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On a plausible triple electro-gravito-informational significance of the fine structure constant and its implications in the four fields unification and the existence of life forms in our universe DOI: 10.13140/RG.2.2.13114.39365 Version 3.2 Andrei-Lucian Drăgoi MD Pediatric specialist and independent researcher in theoretical physics and fundamental biology (Bucharest, Romania); E-mail: [email protected]
Abstract
In the last century, a small minority of physicists considered a hypothetical binary logarithmic connection between the large and the small constants of physics, which also implies a base-2 power law (Fürth, 1929; Eddington, 1938; Teller, 1948; Salam, 1970; Bastin, 1971; Sirag, 1980, 1983; Sanchez, Kotov and Bizouard, 2009, 2011, 2012; Kritov, 2013). This paper brings to attention a plausible triple electro-gravito-informational significance of the fine structure constant, with its implications in the four fields unification and the existence of life forms in our universe: this triple significance is based on the existence of a unifying global scaling factor of nature which appears in a hypothetical fine tuning of all the non-zero rest masses of the all the elementary particles in the Standard Model. Furthermore, this paper also proposes dimensional relativity hypothesis (DRH) stating that the 3D appearance of space (or the 4D nature of spacetime) may be actually explained by the relative magnitude of the photon momentum quanta (and the hypothetical graviton momentum quanta respectively) and this global scaling factor (GSF): DRH also includes a generalized electrograviton model (EGM) for any hypothetical graviton. This paper also proposes a set of strong (and very strong) gravity constants and a gravitational field varying with the energy (and length) scale, all with potential importance in the unification of the four fundamental fields.
Keywords: fine structure constant with triple electro-gravito-informational significance; unifying global scaling factor of nature; the four fields unification; the Standard Model of particle physics; dimensional relativity hypothesis; electrograviton model; life forms
that square root of NEdd should be close to Dirac’s big number (which he invoked in his large number hypothesis) I. Introduction [1] 256 128 such as NEdd 136 2 136 2 In 1929, the German physicist R. Fürth proposed the 3.97 1039 . Later on, Eddington changed 136 to 137 adimensional constant 16232 128 as a possible (using the new experimental values of [re]determined in “connector” between gravitational and quantum mechanics his life time) and (re)insisted that had to be precisely constants [2]. Arthur Eddington (1937) and Dirac (1937) have 1/137 , a fact which attracted irony at that time [3]. remarked the coincidence of the large adimensional However, Eddington’s statement also implied the numbers in physics which can be reformulated as: adimensional constant 2128 , which wasn’t given proper 1/2 40 attention for the next 10 years (Kritov, 2013) [4]. a/ aGve RH / r N 10 ( a 1/ 137 is the In 1948, Edward Teller proposed a possible logarithmic inverse of the fine structure constant [FSC] at rest connection between and Gm239/10 hc of the 2 41 N kqee / c 1/137 ; aGGvv1/ 3.1 10 is the form 12 lnGm / hc , with m being the inverse of a variant of the gravitational coupling constant N N 41 standard rest mass of a nucleon (proton or neutron) [5]. [GCC] Gv Gm p m e / c / 1/ 3.1 10 ; In 1970, Abdul Salam also brought in attention a R c / H14.5 109 light years is the Hubble H 0 possible logarithmic connection between Gv and [6]. radius of the observable universe, which is a function of the In 1971, Edward Bastin invoked the observation Hubble constant H 71.9 km / s / Mpc ; 99% 0 2 38 127 aGvv // Gm p c 1.7 10 2 and proposed r k q22/ m c 2.8 1015 m is the classical radius e e e e the derivation of a 1/ 137 from the exponent 127 by of the electron at rest; N 1080 is the approximate number summing 127 with its series of digits, such as of nucleons in our observable universe, a number which can 127+(1+2+7)=137 [7] be estimated by astrophysical methods) In 1980, Saul-Paul Sirag also proposed an alternative In 1938, Arthur Eddington proposed that the number of interpretation of the binary logarithmic relation between protons in the entire Universe should be exactly equal to: a 1/ and aGGvv1/ , such as 256 79 N 136 2 1.57 10 ( N was later called the 100.6%
log2 aav 137.84 . (Sirag, 1980, 1983) [8]. Eddington’s number NEdd ) and Eddington hypothesized G 2 John D. Barrow and Frank Tipler probably didn’t know about Salam’s (1970), Bastin’s (1971) and Sirag’s (1980, 1983) works on this subject, when they wrote in 1986 that: II. The existence of unifying gravitational scaling factor „Edward Teller appears to have been the first who speculate based on a hypothetical electro-gravitational that there may exist a logarithmic relation between the fine significance of the fine structure constant structure constant and the parameter Gmhc239/10 of the form N Let us consider a function f mxy, m of any two 12 identical or distinct non-zero rest masses m and m of ln/GmhcN [equation 4.23] (in fact x y any pair of elementary particles (EPs) in the standard