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N.T.Anh The Variant Principle THE UNIVERSE’S EVOLUTION N. T. Anh Institute for Nuclear Science and Technique, Hanoi, Vietnam. Email: [email protected] (1999) 0 Based on anewtheory ofcausality [1] and itsdevelopmenttothetheoryof theUniverse[2], we 0 show, in this paper, new ideas for building a theory of everything. 0 2 PACS No. : 01.55.+b n a J I. INTRODUCTION article will find out that the law of causality is just the 2 law of all laws, the theory of causality is just the single 2 The discovery of natural world around us is an indis- theory of everything, and perhaps they will be the ones pensable activity of mankind. And looking for a sin- to complete the quest for the Theory of the Universe. ] h gletheorythatcanexplaineveryphenomenonandevery The article is organizedas follows. In Section 2 we in- p processisagooddreamofscientistsandespeciallyphysi- troduce the ideas and concepts for leading the equation - cists. Nowadays,physicistshavebeentryingtofindasin- of causality [1]. In Section 3, as the main part of the n e gletheorythatunifiesfourfamiliarinteractions,andthey article, we attempt to simulate briefly the process of the g hope that it develops the theory of everything. A the- Universe’s evolution [2]. The conclusions and prospects . ory they believe to be the theory of everything is called are given in Section 4. s c the superstring theory. Notably, it is necessary to un- si derstandthatthe superstringtheorygivesusdescription y which only can unite four familiar forces into a single II. THE EQUATION OF CAUSALITY h framework. p Of course, whether it is really called the theory of ev- WecanalwaysconceivethattheUniverseisinunifica- [ erything or not since there are many unknown interaction. AndasurefirefactisthattheUniverse’sunification 5 tions(besidesfourfamiliarinteractions)absentinginthe isonlyinageneralintrinsicrelationshipwhichisnothing v theory. Moreover, the theory of everything must give us buttherelationshipofcausality,andtheunificationonly 6 a correct solution in every phenomenon and process (in manifests itself in that causal form. Then, a question is 0 all universe’s dimension, in all energy level, in all uni- putonwhatistheultimatecauseofeverything? Onfur- 0 verse’s status and so fourth). The theory of everything ther reflection, we find out that there exists an ultimate 2 1 isnecessarilyatheoryofCreation,thatis,itmustneces- cause - that is the difference. 9 sarily explain everything from the origin of the Universe Truly,therewouldnotexistanythingifthere werenot 9 down to the lilies of the field. A theory of everything is the difference. If there were no difference, this world did / also a theory of everyday. Thus, this theory, when fully not exist. And there is a fact that since the difference s c completed, will be able to explain the existence of every is the ultimate cause, it is the cause of itself, in other i phenomenon, the variation of every process, and many words,it is also the effect of itself. The difference causes s y others. thedifference,thedifferenceisthecorollarygeneratedby h However, there is another way on which we can reach the difference. p thetheoryofeverything. Thatistofindasinglelawthat Inanotherway,wecanimagineabstractlythattheNa- : v implies all known laws and, therefore, predicts unknown ture is a set of positive actions1 and negative actions2. i laws. Thepresenceofthis lawhasineveryphenomenon, Then,whatdoestheNatureactpositivelyon? andwhat X process and thing in nature. It is really to be the ulti- does the Nature act negatively on? The answer to these r a mategoalofallknowledge,thetheorytoendalltheories, questions gives us a law. That is, what do not have the ultimate answer to all questions. any intrinsic contradiction is acted positively on, what The present article is the first one of a series that we do have some intrinsic contradiction is acted negatively wouldliketosayaboutthe lawandthe theoryofcausal- on. Both the positive action (in front of a process) and ity as well as its implementation for building a theory of the negative action (in back of the process) have a final the Universe. We hope that some of the readers of this goal that is to reach and to end at a new action. 