computer Posted November 3, 2022 Report Share Posted November 3, 2022 The hypothesis is an extension of field theory and an attempt to explain the internal structure of elementary particles. Basic equations Presumably, in three-dimensional space there is a field formed by vectors of electric intensity E = (Ex, Ey, Ez), magnetic intensity H = (Hx, Hy, Hz), and velocity V = (Vx, Vy, Vz). Also later in this article, the vectors of electrical induction in vacuum D = ε0 · E and magnetic induction in vacuum B = μ0 · H can be used. E and H are "energy carriers" local density of energy is expressed as follows: u = ε0/2 · E2 + μ0/2 · H2 where E2 = Ex2 + Ey2 + Ez2 and H2 = Hx2 + Hy2 + Hz2 Law of energy conservation: time derivative u′ = - div W where W = (Wx, Wy, Wz) is the energy flux vector. In this case, W = [E × H] + ε0 · (E · V) · E The scalar product EV = E · V = Ex · Vx + Ey · Vy + Ez · Vz expresses the cosine of the angle between E and V. In more detail, Wx = Ey · Hz - Ez · Hy + ε0 · EV · Ex Wy = Ez · Hx - Ex · Hz + ε0 · EV · Ey Wz = Ex · Hy - Ey · Hx + ε0 · EV · Ez Respectively, div W = H · rot E - E · rot H + ε0 · E · grad EV + ε0 · EV · div E Derivatives of the magnetic and electric field by time: H′ = - 1/μ0 · rot E E′ = 1/ε0 · rot H - grad EV - V · div E In this case, div E is proportional to the local charge density q with a constant positive multiplier: q ~ div E, in the SI measurement system q = ε0 · div E. Having performed the necessary transformations, we get: u′ = ε0/2 · (2 · Ex · Ex′ + 2 · Ey · Ey′ + 2 · Ez · Ez′) + μ0/2 · (2 · Hx · Hx′ + 2 · Hy · Hy′ + 2 · Hz · Hz′) = Ex · (∂Hz/∂y - ∂Hy/∂z - ε0 · ∂EV/∂x - ε0 · Vx · div E) + Ey · (∂Hx/∂z - ∂Hz/∂x - ε0 · ∂EV/∂y - ε0 · Vy · div E) + Ez · (∂Hy/∂x - ∂Hx/∂y - ε0 · ∂EV/∂z - ε0 · Vz · div E) - Hx · (∂Ez/∂y - ∂Ey/∂z) - Hy · (∂Ex/∂z - ∂Ez/∂x) - Hz · (∂Ey/∂x - ∂Ex/∂y) = E · rot H - H · rot E - ε0 · E · grad EV - ε0 · EV · div E = - div W A term in the form of "grad EV" for E′ arises from the need to make an adequate expression of the energy conservation law, and although in the "natural" structures discussed below E is everywhere perpendicular to V, that is, EV = 0, it can play a role in maintaining the stability of field formations. Velocity derivative by time From the point of the energy-flux view, the time derivative V′ can be any expression, but should not contain a common multiplier V or 1 - V2/c2, since when approaching zero or the speed of light, the vector would practically cease to change locally, which contradicts many experimental facts and theoretical studies. The most likely are the two-membered constituents for V′, where one part contains V as a multiplier in the scalar or vector product, the second does not. For example, the pure field similarity of the Lorentz forces is of interest: V′ ~ (D · V2 - [H × V]) · div E where V2 = Vx2 + Vy2 + Vz2 The expressions D · V2 and H × V have the same dimension, A/s in SI, and after multiplying by the div E, it is still necessary to enter a coefficient to convert the resulting units into acceleration m/s2. The numerical value of the coefficient will probably have to be determined experimentally. Although there are no strict restrictions on the absolute value of V, as we shall see later, for field formations common in nature, it is uncharacteristically |V| > c, and the speed of light is achieved at a mutually perpendicular arrangement of E, H, and V, when the local "E-energy" is equal to "H-energy", that is, E2 ~ 1/ε0, H2 ~ 1/μ0. The exception is artificially created or simulated on the computer situations. Another hypothetical set of terms for the velocity derivative over time is V′ ~ W - u · V. In the models of particles discussed below, in this case, there is a "longitudinal" effect on the velocity vector, in contrast to the "transverse" one under the influence of an electric and magnetic field, with the mutual perpendicularity of all three vectors. If indeed V′ ~ W - u · V, then although there is still no hard limit |V| ≤ c, the unlimited increase of the velocity in the absolute value is more explicitly limited by the member u · V with a negative sign. If the magnetic or electric field somehow disappears, the velocity will rush to zero, although the energy density may remain non-zero. Modulus of V reaches its maximum value (= c) when E and H are perpendicular and ε0/2 · E2 = μ0/2 · H2. When the charged particle is in an external electric field, like created by another particle in the vicinity, due to the multiplier V2 in the expression V′ ~ (D · V2 - [H × V]) · div E is independent of the sign of V, and the presence of significant velocities close to the speed of light inside the particle, the total acceleration acts in one direction (on average, although internal deformations may occur). In an external magnetic field the velocity vector is involved in the first degree, in any projection about half of the currents are directed in one direction, and about half in the opposite direction, so only internal deformations occur. The shift of a particle as a whole is observed when it moves in an external magnetic field. Let us consider the alleged structure of some elementary particles. To do this, we will use a cylindrical coordinate system (ρ,φ,z), where ρ2 = x2 + y2, φ is the angle counted from the positive direction of the x-axis counterclockwise if it is directed to the right, the y-axis upwards, and the z-axis is directed towards us (the right coordinate system). Also, for the particles under consideration, we will set the condition of cylindrical symmetry, that is, ∂/∂φ = 0 for any variables. Quote Link to comment Share on other sites More sharing options...
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