model 159 ln 3.27 10 [corrected estimation] and the (SM): formula is too insensitive to be of very much use in predicting exact relations)“[9,10]. ( also stands for the mN log2 c / Gmxy m nucleon [proton/neutron] rest mass) f mxy, m 2 (II-1a) Regrettably, Barrow and Tipler also ignored Eddington’s c/ kee q works on the subject which could have inspired them to analyze the binary logarithm variant Interestingly, the function has its values log/ Gmhc2 instead of the natural logarithm 2 N relatively close to 1, in the double closed interval 2 0.817, 1.085 with an arithmetic average of 0.93 variant ln/GmhcN . This paper proposes additional which is also respected on the “diagonal” values (as detailed arguments against Barrow and Tipler superficial analysis of in the next table and figure: obviously, the values of this subject and continues the works of all the authors previously cited who “advocated” in the favor of this binary f mxy, m tend to be super-unitary for the combinations logarithm connection. of the lightest EPs and sub-unitary for the rest of EPs. The recurrence of 2128 and 22a 1/ factors in these (probably just apparent) numerical coincidences suggests that base-2 power law may have a significant role in numerical relations of these physical constants, predicting the existence of a universal (large) scaling factor of nature (indissolubly related to the fine structure constant) with important implications in a possible fine-tuning of all non- zero rest masses of all known elementary particles in the standard model, with implications for the existence of life forms in our universe. Table and figure II-1. The values of the function f m, mc Gm log m / in the double closed x yx y 2 interval Elementary Quarks* Leptons** Bosons*** particles u2/3 d 1/3 c2/3 s1/3 t2/3 b1/3 e W / Z 0 H 0 1.053 1.046 0.987 1.014 0.935 0.974 1.069 1.013 0.983 0.943 0.942 0.938 1.046 1.038 0.979 1.006 0.927 0.966 1.061 1.005 0.976 0.935 0.934 0.931 0.987 0.979 0.92 0.947 0.868 0.908 1.002 0.946 0.917 0.877 0.875 0.872 1.014 1.006 0.947 0.974 0.895 0.935 1.029 0.973 0.944 0.903 0.902 0.899 0.935 0.927 0.868 0.895 0.817 0.856 0.951 0.895 0.865 0.825 0.824 0.82 0.974 0.966 0.908 0.935 0.856 0.895 0.99 0.934 0.904 0.864 0.863 0.859 1.069 1.061 1.002 1.029 0.951 0.99 1.085 1.029 0.999 0.959 0.958 0.954 1.013 1.005 0.946 0.973 0.895 0.934 1.029 0.973 0.943 0.903 0.902 0.898 0.983 0.976 0.917 0.944 0.865 0.904 0.999 0.943 0.913 0.873 0.872 0.868 0.943 0.935 0.877 0.903 0.825 0.864 0.959 0.903 0.873 0.833 0.832 0.828 0.942 0.934 0.875 0.902 0.824 0.863 0.958 0.902 0.872 0.832 0.83 0.827 0.938 0.931 0.872 0.899 0.82 0.859 0.954 0.898 0.868 0.828 0.827 0.824 Note: the super-unitary values (corresponding to the combinations between the lightest elementary particles) were marked in italics. *only the average estimated rest mass of quarks was considered (without their individual rest mass determination uncertainties); ** only the leptons with known rest masses were tabled (such as the three leptonic flavors of neutrinos were excluded for the moment); *** only the bosons with non-zero rest masses were tabled; 3
1.2 1-1.2 1
0.8-1 0.8
0.6
0.4
0.2
0
more super-unitary values to it and equilibrating the As seen from the previous table and figure, the sub- previous “mix” which was dominated by sub-unitary unitary values seem to predominate, as the three leptonic values): this last interval is approximately centered in value flavors of neutrino (which are probably lighter than the 1 and is relatively symmetrical and “equilibrated” around electron) weren’t yet graphed, given the difficulty in this value with two sub-unitary and super-unitary “wings” determining their exact non-zero rest masses. 1 0.2 ; the arithmetic average of this extended interval The denominator c/137 k q 2 is actually the ee of f values increased to 0.97 . See the next figure. inverse of the fine structure constant (FSC) at rest and can be noted with ac1//137 k q 2 , so that ee 1.25 f mxy, m can be simplified as: 1.2 1.15
f m, mGm m logca / / 1.1 x yx y 2 (II-1b) 1.05
1 The values of the function f are also plotted in a graph, sorted in ascending order: see the next figure. 0.95 0.9 1.1 0.85 0.8 1.05 Figure II-2b. The values of the function (also 1 considering three neutrino rest mass of ~1eV combinations) sorted in ascending order 0.95 hyp. f m, m 1.349 also adds to this interval 0.9 ee as an apparently “isolated” value, but which 0.85 pushes the arithmetic average of values to 0.98 and 0.8 1.01(for the diagonal values only) (values even closer to Figure II-2a. The values of the function f (without 1) and which may suggest the existence of EPs (with non- considering neutrino rest mass combinations) zero rest masses and probably zero-charged) even lighter sorted in ascending order than the neutrinos to fill the gap between 1.2 and 1.349 and even to extend this interval. The most plausible candidates 0 are the lightest supersymmetric particles (hypothetical The electron neutrino e rest mass is estimated to be particles proposed by supersymmetric models), probably 2 in the interval 0.2, 2eV / c [11]. For neutralino (which is the most plausible candidate for the hyp. main constituent of the hypothetical dark matter), the 2 m 1.85 eV / c (which is the last