyclic universe [6], dark energy started in 4.28 bil lion years ago in agreement with the observed value. After the appearance as the dark energy, the negative energy univers e will move b ac k to D > 4 dimensi on b y di mensi on, and d is appe ar fr om the p o sit ive ener gy univer se sta rt ing the contraction until the Big Crush followed by the deflation. Then, the universe will repeat the cycle starting the inflationBig Bang or go back to the interuniversal void as in Figure 1. The multiverse can be considered as the digital multiverse consisting of +1 for positive energy universe, −1
D.Y. Chung for negative energy universe, and 0 for the interuniversal void. The sum in the digital multiverse is 0, so the multiverse is the reversible digital zerosum multiverse. During the Big Bang, the combination of the positive energy universe as 1 and the interuniversal void as 0 in the digital multiverse led to the digital space structure consisting of attachment space (the Higgs field) as 1 and detachment space (the reverse Higgs field) as 0 in the positive ener gy unive rse as in Eq uation (1 8). ( )( ) ( )( ) positive energy universe1interuniversal void 0 attachment space as Higgs field1detachment space as reverse Higgs field0 + →+ (18) The digital space structure is described in the previous paper [5] [14]. Derived from the space of the universe before the Big Bang, attachment space is the Higgs field, and attaches to massenergy continuously or reversibly. Derived from the interuniversal void outside of the universe, detachment space is the reverse Higgs field, and detaches adjacent massenergy continuously. Attachment space relates to massive particles, rest mass and reversi ble movement, while detachment space relates to massless particles and kinetic energy adjacent to detachment space continuously. The combination of n units of attachment space as 1 and n units of detachment space as 0 brings about three dif ferent spa ce s tructures : binary p arti tion spa ce, misci ble spa ce, o r b in ary lattice space as below. ( )()( )()()() combination 1010,10,or1 0 attachment spacedetachment spacebinary partition space,miscible space,binary lattice space nnnnnn + →+ (19) Binary partitio n space, (1)n(0)n, consists of two separated continuous phases of multiple quantized units of at tachment space and detachment space. In miscible space, (1+0)n, attachment space is miscible to detachment space, and there is no separation of attachment space and detachment space. Binary lattice space, (1 0 )n, co nsists of repetitive units of alternative attachment space and detachment space. Binary partition spa ce is the space for wavefunction i n quantum mecha nics. I n wa ve fu nct i o n, (20) Each basis element, , has both attachment space and detachment space as binary p artition space . Neither at tachment space nor detachment space is zero in binary partition space for a basic element. The measurement in the uncertainty principle in quantum mechanics is essentially the measurement of attachment space size and momentum from the detachment space in binary partition space: large momentum from detachment space has s mal l no nzero attachment space size, while large attachment space size has low nonze r o mo me nt um fr o m de tachment space. In binar y part itio n spa ce, an e ntity is bo t h in constant motion as wave for detach ment space and in stationary state as a particle for attachment space, resulting in the waveparticle duality. In binary partition space, for every detachment space, there is its corresponding adjacent attachment space. Thus, no pa rt of t he mas senergy can be irreversibly separated from binary partition space, and no part of a dif ferent massenergy can be incorporated in binary partition space. Binary partition space represents coherence as wavefunction. Binary partition space is for coherent syste m. Any destruction of the coherence by the addition of a different massenergy to the massenergy causes the collapse of binary partition space into miscible space. The collapse is a p hase tr a nsition from binar y partition space to miscible sp a c e . ()( )( ) collapse 0 101 binary partition spacemisciblespace nn n →+ (21) The information in miscible space is contributed by the miscible combination of both attachment space and detachment space, so information can no longer be nonlocalized. Any value in miscible space is definite. All observations in ter ms of measure ments brin g about the co llapse o f wavefunctio n, resultin g in miscible sp ace that leads to eigenvalue as definite quantized value. Such collapse corresponds to the appearance of eigenvalue, E, by a measurement operator, H, on a wavefunction, Ψ. (22) In miscible space, attachment space is miscible to detachment space, and there is no separation of attachment space and detachment space. In miscible space, attachment space contributes zero speed, while detachment space
