Chapter 6

The constant To, quantum parameter

The elementary electric charge e

We indicated, in chapter 5, that the temporalist model postulated the existence of the parameter To in the physics of the photon. The redshift of the galaxies is not any more interpreted like a Doppler or cosmological effect but is regarded as an intrinsic quantum property of the photon.

According to quantum physics, there is not essential difference between the photon and the electron. The emission of the photons in the atoms results from the transitions from the energy levels from the photoelectrons. The photoelectric effect illustrates the transfer of energy of the incidental photons to the electrons of irradiated metal, with the disappearance of the incidental photons. The particles of matter (electrons) or energy (photons) appear and disappear, the ones to the profit of the others, but energies and the impulses are preserved. A positron and an electron entering in collision can be destroyed and form 2 y rays. One can consider, at first approximation, the photon like a kinetic particle of energy in translation in space and the electron like a corresponding matter particle, relatively static, in rotation. If this analysis is correct, the physics of the electron, like that of the photon, must integrate the temporalist quantum parameter To. We will see in chapter 8 how the physics of the photon is affected by To. We will examine here how the physics of the electron integrates the parameter To.

In the quantum standard model of the particles, a significant property of the particles is their spin of which the unit is h. This spin can be defined like one intrinsic kinetic moment of the particles. In addition, another quantum significant property of particle is their electric charge e. The value of this charge is the same for all the free charged " elementary particle " (whereas the quarks and anti-quarks be confine): it is the elementary electric charge ± e is 4,8032068 10-10 ues cgs or 1,60218 10-19 coulomb in S.I MKSA.

We saw, in chapter 5, that constant To can be considered, in a way parallel to constant c, like a quantitative and restrictive constant of the quantum phenomena. Just like c is a restrictive parameter of physical speeds and quantitative of the energy of the rest mass E = mc², To can't seem a restrictive and quantitative temporalist parameter of the movement of the particles? In fact, intrinsic kinetic moment of the particles, i.e. of their spin h ? Accordingly, we can pose the equation total spin = h (spin or kinetic moment) x To (time) = hTo (total kinetic moment). In dimensions ML²T-¹ x T = ML² (moment of inertia). In cgs numerical values : 1,05457266 10-27 erg sec x 4,5423 10.17 sec = 4,790185 10-10 erg sec². The numerical value of the kinetic moment or total spin is strangely close to the numerical value of e = 4,8032068 10-10 ues cgs. Simple act of a coincidence? We do not think so. The numerical value of the total spin hTo, so near to that of e, would be probably identical if the numerical value of G' (6,60 10-8 cm/sec²) had been established in experiments starting from quantum and nonmacroscopic measurements (experiment of the torsion bars of Cavendish).

The temporalist assumption of constant To, quantum parameter, leads us to propose that the electric elementary charge e can thus be consider like the total action or the total spin (kinetic intrinsic total moment) of particle be e = hTo. In this prospect, as we base our argument on the experimental numerical quantum value h / e = 6,6260755 10-27 / 4,8032068 10-10 = 1,379510 10-17, we can allot with To the final " quantum " numerical value of e / h = hTo / h either 2 µ / 1,379510 10-17 = 4,55465 10.17 sec, is approximately 14,43 billion years, and for G' the " quantum " value c / To = 2,99792 10.10 / 4,55465 10.17 = 6,58210 10-8 cm/sec², very near to its macroscopic value (6,60 10-8).

Now let us examine the numerical and dimensional problems posed by this temporalist definition of the electric elementary charge e.

a) In the cgs ues system - In the temporalist model, the numerical value of e is given by e = hTo = 1,05457266 10-27 erg sec x 4,55465 10.17 sec = 4,8032068 10-10 erg sec². In the cgs ues system, e = 4,8032068 10-10 ues cgs. The dimension of e is specific. In the temporalist model, the dimension of e (hTo) is ML²T-¹ x T = ML² (ergs sec²). It is the dimension of a moment of inertia. The electric charge e, in temporalist model, does not have any specific size cgs and can thus be integrated into three dimensions L, M and T. It does not require any more the existence of a dimension of the electric charge in ues.

b) In MKSA system - Let us compare the values of h and e in cgs ues and MKSA systems.

h (cgs ues) / h (MKSA) = 1,05457266 10-27 erg sec / 1,05457266 10-34 Joule sec = 10.7

e (cgs ues) / e (MKSA) = 4,8032068 10-10 ues / 1,6019 10-19 coulomb = 2,99792 10.9

