Particles and Fields in Physics

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    Gyula Szász

    Particles and Fields in Physics

    At first, there is a list of the different types of particles presented what are found (or believed to exist) in the whole of the universe, according to modern physics:

    “In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles. Known elementary particles include the fundamental fermions (quarks, leptons, antiquarks and antileptons), which generally are “matter particles” and “antimatter particles”, as well as the fundamental bosons (gauche bosons and the Higgs boson), which generally are “force particles” that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.

    Everyday matter is composed of atoms, once presumed to be matter’s elementary particles -atom meaning “unable to cut” in Greek – although the atom’s existence remained controversial until about 1910, as some leading physicists regarded molecules as mathematical illusions, and matter as ultimately composed of energy. Soon, subatomic constituents of the atom were identified. As the 1930s opened, the electron and the proton had been observed, along with the photon, the particle of electromagnetic radiation. At that time, the recent advent of quantum mechanics was radically altering the conception of particles, as a single particle could seemingly span a field as would a wave, a paradox still eluding satisfactory explanation.”

    “All elementary particles are – depending on their spin – either bosons – an ultimate constituent of substance – was mostly discarded for a more practical outlook, embodied in particle physics’ Standard Model, science’s most experimentally successful theory. Many elaborations upon and theories beyond the Standard Model, including the extremely popular supersymmetry, double the number of elementary particles by hypothesizing that each known particle associates with a “shadow” partner far more massive, although all such superpartners remain undiscovered. Meanwhile, an elementary boson mediating graviton – the graviton – remains hypothetical.”

    So long a short summary what modern physics suggest about particles. Many paradoxes remain unsolved. In the last decades, mathematically constructed theories (strings and membranes) appear in very small space-time ranges – in 10^-30 cm regions – as deformations of more dimensional space-time continuums. However, the gravitation – one of the fundamental interaction – could not be incorporated in particles physics.

    The matter is composed of four kinds of stable elementary particles

    I have broken with the modern physics on a most fundamental theoretical level in order to explain the particles found (and believed to exist) in the whole of the universe.

    First of all, I didn’t theoretically assume that the energy is quantized with the Planck constant, h, – according to E = h∙ν – since h play the role of a Lagrange multiplier. Lagrange multipliers occur as consequences of subsidiary conditions for particle numbers conservations at the variation principle of the action integral for the derivation of the equations of motions for the interacting fields and for the stable particles. Furthermore, I didn’t assume the equivalence of energy and mass.

    The interacting fields between the stable particles are non-conservative fields and propagate with a constant velocity c. The velocity c of the fields is independent of the state of the emitting particles. The stable particles have two kinds of conserved charges, qi and gi, which cause simultaneously the two fundamental fields and fix the physical properties of the elementary particles. However, the positions and the velocities of the particles are never known exactly. I notice: no more fundamental assumptions are needed in order to explain the whole universe.

    The physical realization

    The four point-like stable elementary particles are the electron (e), the positron (p), the proton (P) and elton (E). All four elementary particles are experimentally well known, the elton is labeled in particle physics with the name “antiproton”. That means, we are knowing their elementary electric charges, ± e, and their elementary masses, mP and me. Never are decays of these elementary particles observed. No more elementary particles exist as the four particles, e, p, P and E; also photons and quarks don’t exist. Physically, I assumed that the elementary particles appear point-like and are substructure-less in very small relative distances. I could show that the entire known composite particle are greater that 10^-17 cm.

    The elementary particles, e, p, P and E, have only two kinds of conserved physical properties; two kind of conserved charges – the elementary electric charges, qi = {± e}, and the elementary gravitation charges, gi = {± g∙mi}. Since the universal gravitational constant is G = g^2/4∙π, the elementary gravitation charges determine the elementary masses of proton and electron, mP and me. The positron has the same mass as the electron and the elton has the same mass as the proton.

    On this place, I notice that
    – the gravitational and rest inertial masses of the elementary particles e, p, P and E, are the same, because the elementary particles are not composed of other particles,
    – the elementary masses, mP and me, of the elementary particles are not equivalent to energy; the elementary masses can be neither annihilated, nor created.

