New Basics in Physics

[Gyula Szász]

New Basics in Physics as a Memorandum

The Memorandum is addressed on each particle physicist and on each astrophysicist worldwide and on journals such as Phys. Rev., European Journal of Physics, ZNA, and Foundation of Physics who has rejected the New Basics of Physics. The rejections were founded because the editors did not found the papers suitable for publication invoking very tough standards based on SR, GR and QT. The memorandum is putted in the forum Gravitation in http://www.atomsz.com as thread New Basics in Physics.

New Fundamental Principles in Physics are formulated in a paper in which it is shown that the currently accepted principles of the relativity theories, SR and GR, and of the quantum theories (QT) have physically invalid basics. These were only scientifically conventions; however, they are physically unusable for the creation of comprehensive physical theories. Generally, the energetic physics is unsuitable for physical theories and must be replaced by the Atomistic Theory of Matter.

The basic postulates in physics are, see the article “Fundamental Principle in Physics”.

1. The continuous interaction field is always propagating in empty space with a definite velocity c and it is independent of the state of motion of the interacting body. Or: The speed of interaction in free space has a constant value c and it is independent of the motion of the sources. (Invariance of Interaction)
2. The sources of the interaction field are quantized with conserved elementary charges. The sources of the interacting field are the stable elementary particles. (Principle of Quantization).
3. All physical systems are to be described in finite range of space-time and neither the positions, nor the velocities of particles can be ever observed exactly. (Principle of Uncertainty)

The continuous interacting field is the addition of the time-dependent electromagnetic field, A(em)ν (x), and the time-dependent gravitational field, A(g)ν (x), in a finite range of the Minkowski space, {x}ε Ω. These fields are non-conservative fields in presence of charges and they propagate with c.

The quantized sources of the fields are the elementary electric charges, qi = {-e, +e, +e, -e}, and elementary gravitational charges, qi = {- g∙me, +g∙me, ++g∙mP, -g∙mP}, in the sequence of the electron (e), positron (p), proton (P) and elton (E), The name elton is one other label for the fourth elementary particle, instead of “antiproton”. The masses me and mP are the elementary masses of the electron and the proton. The universality of gravitations is embodied in the fact that all elementary particles have the same specific gravitational charges; that means the universal gravitational constant G is G = g^2/4π. The elementary particles e, p, P and E have two conserved charges, qi and qi. They are stable particles and they are the quantized sources of the interaction fields. Natural, the particles e, p, P and E can never annihilated or created and natural, their masses multiplied with c^2, me∙c^2 and mP∙c^2 are not equivalent of energies.
The static force equations between two elementary charges
F(Coulomb)(rij) = + qi∙qj∙rij/4∙π∙rij^3 and

F(Newton)(rij) = – gi∙gj∙rij/4∙π∙rij^3,
distinguish formal only on the signs. However, the difference of the strength of the forces is enormous, e^2/(g∙mP)^2 ≈ 10^42. The different signs between the electromagnetic and the gravitational forces appear also in the equation of motions of the fields

∂α ∂αA(em)β (x) = + j(em)β (x),
∂α ∂αA(g)β (x) = – j(g)β (x).

The first equation is known as the Maxwell equation; the second equation is new and is derived within the Atomistic Theory of Matter on basics of the new physical basic postulates from a Lorentz-invariant Lagrange density. Both fields must fulfill its own subsidiary condition

∂β A(em)β (x) = 0, respectively ∂β A(g)β (x) = 0.

Also the “particle fields” must fulfill subsidiary conditions expressed by the conserved particle number currents

∂β ji(n)β (x) = 0, i = e, p, P, E.

The main mistake of the current energetic physics is that the scientists did not distinguish between the physical meaning of the continuous fields A(em)ν (x) and A(g)ν (x) and the probability current densities of charges

ji(em)β (x) = qi∙ji(n)β (x) and ji(g)β (x) = gi∙ji(n)β (x).

I would say the scientists did not reconcile the Maxwell equation with the quantized electric charges. It is an enormous difference between a continuous function, such as the fields, and probability current densities of elementary particles carrying quantized charges qi and gi. Even if the differentiability of the functions describing the probability current densities is always assumed, the particles described with the probability densities are still discrete objects. The Noether-theorem as the connections of the conserved charges and the space-time symmetry carries also this mistake. The so called Noether-charges