1Positive action means ’affirmation’. 2Negative action means ”negative’. 1 (cid:13)c 1999 N.T.Anh N.T.Anh The Variant Principle Thus, we have started to come to a theory, axiom of Thus, which is the difference, object of which is actions3 [1]. Consider two actions, we obtain a definition that co- ∆M 1 ′ existence of two actions which reject mutually generates lim∆T→0,∆M→0,∆t→0 ∆t =−T =−a|M |M. contradiction. That is represented as follows: Therefrom, we obtain the equation of causality, A6=A −Action K M = 1 . (cid:26)A=A −Action K2 dM ′ =−a|M (x,y,z,...)|M(x,y,z,...). (1) dt This means the higher the power of mutual rejection between two actions K and K is the more severe the 1 2 Truthly, the difference is the origin of all, but it has contradiction M will be. And the power of mutual re- the meaning in direct relationship, in direct comparison. jection of two actions is estimated from the degree of Some state which has any intrinsic contradiction must difference. A contradiction which is solved means that vary to reach a new one having no intrinsic contradic- the difference of two actions diminishes to zero. Herein, tion, or exactly, having infinitesimal contradiction. The two actions K and K all vary to reach and to end at a 1 2 greater the value of the contradiction derivative with re- new action K . 3 spect to some degree offreedomis, the better the ’scent’ The change, and one kind of which - the variation, is forwayoutinthatdegreeoffreedomwillbe,the greater generated by contradiction. In exact words, the varia- the strength of the solvedcontradictionover that degree tion is the manifestation of contradiction solving. The of freedom will be. moreseverecontradictionbecomesthemoreurgentneed It is easy to see thatequationof causality(1) is repre- of solving out of contradiction will be, and hence the sented as a ’classical’ form. It can be developed to more more violent the change, the variation of the state, i.e. general form in which the time is considered as a new of contradiction will become. Call the violence, or the degree of freedom. However, Eq. (1) looks like famil- quicknessofthe variationofcontradictionQ,thecontra- iar equations, and we will use it for applying to concrete dictionstateisM,theaboveprinciplecanberepresented problems. Though the law of causality (1) is abstract as follows: its concrete form in each problem is very clear. And in Q=K M the next Section we show the process of the Universe’s (M) evolutionwhichlaysthefoundationforbuildingatheory whereK(M) ismeanstosolvethecontradictionM. K(M) of the Universe. canbeafunctionofthecontradictionstate. Itrepresents thedegreeofeasinesstoescapethecontradictionstate. If thecontradictionischaracterizedbyquantitiesx,y,z,..., III. THE PROCESS OF THE UNIVERSE’S these quantities themselves will be facilities to transport EVOLUTION thecontradiction,degreesoffreedomoverwhichthecon- tradiction is solved. Hence, the degree of easiness is val- uedasthe derivativeofthe contradictionwithrespectto A. The general mechanism its degree of freedom ′ K(M) ∼|M (x,y,z,...)