    The two kind of conserved elementary charges, qi and gi, cause the two kinds of fundamental interactions; the electromagnetism, A(em)ν(x), and the gravitation, A(g)ν(x), in finite ranges of Minkowski space, {x}ε Ω. The Minkowski space connects space and time because the interactions propagate with the constant velocity c. Thus, the gravitation, A(g)ν(x), is a time-dependent field caused by conserved elementary gravitational charges, gi; so the gravitation is incorporated in the particle physics. These fundamental interactions don’t need particles, such as photons or/and gravitons.

    Since neither the exactly positions, nor the exactly velocities of the elementary particles are ever known, the particles have to be described with more component objects in Minkowski space. I proposed the four-component and normalized spinors for the description of elementary particles, i = e,p,P,E, like the Dirac spinors, ψiν(x), with a definite transformation property under Lorentz-transformations. The introductions of spinors have nothing to do with spin ½ of the point-like elementary particles; I don’t use the terms of fermions and bosons.

    The action integral, I, is constructed with a Lorentz-invariant Lagrange density in finite ranges of Minkowski space, Ω. The Lagrange density is set up with the two non-conservative fields, A(em)ν(x) and A(g)ν(x), with the two conserved charges, qi and gi, and with the four spinors ψiν(x) in order to derive the invariant equations of motions for the fields and the particles. The equations of motions of the field are wave equations with the velocity c,

    ∂α∂α A(em)β (x) = + j(em)β (x),

    ∂α∂α A(g)β (x) = – j(g)β (x).
    The electromagnetic and the gravitation waves are caused by the probability current densities, j(em)β (x) and j(g)β (x), of the elementary charges, qi and gi. The probability current densities are constructed with the spinors, ψiν(x).

    On the other side, the equations of particle motions contain, beside the elementary charges, qi and gi, also Lagrange multipliers; the Planck constant, h, is such a Lagrange multiplier. Beside h, there exist also other constants: For instance, the Lagrange multiplier, h0 =h/387, is responsible for the known instable composite particles, for two kinds of neutrons, two kinds of basic neutrinos, the myons, pions, kaons and baryons and self-evident, for the several kinds of nuclei of atoms. Our known nuclei are composite of protons, electrons and positrons; the eltons are apparently not present in the nuclei. Thus, we have variation principles for the calculations of the bound energies of composite particles, E((NP,NE,Ne,Np),bound).

    Simultaneously, I notice that the inertial masses, mi(NP,NE,Ne,Np), of the composite particles can be expressed with the elementary masses, mP and me, with the number of elementary particles Ni and with the bound energy, in the rest system of center of mass (COM),

    mi(NP,NE,Ne,Np) = (NP+NE)∙mP +(Np+Ne)∙me – E((NP,NE,Ne,Np),bound)/c^2.

    Since the gravitational masses of composite particles

    mg(NP,NE,Ne,Np) = |(NP-NE)∙mP +(Np-Ne)∙me|,

    are different from their inertial masses, the Universality of Free Fall (UFF) is violated.

    My efforts lead obviously to an Atomistic Theory of Matter and are opposite to the energetic theory of modern physics.

    The theory is described in

    Gyula I. Szász


    Gyula Szász

    The energetic lowest state of a composite particle is the ground state of a many particle system. That is the case if the inertial mass mi(NP,NE,Ne,Np) is zero. Thus, if

    (NP+NE)∙mP +(Np+Ne)∙me = E((NP,NE,Ne,Np),bound)/c^2.

    The ground state of the hydrogen atom at the bound energy E(H,bound) = 13.8 eV is surely not the ground state of the proton-electron two-particle system.

    Gyula Szász


    Gyula Szász

    Generally, the gravitational masses of composite particles are conserved and the inertial masses are changing. Newton’s equation of motion in gravitation field must be enhanced.


    Gyula Szász

    My efforts, a quantum field theory based on conserved charges of elementary particles, lead obviously to an Atomistic Theory of Matter and are opposite to the energetic theory of modern physics.

    The quantum field theory based on conserved charges is described in

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