--- In TheAoISCT@yahoogroups.com, "HKurtRichter" <hkurtrichter@...>
wrote:
>
> Stay tuned for a new article on my mathematical invention, The
> Imagination Unit, also referred to as Richter's Tachyon Operator.
>
> I intend to provide a formal representations theory that explains
how
> the imagination-unit can be used to represent tachyonic variables.
>
> The purpose for employing such an operator is as follows.
>
> Given a particle of mass m, moving at velocity v, which may or may
> not equal lightspeed c, there are three relativistic cases;
> (1) v < c, so that m is real (such as for electrons, protons, etc.),
> (2) v = c, so that m is zero (such as for massless photons), and
> (3) v > c, so that m is imaginary (such as for tachyons).
>
> This above a commonly-used introduction to the idea of tachyons.
>
> The standard representation of a tachyon, therefore, is obtained by
> multiplying the mass m by the standard imaginary-unit, i, to make it
> a pure imaginary, im, where i = (-1)^(1/2) ; i^2 = -1 .
>
> One problem with the standard representation, however, is that we
> have no way to distinguish between different types of tachyons.
> All such tachyons are essentially the same, and could travel at any
> velocity above lightspeed, up to, and including, infinite speed.
>
> Also, the standard imaginary-unit, i, is used in other ways that are
> not associated with tachyons. For instance, due to the manner in
> which the imaginary-unit comes about in the representations of
waves,
> it appears as an operator in the Schroedinger equation of Quantum
> Mechanics, which is used to describe the behavior of a particle with
> wavelike characteristics, which are themselves represented, in turn,
> by a wavefunction. But the use of i in the Schroedinger equation
> does not imply that the particle is a tachyon. So, if we have a
> particle of mass m, described using the Schroedinger equation, but
we
> also wish to discuss a tachyon of mass im in the same context, then
> how are we to know that the i in the Schroedinger equation is used
> differently than the i in the definition of the tachyonic mass, im?
>
> We could use two different symbols for i, but that does not solve
the
> problem of the confusion caused by using two different applications
> of the same operator, (-1)^(1/2), in the same context.
>
> To solve this problem, we need an entirely new imaginary-unit; one
> with a different definition than the standard imaginary-unit, i.
>
> To the point, we can use an operator i^i that is defined as causing
> the mass m to be transformed into its tachyonic analog. Thus, if m
> denotes the mass of a standard particle, then (i^i)m is its
tachyonic
> analog, so that im no longer indicates a tachyon, but is simply the
> pure imaginary obtained from m, by multiplying m by i.
>
> To illustrate the significance of this representation, consider the
> complex mass M obtained as the sum of a real mass m and an imaginary
> mass im, defined according to the equation denoted;
> M = m + im.
> Here, m is the real component of M, and im is the imaginary
component
> of M, but im is not tachyonic.
> A corresponding tachyonic version of M is defined;
> (i^i)M = (i^i)(m + im) = (i^i)m + (i^i)im .
>
> Now, the sum M + (i^i)M is a special case, called a "supercomplex"
> mass. It is the sum of the standard complex mass and the tachyonic
> complex mass. The concept of such a supercomplex mass would not be
> possible without the use of a tachyonic transformation operator,
such
> as the new imaginary-unit, i^i, which I call the "imagination-unit".
>
> Now, in Quantum Mechanics, all particles are described using complex
> variables. Employing the imagination-unit to define tachyons allows
> us to discuss ordinary particles and tachyons in the same
theoretical
> context without changing the meaning of the standard imaginary-unit.
>


I have, of course, already made use of the imagination-unit in my
thesis on tachyonic gravity, where I suggest that the quantum of
gravity is a special kind of waveless tachyon. There, I employ my
new imagination-unit to describe this tachyon, which I refer to as
an "imaginary gravitational exchange tachyon", or "IGET".

For a short version of the thesis, click-on "Tachyonic Gravity" at
www.TachyonicsSociety.com.
Or, for the extended version, go to
http:hometown.aol.com/TachyonicGravity/TLQTtGR01.html.

The imagination-unit can also be used for other purposes; in any
situation requiring a description of tachyons that does not depend on
defining them by applying the standard imaginary-unit, so that
tachyonic quantities are not easily confused with other imaginary but
non-tachyonic quantities discussed in the same contexts.

How this information applies to the effort of constructing a Proto-
Core of data for an Interdiscipline Synthesis Cosmology, ISC, is that
the first fundamental assumption on which to justify ISC is that the
new endeavor of Tachyonics (the study of the tachyon) is required for
an accurate understanding of reality. And, therefore, some means of
representing tachyonic quantities is necessary. But the standard
representation causes problems when both tachyonic and tardyonic
(slower-than-light) complex quantities are discussed in the same
mathematical context. Hence, knowledge of the best way to represent
tachyons is necessary for acquiring a complete ISC.