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The Atomistic Theory of Matter

After the fundamental knowledge that neither the positions, not the velocities of particles can ever be exactly known, we must look how many different kinds of elementary particles exist. The experimental observations tell us, there are four: the electron (e), the positron (p), the proton (P) end the elton (E). How many different kind of elementary properties have these particles? We count two: the electric charges and masses. We have observed two kinds of elementary electric charges qi = ± e and two different elementary masses me and mP with mP/me = 1936.152. For the characterization of each particles e, p, P and E is enough to know the electric charge qi and the mass mi. However, this is uncomfortable and is not on the same level. The electric charges have the same amount e, but different signs; the masses mP and me have different amounts and are > 0.

However, we can achieve the same kind of characterization of the elementary particle properties if we assign to the particles instead of the masses, the elementary gravitational charges gi = {- g me, + g me, + g mP, – g mE}, i=e,p,P,E. At the introduction of gravitational charges we have arbitrary decide that proton has a positive gravitational charge, as we decided that proton has positive electric charge. The relative sings of the other elementary particles follow then. Furthermore, we do not only want set up the elementary properties of particles, but we want use these also for the interactions between the particles. For this reason we use the observed static forces, in the shape of the Coulomb law and of the Newton law between two charges

F(Coulomb) = + qi∙qj/4πr^2 = ± e^2/4πr^2,

F(Newton) = – gi∙gj/4πr^2 = – (±) g^2∙mi ∙mj/4πr^2 = – (±) G∙mi ∙mj/r^2.

We notice, the two laws are completely equivalent only the overall signs are different. Under the assumption of universal gravitational forces expressed with the constant G we can express the factor g in the elementary gravitational charges as g =(G∙4∙π)^1/2. Now, we are ready with the complete characterization of elementary particles. Particles with the same signs of electric charges repulse each other; with different electric charges they are attractive. For the gravitational charges it is reserved: particles with the same signs of gravitational charges are attractive; they repulse each other if the signs are different. The observed electric force is by a factor of ca. 10^42 greater than the gravitational force.

We have to complete the description of particles and interactions with the observed properties that the fields propagate with c and the speeds of the fields do not depend of the motion of sources. The unique speed c allows constructing a space-time connection which we call the Minkowski space. In the Minkowski space the elementary charges qi and gi appear as invariants. The interacting time dependent fields can be described with four-vector potential A(e.m.)ν(x) and A(g.)ν(x) in finite ranges of Minkowski space {x}εΩ. With the two kinds of four-vector potentials and with the two kinds of four-charge probability currents

j(e.m.)ν(x) = Σ(i=e,p,P,E) qi∙ji(n)ν(x)

and

j(g.)ν(x) = Σ(i=e,p,P,E) gi∙ji(n)ν(x)

we can construct a Lorentz invariant Lagrange density with the elementary charges, with the four-particle number probability densities ji(n)ν(x) and with the two kinds of four-vector potentials. The integration runs about Ω and delivers a Lorentz invariant action integral for the variation calculus in order to get the covariant equations of motions. The action integral is not an expression for the energy.

However, appropriate subsidiary and boundary conditions must be applied. The boundary conditions are such that the physics within Ω cannot depend on the surface of Ω. Within Ω the following subsidiary conditions must be applied

∂νA(e.m.)ν(x) = 0, ∂νA(g.)ν(x) = 0 for the fields (Lorenz conditions) and

∂νji(n)ν(x) = 0, i=e,p,P,E for the particles.

The subsidiary conditions of the particles are equivalent with the particle number conservations. The particle number conservations cause the appearance of Lagrange multipliers in the equations of particles motions. For instant the Planck constant is connected with a Lagrange multiplier. This theory is also a quantum theory; however in this are only the sources of the fields quantized.

This theory is obviously a mathematic correct constucted Atomistic Theory of Matter based on the four kinds of elementary particles e, p, P, and E. This theory is quite the contrary to the energetic oriented physics developed in the 20th century. Again the energetic physics speak that the energy is none conserved and none quantized. The emission of light by atoms is a wave process and not a corpuscular phenomenon. The energy decreases continuously during the emission and not in discrete energy packages. The atomistic theory is able to replace completely the developed, but invalid energetic theory.

Gyula Szász

P.S. Unfortunately the text editor does not transfer the lower and upper indices.