From where the ratio h (cgs) / h (MKSA) / the ratio e (cgs ues) /e (MKSA) = 10.7 / 2,99792 10.9 = 1 / 2,99792 10.2

If we pose, in the MKSA system, e = hTo, we obtain e = 1,05457266 10-34 Joule sec x 4,55465 10.17 sec = 4,8032068 10-17 Joule sec², homogeneous to = 4,8032068 10-10 erg sec² but different from 1,6019 10-19 coulomb. To obtain this value, we must take account of the inhomogeneousness of the relationship between h in the cgs ues and MKSA systems on the one hand and of e in these same systems, is e in the MKSA system = hTo = 1,05457266 10-34 Joule sec x 4,55465 10.17 sec x 1 / 2,99792 10.2 = 1,6019 10-19 Joule sec². In MKSA system, the temporalist dimension of e, as in the cgs ues system, is defined by e = hTo is ML²T-¹ x T = ML² (moment of inertia). It does not require any more the existence of a specific dimension of e in coulomb (or ampere).

Temporalist dimension of e (ML²) as well as its numerical value will be justified by its coherence in the quantum phenomena. Let us note here that the identical value, for all the " elementary particles ", of the electric elementary charge e, noted in quantum electrodynamics, but not to be understood, is explained easily in the temporalist model. Its definition (the product of two universal constants h and To) does not use the specific properties of the particles (a mass number, energy, a baryon or lepton number, etc...). The identical electric charge of two completely dissimilar particles, like the positron and the proton, is thus justified. The fractional charge of the quarks is not operational since they are confined. Besides one can, on this subject, call upon a quantum principle: conservation of the total kinetic moment in the quantum systems. It is probable that a similar principle applies to the fractional charge of the quarks, the electric elementary charge e seeming the total kinetic moment of the particles.

Let us note that the electric charge hTo is the double of the total spin of the fermions as the electron (h / 2 x 2 To) whose kinetic moment is equal to h / 2. It is probable that this is due to the fact that a boson, like the photon, has one kinetic moment of an unit h and that it can result from the fusion of two fermions, a positive electron and a negative electron, of kinetic moment h / 2.

The temporalist proposal of the electric elementary charge e = hTo enables us to pose e / h = To or h / e = 1 / To. Constant To, leads us directly to the heart of quantum physics, where this relationship between e and h appears in the Josephson effect, the photoelectric effect and indirectly in the constant of fine structure.

The Josephson effect

The Josephson effect appears by the passage of a stream of electrons between two superconductor ribbons (lead, aluminium, nobium, etc...) separated by an insulating barrier. When these superconductors are brought up to very low temperature (some Kelvins), the free electrons form pairs of Cooper. Quantum mechanics translates this effect by saying that all the pairs condense in the same quantum state described by only one function of macroscopic wave. The intensity of the produced current depends only on dephasing between the function of wave on both sides of the barrier. It varies like the sine of dephasing, dephasing whose derivative compared to time is itself on both sides proportional to the tension of the barrier. The factor of proportionality is proportional to e / h. For a tension V constant, measured at the boundaries of a Josephson junction, one observes the passage of a sinusoidal current of frequency v = 2 e / h x V. The Josephson effect makes it possible to connect, by the intermediary of the 2 universal constants e and h, the tension to the frequency. By International Convention, the value of the frequency/tension ratio proportional to 2 e / h was fixed at 483594 Ghz/V.

Let us write the equation with dimensions of the factor of proportionality 2 e / h : Q/ML²T-¹ = coul/joule sec = ues/erg sec or frequency/tension = T-¹/ML²T-²Q-¹ = 1/ML²T-¹Q-¹ = Q/ML²T-¹ = coul/joule sec = ues/erg sec from where v = 2 e / h x V = 2 x coul/joule sec x joule/coulomb = 2 x Q/ML²T-¹ x ML²T-²Q-¹ = 2 T-¹.

In numerical values, the factor of proportionality is 2 x 1,60217 10-19 coul / 6,626075 10-34 joule sec = 2 x 2,41797 10.14 coul/joule sec = 4,83594 10.14 coul/joule sec or 483594 Ghz/V. We can calculate the angular frequency w = 2µ v is 2µ x 2,41797 10.14 Hz = 1,519259 10.15 Hz and the corresponding factor of proportionality 2 x 1,519259 10.15 Hz/V.