gi = ∫R^3 ji(em)0(r,t) d^3r and gi = ∫R^3 ji(g)0(r,t) d^3r, i=e,p,P,E,

are not Lorentz scalars, as some times argued, but they are really invariant charges. The charges cannot be defined for instance by a scalar product of two vectors of the Minkowski space. The quantized elementary charges, qi and gi, which generate the fields, A(em)ν (x) and A(g)ν (x), are another kind of invariants, as the invariants which can be constructed by spinors, vectors and tensors of the Minkowski space. The generalizations of the Noether-theorem as used in the current particle physics for symmetry considerations and conservation laws, for instance for energy, impulse and angular momentum, must be taken on a justified revision. For instance the invariant construction of Lagrange density with the fields, A(em)ν (x) and A(g)ν (x), and probability current densities, ji(em)β (x) and ji(g)β (x) – in order to derive the covariant equations of motions for the fields and for the particles – is not covered by the Noether-theorem. Even if the positions and velocities of particles cannot be measured ever exactly (Principle of Uncertainty) and they must be described with probability densities, the stable particles are still discrete objects.
It should be also noticed that with the elementary masses me and mP as well the gravitational masses, mg, as the inertial masses, mi, of each particle systems can be expressed

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

with the help of the particle numbers Ni, i=e,p,P,E and the inertial masses, with the bound energies E(bound) divided by c2. The energies E(bound) are radiated at the bound of particles. Both kinds of masses are different and they are always greater or equal zero. Therefore, for instance the Newtonian equation of motion in the gravitational field must be enhanced

mi(body)∙a(body) = – G∙M(Body)∙m(body)/r^2.

The acceleration a(body) depends on the composition of the body
a(body) = a0∙mg(body)/mi(body) = a0∙(1 + Δ(body)),
with the mass defect – 0.109% (hydrogen) < Δ(body) < 0.7084% (56Fe isotope).
Newton, Euler and Lagrange did not account with gravitational charges of two signs.
In two-particle-systems, the electron-neutrino (e,p) and proton-neutrino (P;E) have the gravitational and inertial masses zero and they are 0.703∙10^-8 cm, respectably 0.383∙10^-12 cm large. Also the proton-electron system (P,e), generally known as hydrogen atom, could also have an inertial mass zero if E(bound) = (mP +me)∙c^2, In this case the bound system is 0.382∙10^-12 cm large. The size of the stable neutron N0 = (P,e) has a size of 0.382∙10^-12 cm. The sizes of the possible two-particle systems confirm that the particles (e,p) and (P,E) are not annihilated at their physical merging.
The physics according to the three basic postulates is also a quantum theory, however, only the sources of the fields are quantized by the stable elementary particles. The quantization procedure according to Max Planck and Albert Einstein with the Planck constant h had no physical sense. The Planck constant is connected to Lagrange Multipliers appearing in the equations of motions of the particles in course of subsidiary conditions caused by conserved particle numbers, respectively by conserved charges. The electromagnetic and gravitational fields, the interactions, are not quantized. Also further Lagrange Multipliers appear in particle processes, for instance the h0 = h/387 which is responsible for the occurrence of the neutrinos νe = (e,p) and νP = (P,E).

Summary with conclusion

The particle physics deal with four stable particles e, p, p and E in finite ranges of the Minkowski space. The currently used Standard Model of Particle Physics which consider a confused list of particles https://en.wikipedia.org/wiki/List_of_particles
is not based on physical valid postulates. Also the list of so called elementary particles https://en.wikipedia.org/wiki/Elementary_particle
is not valid because the quark-substructure of the elementary particles e, p, p and E is invalid. Also the Higgs-boson is not needed to explain the masses of particles. Furthermore, the interactions are not quantized and there are not more interactions needed as the electromagnetic and the gravitational interactions.

The currently used Standard Model of Astrophysics which is based on Einstein’s field equation with the deformation of space-time around masses was also a physical invalid trial. The gravitational field is caused by conserved gravitational charges, gi, Such implications of the Standard Model of Astrophysics as the Big Band, Black Holes, Dark Matter, the accelerated expansion of the Universe lack any physical basis. However, in the Universe there are galaxies which attract and which repel each other. The whole Universe can be most probably described only with five natural constants, c, e, me, mP and G=g^2/4π. The gravitation is experimentally found not to be such simple as the current theories say

Unfortunately the upper and lower indexes are not transmitted by the text editor.

Gyula I. Szász

[Gyula Szász]

Enhanced version

New Basics of Physics; a Memorandum

The Memorandum is addressed on each researcher in physics, on each particle physicist and on each astrophysicist worldwide, and on the physical journals, Phys. Rev., European Journal of Physics, ZNA, and Foundation of Physics, who have rejected the New Basics of Physics. The rejections were founded because the editors did not found my submitted papers suitable for publication violating very tough standards based on SR, GR and QT.
The memorandum is putted in http://www.atomsz.com, in the forum Gravitation as a thread New Basics in Physics.

