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The rotating lepton model: Combining fundamental theories

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For decades, physicists have known that their descriptions of the universe’s fundamental building blocks have been incomplete. So far, however, no conclusive theories have emerged to propose more suitable alternatives. Now, Professor Costas Vayenas at the University of Patras in Greece believes that the problem could be solved through the ‘Rotating Lepton Model’ – in which particles named neutrinos rotate at close to the speed of light. By combining the theories of Quantum Mechanics and Special or General Relativity, his theories could prove to transform the way we view the universe on the smallest
of scales.

The Standard Model of particle physics has long provided physicists with a basis for understanding the basic structure of all observable matter in the universe. Among the indivisible particles it describes are quarks – which make up ‘hadrons’ including protons and neutrons; and leptons – which include electrons, and the far more elusive neutrinos.

In addition, the model describes four fundamental forces, which mediate all interactions between observable matter – often via exchanges of particles named ‘bosons.’ These include: gravity, which acts between massive objects; electromagnetism, which regulates interactions between charged particles via photons; the strong nuclear force – which acts between quarks via ‘gluons’; and the weak nuclear force – involving exchanges of ‘W’ and ‘Z bosons’ characteristic of radioactive decay.


So far, the Standard Model has been an excellent basis for researchers to explain their observations, with experimental results rarely deviating far from theoretical calculations. Yet despite its success, physicists have now known for some time that the model in its current form cannot be complete. Among its most glaring discrepancies is the fact that it appears to be incompatible with Einstein’s robust theory of General Relativity. To date, researchers have now conceived a diverse variety of ideas about how the Standard Model could be altered to reproduce this important law. So far, however, their ideas have yet to be proven through real experiments.

Introducing the Rotating Lepton Model

Einstein first published his groundbreaking Special Relativity and General Relativity theories in 1905 and 1915, respectively. The former provided the means to account for the pronounced increase in inertial and gravitational particle mass with particle speed. The latter provided the first long-awaited description of how Newton’s ideas about gravity arose from a more fundamental property: namely, the curvature of spacetime, whose effects can be readily observed on astronomical scales. However, even over a century later, no concrete theories have emerged which unify Relativity with Quantum Mechanics – which describes how the universe behaves on the very smallest of scales, and forms the basis of the Standard Model.

“Yet according to Special Relativity, objects travelling or rotating at extremely high speeds – approaching the speed of light – appear to become dramatically heavier.”

One particularly important consequence for Einstein’s theories is the idea of ‘relativistic mass.’ The phenomenon stems from the universe’s steadfast speed limit – the speed of light – which cannot be surpassed by any particle according to Special Relativity. If any massive object approaches this limit from the point of view of an observer, its mass must increase in relation to its rest mass and velocity. Since photons are completely massless particles, they don’t experience this alteration; but if even the tiniest particle comes very close to this limit within our frame of reference, it could take on the mass of a resting object many orders of magnitude larger.

As Professor Vayenas argues, particles don’t necessarily need to travel through space to experience this effect: instead, they can take on relativistic speeds by spinning at angular velocities very close to the speed of light. In turn, these particles could generate appreciable gravitational fields, allowing them to interact with similarly spinning objects according to the laws of Mechanics and Special Relativity. So far, this idea has barely been considered by physicists – but for Vayenas, it could provide new routes towards the long-awaited unification between Quantum Mechanics and General Relativity.

As a result, Vayenas emphasises in his research that contrary to previous theories, the Standard Model doesn’t need to be expanded in order to achieve this unification. Instead, the number of indivisible particles and forces it describes should be cut down significantly. His ideas have culminated in the ‘Rotating Lepton Model’ (RLM): an elegant theory which Professor Vayenas believes could unite Quantum Mechanics with Special and General Relativity for the first time, through a thorough re-vamp of the Standard Model in its current form. Broadly speaking, the RLM entirely eliminates the need for quarks, and reduces the four fundamental forces down to just two. Such sweeping changes may seem ambitious, but according to Vayenas, they are firmly rooted in existing theories.