Let us now introduce the dimensions and the numerical values of the temporalist model, in the cgs system. The equation with the dimensions of the factor of proportionality 2 e / h = ML² / ML²T-¹ = T = frequency / tension = T-¹ / ML²T-²Q-¹ = T-¹ / T-² = T. In numerical values, 2 e / h x 2µ (in angular frequency) = 2 x hTo/h x 2µ = 2 x To is 2 x 4,8032068 10-10 erg sec²/6,626075 10-27 erg sec x 2µ = 2 x 4,5546 10.17 sec.

The temporalist interpretation, if it is exact, must be coherent with the quantum interpretation of the Josephson effect. Let us check it. In the temporalist model, the factor of proportionality 2 e / h has the dimension of a time: To = T and, as a value 2 x 4,5546 10.17 sec/2µ in units ues cgs. In quantum theory, the factor of proportionality has the dimension of a frequency/volt and for value 2 x 1,51925 10.15 Hz/V. We know that, in S.I. MKSA, the electric potential of an electrostatic unit is 299,792 volts. It is thus equivalent to give for the factor of proportionality the value 2 x 1,51925 10.15 Hz/V or 2 x 4,5546 10.17 Hz (1,519259 10.15 x 299,792) / 299,792 volts (1 ues). In dimensions, the factor of proportionality is worth, as we saw, Hz/V = T-¹ / ML²T-²Q-¹ = T-¹ / T-² = T, coherent with the dimension of the temporalist factor of proportionality To (T).

The factor of proportionality of the Josephson effect 2 e / h is 2 e / h x 2µ, in angular frequency, is thus 2 To, which indicates in this quantum effect the presence of the temporalist constant.

The photoelectric effect

After the discovery of the Planck's constant h, Einstein put forth the assumption of the corpuscular nature of the photon and stated his famous equation of the photoelectric effect E cin = hv - W where W is the energy of extraction of the electron of material.

Later on, the experiments of Millikan made it possible to establish a linear relation between the potential of stop Vo and the frequency of the incidental light Vo = h / e x v - We.

If one traces in a graph the potential of stop Vo according to frequency v, one finds a straight line equal to h / e and, by neglecting the work of extraction of material, the potential of braking of the photoelectric emission will be proportional to constant h / e : Vo = h / e x v or Vo / v = h / e. Let us take numerical values: h / e = 6,626075 10-34 joule sec / 1,602177 10-19 coul = 4,1357 10-15 volt sec. The equation with dimensions from Vo / v gives ML²T-²Q-¹ / T-¹ = ML²T-¹Q-¹ = ML²T-¹ / Q. The factor of proportionality of the potential of braking is thus 4,1357 10-15 volt sec and the potential of Vo braking = 4,1357 10-15 volt sec x v or, by angular frequency w = 2µ v = 4,1357 10-15 / 2µ x v = 6,582 10-16 volt sec x v.

The photoelectric effect can be brought closer to the Josephson effect. In these two quantum effects, an electrical current is produced. In the Josephson effect, an electrical current is created through an insulating barrier, under certain conditions. There is a factor of proportionality between the frequency of the current created and the tension at the terminals of the Josephson junction. This factor of proportionality, in cgs units, is e / h, i.e. the temporalist constant To / 2µ. In a parallel way, we can find, in the photoelectric effect, a factor of proportionality between the potential of stop of the electrical current created by the photoelectrons and the frequency of the incidental radiation. This factor of proportionality is h / e, i.e., in the temporalist model, 2 µ / To, the reverse of the temporalist constant.

Let us introduce the dimensions and the numerical temporalist values.

The equation with dimensions of the factor of proportionality of the potential of braking gives h / e = tension / frequency is h / e = ML²T-¹ / ML² = T-¹ or tension / frequency = ML²T-²Q-¹ / T-¹ = ML²T-¹Q-¹ = T-¹.

In the cgs system, in numerical values, we obtain h /e = h / hTo = 2µ / To; by using the angular frequency w = 2µ v, we obtain h / hTo 2µ = 1 / To is 6,626075 10-27 erg sec / 4,8032068 10-10 erg sec² x 6,2832 = 2,1955 10-18 sec.

The temporalist model, to be exact, must converge with the quantum interpretation of the photoelectric effect. The equation with dimensions of the factor of proportionality of the potential of braking is, in the temporalist model, T-¹ (1 / To). In quantum theory, it is h / e either ML²T-¹Q-¹ (volt second) or, translated into temporalist dimensions, ML² (e) T-¹Q-¹(- e) = T-¹.