The Fundamental Principles in Physics is formulated in my basis paper in which it is shown that the currently accepted principles of the relativity theories, SR and GR, and of the quantum theories (QT) have physically invalid basics. These theories are only scientifically conventions; however, they are physically unusable for the creation of comprehensive physical theories. Generally, the energetic physics is unsuitable for physical theories and must be replaced by the scientifically more appropriate Atomistic Theory of Matter.
The Basic Postulates of Physics are, see my article “Fundamental Principle in Physics”,

1. The continuous interaction field is always propagating in empty space with a definite velocity c and it is independent of the state of motion of the interacting body. Or: The speed of interaction in free space has a constant value c and it is independent of the motion of the sources. (Invariance of Interaction)
2. The sources of the interaction field are quantized with conserved elementary charges. The sources of the interacting field are the stable elementary particles. (Principle of Quantization).
3. All physical systems are to be described in finite range of space-time and neither the positions, nor the velocities of particles can be ever observed exactly. (Principle of Uncertainty)

The continuous interacting field is the addition of the time-dependent electromagnetic field, A(em)ν(x), and the time-dependent gravitational field, A(g)ν(x), in a finite range of the Minkowski space, {x}ε Ω. These fields are non-conservative fields in presence of charges and they propagate with c. The elementary particles are to be described with probability densities.

The quantized sources of the fields are the elementary electric charges, qi = {- e, + e, + e, – e}, and elementary gravitational charges, gi = {- g∙me, + g∙me, + g∙mP, – g∙mP}, in the sequence of the electron (e), positron (p), proton (P) and elton (E), The name elton is another label for the fourth elementary particle, instead of the name “antiproton”. The masses me and mP are the elementary masses of the electron and the proton. The universality of gravitations is embodied in the fact that all elementary particles have the same specific gravitational charges, g; that means the universal gravitational constant G is G = g^2/4π. The elementary particles e, p, P and E have two conserved charges, qi and gi. They are stable particles and are the quantized sources of the interaction fields. The particles e, p, P and E can never be annihilated or created and of course, their masses multiplied with c^2, me∙c^2 and mP∙c^2, are not equivalent to energies.

The static force equations between two elementary charges are known

F(Coulomb)(rij) = + qi∙qj∙rij/4∙π∙rij^3 and
F(Newton)(rij) = – gi∙gj∙rij/4∙π∙rij^3.

They distinguish formally only by the signs. However, the difference of the strength of the forces is enormous; it is e^2/(g∙mP)^2 ≈ 10^42. The difference of the signs of the electromagnetic and the gravitational static forces appear also in the equations of the field motions

∂α ∂αA(em)β(x) = + j(em)β(x),
∂α ∂αA(g)β(x) = – j(g)β(x).

The first equation is known as the Maxwell equation; the second equation is new; it is derived within the Atomistic Theory of Matter on the basics of the new physical basic postulates from a Lorentz-invariant Lagrange density. Both fields must fulfill its own subsidiary condition

∂β A(em)β(x) = 0, respectively ∂β A(g)β(x) = 0.

These subsidiary conditions accomplish that the fields propagate with the constant velocity c. Also the “particle fields” must fulfill subsidiary conditions; they are expressed by the continuity equations of the conserved particle number currents

∂β ji(n)β(x) = 0, i = e, p, P, E.

The main scientifically mistake of the current energetic physics is that the researchers did not distinguish between the physical meaning of the continuous fields, A(em)ν(x) and A(g)ν(x), and the probability current densities of charges

ji(em)β(x) = qi∙ji(n)β(x) and ji(g)β(x) = gi∙ji(n)β(x) , i = e, p, P, E.

The researchers did never really reconcile the Maxwell equation with the quantized electric charges. There is a big scientifically difference between continuous functions, such as the fields, A(em)ν(x) and A(g)ν(x), and probability current densities, ji(n)β(x), describing the elementary particles carrying quantized charges, qi and gi. Since the positions and velocities of particles can never be exactly observed (Principle of Uncertainty), the particles must be always described with probability densities as continuous functions of space and time, but the stable particles are still discrete tiny objects. The Noether-theorem – connecting conserved charges and space-time symmetry – carries also this mistake. The so called Noether-charges