experimental gravitino and the lightest sneutrino. e Furthermore, even if the proton and the neutron aren’t m,m,m,m,m,m,udb c s t estimation) and m , elementary particles, f mpy, m and f mny, m also y m , m , m , m,, m m e W Z H have values that “fit” in the same approximate interval 1.201, 1.193, 1.134, 1 0.2 , as those nucleons have rest masses relatively close (with the same order of magnitude) to the tauon rest mass, hyp. 1.161, 1.083, 1.122, f m , my , which extends for which f m , me 0.999 : f mN , me 1.006 . e 1.217, 1.161, 1.131, This paper considers that it is very unlikely for the 1.091, 1.09, 1.086 relatively large diversity of EPs non-zero rest masses to be strongly centered logarithmically around a 1/ 137 the interval of values of f to 0.817, 1.217 (by adding 4 only due to a “simple” coincidence: by contrast, it is very ff Rl, 1.49, ff Rr, 0.99 , ff Rr, 1.01, plausible that the existence of this “unity in diversity” to be ou Pl ou e ou p the consequence of a more profound law of nature, as is ff rl, 0.48 , ff rl, 0.49 . Interestingly, all also the expression of a charge-anticharge symmetry (which p Pl e Pl was verified to be exact with very high accuracy) with no these values tend to concentrate around values 1/2, 1 and 3/2 clear and definitive explanation yet. which are multiple integers of 1/2. The length 26 na rm ec 5 10 is relatively close to In conclusion, f mxy, m appears to help in predicting the products of any pair of elementary non-zero rest masses , so that na rR ecou 1.14 and
mmxy as a function of Planck mass mPl cG/ , so 99.9% that: log2 (Rou / raec ) 136.85 . The length 2 nr 1.6 1026 m is also relatively close to R so cG/ mPl (II-2a) ap ou mmxy 22aa1 0.21 0.2 101.1% that n rR 0.35 and log (R / ra ) 138.54 . a pou 2 ou p a 1/ 41 In other words, when expressed in r and r units, the The factor na 221.8 10 which p e emerges in the previous equation can be proposed as a observable universe has ~137 length “octaves” which also unifying gravitational/mass scaling factor of the Standard suggests the gravitational significance of FSC. The next model, so that: “natural” ff-value in the series nwith/2() n * is
ff Rlx , Pl 2 , which predicts a radius 2 m 221 Pl (II-2b) R l nR 10 which is a potential candidate for mmxy1 0.2 xaou Pl na the real radius of our present universe (which is already predicted by superstring theory to be with at least 3 orders m Pl (II-2c) of magnitude larger than Rou ) mmxy n 0.5 0.1 282 a na 3.2 10 is also close to the gravity-related ratios between the rest-mass of our observable universe (ou) 54 a 1/ Mkgou 3.1 10 and the non-zero rest masses of the The existence of na 22 in the function proton mp and electron me , such as: f mxy,1 m justifies the hypothesis that the fine 81 84 structure constant may have a dual/hybrid Mou/ mN p (1.8 10 Edd ) , Mmou/ e 3.4 10 electromagnetic and gravitational (electro-gravitational) 82 and Mou/7.9 m p 10 m e . significance, so that na may be regarded as a unifying electro-gravitational scaling factor with the propriety c 105% a 41 Additionally, 75.75km / s / Mpc H , that mPl / mx m y n a 2 1.8 10 and 0 /4 rpan log na . 2 a with Hkm0 71.9 s Mpc / / being the Hubble constant as determined by the latest measurements from A similar base-2 logarithmic function ff rrxy, can 2016 with the Hubble telescope [12]. This n -based be conceived to compare the most important length scales of a predicted value is very close to the first good estimate our universe in pairs rrxy, such as: H0 75 km / s / Mpc proposed in 1958 by the influent American astronomer Allan Sandage [13]. ff r, r log r/ r / a (II-3a) x y 2 x y 3 23 Additionally, / 4ana 6.01 10 is very close
to the numerical value of the Avogadro constant ff rx, r y logn a r x/ r y (II-3b) 23 NA 6.023 10 molec / mole , so that
99.8% 3 /4 a n N . Given the estimated radius of our observable universe a A 26 (ou) Rmou 4.4 10 , the classical electron radius
22 15 rec k e q e/ m e c 2.8 10 m , the radius of the III.The hypothetical electrograviton as based on the proton (as determined by scattering using electrons) electro-gravitational significance the fine structure 15 constant rmp 0.87 10 and the Planck length 3 35 can be also written as: lPl G/ c 1.62 10 m , for rrxy,
Rou,,, r ec r p lPl , has the following values: 5 individual eg adds a distinct supplementary possible c / subquantum state to a receiver PS then (so that N a log gS 2 (III-1a) Gmxy m / increases with one unit, one additional possible gravitonic/subquantum state), the absorption of (a number