|. To survey clearly the evolution of the Universe, we firstlyreviewfour importantconcepts: time, space,mat- Thus, ter, and motion. Q=a|M′|M Aboutthetime. Canthetimeexistindependently,ifit is separatedfromspace, matter, and motion? Evidently, where the coefficient a generates from choosing the di- no. If the time were separated from motion, the con- mension. ception of it would have no meaning. The time cannot Advance a quantity T, inverse of Q, to be stagnancy self-exist, it is the effect of motion. No motion, no time. of contradiction solving. The sum of stagnancy in the About the motion. The motion also would not self- process of contradiction solving from M to M −∆M 0 0 exist if it were separated from matter and space. we call the time is generated by this variation And about the matter. The matter also cannot self- T +(T +∆T) exist without space. It exists owing to not only itself ∆t≈− ∆M. but also the coexistence of the space surrounding it. In 2 3Action here is a general concept of anything, it may be a function, a generator, an operator, or even a force, an interaction, a field,ect. dependingon each considered subject. 2 N.T.Anh The Variant Principle essence, the matter is nothing but just some space with where n is total of quanta, i is quantum number gen- intrinsic relationshipdifferent fromfamiliar space we see erated by each step of expansion of the Universe, Cn is i around us. binary coefficient. Imaginethatallarevanished: matter,space,...,andin It is easy to realize that Eq. (2) is also a form of general, every difference is vanished. Then, there exists equation of causality (1). But Eq. (2) gives us an im- only one. It is homogeneousandlimitless everywhere. It portant application in modelling the multiplication and canself-exist. Itisthefirstelement. Inthisunique there the combination of quanta. There are two objects from is nothing, but there exists the ’Nothing’. The Nothing Eq. (2) we can use to study: one is actions, the other is is the origin of all, the cause of all, since it has the first quanta. Studyingactionsgivesuslaws,equations,repre- difference. sentationsineachconsideredfield. Andstudyingquanta In Section 2, we have said the axiom of the theory of gives us models, classifications, arrangements of quanta. causality. That is the difference. Imagine that if the To describe the evolutionof the Universe,it is better for present Universe has many differences, the first state of us to investigate quanta. the Universe will be the state which has fewest differ- Call α,β,γ,... quanta. For each quantum there is a ences. It is logicalto show that the first Universe’s state rule of multiplication as follows istheNothing,andthetransformationchain”difference- contradiction- solving”isthe expansionofthe Universe. n A remarkable consensus has been developing recently αn →e∂ααn = Cnαn−i =(α+1)n (4) around what is called ”quantum cosmology”,which pro- i poses a beautiful synthesis of seemingly hostile view- Xi=0 points. In the beginning it was Nothing. No space, no matter or energy. But according to the quantum princi- where n is order of combination. Although Eq. (4) is ple,evenNothingwasunstable. Nothingbegantodecay, obtained from Eq. (2) in considering for quanta, it can i.e. it began to ’boil’, with billions of tiny bubbles form- be found meaningly using the evolution principle shown ing and expanding rapidly. Each bubble became an ex- in Ref. [2]. Eq. (4) itself represents the evolution of the pandingsub-universe4. Sub-universescanliterallyspring Universe. intoexistenceasaquantumfluctuationofNothing. Res- onances of vacuum fluctuations create first elements of matter. In Ref. [2] we show the elementary equation of Evolu- B. Examples for the doublet and the triplet tion eΣaM∂M =eΣ(−)∆t∂.M, (2) b and the conservation relation of quanta Using Eq. (4) we consider two stages in the process of n (−)i the Universe’s evolution: doublet and triplet. n! CinMj...Mk =0, (3) For two interactive quanta the rule of multiplication jX,...,kXi=0 reads n 1 αn,βn → (eβ∂ααn+eα∂ββn)= Cnαn−iβi =(α+β)n. (5) 2 i Xi=0 And similar to three interactive quanta 4Ouruniverseisactuallypartofamuchlarger”multiverse” of sub-universes. Our sub-universe may co-exist with other sub-universes, but our sub-universe may be one of the few compatiblewithlife. Thiswould answertheage-old question of why the physics constants of the universe fall in a narrow band compatible with the formation of life. If the universal constants were changed slightly, then life would have been impossible. 