qi = ∫V ji(em)0(r,t) d3r and
gi = ∫V ji(g)0(r,t) d3r, i=e,p,P,E,

integrated about a small volume V, are not Lorentz scalars, as some times argued, but they are really invariant quantities. However, these invariant charges cannot be defined for instance by scalar products of two vectors of Minkowski space. The quantized elementary charges, qi and gi, which generate the fields, A(em)ν(x) and A(g)ν(x), are another kind of invariants as the invariants which can be constructed by spinors, vectors and tensors in Minkowski space. A special case occurs with the invariant gravitational charges, gi. Since the universality of gravitation means that the special gravitational charge, g, is the same for all elementary particles, the elementary masses me and mP can also be considered also as invariants. The generalizations of the Noether-theorem – used in the current particle physics theories for symmetry considerations and conservation laws, for instance for energy, impulse and angular momentum conservation – must be taken under a legitimate revision. The invariant construction of the Lagrange density with the fields, A(em)ν(x), A(g)ν(x), with the probability current densities, ji(em)β(x) and ji(g)β(x), and with mi and c – to derive the covariant equations of motions for the fields and for the particles – is not covered by the Noether-theorem.

It should be also noticed that with the elementary masses me and mP can be expressed as well the gravitational masses, mg, as the inertial masses, mi, of each particle systems. From the static force follow the gravitational masses

mg = |(NP – NE)∙mP + (Np – Ne)∙me|.

The gravitational interaction between two particles contains always a product of two gravitational masses. The inertial masses are resulting from the action integral, see later,

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

Ni are the particle numbers for i=e,p,P,E. The inertial masses contain additionally the bound energies of the particle systems, E(bound), divided by c^2. The energies E(bound) are radiated from the bound particles. The Mach’s principle that the inertia of bodies depends on the whole mass of the Universe is obviously invalid. The two masses, mg and mi, are always greater or equal zero; however, and they are generally different. Therefore, the more that 300 year old Newtonian equation of motion of bodies in the gravitational field must be enhanced

mi(body) ∙ a(body) = – G∙M(Body) ∙ m(body)/r^2.

The accelerations of bodies, a(body), depend on the composition

a(body) = a0∙mg(body)/mi(body) = a0∙(1 + Δ(body)),

through the mass defect Δ(body). The mass defects are phenomenological known for each isotope, Δ(isotope); it can be calculated from the experimentally known inertial masses of isotopes, mi(isotope), and the associated gravitational masses, mg(isotope), to be

– 0.109% (hydrogen) < Δ(body) < 0.784% (56Fe-isotope).

With a knowledge of the isotope compositions of bodies and with Δ(isotope) the mass defect, Δ(body), can be sufficiently accurate calculated for each body. It follows that the hypothesis of Galileo about the Universality of Free Fall (UFF) with the assumption

a(body) = a0 = constant,

for each body is obviously physical invalid. The planets Uranus and Mars offer already violations of the UFF, since the difference of their R^3/T^2-values is 0.15%. Newton, Euler and Lagrange have not recognized and could not count with gravitational charges of two signs. They belief that the gravitation is a universal mass attraction and have calculated with the equality of the gravitational and the inertial masses, mg = mi which are obviously invalid.

Now, we shall consider two-particle-systems. Within two-particle-systems, the electron-neutrino, νe = (e,p), and proton-neutrino, νP = (P,E), have the gravitational masses and inertial masses zero; this is the appropriate definition of the neutrinos. The sizes of the neutrinos are 0.703∙10^-13 cm, respectively 0.383∙10^-16 cm. The proton-electron two-particle-system, (P,e), generally known as hydrogen atom, could also have the inertial mass zero, if it is E(bound) = (mP +me)∙c^2. In this case, the bound (P,e)-system is 0.382∙10-16cm large. The (P,e)-system can also build a stable neutron N0 = (P,e) at the energy E(bound) = 2.04 MeV. The size of N0 is 0.702∙10^-13 cm. Since νe = (e,p) and N0 = (P,e) have almost the same size, we conclude that the nuclei on the Earth, with sizes somewhat greater than 10^-13cm, are composed of protons, electrons and positrons. The neutron is obviously not elementary particle. The sizes of νe = (e,p) and νP = (P,E) confirm that the two particles (e,p) and (P,E) are not annihilated at their physical merging; that is in opposition to the assumptions what the Standard Model of Particle Physics currently uses, based on the equivalence principle of energy and mass, E = m∙c2.

The masses of bodies are non-equivalent to the energy. Form a particle system with the mass
m = (NP + NE)∙mP + (Ne + Np)∙me,
the energy E = m∙c^2 can be only gained if, and only if, the particle system had before a bound state with the energy
E(bound) = ((NP + NE)∙mP + (Ne + Np)∙me)∙c^2
The particle system exists completely also in such a bound state. From vacuum can never gained energy and vacuum is not the fluctuation of virtual particle-antiparticle pairs. Virtual particles do not exist in Nature.

