Gravitational catalysis of nuclear synthesis from positrons, electrons and neutrinos

Abstract

This article presents a model which describes the catalytic gravitational action between positrons, electrons and ambient neutrinos for the generation of quarks, protons and neutrons, i.e. for the generation of visible matter. This gravitational catalysis model, termed the Rotating Lepton Model (RLM), contains no adjustable parameters and leads to quantitative agreement with the experimental hadron and boson mass values. Thus, the article examines three gravitating neutrinos rotating on a circle around a positron or electron or neutrino and shows that, surprisingly, the three rotating neutrinos reach highly relativistic speeds with a concomitant dramatic relativistic increase in their masses which thus increase from the meV/c² range and reach the mass range of quarks and hadrons, i.e. the GeV/c² range. Using this Rotating Lepton Model (RLM) one finds that the total mass of the rotating neutrino trio equals the mass of a baryon, e.g. of a neutron if the central particle is a neutrino, or of a proton if the central particle is a positron. This simple hadronization mechanism shows the feasibility of electron-positron catalyzed neutrino hadronization which is extremely exothermic and which may have played and continues to play a significant role in the history of our Universe. In this way, positrons and electrons can accelerate ambient neutrinos to super-relativistic speeds, thus causing a very strong increase in their masses which reach those of quarks, and a concomitant dramatic relativistic increase in their gravitational attraction which reaches the value of the Strong Force. Whereas catalysis in chemistry and biology is based on electrostatic forces, in the present case of catalysis in nuclear physics, the neutrino conversion to quarks and hadrons is based on gravitational forces, computed via the brilliant legacy of Newton, Einstein, De Broglie and Bohr.

Introduction

Catalysis and electrocatalysis have been known for almost two centuries¹ to play a dominant role in chemical^1,2, biochemical and biological³ synthesis via electrostatic (Coulombic) interactions between positrons, electrons and neutral chemical species. Here we show that, surprisingly, the “Strong Force”, which keeps nucleons together in nuclei, is Newtonian gravity between fast rotating superrelativistic neutrinos whose masses increase dramatically with speed according to Einstein’s theory of Special Relativity^4,5. Consequently their relativistic masses (γm_o, where γ is the Lorentz factor (1-v²/c²)^−1/2) reach the values of quark masses (~ 1 GeV/c²) and the gravitational attraction between any two of them at a distance d reaches the value of the Strong Force, i.e. (h/2π)c/d²⁶. This value is a factor of 10²⁰ stronger than Newtonian gravity at the same distance and α^-1 (~ 10²) times stronger than the Coulombic attraction of a positron -electron pair again at the same distance. It therefore follows that the Strong Force is the gravitational force between two such rotating super-relativistic particles (each with γ≈10¹⁰, thus relativistic mass γm_o= 0.313 GeV/c² and gravitational mass γ³m_o= 3.13⋅10²⁸ eV/c²). This force is also a factor of 10¹⁰ stronger than the force between an electron and a fast neutrino rotating around it, which corresponds to the Weak Force⁷. It thus follows that the “Weak nuclear Force” can be viewed as gravity between super-relativistic neutrinos and positrons or electrons, showing that gravity and electromagnetism are the only forces in our Universe.

On the other hand, close examination of the Tables of particle decays⁸ reveals that, surprisingly, the eventual products of all composite particle decays are only five, i.e., the positron (e⁺), the electron (e^-) and the three neutrino types⁶, i.e. type 1 (denoted ν₁, of mass m₁), type 2 (denoted ν₂, of mass m₂) and type 3 (denoted ν₃, of mass m₃)⁹. According to the principle of Microscopic Reversibility¹¹ this implies that all other particles can be synthesized via appropriate combinations of the above five elementary particles, i.e. e⁺, e^-, ν₁, ν₂ and ν₃. Due to their extremely light rest masses (~ 1–5 meV/c²) neutrinos can be easily accelerated gravitationally by adjacent electrons or positrons to highly relativistic speeds with Lorentz factor γ values of the order of 10¹¹, thus reaching relativistic masses, γm_o, of the order of quark masses (~ 1GeV/c² ) and gravitational masses, γ³m_o, of the order of 10¹⁹ GeV/c², which is sufficient to cause neutrino hadronization, also known as baryogenesis, i.e. the formation of protons, neutrons and other hadrons from neutrinos. Consequently, positrons and electrons can act as gravitational catalysts for hadronization, i.e. for the production of hadrons from ambient neutrinos.