of) n egs means receiving log n 137gbits c / a a 2 a 2 na ([subquantum] gravitonic bits): on the other hand, the Gmxy m / (III-1b) energy-absorption of egs with Eceg eg / is equivalent to the absorption of one photon with the same / nca Gmxy m wavelength and energy Ec n E / ; (III-1c) ph a eg if the absorption of each individual photon adds a distinct supplementary possible quantum state to a receiver PS then, Based on previous equations, this paper proposes a the absorption of a photon means receiving model for the hypothetical spin-2 graviton analogous to the spin-1 photon (with wavelength and energy 1qbit 137gbits . Each gbit represents a group of gravitonic states similar to the “octave” interval used in Ecph / ), with zero-rest mass and moving with music to define any (double closed) interval of frequencies maximum speed c (or close to c , as the speed of gravitational waves [14]). As it is modeled analogous to the (f) ff,2 Hz . electromagnetic field quanta (the photon), this hypothetical FSC expresses an informational equivalence between graviton may be called “electrograviton” (eg), as it is also electromagnetism and gravity and a 137 may be used based on a (reduced) gravitational Planck-like constant as an interconversion factor between qbits and gbits, so that 76 ega/5.1nJs 10 , so that an eg with FSC 1/a can be regarded as the probability of wavelength is predicted to have an energy defined by: targeting a specific subquantum (gravitonic) octave of states (defined by each gbit) of any PS. In this view, a photon can be defined as an EP containing 1qbit 137gbits so that Ecegeg / (III-2) the probability of a real electron/positron (at rest) to emit a real photon (Feynman’s interpretation of FSC) may measure Measuring the value of FSC at rest (with very high in fact the base-2 logarithmic probability of an accuracy attained by using experiments based on the electron/positron to emit a photon in a specific subquantum quantum Hall effect) may be considered an indirect method (gravitonic) state. to essentially determine the electro-gravitational scaling The author of this paper had also demonstrated that na 1/ a factor na 22, which can further be used to redefine FSC at rest, such as: and the redefined can both help
predicting a quantum gravitational coupling constant aGq redef . (III-3a) for an electron/positron pair which approximates the a log2 na empirical Gm 2 / c 1.75 1045 with very redef . G e (III-3b) high accuracy[1], such as: 1/an 1/ log2 a
The existence of the hypothetical graviton (modeled in 1 99.6% 45 (III-5a) this paper as an electrograviton) may also imply the GqG 1.74 10 a 2an3/2 existence of subtle (at least theoretically distinguishable) a subquantum states for any physical system (PS) (composed of one or more EPs) generated by the absorption of one or This quantum a can also be used to predict a quantum more egs [15,16,17]. The total number of possible (at least Gq big G scalar G with the same high accuracy, such as: theoretically) distinguishable states of a PS NS can be q calculated as the product between the total number of 2 quantum states NqS and the total number of gravitonic Gqe Gq c/, m with (III-5b) 99.6% (subquantum) states NgS , such as [18]: 11 3 1 2 Gq 6.648 10 m kg s G
NNN In conclusion, FSC may actually have a triple electro- S qS gS (III-4a) gravito-informational significance, so that na can be log2NNNS log 2 qS log 2 gS (III-4b) [1] Discovered in 2014 and included in a document registered at The absorption of one photon by a PS increases NS the Romanian Copyright Office (ORDA) with the registration with one unit (one additional possible quantum state). number 2546 / 26.03.2015. URL
Analogously, if hypothesized that the absorption of each
6 considered a unifying (quantum/subquantum) electro- also implies a strict correlation in the variation of all the gravito-informational scaling factor, such as elements of the triad L ,,Nh. 41 xxx 1/1/10na can be interpreted as the probability to Given the relativity of from the target a specific subquantum (gravitonic) octave of states of any EP and 1/ log1/1372 na can be interpreted triad , this paper launches the dimensional as the base-2 logarithmic variant of that (same) probability. relativity hypothesis (DRH) which states that: “the dimensions (D) of the observable universe (ou) may not be Euclidean but fractal and the number of dimensions IV. The dimensional relativity hypothesis (DRH) based (d) of ou may not be absolute (a priori defined) and on the unifying scaling factor na [1] integer but relative and fractionary, depending on the electro-gravito-informational unifying scaling factor na An interesting (probably just apparent) coincidence and the (angular) momentum “key”-quanta we use to emerges when comparing h and ega / n with a study the global angular momentum Lou (using our global (angular) momentum parameter of the observable mind, senses and their extensions as 89 observational/measuring tools)”. As we generally use light universe (ou) at rest Lou E ou tJs ou 1.37 10 : (photons) to perceive and study space (together with virtual 71 photons which were demonstrated to permeate all space, as EJ3.14 10 is the approximate resting energy of ou 3 ou determined from the experimental measurements of the proved by the Casimir effect), the fact that Lnou a may generate the “3D space” appearance: there are studies which average energy density of ou which is estimated to ou also show that time may not exist as a “4th dimension” in the be very close to the critical energy density established by relativistic microcosm (the quantum level of reality). The 22 fact that we perceive time at the macroscopically level (as the Friedmann model as c 3H0 / 8 G / c so that part of an apparent “4D spacetime”, with a 4th dimension 10 3 ou c 8.73 10Jm / and the volume of ou modeled and measured using a classical linear time 3 80 3 function) may be also an appearance generated by gravity Vou 4 / 3 R ou 3.6 10 m (derived from the (mediated by [electro]gravitons with the very small eg 26 9 radius of ou Rmou 4.4 10 ); tyearsou 13.8 10 4 momentum-quanta) and to the relation Lnou eg a . is the age of the present ou (as determined by specific astrophysical methods). The human brain uses photons (light) to observe an apparent “empty” space, so that it may be the “victim” of (IV-1a) the illusion governed by d ph 3 , which generates the dlog LL / n 2.98 3 ph na ouou a appearance of a “3D spacetime”, in which time is not an (IV-1b) additional 4th dimension, but only an abstract/artificial dlog LL / n 3.98 4 egna ou eg ou eg a function which records a sequence of changes/events in that 3D space. The human brain also uses a combination of photons (light) and (quantized) gravity to observe the The closeness of the positive reals d and d to the ph eg movements of objects in space, so that it may be also the positive integers 3 and 4 respectively (denoting the number “victim” of the illusion governed by d 4 , which of apparent/perceptual dimensions of the 3D space alone eg generates the appearance of a “4D spacetime”, with an and the 4D spacetime respectively, as gravity is modeled by th General Relativity in a 4D Minkowski space) may suggest additional spatial 4 dimension attached to a perceptual “3D that the number of dimensions of ou may not be absolute, so space”. that it may not be correct to (a priori) predefine the This hypothesis can also offer an escape from a potential number of dimensions of space/spacetime as pure tautology, as when we measure different parameters of a observational arbitrary parameters without also quantum particle (QP), we use algorithms and equations considering the type of gauge boson (photon, based on the a priori assumption that space has three electrograviton, etc. and its specific momentum quanta (Euclidean or non-Euclidean) dimensions dx 3 , which , , etc.) used to observe/measure that eg may be essentially an illusion created by : it is also space/spacetime and its number of dimensions dx . the case in this paper, when Vou was calculated using the An arbitrary dx may be extracted from an arbitrary triad same 3D space a priori assumption. As L E t is a function of both the energy Lx,,nh x x as dx logn x L x / h x : this fact suggests ou ou ou E and age t of ou, a generalized function that it may not be correct to define dx a priori, based only ou ou on empirical/experimental observation, without also dx E x, t x, h x can be defined next: defining the triad from which this dx was extracted: this is because a fixed (as we associate space d E, t, h log E t / h d x x x x x n a x x x (IV-2a) with a 3D reference frame) also implies a fixed ratio
dxlogn x L x / h x log22 L x / h x / log n x , which dx E x, t x, h x predicts that if we could (theoretically) existed and could have used the same photons with the same 7
hx (as the present photons have) in a very early hf 3 2.4 1035 Js is relatively close (with historical epoch of ou (defined by txou t , the same approximately the same order of magnitude) to the reduced EE and the same n ) our space would have looked xou a Planck constant , so that hf 3 0.23 . The rest more like a ~2.5D space (like in the first second after the hypothetical Big Bang) or even ~1.5D (like in the first energies of W/Z bosons EW 80.4GeV , EZ 91GeV 544 25 Planck time interval tGPl cs / 5.39 10 after and their mean (measured) lifetimes ttWZ 3 10 s the hypothetical Big Bang): may help defining two reduced (angular) momentum-like
quanta W and Z (with 2 being associated with a full
d E,1 s ,2.56 x ou (IV-2b) mean lifetime tWZ/ ), such as:
dx E ou , tPl ,1.51 (IV-2c) Et WW6 26hf (3) (IV-3b) W 2 dExx t x, h x , also predicts that if we would (at least theoretically) exist and use the same photons with the same h E t 7 29 hf (3) ZZZ (IV-3b) (as the present photons have) in a very distant future of ou (defined by txou t , the same and hW and hZ are relatively close but larger than the same ) our space would have looked more like a ~4D (with ~1 order of magnitude), and that is space, for example in the future moment corresponding to why the W/Z bosons may be considered “heavy” photons, the age of tyears 1050 measured after the hypothetical or high-momentum photons (unstable excited states of the x photon with non-zero rest energies/masses and tendency to Big Bang: decay asymmetrically into pairs of distinct leptons) which is also the essential part in the successful unification of 50 electromagnetic field (EMF) and the weak nuclear field dx Eyears ou ,10, 3.95 (IV-2d) (WNF) as the electroweak field (EWF). As
More interestingly, all known elementary particles (EPs) dLW( ZW )( Z )logna ou / 2.97 3 , observing (including those EPs with extreme low/high non-zero rest our space by using W/Z bosons also generates the same 3D masses like the neutrinos [nn] and the Higgs [H] boson, space appearance. except the photon and gluon) have non-zero rest energies in Analogous to and , one can also calculate a the interval EE1.85eV, 125 GeV which W Z nnH reduced (angular) momentum-like quanta for the Higgs is relatively “centered” in EEnn H 0.5MeV (more or boson (HB) H by using the HB non-zero rest energy less ~5-6 orders of magnitude): 22 EGeVH 125 and its mean lifetime tsH 1.56 10 dEEPEP log E na ou / has values in the interval (with being associated with a full mean lifetime tH ), 1.9, 2.2D which is relatively centered around 2(D). such as:
This may explain why QPs (first treated as superstrings by the string theories [STs]) can also be generalized and Et HH4718 20770hf (3) (IV-3c) modeled as 2D surfaces (supermembranes or 2-branes) that H 2 may exist in an 11D spacetime as proposed by M-Theory (MT) and supergravity theory (which combines the L is with ~3-4 orders of magnitude larger than principles of supersymmetry and general relativity). A na - H based 11D universe may have a total angular momentum and that is why HB may be considered a Ln 11 . In this view, bosons may be modeled as “very heavy” photon, or very-high-momentum photon (a tot eg a very high and unstable excited state of the photon with a open 2-branes and fermions may be modeled as closed 2- non-zero rest energy/mass and tendency to decay branes [19,20]. The same QPs may be regarded as 2-branes symmetrically into pairs of identical/opposite-charge W/Z in 4D spacetime or as 1-branes (strings) in a 2D bosons, photons, leptons). As (holographic) universe: this sustains the holographic dLlog / 2.9 3 , observing our space principle (HP) proposed by Gerard't Hooft’s but also the HHna ou AdS/CFT correspondence (aka Maldacena duality or by (at least theoretically) using HBs may also generate the gauge/gravity duality). same 3D space appearance. Based on hf d function, DRH also predicts and The definition dx logn a L ou / h x , can be used to inversely define a specific momentum quanta associated to defines a quantum G function Gfq associated to any any d-frame of reference (with a number of d dimensions) integer/fractional dimensional d-frame (with such as: dimensions), such as:
d hf d Lou/ n a (IV-3a) 8
2 hf dL / d Gfqe dc mGq hf / d , (IV-4a) egou a n (IV-7a) with GGfG4 (IV-4b) 2 qq and Gfqe dc m egGq hf / d (IV-7b)
Based on the Gfdq general definition, DRH predicts In this view, the Newtonian/relativistic gravity is a hypothetical (very plausible) strong gravity constant mediated by the 4D-frame electrograviton (4-eg), with an (SGC) associated with a 3D frame and generated by a angular momentum quanta measured by egeg hf 4 strong gravity field (SGF) measured by a momentum quanta which generates a gravitational field with strength measured close to hfh3 , such as: by GGf 4. In the same view, SGF is predicted to be q mediated by a 3D-frame electrograviton (3-eg) with 31 3 1 2 Gfmq 3 kg s10 and (IV-5a) hfeg 3 , which has a strength also measured by 41 (IV-5b) 41 1.5 10 G GfGq 3 1.5 10 . The photon (which is its own antiparticle), the W/Z bosons and HB may all be considered The majority of authors have calculated a value for this different types of 3-egs because dddH W() Zph 3 . hypothetical SGC from 1025m 3 kg 1 s 2 inf In this way, the DRH-based SGF may co-predict (corresponding to dinf 2.84 ) up to (retrodict) the existence of the Higgs field (HF), as the 3D- 37 3 1 2 frame eg (3-eg) has some striking scalar similarities with sup 10 m kg s (corresponding to dsup 3.14 ), HB, which is a scalar QP (the only known scalar QP in with most of estimations between 1028m 31 kg 2 s and nature, first predicted to exist in 1960s) with 0-spin and even parity. HB is defined as the quantum excitation of one 32 31 2 10 m kg s , with a average davr 3 . (Seshavatharam [of the four] components of HF: HB is a very plausible and Lakshminarayana S. , 2010, 2012, 2015 [21,22,23]; candidate for the 3-eg (predicted by DRH) and vice versa. Perng, 1978 [24]; Fisenko et al., 2006, 2008, 2010 This DRH sub-hypothesis also implies that [25,26,27]; Recami et al., 1994, 1995, 1997-2001, 2005 Gf dGf 3 . However, the mainstream [28,29,30]; Fedosin, 1999, 2009, 2012, 2014 [31,32,33]; qqH Tennakone, 1974 [34]; Stone, 2010 [35]; Oldershaw, 2007, considers that more studies are needed to firmly confirm if 2010 [36,37]; Mongan, 2007-2011[38]; Sivaram and Sinha, the ~125GeV boson discovered in CERN's Large Hadron 1977 [39]; Dufour, 2007 [40]). Collider (LHC) has properties matching those predicted by SGF may act as a confinement force between the 2- Standard Model (SM) for HB, or whether, more than one branes contained in the same 3-brane (like our 3D space) type of HB exist (as predicted by some theories). The 100% stabilizing that 3-brane. confirmation of HF existence depends on the final Furthermore, DRH also predicts that there may exist a confirmation of HB existence, as HF is detected through its set of very strong gravity fields (VSGF) associated to the excitations (the HBs, which are difficult to obtain and 2D (the frame of 2-branes) and 1D (the frame of strings/1- detect). branes) which may manifest at scales progressively smaller HF is predicted to be tachyonic (as the symmetry- and even smaller the Planck length scale, such as: breaking of HB [through condensation] only occurs under certain conditions), and has a "Mexican hat" shaped Gf2 101072 m 3 kg 1 s 2 82 G (IV-6a) potential with non-zero strength at any distance (also q manifesting in empty space and permeating the entire 113 3 1 2 123 (IV-6b) Gfq 1 1010 m kg s G observable universe and possibly all our universe, similar to both electromagnetic field (EMF) and the predicted SGF.