The physics according to the three Basic Postulates is also a quantum field theory. However, only the sources of the interacting fields are quantized by the four kinds of stable elementary particles. Thus, this quantum field theory is an Atomistic Theory of Matter based on e, p, P, and E. Moreover, since the sizes of all microscopic objects are much smaller than the wavelengths of their electromagnetic radiations, their light emissions are continuous wave processes with continuous submission of energies and not corpuscular phenomena. The quantization procedure of the electromagnetic field and the energy, according to Max Planck, Albert Einstein and Niels Bohr, with the Planck constant, h, makes physically no sense.

The Planck constant, h, is connected to Lagrange Multipliers appearing in the equations of motions of the particles due to subsidiary conditions caused by conserved particle numbers, respectively caused by conserved charges. The field equations of the electromagnetic and gravitational fields, the interactions, are not quantized. However, several Lagrange Multipliers, λj, appear in particle processes. The Lagrange Multipliers with the additional conditions that the particle systems in the mutual interactions are temporary stationary lead to different bound states, with different bound energies E(bound). For such Lagrange Multipliers, h, a phenomenological relation is known since Sommerfeld for the hydrogen atom

h = e^2 /2c ⋅ (m‘⋅c^2 /2⋅E(bound))^1/2 = e^2 /2c ⋅ 1/ α .

This relation connects the reduced mass,
m‘=me∙mP/(me + mP),
and the bound energy, E(bound), to the values of h with the invariants, e and c.
α = (2⋅E(bound) / m’⋅c^2 )^1/2 is considered as the relative velocity of particles, v/c, in the bound state in relation to c. In case of the hydrogen atom with the bound energy E(bound) = 13.8 eV we get for h the value of the Planck constant h and for α the value of α = 1/137.036. Up to nowadays, the quantum physicists do not know why α has this value. In the case of the electron-neutrino, νe = (e,p), with the bound energy E(bound) = 2∙me∙c^2 we get another value for the Lagrange Multiplier, h0 = h/387. h0 is responsible for the occurrences of both neutrinos νe = (e,p), νP = (P,E), and of the stable neutron N0 = (P,e). At the nuclei, h0 is responsible for all the physical processes and not the Planck constant, h. The instable neutron N is composed on four particles, N = (P,e,p,e).

Additionally, another phenomenological relation is also known for the radius of bound states

r(bound) = h^2/(4∙π^2∙m’∙e^2).

This relation dependents on the reduced mass, m’, and on h beside on the invariant elementary electric charge, e, and allows the calculation of the size of the bound states.

We can also calculate as well the sizes, r(bound), as the relative velocities of particles,

(v/c)/(1 – (v/c)^2)^1/2 = (2⋅E(bound) / m’⋅c^2)^1/2,

with the reduced mass m’ and with the bound energy E(bound) for each bound state of two-particle systems, it does not matter how great the bound energy, E(bound), is compared with m’.
For the calculation of E(bound) we have a variation principle containing Lagrange Multiplier, h, in the mutual interaction of particles. The bound states are characterized by the fact that no radiations and no particles currents occur from the bound states; that means within the bound states, the particle number densities are time independent and the particle number currents vanish.

The action integral

I = ∫Ω L(x) d^4x,

integrated over a finite range of Minkowski space Ω, is constructed with a Lorentz-invariant Lagrange-density,

L(x) = L(A(em)ν(x), ∂βA(em)ν(x),A(g)ν(x), ∂βA(g)ν(x),ji(n)ν(x), ∂βji(n)ν(x),qi,gi,mi,c), i = e,p,P,E.

The Lagrange-density can also be expressed instead of the invariant constants, qi, gi, mi, and c, with the five natural constants, c, e, me, mp and g = (4∙π∙G)1/2, since qi, = {±e}, gi = {±g∙mi},

L(x) = L(A(em)ν(x), ∂βA(em)ν(x),A(g)ν(x), ∂βA(g)ν(x),ji(n)ν(x), ∂βji(n)ν(x),mP,me,g,e,c).

However, it should be noticed that during the fields, A(em)ν(x) and A(g)ν(x), are continuous functions of x, the ji(n)β(x) are x dependent probability density currents of the particles.

According to the continuity equations of the particles with particle numbers conservations

∂β ji(n)β(x) = 0, i = e, p, P, E

the subsidiary conditions

Gi = ∫Ω ∂β ji(n)β(x) d^4x = 0,

must be take into account at the variation of the action integral I, in order to derive the equations of particles motions. That means, the Lagrange Multipliers, λj, shall appear in finite ranges of Minkowski space at the variation of the action integral for the subsidiary conditions

δ I = δ ∫Ω L(x) d^4x + Σj Σi=e,p,P,E ∙ λj ∙ δ Gi =0.