Hadronization and baryosynthesis

The question thus arises on how nature could build from these five particles (e⁺, e⁻, ν₁, ν₂, ν₃) the incredibly complex and fascinating environment in which we live. In particular it is difficult to understand how these five particles have combined to form atoms, molecules, cells and, at the end, living organisms who can think. This question becomes more intriguing upon recalling that, at least macroscopically, there exist only two types of forces: (i) gravitational, governed by Newton’s Law:

1

where and are the gravitational masses of components 1 and 2 and (ii) electrostatic forces governed by Coulomb’s Law:

2

While electrostatic (Coulombic) forces are known to be sufficient for the synthesis and transformation of chemical compounds using e⁺ and e⁻ electrocatalysts, on the contrary, gravitational forces (which are commonly thought to be extremely weaker) do not seem (at a first glance) capable of forming anything useful from positrons, electrons and neutrinos. However the formation of hadrons from neutrinos has been already proposed and discussed¹⁰.

Such a composite particle formation is theorized in the Standard Model to occur via the Strong Force, which is mediated by gluons⁶. Such particles have never been isolated and studied experimentally and thus are not a useful option for the unambiguous description of hadron formation.

Therefore it appears, at a first glance, (Fig. 1) that there is nothing which can bridge the mass gap between neutrinos and quarks or hadrons and thus can describe the formation of protons, neutrons and other hadrons out of, say, neutrinos, which are the only available option⁸, particularly since the masses of neutrinos are ten orders of magnitude smaller than those of hadrons.

The central role of special relativity and quantum mechanics

The solution to this mass gap problem is provided by Einstein’s Special Relativity (SR), coupled with Bohr’s simple quantum mechanics (QM). The answer is simple and straightforward^4,5: It is the simple combination of QM and SR which describes hadronization in a simple and direct manner: The relativistic masses (m_r) and gravitational masses (m_g) of particles, such as neutrinos, approaching the speed of light c, increase dramatically with speed according to:

3

where m_o is the rest mass of the particle, and

4

is the Lorentz factor, which approaches infinity as the particle speed v approaches the speed of light c. Thus, if neutrinos can, due to their miniscule rest mass, be accelerated to speeds v, approaching c, then the neutrino mass will increase dramatically from the meV/c² range to the MeV/c² range, thus creating “quarks” and baryons (Fig. 1).

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Fig. 1

The marvel of catalytic neutrino hadronization via special relativity: Rest masses (m₁, m₂ & m₃)⁸ and relativistic masses (γ₁m₁, γ₂m₂ and γ₃m₃) of the three neutrinos ν₁, ν₂ and ν₃ compared with the masses of protons (p) and neutrons (n) and with the masses of quarks (u, d, c, s, t and b)^6,8. The γ₃ Lorentz factor expression shown in the figure follows directly from Eq. (7). Note how these huge (~ 10¹⁰) γ_i values bring the corresponding neutrino masses from the rest neutrino mass range (~ meV/c²) to the relativistic neutrino mass range (~ GeV/c²) which is in the quarks and baryons rest mass range. It is also worth noting that protons and neutrons are formed from the heaviest neutrinos ν₃ of rest mass m₃ via the action of special relativity. The lightest neutrinos, ν₁, have a mass which is 4π² times smaller than the ν₃ neutrinos and, as recently shown¹², play a central role in light transmission, since their mass, m₁, defines the speed of light, c, via the Newton-Laplace equation¹³; T_cmb: Cosmic background radiation temperature (2.725 K).

Such highly relativistic speeds can be easily reached and sustained when neutrinos are caught in gravitationally confined relativistic circular orbits (Fig. 1). This is apparently the simple mechanism developed by nature to generate mass¹⁴ as demonstrated in Fig. 1, which depicts how gravity increases the neutrino speeds, thus increasing via Eqs. (3) and (4) the neutrino masses by a factor of roughly 10¹⁰ from the rest mass values (in the meV/c² range) to the relativistic mass values (in the GeV/c² range). In this way the mass values of hadrons and quarks, which are relativistic neutrinos^7,14, are reached.

