Re: Propagation of EM waves in a relativistic medium - some mathematical details

From: Ole D. Rughede (ole.rughede_at_privat.dk)
Date: 07/01/04 

Date: Thu, 1 Jul 2004 05:05:19 +0200

"LEJ Brouwer" <intuitionist1@yahoo.com> skrev i en meddelelse
news:4487dad1.0406301357.75407f64@posting.google.com...
> I wrote a short paper a while ago describing how classical
> electrodynamics might be derived from the motion of an underlying
> space-filling relativistic continuum (which some may wish to interpret
> as a kind of `luminiferous aether'). I have now added a section to
> that paper (which is work ongoing in my spare time) which describes
> explicitly how oscillations of the medium describe the propagation of
> electromagnetic waves. The paper is here:
>
> http://www.seventh-sense-software.com/aether.pdf
>
> Steve Carlip had raised the objection earlier that the medium would
> have to satisfy a rather complex third order PDE in order for the
> Lorentz force equation to hold, which was therefore less than
> satisfying. While these objections still hold (how serious they are is
> possibly a matter of opinion), one can still hope that the underlying
> equations (if and when they are found) governing the motion of the
> relativistic continuum/medium/fluid may actually be much simpler than
> 3rd order PDE that they are constrained to satisfy. [If anyone
> succeeds in deriving a satisfactory equation of motion, I would be
> delighted to hear about it].
>
> As I mention in the paper, the formulation in terms of 4-velocities of
> a medium contains more information than the standard 4-potential (such
> as a way of potentially incorporating vacuum energy density
> classically), which may be significant for further development of the
> theory.
>
> Best wishes,
>
> Sabbir.

Thank you for your communiction.
I would stress the importance of the energy density u erg/sec and
the energy U = uV erg of the aether medium of pure electromagnetic
energy irradiated from all astrophysical objects and filling all of space,
cf. your parenthetic remark in summary. Should also note that the
aether energy is of only one positive quality, while discrete wavelets
may have right or left chiralty which I assume has meaning with regard
to the creation and annihilation of electric positive and negative
particles.

The wave characteristic velocity c of the aether medium (as function
of u) may be found from my following equation (CGS):

                        kappa * U * V = G * h * c^2

where V = 1 cm^3, and kappa =1 erg/(sec * g^2) provides a radiant
flux Phi = kappa * M * m erg/sec, proportional with the product of
any two gravitating masses M and m in relative distance a = n * L cm
with L = 1 cm, so that Phi as an enduring flux of radiant energy, which
is continually exchanged between the masses M and m by way of the
aether medium, is the exact cause of gravity.

G*M*m/a * c/a*Phi = G*m_e/a*c^2 * E*c/a*Phi´ = U*L/n^2*h*c.
(Phi = kappa*M*m, and Phi´ = kappa*(m_e)^2 erg/sec respectively).

G*m_e/r_e*c^2 * e^2/L * c/L*Phi´ = U*L/h*c =
G*c/kappa*L^2 = 2.000343E3 diminsionsless constant, where

Phi´ = kappa*(m_e)^2, and G*c/L^2 = K erg/(sec*g^2) so that
K/kappa = 2.000343E3 (at present u = 3.973837E-13 erg/cm^3),
why K may conveniently be used in stead of kappa for calculation
of the radiant flux Phi causing exactly the virtual gravitational energy
G*M*m/a erg, and the gravitational force G*M*m/a^2 dyn, when
G*c/K*L^2 = U*L/K*h*c = 1 dimensionless.

As may be seen, the derivation of K confirms my arbitrarily defined
kappa in the above fundamental aether equation with the energy
density of the aether, u = 3.379637E-13 erg/cm^3 at the temperature
of cosmic microwave bacground radiation T(CMBR) = 2.692064 K.
(K = Kelvin not to mistake for the former mentioned constant K).
G = 6.672426E-8, h = 6.626176E-27, c = 2.99792458E10.

Generally we therefore have as definition of the concept of mass:

                        m^2 = Phi*U*V/G*h*c^2 .

The Schwarzschild expression for the electron as a black hole
G*m_e/r_e*c^2 = G*(m_e)^2/e^2 = 1/rho, gives
rho = 4.166705E42 as proportionality between electrostatic
and gravitational forces for any electron or electron-positron pair
at any relative distance a = n*L cm, leading to a definition of the
fundamental unit of charge, +/- e = 4.803242E-10 esu, where
Phi_e = kappa*(m_e)^2 erg/sec

                        e^2 = rho*Phi_e*U*V/h*c^2 .

Clearly, if the mass m_e and charge e of the electron/positron as
well as Planck's constant h are in fact universal constants, both the
Newtonian G and the velocity of light c are variables depending of
the local energy density of the aether, which of course will attain
enormous values, say in the center of a galaxy or a "black hole" as
compared with the T(CMBR) value far from all radiating bodies.

I assume from considerations on coefficients to my aether equation,
x*U, y*G, and z*c, that G may tend to equal y*G = x*G/2
for very great values of x, and (z*c)^2 -> 2*c^2 as a maximum
for the velocity of light, meaning ½*m*v^2 -> E = m*c^2 for
v = c, meaning shift of phase from constituent mass to radiant energy.

If such speculations hold, we necessarily will see a differential effect
of gravitational action in the galaxies. The "missing or black mass" in
the universe would be the mass equivalent of the aether energy, and the
universal red-shift should be explained as a phenomenon of gravitational
work done by the aether energy as a simple function of distance through
space distributions of ponderable gravitating massive bodies, including
dust and elementary particles of gasses in space left from "dead" astro-
physical objects.

These gasses and clouds of dust, I believe, are generally concentrated
by the mock-gravity of light pressure and the ordinary gravity to create
new galaxies and new stars in relatively "small bangs", whereby an
enduring creation works as part of a general life-death cycle of all
matter in the eternal universe of infinite dimensions, only observable to
the limit of observation from any thinkable position in the universe due
to the ever greater reddening and darkening of light by distance.

Best regards,
Ole D. Rughede

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