Now, we are seeking stationary solutions of this variation principle. The bound states are fixed at temporary stationary solutions of the variation principle for the mutual interactions of particles. The mutual interactions mean conditional probability densities current of particles as a function of relative distances and relative velocities of the particles. The relativity enters on this place in the theory. The variation principle shows that the Planck constant h appears only in the equations of particle motions and it is missed in the equations of field motions. With other words, the interaction is not quantized; only the sources of the interacting fields are quantized. This corresponds to a quantum field theory, to the Atomistic Theory of Matter.

Summary with conclusion for the used Standard Models

The New Basic Postulates in Physics deal only with four kinds of stable particles e, p, P and E having two invariant charges in finite ranges of the Minkowski space. This is a quantum field theory quite different from theories used in the currently accepted Standard Model of Particle Physics resulting the confused list of particles https://en.wikipedia.org/wiki/List_of_particles. This list of particles is not based on physical valid postulates. Also the list of the elementary particles of the Standard Model, https://en.wikipedia.org/wiki/Elementary_particle, is questioned, because the quark-substructure of the elementary particles e, p, p and E was donned as a trial, but is experimentally not confirmed. The Higgs particles are not needed to explain the masses of particles, we have the explanation with the elementary masses me and mP. Gauge bosons are also not need for the constructions of interactions. In the new quantum field theory the interactions between the particles are not quantized and no more interactions are needed than the non-conservative electromagnetism and gravitation, however, without the relation E = m∙c^2. The gravitation is also built in the particle physics and there is no need for the search of the so called “quantum gravitation” in more than three dimensional spaces and in distances less than 10^-30 cm. The wave-particle dualism lacks physical basics.

The currently used Standard Model of Astrophysics which is based on Einstein’s field equation with the deformation of space-time around masses is also a physically questionable trial because the UFF is violated. In the new quantum field theory the gravitational field is caused by conserved gravitational charges, gi = {± g∙mi}, and the gravitation, A(g)ν(x), is a continuous time-dependent field in finite ranges of Minkowski space. The currently obtained implications of the Standard Model of Astrophysics, the Big Band, the Black Holes, the Dark Matter and the accelerated expansion of the Universe, are lacking any physical basics. Since proton and elton have a repulsive gravitation, in the Universe exist galaxies which attract and which repel each other. The neutrino-like particles, all with the gravitational masses zero, convey as particles between this two kinds of galaxies, apart from the electromagnetic and the gravitation fields. Most probably, the whole Universe can be described with only five natural constants, c, e, me, mP and G = g^2/4π. The Lagrange Multipliers are not natural constants and the Boltzmann constant, k, is responsible only for one kind of equilibrium condition of matter.

The experimentally found gravitation is not such simple as the accepted gravitation theory said about more than 400 years; the UFF is violated

The revision of physics must begin with an enhanced theory of Kepler, Galileo and Newton for the gravitation; the basic theories within the energetic physics, SR, GR and QT, developed since the beginning of 20th century were not suitable to describe comprehensibly Nature.

Ingelheim, 17.04.2016,
Gyula I. Szász

[Gyula Szász]

Consequences of the relation of the gravitational and the inertial mass

The gravitational mass

We begin with the gravitational mass of a body consisting of NP protons (P), NE eltons (E), Ne electrons (e) and Np positrons (p). Since the stable elementary particles carry the conserved gravitational charges gi = { – g∙me, + g∙me, + g∙mP, – g∙mE}, i= e,p,P,E, whereby the universal gravitation constant is G = g^2/4∙π and mP/me = 1836.1528, the gravitational mass of a body is
mg(NP,NE,Np,Ne) = |(Np – NE)∙mP + (Np – Ne)∙me|.
The gravitational mass is always greater or equal zero. Since the gravitational interaction is a product of two elementary charges, the different signs of gravitational charges can be put in the interaction part. We have chosen conventionally the gravitational charge of proton positive, gP = + g∙mP.
Now, we consider only electric neutral particle systems for which all the particles are bound. It is easy to see that an electron-positron pair, or a proton-elton pair, has the gravitational mass zero
mg(e,p) = me – me = 0; mg(P,E) = mP – mP = 0.
These two-particle systems correspond to the positronium and protonium and to the electron-neutrino and proton-neutrino. The proton-electron system, N0 = (P,e), has the same gravitational mass as the elton-positron system, N0 = (E,p),
mg(N0) = mg(P,e) = mg(N0) = mg(E,p) = mP – me,
and the same gravitational mass as the instable neutron, N = (P,e,p,e) with the decay N → P + e + electron-neutrino,
mg(N) = mg(P,e,p,e) = mg(P,e) = mP – me.
In absence of eltons, an electric neutral isotope, with NP = A protons, has the gravitational mass
mg(A) = A∙(mP – me).
The numbers of positrons don’t appear in the gravitational mass of an electric neutral isotope.