In its vacuum state, HF breaks the weak isospin VSGF (2) is associated with Gfq 2 and may act as a symmetry of the electroweak field (EWF) and generates the confinement force between the strings contained in the same W and Z bosons of WNF, which have very large non-zero 2-brane stabilizing that 2-brane. VSGF (1) is associated with rest masses of about (80-90)GeV. HF may also explain the Gf 1 and may act as a confinement force between the non-zero rest masses of other elementary QPs like quarks q and leptons (that are predicted to be normally massless points contained in the same 1-brane (string), stabilizing that when considering the symmetries controlling their 1-brane. interactions), by using other HF-based mechanisms Gfq 1 is a potential candidate for the upper bound of a alternative to the Higgs mechanism. plausible finite G that limits the growth to infinity of the f mxy, m can be generalized/extended for any strength of gravity when approaching infinitesimal length scales possibly inferior to the Planck length scale (as (reduced) Planck-like constant x ,,,WZH , possibly in the black holes): the predicted hypothetical such as: asymptotical freedom of gravity. DRH also proposes a generalized electrograviton model logc / Gm m (EGM) in which there is a distinct electrograviton (0-spin, 2 x x y (IV-8) f m,, m 1-spin or 2-spin) associated with each dD frame (with d x y x 2 being a positive integer number of dimensions) with its own xc/ k e q e specific angular momentum quanta, such as:
9 All fermionic EP non-zero rest masses can be considered 2 the result of symmetry breaking of high-momentum bosons GqGq33 EE c m / e (V-1f)
(like the W/Z and HB) but keeping f mxy,, m x close 31 3 1 2 and centered on value 1. Not only “injecting” energy in a Gq1 EmPl kg1.2 s 10 reaches Gfq 3 , photon (by frequency increase of that photon) may generate 72 3 1 2 G Em kg 10 s reaches Gf 2 and fermionic particle-antiparticle pairs (with non-zero rest q2 Pl q masses), but also injecting momentum in a photon may 113 3 1 2 Gq3 EmPl kg 10 s reaches Gfq 1 . The base- generate “(very) heavy photons” (like W/Z bosons and HB) which further decay in fermionic pairs. 10 logarithmic variation of the functions DRH considers very plausible the possibility that the pE1 log101Gq E , pE2 log102Gq E symmetry-breaking condensation of HB to also generate not-only the W/Z-bosons (also 3-egs), but also the 4-egs and pE3 log103Gq E for EE Ee , Pl are which mediate the gravitational field (GF): this implies GF represented in the next graph: to be a residual SGF (SGF may also be a residual VSG[2], as VSG[2] may be a residual VSG[1]), and may contribute to the na -based explanation of the hierarchy problem, as Gfqa dH / Gf4 3 n (with an approximate same order of magnitude) DRH also predicts that VSGFs are probably mediated by the 1/2D-frame egs (1-egs and 2-egs) quantized by hfeg 1 and hfeg 2, which generates Gfq 1 and Gfq 2 and may also have 0-spin and even parity (like HB and the 3- eg). In conclusion, DRH (as based on the universal scaling factor n ) offers important explanations and predictions a Figure V-1. The variation of the gravitational field strength (mainly the generalization of the electrograviton model for described by the functions pE1 , pE2 and pE3 any relative frame with d dimensions) This paper also proposes the replacement of G in Einstein's Field Equation (EFE) with the quantum G V. The prediction of a gravitational field varying with function GE . In this way, the compact EFE based the energy scale q(1,2,3) on the predefined (symmetric second-rank) Einstein tensor 1 This paper also proposes a set of three simple na -based Gv R vv Rg (function of the metric tensor gv ) functions to describe three hypothetical variations of the 2 gravitational field (GF) strength as measured by the 8G quantum gravitational coupling constants a , a and Gvv gTv becomes a unifying equation Gq1 Gq2 c4 aGq3 , with a variable energy scale EEE e , Pl , with for both quantum mechanics and general relativity, 2 describing a quantum GF mediated by gravitons (modeled Emc 0.51 MeV and ee as electrogravitons) with a -based variable strength: EGeV cG5 / 1.22 1019 (the Planck energy Pl 8GE q(1,2,3) (V-2a) at which unification of all the four fundamental forces is Gv gT vv 4 predicted to occur), such as: c
Evar This approach also has the potential to solve the E 1 En Pl cosmological constant problem by offering the possibility of Gq1 a 3/2 (V-1a) 2ana a vacuum energy density vac that varies inverse- 2 proportionally to the length scale (and direct- Gq1 E Gq E c/ me (V-1b) proportionally to the energy scale E ), which may fill the huge “gap” (varying from 40 to more than 100 orders of E 2 var E 1 magnitude) between the observed small used by En Pl Gq2 a 3/2 (V-1c) 2ana general relativity and the very large predicted by the
2 quantum field theory. Gq22 E Gq E c/ me (V-1d) 2 Evar c 3 1 (V-2b) EPl vac En a Gq3 3/2 (V-1e) 8Gq(1,2,3) 2ana
10 VI. The unification of all the four fundamental fields at p EE log , pEf E log , Planck energy scale GFGq310 3 EMF 10
pEfWNFW E log10 , pSNFS Ef Elog10 : The running coupling constant of the electromagnetic field (EMF) determined in quantum electrodynamics see the next figure.
