Universal Journal of Physics and Application 10(6): 198-206, 2016 http://www.hrpub.org DOI: 10.13189/ujpa.2016.100604 Scale Independent Workable Model of Final Unification U. V. S. Seshavatharam1,*, S. Lakshminarayana2 1Honorary Faculty, I-SERVE, Survey no-42, Hitex road, Hitech city, Hyderabad-84, Telangana, India 2Department of Nuclear Physics, Andhra University, Visakhapatnam-03, AP, India Copyright©2016 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract We show that, Schwarzschild radius of Planck simple relations among the Newtonian gravitational mass plays a vital role in electroweak and strong interactions. constant, Fermi’s weak coupling constant, Strong With reference to the observed large proportionality ratio, coupling constant and nuclear charge radius. 12 B). With reference to the proposed semi empirical relations, 0.1153()mmpe , it seems appropriate to consider a large it is possible to show that, proportionality ratio is of the 3 -1 -2 nuclear gravitational constant, G ≅ 3.3295608 m kg sec . 12 s order of 0.1153mm . Qualitatively this idea is in agreement with “Strong gravity” ()pe concept proposed by Abdus Salam and C.Sivaram [Mod. C). By replacing the large proportionality ratio with a large Phys. Lett., A8(4), 321- 326. (1993)]. We would like to 3 -1 -2 gravitational constant, Gs ≅ 3.3295608 m kg sec , suggest that, by replacing the Newtonian gravitational assumed to be associated with nuclear structure, we constant with the proposed nuclear gravitational constant, eliminated the higher powers of proton-electron mass predicted high energy levels of String theory can be brought ratio and proposed unified and simplified semi down to the current hadronic scale. Based on this idea, we empirical relations. defined the nuclear Planck mass, D). By replacing the Newtonian gravitational constant with 2 mnpl ≅≅ cGs 546.7 MeV/c and proposed a quantized the proposed nuclear gravitational constant, we defined 2 model mechanism for understanding the hadronic mass the nuclear Planck mass, mnpl ≅≅ cGs 546.7 MeV/c spectrum. and developed a quantized model mechanism for Keywords Final Unification, Nuclear Gravitational understanding the hadronic mass spectrum. Constant, Newtonian Gravitational Constant, String Theory, Nuclear Planck Mass, Neutral Charge Nuclear Dark Baryon, Quantized Hadronic Mass Spectrum 2 . Conceptual Thought Connected with Final Unification Conceptual thought: Schwarzschild radius of Planck mass plays a vital role in electroweak and strong interactions. 1 . Introduction -11 3 -1 -2 Let, GN ≅×6.67408 10 m kg sec . A Grand Unified Theory (GUT) is a model in particle physics in which at high energy, the three gauge interactions c -8 Planck mass = M pl ≅≅2.176471826 × 10 kg of the Standard Model which define the electromagnetic, GN weak, and strong interactions, are merged into one single force. Unifying gravity with the other three interactions Rspl ≅ Schwarzschild radius of Planck mass would provide a theory of everything (TOE) [1-4]. In general, 2GMN pl G GUT is often seen as an intermediate step towards a TOE. ≅ ≅≅N ×-35 232 3.2324592 10 m The most desirable cases of any unified description [4] are: cc 1) To simplify the complicated issues of known physics. 2) To predict new effects, arising from a combination of the fields inherent in the unified description. 3 . Strange Result Connected with So far it has never been achieved. In this paper, we geared Planck Scale Schwarzschild Radius up the following things. mp A). By considering the Schwarzschild radius of Planck Let, be the proton-electron mass ratio and G be F mass and proton-electron mass ratio, we proposed very me Universal Journal of Physics and Application 10(6): 198-206, 2016 199 the Fermi’s weak coupling constant. 5. Strange Result Connected with It is noticed that, Strong Coupling Constant 1 1 10 2 10 mp GFF Gc ≅≅ (1) Let, αs ≅ 0.1153 be the strong coupling constant. m 22 e cRspl 4 GN It is noticed that, Based on this relation, 12 mp 1 c 10 ≅ 2 2 (8) mp 4G -62 3 m α G ≅N ≅×1.438965 10 J.m (2) esGmNp F m 2 e c From relations (6) and (7) 10 2 me GcF 12 2 G ≅ (3) m ccRspl N 2 α ≅≅e mp 4 s 22 mRp GmNp 0 GmNp 10 (9) m 2 22 22 GF p 4 MRpl spl MRc pl spl 2 ≅ (4) ≅≅ ≅ Gm2 22 m Rc m Rc Ne c mRp 0 pp00 -62 3 If, recommended GF ≅×1.435850984 10 J.m , From above relations, we would like to say that, magnitude of α seems to be around 0.1153. The same obtained G ≅×6.65963739 10-11 m 3 kg -1 sec -2 s N conclusion can also be extracted from Particle data group’s (PDG) review on Quantum chromodynamics [5]. See the 4. Strange Result Connected with following table-1. Fermi’s Weak Coupling Constant Let, ≈ be the nuclear charge radius. 