Some meditations

 

Field equations for individual photons and relativistic field equations for moving massive particles

André Michaud

SRP Inc, Quebec, Canada

Service de Recherche Pédagogique

22 Godbout, Québec, QC, Canada, G1L 1T9

 

Here some meditations are presented, that were generated by paper of Prof. Paul Marmet (Paul Marmet. Fundamental Nature of Relativistic Mass and Magnetic Fields. Problems of nonlinear analysis in engineering systems, No. 3 (19), Vol. 9, 2003, Kazan, Russia. (Also available from the Internet site www.newtonphysics.on.ca)).

When localized electromagnetic particles are considered, the only way ever devised to sum up by integration their total complement of energy, which is deemed to be spherically isotropic and mathematically deemed to radialy decrease to infinity, involves setting the upper limit of integration to infinity, and setting the lower limit to a specific distance from zero simply because integrating up to the center of the particle (r = 0) would integrate an infinite amount of energy.

Using this established method, and quantizing the unit charge in the Biot-Savart equation, Paul Marmet established an equation allowing calculating the total relativistic mass of the magnetic field of a moving electron, from which can be deduced the invariant mass of the magnetic field of an electron at rest. The lower limit of integration in the case of an electron turns out to be the electron Classical Radius (r = 2.817940285E-15 m).

From working on other aspects of electromagnetic theory, I had previously come across the fact that the classical radius of the electron was obtained by multiplying the amplitude of the electron Compton wavelength by the fine structure constant (r_e=l_ca/2p=2.817940285E-15 m) and that the Compton wavelength itself was the actual absolute wavelength of the energy making up the rest mass of the electron (l_c =h/m₀c=2.426310215E-12 m).

This led me to consider the possibility that the total complement of energy of any localized electromagnetic particle could possibly be obtained by integrating their energy in the same manner, that is by setting the upper limit of integration to infinity, of course, and by setting the lower limit to the product of the amplitude of the absolute wavelength of the particle and the fine structure constant (la/2p), which upon verification turned out to be confirmed.

The equations obtained effectively allow calculating the energy of any localized electromagnetic particles by integrating energy fields mathematically deemed spherically isotropic and whose density radialy decreases from a lower limit of la/2p to an infinite upper limit (¥)

The possibility also came to light that general equations for electric and magnetic fields specific to localized particles could also be established from the same considerations.

By associating quantization of unit charge and integration of the energy associated to the very precisely known dipole moment (the Bohr magneton) and magnetic field of the ground state of the hydrogen atom to the Biot-Savart law,љ an equation was then developed to calculate the magnetic field of any photon with the absolute wavelength of the photon's energy as the only variable (l), all other parameters being known constants (p, m₀, e, c, and a).

From the known equality of density of magnetic and electric energy per unit volume in any electromagnetic field, an equation was then derived from this discrete magnetic field equation to calculate the electric field of any photon with the absolute wavelength of the photon's energy as again the only variable (l), all other parameters being known constants (p, e, e₀ and a).

At this point, there remains to be addressed the possibility of relativistic discrete field equations for moving scatterable massive particles, for which the carrying energy must be considered on top of the energy making up the rest mass of such particles.

The natural starting point for such an exploration is the Lorentz equation, which, for straight line motion of a charged particle, provides the only existing equation making use of both E and B fields to calculate the relativistic velocity of the particle.

By making use of the magnetic field equation previously obtained for photons, that makes use of the absolute wavelength of the particle as the only variable, it is possible to calculate the magnetic field of the electron at rest from its absolute wavelength (the electron Compton wavelength), and to separately calculate the magnetic field of the carrying energy of a moving electron.

From Marmet's demonstration, it is clear that the composite magnetic field of an electron in motion can be obtained from the simple sum of the magnetic field of the carrying energy and the magnetic field of the electron at rest.

From relativistic equation (E=gmc²), an equation for relativistic velocity can then be obtained, making use of only the absolute wavelength of the carrying energy and the absolute wavelength of the energy making up the rest mass of the electron.

Having then resolved the B element of equation (E=vB) from only fundamental constants (p, m₀, e, c, and a) and two absolute wavelengths (l and l_c) and the v element from the same two absolute wavelengths (l and l_c), a discrete electric field equation can easily be resolved making use of only fundamental constants (p, e, e_o, and a) and absolute wavelengths (l and l_c), which, when used in conjunction with the associated composite B field allows calculating the relativistic velocity in straight line of any material particle in motion from only electromagnetic considerations.

These equations support the idea that photons, as well as moving massive particles self-propel at the observed velocity from the interaction of their own internal uniform and orthogonal electric and magnetic fields.

Moreover, in accordance with the only case that allows straight line motion of a charged particle with Lorentz equation, that is, relative E and B values of external uniform fields that verify equation (E=vB), the new composite discrete field equations for massive moving particles directly explain why moving particles tend to self-propel in straight line, in accordance with Newton's first law; and by similarity, as a limit case with no massive particle involved, (E=cB) for photons from Maxwell's fourth equation provides the same explanations for default straight line motion of photons if no external force is acting on the particle.

Establishing the value of individual electromagnetic fields of electrons, quarks up and quarks down (which are the only scatterable elementary particles known to exist inside atoms) and of their carrying energy inside atoms and nuclei may finally allow determining with precision the contribution of each one of them to the resulting electromagnetic equilibrium inside atoms.

Finally, the fact these equations support the idea that electromagnetic particles may be self-propelling, directly hints at the possibility that they may exist without the need for underlying fields nor medium of any sort, and that a space geometry that would not impose that energy becomes infinite at r=0 could possibly be conceived of that would allow spherically integrating the energy of scatterable electromagnetic particles from a maximum more realistically compatible with a transverse velocity of energy not exceeding the speed of light, which would be more coherent with the concept of locality.

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