In a recent Springer Nature book⁷ and in several recent publications^{14, 15–16} the mechanism of this violently exothermic formation of hadrons (e.g. neutrons and protons) from ambient neutrinos and electron/positron gravitational catalysts has been presented for the first time in the context of the Rotating Lepton Model (RLM)⁷. This very important hadronization reaction is apparently closely related to the Big Bang itself¹⁷ and to the “Little Bang hadrosynthesis”¹⁸, which produces hadrons or bosons from ambient neutrinos. This has been recently demonstrated nicely by the CERN experiments^{19, 20–21} in which positron – electron beams have been fed into a “vacuum system” which unavoidably is filled with neutrinos. This results in a very pronounced production of Z bosons²¹ (Fig. 2), which have been recently shown via the RLM to comprise rotating positron -electron-neutrino triads²². Thus the mass of the Z boson has been computed via the RLM to equal 91.72 GeV/c²²² which differs less than 1% from the experimental value of 91.19 GeV/c²⁸.

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Fig. 2

Positron-electron annihilation products observed at CERN²¹.

The Rotating Lepton Model (RLM)

In general the Rotating Lepton Model (RLM) considers the circular motion of three gravitating leptons (e.g. neutrinos) and uses special relativity to express the relativistic (γm_o) and the inertial thus gravitational mass (γ³m_o) of the rotating neutrinos of rest mass m_o on a circle of radius r due to their gravitational attraction by the two other symmetrically rotating neutrinos. It also utilizes Newton’s gravitational law in terms of the relativistic particle masses i.e.,

5

This SR based equation establishes the relationship between particle speed v(or γ) and rotational radius r.

A second, quantum mechanics based, equation relating γ and r is established by the de Broglie equation of quantum mechanics which dictates that:

6

where n is an integer.

Upon combining Eqs. (1), (3), (4), (5) and (6) and recalling the definition of the Planck mass, m_Pl, from m_Pl=(ηc/G)^1/2, one derives the following expressions for the neutron mass m_n:

7

where is the Planck mass.

For the m₃ neutrino mass value

8

which is the heaviest neutrino mass^7,9, Eq. (7) gives:

9

which is in excellent agreement with the experimental neutron mass value⁸. This model is known as the Rotating Lepton Model (RLM) of composite particles^{7,12,14, 15–16,22, 23–24}.

By applying the same RLM approach to compute the masses of all other simple hadrons and bosons one obtains Figs. 3 and 4⁷.

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Fig. 3

Compositions, structures and masses of composite particles computed via the RLM (compared with the experimental ones) of Baryons (n, p), Mesons (µ^±, π^±, Κ^±), Βosons (W^±, Z^o, Higgs) and the Deuteron Nucleus (d) created by the five leptonic building blocks, which serve either as reactants (ν₁, ν₂, ν₃) or as catalysts (e⁺, e⁻) for composite particles synthesis. Particle volumes are drawn proportionally to their masses^{6,7,16,22, 23–24}.

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Fig. 4

Comparison of the RLM computed masses of composite particles with the experimental values⁶. Agreement is better than 2% without any adjustable parameters. The three approximate mass expressions shown in the Figure provide the order of magnitude of hadron and boson masses¹⁶.

One observes the very good agreement, typically within 1%, between the RLM and the experimental data⁸ which becomes more impressive by recalling that, as Eqs. (3), (4) and (5) show, the RLM does not contain any adjustable parameters⁷.

The question then arises about how the three neutrinos of a proton or a neutron have reached such amazingly high speeds.

The answer can be provided by considering a gravitationally confined rotating positron (or electron) – neutrino pair.