6. To Eliminate the Higher Powers of R0 1.24 fm It is noticed that, Proton-electron Mass Ratio 2 mp cR It is true that, unless stringent requirements are met, in ≅ 0 (5) mGeF general, speculative alternatives to currently accepted theories cannot be accepted or published. Scientific papers From relations (1) and (5), having content that lie outside the mainstream of current 66 mmpp4G research must justify by including a clear, detailed RR≅≅N (6) 0 3 spl discussion of the motivation for the new speculation, with mmeec reasons for introducing any new concepts. If the new 6 2 12 formulation results are in contradiction with the accepted RR00mmppp ≅≅ Or (7) ( ) 2 theory, then there must both be a discussion of which Rmspl e p R me spl experiments could be done to verify that the conventional -11 3 -1 -2 If, GN ≅×6.67408 10 m kg sec , obtained theory needs improvement, and also an analysis showing the consistency of the new theory with the existing experiments. R0 ≅ 1.238755fm . Table 1. Magnitude of αs close to 0.1153 2 +0.0041 2 1 αsZ(M ) = 0.1161-0.0048 7 αsZ(M ) = 0.1158± 0.0035. 2 +0.0093 2 2 αsZ(M ) = 0.1151-0.0087 . 8 αsZ(M ) = 0.1154± 0.0020. 2 αsZ(M ) = 0.1148± 0.0014(exp .) 2 +0.0028 3 9 αsZ(M ) = 0.1131-0.0022 ± +0.0050 0.0018(PDF )-0.0000 2 2 +0.0021 4 αsZ(M ) = 0.1134± 0.0011, 10 αsZ(M ) ≅ 0.1156-0.0022 2 2 +0.0041 5 αsZ(M ) = 0.1142± 0.0023, 11 αsZ(M ) ≅ 0.1156-0.0034 2 +0.0033 2 +0.0093 6 αsZ(M ) = 0.1151-0.0032 12 αsZ(M ) ≅ 0.1151-0.0087 200 Scale Independent Workable Model of Final Unification In this context, by considering a proportionality ratio of 2 2 12 2c αs ≅ ≅≅0.1153 (11) 0.1153(mmpe) , we propose the following workable 2 mp Rc0 Gmsp assumption: In nuclear structure, there exists a very large 3 -1 -2 gravitational constant, Gs ≅ 3.3295608 m kg sec . We Application-2 estimated this magnitude by the following ad-hoc relation. 1 1 2210 10 Gs Gm se Gmse 2 2 Proton rest mass, mp≅≅ mm ee mpe Gmsp Gc 2 Planck's constant, h ≅ N GmN npl me 4pe0 cc c 2 (10) where ≅≅546.7 MeV/cm Nuclear Planck mass ≅npl 4pe hcm22 Gs →≅G 0 e s 23 (12) emp Application-3 Qualitatively, this assumption is not new and is having a long standing history [6-14]. For more information, readers Nuclear charge radius, are encouraged to see Abdus Salam’s ‘Strong gravity’ 2Gmsp ≅≅ (13) concept [12]. In the early seventies Abdus Salam and his R0 2 1.238755 fm co-workers proposed the concept of strong gravity. In this c context, in physics literature one can see valuable papers on Application-4 ‘strong gravity’ proposed by C. J. Isham, Abdus Salam, C. Root mean square radius of proton, Sivaram, J. Strathdee, K. P. Sinha, Y. Ne’eman and Dj. Sijacki. In Strong gravity, the successive self -interaction of 2Gmsp Rp ≅≅0.875932 fm (14) a nonlinear spin-2 field was used to describe a non-abelian c2 field of strong interactions. This idea was formulated in a two-tensor theory of strong and gravitational interactions, Application-5 where the strong tensor fields are governed by Einstein-type 38 Fermi's Weak coupling constant, field equations with a strong gravitational constant Gf ≈ 10 2 24Gm G22 m 4G (15) times the Newtonian gravitational constant, GN. Within the se s e2 s GF≅ c ≅≅Gmse framework of this proposal, tensor fields were identified to cc43 c 3 play a fundamental role in the strong-interaction physics of 4G 2Gms npl quantum chromodynamics (QCD). Modifying these concepts, s ≅ ≅≅ where 320.36 fm Nuclear Planck length . O. F. Akinto and Farida Tahir recently posted their work in cc arXiv preprint [14]. They elaborately discussed on modified Application-6 strong gravity concepts pertaining to QCD and general relativity. In 2013. Roberto Onofrio [15] proposed a very Stable mass number, interesting concept: Weak interactions are peculiar 2 Gm m 2 manifestations of quantum gravity at the Fermi scale, and AZ≅+2 s pe 2ZZZ≅+ 2 0.00642 (16) s ( ) ( ) that the Fermi coupling constant is related to the Newtonian c constant of gravitation. In his opinion, at atto-meter scale, Newtonian gravitational constant seems to reach a Application-7 magnitude of 8.205× 1022 m 3 kg -1 sec -2 . For Z ≥ 30 , close to stable atomic nuclides, nuclear With this assumption, 10th and 12th powers of mm ( pe) binding energy [18], can be eliminated.