D.Y. Chung contributes the speed of light. For a movin g mass iv e particle cons is ti n g of a rest massi v e part and a mass les s part, th e massive part with rest mass, m0, is in attachment space, and the massless part with kinetic energy, K, is adjacent to detachm en t s pace. The com bin at ion of th e mass iv e part in att a chment s pace and massl ess part in detach ment leads to the prop agation spee d in betwee n zero and the speed of light. To maintain the speed of light consta nt for a moving particle, the time (t) in moving particle has to be dilated, and the length (L) has to be contracted relative to the rest frame. 22 00 0 22 00 1, , ttct LL EKmcmc υγ γ γ =−= = =+= (23) where is the Lorentz factor for time dilation, and length contraction, E is the total energy, a nd K is the kinetic energy. Bo uni as and Krasnoholovets [23] propose that the reduction of dimensi on can be done by slicing di mensi on, such as slicing 3 space dimension object (block) into infinite units of 2 space dimension objects (sheets). The positive energy 10D4d particle universe as our observable universe with high vacuum energy was transformed into the 4D10d universe with zero vacuum energy at once, resulting in the inflation. During the B ig Bang following the inflation, the 10d (mass dimension) particle in attachment space denoted as 1 was sliced by detachment space de noted as 0. For example, the sli cing of 1 0d particle in to 4 d pa rticle is as f oll ow s . ( ) 10 slicing 10444 ,d d5 1 1 01 10d particle4d core particlebinary lattice space n = → ∑ (24) where 110 is 10d particle, 14 is 4d particle, d is the mass dimension number of the dimension to be sliced, n as the number of slices for each dimension, and (04 14)n is binary lattice space with repetitive un its of alternative 4d at tachment space and 4d detachment space. For 4d particle starting from 10d particle, the mass dimension number of the dimension to be sliced is from d = 5 to d = 10. Each mass dimension i s sliced into infinite q uantized units (n = ∞) of binary lattice space, (04 14)∞. For 4d particle , the 4d core p article is surrounded by 6 types (from d = 5 to d = 10) of infinite qua ntized units of binar y lattice space. Such infinite quantized units of binary lattice space represent the infinite units (n = ∞) of separate virtual orbitals in a gauge force field, while the dimension to be sliced is “dimensional orbital” (DO), representing a type of gauge force field. The ma ssenergy in each dimen sional orbital increases with the number of dimension number, and the lowest dimension orbital with d = 5 has the lowest massenergy [7] [11]. 10d particle was sliced into six different particles: 9d, 8d, 7d, 6d, 5d, and 4d equally by mass. Baryonic matter is 4d, while dark matter consists of the other five types of particles (9d, 8d, 7d, 6d, and 5d). ( )() the inflationthe Big Bang 10D4dthe interuniversal void4D10d baryonic matter 4D4ddark matter 4D5d, 4D6d, 4D7d, 4D8d, 4D9dkinetic energy +→ → ++ (25) The mass ratio of dark matter to baryonic matter is 5 to 1. At 72.8% dark energy, the calculated values for baryonic matter and dark matter (with the 1:5 ratio) are 4.53% (=(100 – 72.8)/6) and 22.7% (=4.53 × 5), resp ec tively, in excellent agreement with observed 4.56% and 22.7%, respectively [24]. The dimensional orbitals of baryonic matter provide the base for the periodic table of elementary particles to calculate accurately the masses of all elementary particles, including quarks, leptons, gauge bosons, the Higgs boson, and the kneesanklestoe in cosmic rays [7][9]. The calculated masses of all elementary particles are in good agreement with the ob served values. The lowest dimensional orbital is for electromagnetism. Baryonic matter with maximum number of gauge for ce fields (dimensional orbitals) is the only one with the lowest dimensional orbital for electromagnetism. With higher dimensional orbitals, dark matter does not have this lowest dimensional orbital [5] [6]. Without electromagnetism, dark matter cannot emit light, and is incompatible to baryonic matter with electromagnetism, like the incompatibility between oil and water. Derived fro m the inco mpatibility between dark matter and baryonic mat ter, the modified interfacial gravity (MIG) between homogeneous baryonic matter region and homogeneous dark matter region to separate baryonic matter region and dark matter region explains galaxy evolution and unifies the