The inertial mass (at rest of center of mass)

The inertial mass of the stable neutron, N0 = (P,e), is to be calculate with the bound energy, E(N0, bound) = 2.04 MeV, to
mi(N0) = mP + me – E(N0, bound)/c^2 = mP + me – 2.04 MeV/c^2.
The inertial mass of the instable neutron, N = (P,e,p,e), is in nuclear physics measured,
mi(N) = mP + 3∙me – E(N, bound)/c^2 = 939.565 4133(58) MeV/c^2.
The bound energy, E(N, bound)/c^2, can be calculated with the proton mass, NP = 938.272 0813(58) MeV/c^2 and the electron mass Ne = 0.510998910(13) MeV/c^2 to
E(N, bound)/c^2 = 0.2396647 MeV/c^2.
For the two-particle systems, (e,p) and (P,E), the ground states are defined as states if their inertial masses are also zero: these are the electron-neutrino, νe, and the proton-neutrinos, νP, thus, if mi(νe) = 0 → 2∙me = E(νe,bound)/c^2 and if mi(νP) = 0 → 2∙mP = E(νP,bound)/c^2. From the neutrinos originate the Lagrange multiplier, h0, with the value (e is the elementary electric charge)

h0 = e^2/2∙c∙(2∙m’(neutrino)∙c^2/2∙E(neutrino,bound))^1/2 = e2/2∙c∙(1/8)^1/2= h/387.

Hereby the reduced masses are m’(νe) = me/2 and m’(νP) = mP/2, and h is the Planck constant. With h0 we can then calculate the bound energy of the stable neutron, N0. The Planck constant corresponds to the bound energy E(hydrogen,bound) = 13.8 eV.

The Lorentz-invariant formulation of the equations of motions

Lagrange multipliers, such as h and h0, appear in the Lorentz-invariant equations of particles motions as a consequence of the subsidiary conditions caused by the conserved numbers of the elementary particles, e, p, P and E. The Planck constant play the role of a Lagrange multiplier. The Lagrange multipliers occur in the equations of particles motions derived from an action integral formulated in finite ranges of the Minkowski space and taking the general uncertainty in to account that neither the positions, nor the velocities of particles are ecer exactly known. The action integral is constructed with a Lorentz-invariant Lagrange density, which is however not an expression for energy density, and from which the invariant equations of motions for the fields are also derived http://www.atomsz.com.

Further consequences of the conserved gravitational charges

We should mention, that the proton-electron system could also have inertial mass zero; that means
mi(P,e) = 0 = mP + me – E(bound)/c^2
with
E(bound) = (mP + me)∙c^2.
This state has the lowest bound energy of the proton-electron system. This state is the stable ground state of the (P,e)-system and this is not the ground state of the hydrogen atom.
For two-particle systems, the velocities of particles can be calculated according the formula
(v/c)^2/(1-(v/c)^2) = 2∙E(bound)/mij’c^2,
with the reduced masses mij’ = mi∙mj/(mi + mj). The radii of bound two-particle system are with the Lagrange multipliers, h and h0,