In numerical values, in temporalist model, 1 / To = 1 / 4,5546 10.17 sec = 2,1955 10-18 sec. In quantum theory, in the S.I, h / e = 6,626075 10-34 joule sec / 1,602177 10-19 coul = 4,1357 10-15 volt sec is by angular frequency, 6,582 10-16 volt sec. Let us introduce the potential in ues is 299,7925 volts by ues. The factor of proportionality is thus 6,582 10-16 volt sec x 1/299,7925 volts = 2,1955 10-18 sec.

We can check the adequacy of this value with the calculation of the potential of braking of a blue light of frequency of about 7 10.14 Hz: 2µ x 7 10.14 sec-¹ x 2,1955 10-18 sec x 299,7925 volts = 2,89 volts, which corresponds perfectly to the order of magnitude of the potential of necessary braking.

The factor of proportionality of the potential of braking of the photoelectric effect is equal to 1 / To and one finds in this quantum effect the presence of the temporalist constant.

The constant of fine structure &

The constant of fine structure is one of the fundamental constants of nature. Its role in quantum electrodynamics is major. Let us recall briefly the essential characteristics. & is the constant of coupling which describes the coupling of any elementary particle carrying the electric charge e with the electromagnetic field. The constant of fine structure draws up the relationship between the electrostatic energy of coupling between an electric particle and the electric field, on the one hand, and its energy of rest mass, on the other hand: & = e² / (h / mc) / mc² = e² / hc = 7,2992 10-3 = 1 / 137,036, h / mc being the wavelength of Compton of the electric particle and mc² its energy of rest mass.

The constant of fine structure & also plays a significant role in the diagrams of Feynman relating to the processes of diffusion electrons-electrons. The contribution of each diagram to the rate of the process of diffusion is proportional to a certain power of factor 1 / 137 (of the constant of fine structure &) that is to say (1 / 137) n, n which can be 1, 2,3, etc...

If we consider the constant of fine structure & within the framework of the temporalist model, we come to interesting results. Let us apply the temporalist parameters e = hTo and G' = c / To. We obtain & = e² / hc = e/c x To = e / G'.

1) In the ues cgs system - Let us apply the numerical values. In quantum theory, & = e² / hc = 4,8032068 10-10 x 4,8032068 10-10 / 1,054572 10-27 x 2,997925 10.10 = 7,2974 10-³; in the temporalist model e / G' = 4,8032068 10-10 / 6,582 10-8 = 7,2974 10-³.

In dimensions - In quantum theory: e² / hc = ML³T-²Q-² x Q² / ML²T-¹ x LT-¹ = ML³T-² / ML³T-² = Number without dimension (from where e² = ML³T-²).

In temporalist model e² = ML³T-² from where e / G' = e²/e / G' = ML³T-²/ML² / LT-² = LT-² / LT-² = Number without dimension.

2) In SI MKSA - In numerical values. In quantum theory: e² / hc = 8,987 10.9 (constant K in the void for the S.I.) x 1,602 10-19 x 1,602 10-19 / 1,054 10-34 x 2,997925 10.8 = 2,306 10-28 / 3,16 10-26 = 7,2974 10-³.

In the temporalist model: e / G' = e²/e / G' = 2,306 10-28 / 1,602 10-19 / 6,582 10-8 = 2,1877.

Taking into account the inhomogeneousness of the cgs/MKSA systems = 2,997925 10.2, e / G = 2,1877 X 1/299,7925 = 7,2974 10-³.

In dimensions - In quantum theory: e² / hc = ML³T-² / ML²T-¹ x LT-¹ = ML³T-² / ML³T-² = Number without dimension.

In the temporalist model, e / G' = e²/e / G' = ML³T-² / ML² / LT-² = LT-² / LT-² = Number without dimension.

We note that the temporalist constant To is to be found in the definition of the constant of fine structure & since & = e² / (h/mc) / mc² = e² / hc = e/c x To or e / G'. & is interpreted, in quantum mechanics, like the constant of coupling of the electromagnetic interactions or the relationship between electromagnetic energy and the energy of rest mass of any electric " elementary " particle. In the temporalist model, the constant of fine structure seems to be the relationship between the electric elementary charge e and the parameter G' (c / To).

Next : 7 G' quantum constant

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