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1. Introduction 2. Pregeometry Hidezumi Terazawa 219 218 Proceedings of BGL-4 SPECIAL INCONSTANCY IN PREGEOMETRY for 0.2 < z < 3. 7, which is consistent with a time-varying a . Note, however, that in 1976 Shylakhter f81 obtained the very restrictive limit of 16.a/al < 10- 7 or, more precisely, Hidezumi Terazawa 6.Œ/a6.t = (-0.2 ± 0.8) x 10-17 yr-1 for z ,...., 0.16 (but over a. narrower and latest range of epochs betwcen now and about 1.8 Instu.te of ?article and Nuclear St11dies 1 H'igh Energy Accelemtor Research Organization, billion years ago) from the "Oklo natural reactor". Very lately, Srianand et al. [9] have made Japan a detailed many-multiplet analysis performcd on a new sample of Mg II systems observed in high quality quasar spectra obtained using the Very Large Telescope and found a null result Midlands Acaderny of Bnsiness ël Technology (MABT), 5 United Kingdom of 6.a/cr. = (-0.06 ± 0.06) x 10- for the fractional change in Œ or a 3ri constraint of 16 1 16 1 -2.5 x 10- yr-- -:; (6.a./a6.t) -:; +1.2 x 10- yr- A thcory of spccial inconstancy, in which some fondamental physical constants such as the for 0.4-:; z -:; 2.3, which seems to be inconsistent with the result of Webb et al. [7]. However, fine-structure and grnvitational constants may vary, is proposed Ill pregcometry. In thf~ the­ a careful comparison of thesc different rcsults [7-9] indicates that thcy are ail consistent with ory, the alpha-G relation of a = 3n /[16 ln( 471' /5CM~ )] between the varyin~ fine~structure ;;i,r~d gravitational constants (where Mw is the charged weak Loso.n mass) 1s denved frorn a tirne-varying l~ as the hypothesis that Loth of these constants arc related to the same fu11damcnt:l1 ~en~t~1 ~cale in nature. Furthermorc, it leads to the prediction of G/G = (0.4 ± 0.4) X 10 yr rom for 2.2 < z < 3. 7. the recent observation of <i/a = (5 ± 5) .x 10- 15 yr- 1 by Webb _e{ al . _,_~vhich is n_ot only 2 In this talk, I am going to propose a theory of special inconstancy, in which some consistent with the most precise limit of G /G = (-0.6 ± 2.0) X 10 yr by Thorsett but fondamental physical constants such as the fine-structure and gravita.tional constants rnay also fcasible for future expcrimental tests. In special inconstancy, the pa.<:it and p~escnt of the vary. ln the theory, the alpha-G relation of Univese are cxplained and the future of it is predicted, which is quitc different !rom that m the Einsein theory of gravitation. The coutcnts of this talk include the followmg: Œ = 3n /[16 ln( 411'/5G Mfv )] 1. Introduction 2. Pregeomctry (where Mw is the charged weak boson mass) is derived from the hypothesis that both of 3. Special Inconstancy a and G arc related to the same fondamental length scale in nature. Furthermore, from 4. Further Discussions and Future Prospects. the above result on a , it leads to the prediction of è /G = (0.4 ± 0.4) x 10-12yr-1 1. Introduction which is not only consistent with the limit on G by Thorsett (6) but also feasible for future Is a physical constant rcally constant? In 1937, Dirac (1] discussed possible time vari~­ experimcntal tests. I will organize this talk as follows: in Section II, I will briefly review tion in the .fondamental constants of nature. He made not only the large numbcr hypothes'.s pregeometry in which a theory of special inconstancy is constructed. In Section III, I will (LNH) but also, as a consequences of the LNH, the astonishing prediction that the grav'.~ present the theory and its predictions. Finally in s~) ction IV, I will present further discussions tat.ional constant G varies as a fonction of time. Sincc then, .Jordan (2] and rnany oth<~ 1 s and future prospects. In addition, in special inconstancy I will explain the history of our (3,4] have tried to construct new theories of gravitation or gen~ral _r'.'lativity in order_ ::o Universe and predict the future of it, whid1 is quite difforent from that in the conventional accomodate such a timc-varying G . Although the LNH bas been mspmng many thcoret1c<tl Einstein theory of gravitation. devcloprnents and bas recently led rnyself [5] to many new large number relations, the pre­ diction of the varying G has not yet reccived any experimental cvidence. R.ccently, _Thorsett (6] has shown that measurcments of the masses of young and old neutron stars m pulsar 2. Pregeometry binaries lead to the most prccise limit of Pregeornetry is a theory in which Einstein's geometrical theory of gravit.y in general 1 