D.Y. Chung CDM ( C ol d Dark Matt er) model , MOG (Modified Gra vity), and MOND (Modified Ne wtonian Dynamics) [10] [11]. The digital space structure based on the combination of binary partition space and binary lattice space explains su perconductivity [12] and superstar without singularity to replace black hole with singularity [13] [14]. Singu larity is per manently irreversible b y losing informatio n p e rmanently, forbidden in the reversible multiverse. 5. Temporary Irreversible Entropy Increase In the reversibility theory, all physical laws and phenomena are permanently reversible. The allowed temporary irreversible universes with irreversible entropy increase must be able to return to the reversible universes with permanently reversible physical laws and phenomena. The requirements for temporary irreversible entropy in crease are 1) reversibility breaking, 2) symmetry breaking, and 3) low entropy beginning. The allowed reversibility breaking of the reversible oscillation between 10D and 4D is by kinetic energy de rived from the absorption of the interuniversal void by a universe, The absorption of the interuniversal void forces the direct transformation from 10D to 4D as the inflation followed by the Big Bang, and creates kinetic energy that provides individual momenta for individual particles to produce irreversible entropy increase in a macroscopic collection of particles, resulting in the reversibility breaking of the reversible oscillation between 10D and 4D. Such reversibility breaking can occur only through symmetry breaking where one universe be comes irreversible, while the coexisting universe in the dual universe remains reversible to serve as a guide for the reversible dual universe as a whole. If both universes in the dual universe absorb the interuniversal void, both universes are irreversible and the dual universe will become permanently irreversible which is forbidden in the reversibil ity theor y. The reversibility breaking that starts the beginning of the irreversible entropy increase is caused by the ab sorption of the interuniversal void. In the reversible cyclic dual universe, the absorption of the interuniversal void is the exact timereversed version of the desorption of the intrauniversal void. To have exactly reversible absorptiondesorption of the interuniversal void for the reversible dual universe, the absorption and desorption have to be uniform. The space of the universe where the absorptiondesorption occurs has to be small enough for the uniform absorptiondesorption. The 10D4d universe with a high vacuum energy has a small space. During the inflation, the 10D4d universe was transformed into the 4D10d universe. According to Equation (4b), M10D4d = M4D10d α 12 ≈ M4D10d/13712 = M4D10d/(4.4 × 1025). T he 1 0D 4d univer se whe re t he i nte ru ni ve r sa l vo id was a bs or b ed was much smal ler tha n the 4 D10d uni verse. Kinetic energy eme rged in t he Big B ang ca used the further expan sion of the universe. The reversible absorptiondesorption of the interuniversal void forbids any absorption of the i nteruni versal void in t he lar ge univer se whic h can not be uni form. A small sp ace results in low e ntrop y be ginning such as in the inflationBig Bang for the beginning of the irreversible entropy increase. 6. Summary In the posited reversibilit y theory, 1) all ph ysical la ws and p henomena are per manently reversible, 2) all physi cal laws are derived from the reversible Mtheo ry (e xtens io n of str ing t heor y) in the reversible multiverse, and 3) temporary irreversible entropy increase is allowed through reversibility breaking, symmetry breaking, and low entropy beginning. Dealing with all physical laws and phenomena, the reversibility theory is the theory of eve rythi ng, inc ludi ng ther mod ynamic, cosmo log y, t he co mposit ion ( baryo nic mat ter, dark matter, and dark energy) in the universe, the periodic table of all elementary particles, the galaxy evolution, superconductivity, and black hole. In the reversible Mtheory, spacetime dimension number oscillates between 11D (spacetime dimensio n) and 10D and between 10D and 4D. The reversible Mtheory includes 11D membrane, 10D string, and variable D particle. Spacetime dimension number between 10 and 4 decreases with decreasing speed of light, decreasing vacuum energy, and increasing rest mass. In our d ual unive rs e of p osit ive nega ti ve e nerg y uni verse , t he re ver si ble o sc il la tio n b et we e n 1 0 D with a nd 4 D in t he ne gat i ve ene r g y un iver se witho ut ki net ic e ne rg y is t he r e ve rs ib le cyclic fractionalizationcondensation for the reversible cyclic expansioncontraction of the universe. Without kinetic energy, the individual particles have no individual momenta for entropy increase. The negative energy universe is the locally reversible universe for dark energy. In the positive energy universe where we live, the absorption of the interuniversal void forced the direct transformation from 10D to 4D as the inflation followed by the Big Bang, and created kinetic energy that provided individual momenta for individual particles to pro duce irreversible entropy increase, resulting in the reversibility breaking of the reversible oscillation. The posi tive energy universe is the locally irreversible universe. The dual universe as a whole is reversible guided by the
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