3 N.T.Anh The Variant Principle n m 1 αn,βn,γn → (e(β+γ)∂ααn+e(γ+α)∂ββn+e(α+β)∂γγn)= CnCmαn−mβm−iγi 3 m i Xm Xi =(α+β+γ)n. (6) And so fourth. Eqs. 5 and 6 can be drawn as schemata. . . . ··· ··· ··· ··· 2 1 1 0 (cid:13) 2 1 1 2⊗2=3⊕1 1 2 1 (7) 2⊗2⊗2=4⊕2⊕2 1 3 3 1 . . . 1 4 6 4 1 . . . 1 5 10 10 5 1 . . . ··· ··· ··· ··· ··· ··· ··· is the schema for Eq. (5), where 2 means two quanta And similar to Eq. (6) we have α and β. The numbers in the triangle is the binary coef- ficients which give us weights of classes. For example, 1 2⊗2=3⊕1= . 1 ——– 1 ——– 1 4 N.T.Anh The Variant Principle . . . 1 3 1 1 0 (cid:13) 3 1 1 1 1 2 1 3⊗3=6⊕3 2 2 (8) 1 1 3 3 1 3⊗3⊗3=10⊕8⊕8⊕1 3 6 3 3 3 1 1 4 6 4 1 4 12 12 4 3⊗3⊗3⊗3 6 12 6 4 4 . .. 1 where 3 means three quanta α, β and γ. The coeffi- It is easily to identify that the above schemata have cients in the pyramid give us weights of classes, the forms similar to the SU(2) and the SU(3) groups. This means that for n quanta we have a corresponding 1 1 1 schema according to the SU(n) group, and the multipli- 3⊗3=6⊕3= 1 1 1, cation and the combination of the Universe conform to 1 1 the SU group. And from these schemata we can draw 1 periodic diagrams of the Universe’s quanta. Forsimplification,weshowbelowtheperiodicdiagram of the two quanta’s multiplication made of the schema 1 (7). Remodel (7) with regard to the level splitting we 3⊗3=1⊕8= 1 1 1 2 1. have a new diagram, 1 1 5 N.T.Anh The Variant Principle [] 1 ][ 2 ][ ][ 5 ][ ][ ][ . . . 1 ] 1 [ 2 ] ][ 2 ][ [ 5 ] ][ ][ 5 ][ ][ [ 14 ] ][ ][ ][ 14 ][ ][ ][ [ . . . . . \ / . 1 ] ] 1 ][ 1 [ [ 3 ] ] ][ 3 ][ ][ 3 ][ [ [ 9 ] ] ][ ][ 9 ][ ][ ][ 9 ][ ][ [ [ . . . . . \ / . 28 ][ ][ ][ ][ . . . 1 ] ] ] 1 ] ][ 1 ][ [ 1 [ [ [ 4 ] ] ] ][ 4 ] ][ ][ 4 ][ ][ [ 4 ][ [ [ [ . . . . . \ / . 14 ] ][ ][ ][ 14 ][ ][ ][ [ . . . . . \ / . ... 1 ] ] ][ 1 ][ ][ 1 ][ [ [ ... ... 5 ] ] ][ ][ 5 ][ ][ ][ 5 ][ ][ [ [ ... . . . . . \ / . 20 ][ ][ ][ ][ . . . ... 1 ] ] ] ][ 1 ] ][ ][ 1 ][ ][ [ 1 ][ [ [ [ ... . . . . . . 6 ] ][ ][ ][ 6 ][ ][ ][ [ . . . . . \ / . ... 1 ] ] ][ ][ 1 ][ ][ ][ 1 ][ ][ [ [ ... . . . . . . 7 ][ ][ ][ ][ . . . Arrange this diagram in the order of the levels we obtain the so-called periodic diagram 6 N.T.Anh The Variant Principle • I • (cid:30)(cid:31) •↼•⇀• II • (cid:30)(cid:31) •−•−• III (cid:30) • (cid:31) •↼•(cid:30)•(cid:31)•⇀• •−•−• IV (cid:30) • (cid:31) •−•(cid:30)•(cid:31)•−• , (cid:30) •−•−• (cid:31) V (cid:30) (cid:30) • (cid:31) (cid:31) •↼•(cid:30)•−(cid:30)•(cid:31)−•(cid:31)•⇀• •−•(cid:30)−•−(cid:31)•−• (cid:30) •−−•−−• (cid:31) VI (cid:30) (cid:30) • (cid:31) (cid:31) •↼•(cid:30)−•−(cid:30)•(cid:31)−•−(cid:31)•⇀• •−−•(cid:30)−•−(cid:31)•−−• (cid:30) •−−•−−• (cid:31) VII (cid:30) (cid:30) • (cid:31) (cid:31) •↼−•(cid:30)•−•(cid:30)•(cid:31)•−•(cid:31)•−⇀• (cid:30) (cid:30) (cid:31) (cid:31) which is nothing but the Mendeleev periodic table built in the energy levels, FIG.1. The pine-treeform of theperiodic law and we can paint it as an abstract picture, 7 N.T.Anh The Variant Principle FIG.2. The spiral form of theperiodic law The pictures Fig.1 and Fig.2 have a very special sig- relationships. Transformation, change, or motion, vari- nificance besides the periodic law. Thus, corresponding ation, or exactly contradiction solving, does experience to the SU(2),SU(3), andSU(n)groupswe have the pe- of relationships. Even space and time must be spoken riodic laws of doublet, triplet, and multiplet elements. aboutin terms ofrelationships. There is no sucha thing They give us a model of the evolution in the pine-tree as space independent of that which exists in it and no and the spiral from simplex to complex, from low-level such thing as time apart from change. These mean that to high-level. the universe is in unification, and this unification is cre- ated by relationships of causality. Relationships of causality give us an ultimate law IV. CONCLUSIONS AND PROSPECTS which is called the