G/G == (-0.6 ± 2.0) x 10 .:_ 12yr- relativity can be derived from a more fondamental principle as an effective and approximate theory at low energies (or at long distances). In 1967, Sakharov [10] suggested possible ap­ at the 68% confidence level. proximatc derivation of the Einstein-Hilbert action from quantum fructuations of matter. More recently, on the other hand, Webb et al. [7] have investigated possible tune vanatton A decade la.ter, we [11] demonstrated that not only Einstein's theory of gravity in general in the fine structure constant a by using quasar spectra over a wide range of cpochs, relativity but also the standard model of strong and eleetroweak interactions in quantum spanning redshifts 0.2 < z < 3.7, in the history of our Universe, and derived the remarkable chromodynamics and in the unified gauge theory can be derived as an effective and ap­ result of proximatc theory at low energies from the more fondamental unified composite model of all a/a== (6.40 ± 1.35) X 10-lûyr-l fondamental part.ides and forces (12]. 220 Proccedings of BGL-4 Hidezumi Terazawa 221 Let us explain what pregeometry means more explicitly in a simple rnodel of . One of ~he rnost remarkable consequences of pregeometry is the alpha-G relation, a Slm_ple relat10n between the fine-structure and gravitaional constant, which can be easily de~1_ved from the results for a: and for G by eliminating lh momenf;um eut-off A. In ou.r umfied quark-lepton mode! of ail fondamental forces [14,15] the alpha-G relation is given by [161 ' , where 9µv is the space-time metric, g = det(gµv) , Aµ is an Abelian gauge field, and 'Pi ( i = 1 ,..., n) are n complex scalar fields of matter with the charge e . The fondamental a= 37r/ L, Qiln(l21f/nGm7), Lagrangian Lo consists of the gauge-invariant kinetic terms of the matter fields only as i where 9i and mi are the charge and mass of quarks and leptons, respectively. For three g_enerat10ns of quarks and leptons and their mirror- or super-partners, the alpha-G relation s1mply becornes (where F is an arbitrary constant) but does not contain either the kinetic term of the space­ a':::! 37r/l6ln(47r/5GMti,,) time metric or that of the gauge field so that both of 9µv and Aµ are auxiliary fields. The effective action for the space-time metric and gauge field can be defined by the path-integral wh:re Mw is the chargcd weak boson mass. Note that this alpha-G relation is very well 1 2 over the matter fields as sat1sfied by the experimental data of (l'. ':::! 1/137' a- 1 2:! 1.22 X 1019GeV' and Mw 2:! 80.4GeV. ea:p(iSef J) = JIT[dt.pÎ][dt.pi]exp(iSo) i 3. Special Inconstancy and it can be expressed formally as Special inconstancy is a principle in which sorne fondamental physical constants such as the fine-structure and gravitational constants may vary. Let us first rnake it clear that in this talk we use the nat.ural w.1ili Rystcm ~>f h/2rr = c = 1 (where h is the Planck constant and c is .the speed in vacuum). Note, howcver, that it does not mean that, in discussing the after the path-integration over 'Pi. For small scalar curvature R and Ricci curvature tensor ~f ~i?lit i:elevant pos~1b~ty oI ~·~ :1aryî11.g fu1e-sl;ru t11re and gravitational constants [17], we exclude Rµv , the effective action can be calculated to be anothcr rntngumg p SA1bihty of the varyilJg light velocity reccntly discussed by some authors jJ8] s.ince vur:ying eiLher h or c is in .vi.tably related to varying the fine-structure constant Œ ( = e~ /2hc)(jf th unit charg· e stays constant). It simply means that we must set up a certam reference frame on which we can discuss whether physical quantities such as the with fine-structure, gravitational, and cosmological [19] constants be really constant. Our basic 4 2 1 2>. = [nA /8(47r) ] - p- , hypothesis is that both of the fine-structure and gravitational constants are related to the 2 2 more fondamental length scale of nature as in the unified (pregauge [20] and) pregeometric (1/l67rG) =nA /24(47r) , [10-12] theo? (or "pregaugeornetry" in short) of ail fondamental forces[14,15J reviewed in 2 2 c = nlnA /240(47r) , the last Sect10n. To be more explicit, in the simple mode! of pregaugeometry discussed in the last Section, d= 2, assert that 1 and < (8µ + iA1,)..j=gg w(8v - iAv)'Pi >A= 0, 2 2 2 (1/4e ) = nlnA /3(47r) , 91w = F < [(8µ + iAµ)'PÎ](élv - iAv)'Pi >A, where À and A are the cosmological constant and the momentum eut-off of the Pauli­ and Villars type, respectively.
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