Cutting down on fundamental particles

One key aspect of the Standard Model is a family of leptons named ‘neutrinos.’ Since these particles have no charge, along with minuscule masses, they only interact with other forms of matter extremely rarely, and have virtually negligible gravitational fields. Yet as we have seen, Special Relativity states that these objects can appear to become dramatically heavier when travelling or rotating at extremely high speeds. In their research, Vayenas and his colleagues propose that when combined, these two phenomena provide an alternative explanation to the presence of quarks.

As stated by the Standard Model, quarks have the mysterious property of only existing in groups. Baryons, for example, are made up of combinations of three quarks, which cannot be individually isolated under any circumstances. When these particles were first proposed in the 1960s, questions arose as to how they could interact with each other. Since quarks have such minuscule masses and charges, researchers believed they could only interact through the newly proposed strong force. However, Professor Vayenas argues that this is not necessarily the case.

Since gravity is by far the weakest of the four currently proposed fundamental forces, it is only thought to be relevant when describing masses far higher than those of quantum particles. Yet according to Special Relativity, these masses could be reached if quarks did, in fact, consist of neutrinos, rotating at close to the speed of light. With masses vastly higher than their stationary counterparts, groups of these particles could be held together by gravitational forces, making them virtually impossible to isolate.

Widespread implications for physical theories

Leading on from this, Vayenas and his colleagues propose that the RLM can also remove the need for both the strong and weak nuclear forces. Instead, hadrons could be held together by relativistic gravity, with their constituent rapidly spinning neutrinos following the well-established ‘Bohr model.’ Typically, this model describes the quantum properties of the Hydrogen atom. In this case, neutrinos could adopt characteristic circular orbits, with gravity acting as a centripetal force to keep them in place. To explore this idea further, Professor Vayenas’ team has introduced another important quantum effect into their calculations.

“The Rotating Lepton Model (RLM) is an elegant theory which unites Quantum Mechanics with Gravity and Relativity for the first time.”

One of the founding principles of Quantum Mechanics is the idea that any particle – be it a photon, electron, or neutrino, can also be described as a wave: a principle known as ‘wave-particle duality.’ Through decades of cutting-edge theories and experiments, physicists have now identified the wavelengths of specific fundamental particles – named ‘de Broglie’ wavelengths, after the French physicist who first theorised their existence in the 1920s. Ultimately, accounting for the wave-like nature of matter would prove to be the final piece of the puzzle in the team’s goals to unify Quantum Mechanics with Gravity and Relativity.


Through their research, Vayenas and colleagues have now incorporated the de Broglie wavelength equations of electrons and neutrinos into the RLM and the Bohr model – generating some deeply fascinating results. In one study, they found that stable protons and neutrons could be described simply as groups of rapidly-spinning neutrinos – interacting through their mutual gravitational attraction, without any need for a strong nuclear force mediated by theoretical quarks and gluons. Through a further study, they showed that the W bosons which convey the weak nuclear force are not actually elementary particles after all. Instead, they can be described from first principles as rapidly-rotating neutrinos paired either with rapidly-rotating electrons, or their antimatter counterpart – the positron. The only force not accounted for by this description would be the electromagnetic force – leaving the Standard Model with just two fundamental forces.

If this theory is correct, it would cut down the 16 indivisible particles required by the Standard Model down to just five: including three neutrinos, the electron, and the positron. In their latest research, Vayenas and his colleagues have now used the RLM to calculate, without any adjustable parameters, the masses of 15 composite hadrons and bosons – including protons and neutrons: all to within 1% of their experimentally measured values. Their approach has also enabled them to calculate the masses of stationary neutrinos with less than 3% deviations among the values obtained when using the composite masses of different hadrons and bosons – compared with the 20% error margins associated with far more costly experiments.

Overall, the RLM suggests that many of the fundamental phenomena described by the Standard Model are not so fundamental after all. Instead, they exist as combinations of five truly indivisible particles; or, in the case of gluons, may not need to exist at all. Based on the robust results they have gathered so far, Professor Vayenas’ team believes their model now holds the potential to provide long-awaited solutions to the unification of Quantum Mechanics and General Relativity – with no need for novel, as-yet unproven theories. Ultimately, their discoveries could lead to profound changes in the ways that physicists view the fundamental structure of the universe, and how we explore its many remaining mysteries in the future.

