How am I to prove the notion that tachyonic magnetic monopoles
account for the Dark Matter and Dark Energy of recent cosmological
thought?

I cannot, although the explanation is consistent with the collected
data.

Empirical symmetry is obtained in Maxwell's equations as follows.

The standard representations in differential form (Gaussian) can be
denoted;

div E = 4(pi)p ,

curl E = -(1/c)dB/dt ,

div B = 0 ,

curl B = (1/c)dE/dt + (4(pi)/c)j ,

where
the "d/dt" indicate partial deriviatives, with respect to time t,
E is the vector-valued function for an electric field,
p is the associated electric charge-density,
B is the vector-valued function for the associated magnetic field,
c is the lightspeed constant (approximately 3 x 10^8 meters/second),
the dimensionless pi can be approximated as the number 3.14, and
j is the vector-valued function for the electric current-density.

The Lorentz force F of an electric field of strength |E| on an
electron of unit-charge e, moving at velocity v, is defined;

electric F = e[E + (1/c)(v x B)] ,

where e is approximately 1.6 x 10^-19 Coulomb,
and the "x" in the right-hand term indicates a cross-product.

However, since there are no real magnetic charges, then there is no
real force for the magnetic field corresponding to the electric F.

If magnetic monopoles existed in real spacetime, then the above
equations for the magnetic field would be of the same form as those
for the electric field, and the given equations could be changed so
that;

div B = 4(pi)q ,
and
curl E = -(1/c)dB/dt + (4(pi)/c)k ,

where
q is the magnetic-charge density, and
k is the the vector function for magnetic current-density.

In that case, a magnetic field of strength |B| would impose a Lorentz
force F on a magnetic charge g, moving at velocity v, as follows;

magnetic F = g[B - (1/c)(v x E)] .

This, of course, is not empirical, because magnetic monopoles have
never been detected in real spacetime.

If, however, magnetic monopoles do exist in tachyonic spactime
(having been created as tachyonic particles during the superluminal
Inflation Phase of the first few moments after the Big Bang, and
remaining in superluminal states ever since), then we can make a
simple revision of certain of the terms above, so as to obtain the
desired symmetry, by writing;

div B = (i^i) 4(pi)q ,
and
curl E = - (i^i) (1/c)dB/dt - (4(pi)/c)k ,

where
i^i is not the imaginary unit raised to an imaginary power, but is an
operator that transforms any variable into its tachyonic analog,
evaluated excusively at speeds between lightspeed and infinite speed.

This operator was inspired by the standard imaginary unit, defined;
i = (-1)^(1/2),
and is treated similarly algebraically, but has a totally new
meaning; it is used for converting quantities/symbols to their
tachyonic analogs, but with restricted superluminal velocity.

Consequently, we can also write;

magnetic F = (i^i) g[B - (1/c)(v x E) .

This, then, completes my idea on providing the empirical symmetric
representations of Maxwell's equations.


References:
(1) Maxwell's Equations; article "Search for Magnetic Monopoles ...",
by Bertram Schwarzschild, Physics Today magazine, July 2006, page 16.
(3) Dark Matter, Dark Energy, and Inflation; article "Analysis
and ...", by Frank Wilczek, Physics Today magazine, Oct. 2003, page
10.
(2) Tachyon Operator; online article "Tachyon Math", written by
myself, at
http://hometown.aol.com/HKurtRichter/TachyonMath.html




Previously -

--- In TheAoISCT@yahoogroups.com, "HKurtRichter" <hkurtrichter@...>
wrote:
>
> An article in the latest issue of Physics Today magazine (July
2006,
> page 16) reminded me of something I had contemplated some time ago,
> and I have decided to post the notion below.
>
> The article was entitled: "Search for Magnetic Monopoles at the
> Tevatron Sets New Upper Limit On Their Production".
> It was written by Bertram Schwarzschild, who metioned therein that
> detection of a magnetic monopole, anywhere, would allow us to write
> Maxwell's equations for electromagnetism in a fashion that would
have
> the equations describing the electric field in exactly the same
form,
> symmetrically, as the equations describing the magnetic field.
>
> At present, since we have yet to actually detect magnetic
monopoles,
> we must assume that they do not exist within the "visible"
universe.
> For that reason, in Maxwell's equations the magnetic equivalent of
> the equation for the force F of an electric field on a particle of
> electric charge e is not meaningful (i.e., there is no
corresponding
> magnetic charge), the term for the magnetic current-density in the
> formula for the divergence of the electric field is missing (while
> there is a term for the electric current-density in the formula for
> the magnetic field's divergence), and the curl of the magnetic
field
> is, by convention, made equal to zero, which is the condition that
> establishes the "non-existence" of magnetic monopoles (with curl of
> the electric field a non-zero function of electric-charge density).
>
> Furthermore, as noted in the article, the mass of a magnetic
monopole
> would be nearly 70 times that of the electron, according to the
most
> optimistic interpretation of the situation. That puts it far
outside
> the detection range of all existing colliders, and even beyond the
> capabilities of the coming largest Tevatron ever built (scheduled
to
> go online sometime next year).
>
> In any case, it was largely to explain the lack of magnetic
monopoles
> in the visible universe that some astrophysicists proposed the
theory
> referred to as "Inflation"; a superluminal phase of outward motion
in
> the first moments of the Big Bang, in which, it is said, the
density
> of magnetic monopoles (and, therefore, magnetic "charges") shrunk
to
> nothing (though electrical charges, poles, and currents, and their
> counterparts in the weak-nuclear and strong-nuclear fields, are
still
> very much with us, in large numbers).
>
> So, we have a proposal from respected scientists which implies that
> all magnetic monopoles remained in superluminal states of
existence,
> and that this fact is why we cannot detect them.
>
> In other words, it is suggested that actual magnetic monoples are
> tachyonic in nature. Thus, they can be depicted, theoretically,
> using the tachyonic analogs of their standard representations.
>
> Now, while I noted elsewhere that using the tachyonic analog of a
> magnetic monopole to explain gravitation is not as empirical as the
> tachyonic-gravity model I propose in my thesis, the tachyonic
analog
> of a magnetic monopole does explain the so-called Dark Matter and
> Dark Energy that cosmologists are looking for, to account for the
> extra amount of gravity they have determined must be present in the
> universe (i.e., because there is more gravity than is coming from
the
> detectable mass in the universe), and to account for the
acceleration
> in the rate of expansion of the universe (for which they have
offered
> very few explanations, with none of them satisfactory),
respectively.
>
> So, there you have it. The Dark Matter they seek is the tachyonic
> mass of superluminal magnetic monopoles, and the Dark Energy is the
> virtual quanta of the associated superluminal magnetic fields.
>
> To represent this situation mathematically, then, we can simply
write
> Maxwell's equations for the elecric field as usual, with the
magnetic
> field representations modified to be of the same form as those for
> the electric field (as shown in Schwarzschild's article), except
that
> magnetic charge-density, magnetic current-density, and magnetic
force
> are tachyonic; written as actual imaginary quantities, defined by
> applying a suitable representations theory, such as using an
operator
> (like the imagination-unit I present in my thesis) which transforms
> the standard terms into their respective tachyonic analogs.
>
> In short, we can hold that Tachyonics explains Dark Matter/Energy
in
> a manner that is consistent with the observational data on which
the
> prediction of the existence of Dark Matter/Energy is based.
>
> Of course, the implications for the revision of cosmology theories
> can only be guessed, at this time, but such an explantion, if it
> proves true, is sure to cause a revolution in our understanding of
> the creation, evolution, and present condition of the universe.
>
> EOF
>