If we consider a rotating ring comprising one or more neutrinos together with one or more electrons/positrons, then the requirement for equal angular momenta of all rotating particles leads to , thus the ratio

10

becomes enormous, i.e. equal to for ν₁ neutrinos, 7.35⋅10⁷ for ν₂ neutrinos and 1.17⋅10⁷ for ν₃ neutrinos. If we consider such a rotating e — ν ring as a possible candidate for the W^± boson structure, then its relativistic mass should equal the observed experimental boson mass, i.e. thus,

11

Consequently, for , the corresponding , and Lorentz factor values for the three neutrinos are:

12

These very large γ_i values imply the onset of hadronization via formation of neutrons and protons. The corresponding gravitational masses, i.e. exceed the Planck mass by more than seven orders of magnitude. This amazing result implies that the gravitational force between such relativistic neutrinos at a distance d can reach or even exceed the strong force value of .

One may thus observe (Fig. 5) that such rotating positron (or electron) -neutrino rings, which correspond to W^± bosons, can act as neutrino catapults in that, upon decomposition, they generate extremely active neutrinos suitable for hadronization, i.e. for the formation of hadrons, such as neutrons and protons.

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Fig. 5

The catalytic mechanism of hadronization (or baryogenesis) leading to the formation of a proton or neutron: When a neutrino meets an electron (a) then the huge (by neutrino standards) electron mass accelerates gravitationally the neutrino to highly relativistic speeds and thus a W⁻ boson (which is a rotating ν-e^± pair) is formed. (b) where, according to Einstein’s special relativity (SR) its mass increases dramatically and reaches the quarks (q) mass range. (c) three such fast rotating quarks (i.e. relativistic neutrinos) form a proton; (d) if the positron leaves, then a neutron is formed.

Conclusions

In brief, the success of the RLM summarized in Figs. 3 and 4 shows that:

1. There exist only five elementary (undividable) particles, i.e. positrons, electrons and the three neutrinos^{7,14, 15–16}.

2. Hadrons consist of rotating gravitating relativistic neutrinos (named quarks) arranged in circular orbits^{7,14, 15–16}.

3. Bosons comprise a rotating relativistic neutrino ring which additionally contains a positron or an electron^{22, 23–24}.

4. The Weak Force is the gravitational force between electrons or positrons and highly relativistic neutrinos^{7,14, 15–16}, which initiates the catalytic cycle of hadronization.

5. The Strong Force is the gravitational force between highly relativistic neutrinos^7,8 which completes the catalytic cycle of hadronization.

6. Positrons and electrons (due to their huge relative to neutrino masses) act as “gravitational catalysts” and cause neutrino hadronization, thus forming quarks and hadrons.

7. The role of positrons and electrons in baryosynthesis (due to gravity and their large masses) is as important as their role in chemical synthesis (due to electrostatics and their charge). The above analysis implies that all composite particles can be synthesized from the omnipresent neutrinos via the catalytic action of positrons and electrons.

8. The Rotating Lepton Model (RLM) of elementary particles, is a generalization of the Bohr model of the H atom which, by combining Newtonian Mechanics, Quantum Mechanics and Special Relativity, provides a satisfactory and accurate description of the composite particles (baryons, bosons) of our Universe using the heaviest (ν₃) neutrino type.

9. Similar conclusions regarding the ultrarelativistic behavior of gravity can be reached by the use of General Relativity as discussed in References^25,26 and²⁷. Interestingly, in reference²⁵ Einstein’s field equations are solved in the first post-Minkowskian approximation in the ultrarelativistic limit. Similarly to the present special relativistic approach, it is found that the gravitational attraction between two such relativistic particles can describe the Strong Force.

10. The lightest neutrino type (ν₁) has also a significant role in our Universe, as it mediates the transmission of light, and thus determines via its mass m₁, the speed of light, c in “vacuum” which, of course, always contains billions of neutrinos per cm³. Therefore, while sound is transmitted via molecular vibrations, visible “light” is transmitted via the vibrations of the lightest neutrino¹² of mass m₁ = m₃/4π² with a speed of v_W=(5k_bT/m₁)^1/2 = c.

All the above conclusions result from the simple combination of well-known catalytic principles, classical and quantum mechanics and special relativity.

Acknowledgements

This research has been co-financed by the Foundation for Education and European Culture (IPEP) and by the A.G. Leventis Foundation.

Author contributions

C.V. and D.T. conceived the main idea and wrote the manuscript. E.M. prepared Figs. 1, 2, 3, 4 and 5 and participated in all scientific discussions. All authors reviewed the manuscript.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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