rij = h^2/(4∙π^2∙mij∙e^22),
r0ij = (h0)^2/(4∙π^2∙mij∙e^2).
In two-particle system the particles cannot approach each other under their mutual interactions below the relative distance of 10^-17cm. That means, the electron-positron pairs and the proton-elton pairs do never annihilate.
For all electric neutral isotopes with the mass number, A, and with the nuclear charge, Z, the inertial masses, mi(A,Z), are measured by mass spectrometers, thus in the electromagnetic field. From the formula
mi(A,Z) = A∙(mP + me) +Np∙2∙me – E(A,Z; bound)/c^2,
we could calculate the bound energy of the isotopes, E(A,Z; bound), if we would know the numbers of positrons, Np, in the nuclei. In order to solve this problem, we have a variation principle for the bound energies for many body problems, with A = NP protons, Np positrons and NP + Np electrons, and applying h0 and h. This is a well defined model calculation in order to get the Np numbers from the calculated bound energy, E(A,Z; bound) at known mi(A,Z). The sizes of the nuclei are somewhat greater than the sizes of the electron-neutrino and of the stable neutron, which are r(νe) = 0.703∙10^-13cm and d =2∙r(N0) = 0.702∙10^-13cm.
Since we know experimentally the inertial masse of the isotopes, mi(A,Z), and also the gravitational masses, mg(A,Z) = A∙(mP – me), we can calculate the relation of these masses
mg(A,Z)/mi(A,Z) = 1 + Delta(A,Z).
The mass defect, Delta(A,Z), are varied for different types of isotopes
– 0.109% (hydrogen) < Delta(A,Z) < 0.784% (56Fe isotope).
The static force between two stable elementary particles is always the sum of two interactions
F(rij) = + qi∙qj∙rij/4∙π∙rij^3 – gi∙gj∙rij/4∙π∙rij^3,
whereby the conserved elementary electric charges are qi = {± e}. The modified Newton’s equation of motion for a body composed of different (electric neutral) isotopes is, if the other electric uncharged body, BODY, has the same sign of gravitational charge
mi(body)∙a(body) = – G∙mg(BODY)∙mg(body)∙r/r^3.
The acceleration of the body, a(body), is composition dependent
a(body) = – a0∙ mg(body)/ mi(body) = – a0∙(1 + Delta(body).
Therefore, the Universality of Free Fall (UFF) is violated and it can be measured by fall experiments with different composed test bodies. An experimental verification of the UFF violation is performed by Gy. I. Szász at the drop tower of the University Bremen on the 21.06.2004, and is reported in his book, Physics of Elementary Processes; Basic Approach in Physics and Astronomy, ISBN: 963 219 791 7 (2005) and in his lecture on YouTube https://www.youtube.com/watch?v=WsyJjxC7SRc . However, the editors/reviewers of physical journals, PRD, EJPC, ZNA and Foundation of Physics, rejected the articles that attempted to publish Szász’ results. Therefore, his theory did not came in circulation of physical science.

A comparison with the special relativity theory

All inertial masses discussed up to now are calculated if the center of masses (COM) is at rest. These masses are the so called rest masses, m0(body), which should appear in Einstein’s equation of the special relativity theory
E^2 = (m0(body))^2∙c^2 + p^2∙c^2.
However in particular, the rest inertial masses of composed systems are not invariant masses of bodies. Only the elementary particles e, p, P and E have invariant masses. The equation above is not verified in our theory. Since the bound energies of composed systems are caused finally by interactions between the elementary particles which propagate with c, at velocities of the COM nearby c, the composed systems would decay in the composing elementary particles.
In our theory, we can also not verify Einstein’s energy-mass-equivalence relation
E = mi(v)∙c^2.
The elementary masses mP and me are the invariant masses and they are not equivalent to energies. However, we get the equation for the inertial masses at rest of COM
mi(NP,NE,Np,Ne) = (NP +NE) ∙mP +(Np+Ne)∙ me – E(NP,NE,Np,Ne; bound)/c^2,
which are not invariants. On the other side, the gravitational masses are conserved
mg(NP,NE,Np,Ne) = |(Np – NE)∙mP + (Np – Ne)∙me|.

Conclusions

Here, it is demonstrated that the conclusions of the special relativity for masses and energy are erroneous.

Also the conclusions derived from the general relativity for gravity are erroneous then the gravity is obviously caused by conserved gravitational charges, gi = { – g∙me, + g∙me, + g∙mP, – g∙mE}, of the stable elementary particles i= e,p,P,E. A proof for the existence of elementary gravitational charges is given for instance by the confirmed violation of the UFF. But, these did not fit to the convinced meaning of editors/reviewers of physical journals about their imagination to the validity of the weak equivalence principle.

The physical science needs neither the deformation of space-time in order to explain the gravitation, nor the quantization of energy for the construction of a quantum field theory. After that all, the UFF is violated and the Planck constant h plays the role of a Lagrange multiplier.

The quantum field theory based on two conserved elementary charges of four kinds of stable elementary particles does not need Higgs-particle in order to explain the gravitational and the inertial masses of all particles.

This theory state also that the stable elementary particles are not composed of quarks. In the diploma thesis, SU(3) Symmetry in der starken Wechselwirkung; Ein Vergleich mit den Experimenten, at the University of Mainz, Gy. I. Szász has 1967 shown, that the prognoses of the SU(3) symmetry model of particles are scientifically not acceptable.

In his doctor thesis, Zur quantenmechanischen Beschreibung von Resonanzphänomenen, Szász proposed a new variation principle for the determination of instable states. The work was published in Z. Physik, A275, 403 (1975) and A278, 165 (1976), Fortschr. Physik, 24, 327 (1976), Phys Lett. A55, 327 (1976) and A62, 313 (1977). But, a further article with the significant recognition that the Planck constant play a role of Lagrange multiplier, submitted 1977 in Phys.Lett., has been rejected by the editors.

Gyula I. Szász

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