law of causality. Following the log- ical source of the law of causality, we open up limitless There is a truth that everybody knows: the nature is horizonsofaviewoftheuniverse. TheUniversewasborn difficulttounderstandforuswhenithasnotbeendiscov- from Nothing, and its evolutioncreatedbeautiful worlds eredyet,butitisreallybeautifulwhenweunderstandit. ofnumerousformofthingswhosestructureandcomplex- Thisisscience,wheretheultimateworthofone’sideasis ity can be self-organized. We understand that there are thattheyleadtoagenuineunderstandingofnature. And natural processes, easily comprehensible, by which orga- anidea or a theory not only representsdaily phenomena nization can arise naturally and spontaneously, without but alsomakes predictionsthat survivecomparisonwith any need for a maker outside of the system. That is observation and experiment based on fundamental prin- confirmed in the present article. ciplesandlawsthatunderlietheuniverse. Bythepresent Althoughthe resultsweobtainedinthis articleissim- article,wecanconfirmanexistenceofanultimateprinci- ilar to ones that modern physics discovered, we open to ple or an ultimate law from which others could be found the possibility that the answers to many of the ques- out. tionswehaveaboutwhyphenomena,things,theelemen- We realize that the most important principle of na- tary particles, or the fundamental forces are as they are ture is that all observable properties of things are about andnot otherwise,andwhy the nature createdbeautiful relationships. The difference has meaning in direct rela- worlds in the way we see not otherwise. Moreover, we tionship. Actions are in interaction in mutual relation- have the expectation to answer the greatest questions: ships. Contradictions are generated in mutual-rejection ”Where does the universe come from?” or ”What is the 8 N.T.Anh The Variant Principle evolution, the self-organization, the variety, or the fate are only essential for understanding what happened, is of the universe?” or ”Where does the matter come from happening, and will happen in the universe. and where is the missing matter?”. Ofcourse,thisdoesnotmeanthattheorieswillbedis- Inthepresentarticle’sviewoftheuniverse,everything covered, based on the principle of causality, are proven is fromto nothing, everythingmay be smooth atthe be- to be right; only observation and experiment can, in the ginning but does not stay smooth forever, because to- end,tellusthat. Butadefinitefactthatweenterthe21st day ouruniverse is very inhomogeneous. So the universe century with new ideas and wide horizons,with muchto was not perfectly homogeneous either when it began or do and everything to talk about. shortlyafteritbeganbut,rather,itwasslightlyinhomo- geneous. Ithadsmallregionswherethedensityofmatter wasslightlyhigherthanaverageandotherregionswhere ACKNOWLEDGMENTS it was slightly lower than average. They are really tiny. Yettinyastheyaretobeginwith,theseinhomogeneities areveryimportantbecausetheyaretheseedsfromwhich We would like to thank Dr. D. M. Chi for useful dis- particles, star clusters, galaxies and, eventually, human cussions and valuable comments. beings,willgrowinthe waythattheir structuremustbe The present article was supported in part by the formed systematically from within by natural processes Advanced Research Project on Natural Sciences of the ofself-organizationsuchasperiodic,multiplicative,com- MT&A Center. binative, evolutive, and etc. principles. Our universe has a variety of mysteries to discover. But we cannot say everything in a day. Many and very manybeautifulworldsareinfutureofourdiscovery. This article is only the first one we would like to open up a first view of the universe. The first is the key idea behind evolution of the universe from nothing, the second 1 D. M. Chi, The Equation of Causality, (1979). the idea behind the principle of causality. These themes 2 N. T. Anh,Causality: The Nature of Everything, (1991). 9