Growing fields imply Evanescent Matter

Helder Velez

Abstract:

The conservation of energy in a field that obeys an inverse square law, as Electrostatics or Gravitation, imply that in order to set an exterior field that propagates at a finite speed ‘c’, the energy contents associated to the source mass/charge must obey an evanescent law. It means, namely, that we must have a shrinking matter scenario [AlfCP, AlfAstro]instead of a space expansion one.

A spherical shell of charge ‘q’ and radius ‘a’ sets an electrical field:

(1)

that has the energy U, ignoring :

(2)

Assuming that all of the mass of the electron is due to its electromagnetic field energy and from Einstein's mass/energy equivalence [McDonald]

(3)

(4)

This energy U, proportional to the electron mass, has been considered a constant valued quantity.

- Considering that the above formula for U was derived long time ago when the ‘fathers’ of Electromagnetism ‘presumed’ that the universe was infinite in age, and we know now differently.
- Being able to assign the label ‘zero’ into the arrow of time, as a beginning, we are dealing now with a finite interval of time.
- Being r=ct, c=1, for a stationary universe and uniform time, there exists a maximum r, determined by time ‘now’ and equation for U becomes U(t)

(5)

This energy in the E field evolves from 0 at t=t_{a} growing asymptotically to m_{e} as time evolve.

We must conclude, after dismissing the traceable possibility that q^2 is simply proportional to time, thatU(t) is constant iff

(6)

Conclusions:

The conclusion must be such that the overall energy must remain constant, implying a transfer of energy from particles to its associated fields. Thus, the paradoxes expressed by Mr. Claus got explained[Turtur].

Acknowledging this fact the above equations of the field and energy became inadequate because E field (here and now) depends on the value of the charge at a previous time : q(then).

The scenario of evanescent matter must have consequences on our deeply rooted believes of a constant, thru time, of Time, Length and Mass Units, and the validity of the 'space expansion' must be reconsidered.

References

[AlfCP] A. G. Oliveira and R. Abreu, Cosmological Principle and Relativity – Part I (physics/0205033)

[AlfAstro] A. G. Oliveira and R. Abreu, A relativistic time variation of matter/space fits both local and cosmic data, astro-ph/0208365)

[McDonald] Kirk McDonald, Princeton.edu, ph501, Lecture 3, pages 29/31, Electrostatic Energy (http://www.physics.princeton.edu/~mc...01lecture3.pdf)

[Turtur] Claus W. Turtur, Two Paradoxes of the Existence of electric Charge (physics/0710.3253)