(QED) using the beta function can be also written as the function of a variable energy scale 2 E Eee m cMeV0.51 , EE Pl and 1/137 , such as [41,42]:
f E or (VI-1a) 2 1 lnEE / 3 e
f E may be interpreted/explained and redefined as the consequence of the variation of na with a variable energy scale E , as described by the function: Figure VI-1. The unification of GF(1,2,3), EMF, SNF and WNF at the Planck energy scale ln(4) 3 (VI-1b) nfaae E n// E E ,
with f Enf 1/ E log VII. Life phenomenon as engraved in the laws of our 2 a (VI-1c) universe
The running coupling constant of the weak nuclear field There are some strong arguments that creationism and (WNF) includes the rest energies of the W/Z bosons evolutionism can be unified in a more profound monad, as W also described by the Fine-tuned universe theories, (which are the propagators of the WNF) and is also based on including the Anthropic (Cosmological) Principle. [48]. the Fermi coupling constant It is generally considered that the non-zero probability of exp. 3 G/ cGeV 1.1663787 1052 (with life existence strongly depends on: boson-fermion F dichotomy (BFD) (associated with Pauli’s exclusion 62 3 GJmF 1.43585 10 ), which can be indirectly principle [PEP] which apply to all fermions), some narrow determined by measuring the muon lifetime experimentally. intervals of allowed variations (±4%) for the fine structure
W can be also written as a function of a variable energy constant (FSC) value (at rest) and for the beta constants +/- values at rest mm/ and mm/ (which scale EEE e , Pl , the rest mass/energy of the W p p e n n e influence the formation and the life cycles of the stars, boson m and E m c2 such as [43,44,45,46]: W WW which are the main sources of energy for life forms (LFs) and the only source of atoms heavier that the iron, which are 2 3 vital microelements for LFs); it is also generally admitted EWF G/ c (VI-2) fEW EE/ (and partially proved by some experiments) that and e W values have probably been “decided” (by so-called pn() The running coupling constant of the strong nuclear field natural (pre)selection) in the first moments after the (SNF) S determined in quantum chromodynamics (QCD) (hypothetical) Big-Bang. It was also demonstrated that the (also) using the beta function can also be written as a stability of all chemical structures that compose any LF function of a variable energy scale EESNF , EE Pl mainly depend on BFD-PEP association, and rd and ESNF 210 40 MeV (the QCD energy scale of values. In order for the first LFs to appear by the 3 step of quark confinement as determined experimentally), such as “biological natural selection”, proper chemical structures [47]: (atoms and molecules) must have been produced long before these first LFs, by a 2nd step of “chemical natural 2 (pre)selection”: but this 2nd step strongly and decisively (VI-3) fES redef . 7 lnEE / SNF depends on 1/ log2 na and values (at rest)
The approximated running coupling constants of GF, that were also “naturally (pre)selected” at a relative short EMF, SNF and WNF can all be represented on the same moment after the (hypothetical) Big-Bang and this graph using the base-10 logarithmic functions “selection” may be consider the 1st step of the “natural selection” process, that can be named the “alpha-beta pGF1 E log 10 Gq 1 E , pGF2 E log 10 Gq 2 E , 11 natural (pre)selection”. In this way, this hypothesis proposes a “natural selection” in three “abc” steps: (Physikalische Zeitschrift, 1929), extracted from Helge a. the selection of the main physical principles and Kragh, “Magic Number: A Partial History of the Fine- adimensional constants compatible with LFs Structure Constant” (DOI 10.1007/s00407-002-0065-7), existence (very close to the Big-Bang moment); Archive for History of Exact Sciences, 2003, v. 57, 395– b. the selection of the atoms and molecules compatible 431. URL1, URL2. with LFs existence; [3] Kragh H. (2015). "On Arthur Eddington's Theory of c. the appearance of the first LFs that evolved by a so- Everything” (freely accessible ArXiv article; submitted called “natural selection” process. on 14 Oct 2015). URL1, URL2. [4] Kritov A. (2013). “A New Large Number Numerical With these previously listed arguments, this paper Coincidences”, Progress in Physics, volume 2, April proposes the unification of evolutionism and creationism in 2013, pages 25–28. URL a monad (a seed-like model of the pre-Big-Bang in which [5] E. Teller (1948). “On the Change of Physical this singularity unpacks and repacks itself periodically, Constants”. Physical Review (April 1948) Vol. 73, Issue generating a universe populated with LFs), as it pushes the 7, page 801. URL1, URL2. three abc-steps of “natural selection” very close to the [6] Salam A. (1970). International Center for Theoretical Physics, Trieste, Preprint IC/70/1906. 41 moment “0” of the Big-Bang when na 10 , [7] Bastin E.W. (1971). “Quantum Theory and Beyond redef . (Essays and Discussions Arising from a Colloquium)” (book). Ted Bastin, ed. Cambridge University Press, 1/ log2 na and pn() values were probably London, page 213. URL. “naturally” (but not necessarily randomly!) selected. In this [8] Sirag S-P. (1980, 1983). “Physical constants as view, may be regarded as predesigned for life cosmological constraints” (Received on November 22, 1980), International Journal of Theoretical Physics, forms to exist. 1983, vol. 22, no. 12, pages 1067–1089. URL1, URL2
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