How do you hope to gather experimental evidence for your theories in the future?

We plan to expand the experimental evidence for the validity of the RLM in four directions:

  • Expansion of the number, currently 15, of composite particle mass computations via the RLM by including more complex hadrons (e.g. Kaons) and some simple nuclei (e.g. deuteron) and comparing the RLM computed masses with the measured masses.
  • Comparison of the RLM predictions for the three neutrino mass eigenstates with more recent experimental results from Superkamiokande, SNOLAB, DUNE, IceCube and KATRIN.
  • Analysis via the RLM of the published proton-proton (pp) collision data collected at CERN. We are already collaborating with two prominent CERN researchers in this direction. Agreement with the RLM predictions looks quite good.
  • We also plan to compare the RLM computations with the “World data” of positron-electron annihilation, also obtained at CERN.



  • Vayenas, CG Tsousis, D Grigoriou, D (2020). Computation of the masses, energies and internal pressures of hadrons, mesons and bosons via the Rotating Lepton Model, Physica A: Statistical Mechanics and its Applications, 545, 123679.
  • Vayenas, CG Souentie, S Fokas, A (2014). A Bohr-type model of a composite particle using gravity as the attractive force. Physica A: Statistical Mechanics and its Applications, 405, 360–379.
  • Vayenas, CG Fokas, AS Grigoriou, D (2016). On the structure, masses and thermodynamics of the W±bosons. Physica A: Statistical Mechanics and its Applications, 450, 37–48.
  • Vayenas, CG Fokas, AS Grigoriou, D (2017). Catalysis and autocatalysis of chemical synthesis and of hadronization. Applied Catalysis B: Environmental, 203, 582–590.

Research Objectives

Costas Vayenas has research interests in both physical chemistry and gravity and particle physics.


  • General Secretariat of Research and Technology (GSRT) (MIS 467 ΑΡΙΣΤΕΙΑ)
  • European Union (T1EDK-01631)
  • State Scholarships Foundation (ΙΚΥ) (MIS-5033031)
  • European Space Agency (ESA) (4000109578/13/NL/SC:HT-PEM)


The current collaborators of our U of Patras team are Dr Dimitrios Grigoriou and Mr Dionysios Tsousis, supported by Dr Eftychia Martino (computing) and Ms Chryssa Pilisi (technical support).

Other current collaborators: Professor Marek Gazdzicki, Institut für Kernphysik Johann-Wolfgang-Goethe- Universität, Germany, and Professor Szymon Pulawski, University of Silesia, Poland; Professor Yannis Yortsos, USC, USA; Professor E. Aifantis and Mr K. Parisis, Aristotle University of Thessaloniki, Greece.


Costas Vayenas was born in Athens in 1950. He completed his Diploma (NTU, Athens, 1973), and PhD from University of Rochester, 1976. He was Assistant Professor at Yale (1976-77), Associate Professor at MIT (1977-82). He returned voluntarily as Professor to the University of Patras in Greece (1981-present). He is a Member, Academy of Athens, International Member, National Academy of Engineering (NAE), USA, Honorary Professor, Aristotle University of Thessaloniki. He has supervised 41 PhD students, 18 in Academia.

Dimitrios Grigoriou was born in Athens, in 1982. Has a Chemical Engineering degree (UPatras 2006), an MBA (HEC Paris 2012), and a PhD (UPatras 2018). Holds several patents, has published research in catalysis and particle physics, also published two novels. Member of the Technical Chamber of Greece, and of the Triple Nine Society.

Dionysios G. Tsousis was born in Patras in 1998. He is a graduate Chemical Engineer of the University of Patras (Greece), where he achieved the highest ranking in his class. He did his thesis under the supervision of Professor Vayenas, and he has already co-authored two publications. In the fall he is going to join Stanford University for his doctoral studies.

University of Patras
Department of Chemical Engineering
Caratheodory 1, St.
GR-26504 Patras, Greece

E: [email protected]
T: +302610997576

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