You are invited to join my social network, check my friends list here:
http://femtwofe.zoomshare.com/files/myphoto.htm

--- In TheAoISCT@yahoogroups.com, Jonesalonzo1@... wrote:
>
> What are the most likely sources of possible tachyons?? We would
likely need a source so that we can use them in an experiment in an
effort to prove their existence.? Once we have them we can devise an
apparatus to manipulate them into causing an effect that won't be
explainable by any other means.? To do that though, we not only need
a source but also we will need to know their properties,
specifically, their speed... how many times the speed of light is
it?? and is it a constant speed?? We need to know this so that we can
create the apparatus to manipulate them.? It should be pretty
simple.? It could be based on a version of early atom smashers (so
that we can keep the cost of creating it cheap)... maybe a simple
linear accelerator?? It would have to be redesigned to work at the
faster than light speeds.? The problem here is I think the tachyons
may have to be charged for them to work in the machine though.
> _____


Reply from H.Kurt Richter:
Sorry it took so long for me to respond to this post, but things have
been up in the air for me this whole year.

Anyway, one source for tachyons could be quark interaction activities
called "flavordynamics".  It has long been known that flavor is not
conserved in weak interactions between quarks.  This fact allows for
extremely small amounts of energy to be released from all weakly
interacting quarks; consistent with experimental data.  And since
infinite speed is the tachyon's zero energy level, it is reasonable
to assert that very high speed tachyons (not necessarily inifinte
speed, but say "near infinite") could be produced quite easily in
these types of interactions.

As for detecting the tachyons, I am afraid technonoloy will have to
catch up to theory before that can happen, because we remain bound up
with the electromagnetic spectrum, per-force, as you noted (with
respect to possible tachyon charge), and cannot seem to find ways to
detect things that do not somehow disturb or otherwise affect an
electric, magnetic, or electromagnetic field, or which causes some
detectable change in materials at macroscopic distance scales.  My
contention is; with the implication from M-Thoery, that our universe
is simply one of millions, in a multi-verse of alternate-dimensional
universes, attempts at detecting (not just confirming the existence
of) alternate dimensional energies will enable us to understand how
to detect tachyons  --  if tachyons are not indeed the first
alternate-dimensional objects to be confirmed (which is, in my
opinion, the most likely scenario).  Perhaps the new LHC will provide
some directions for researchers to take, in that respect.

The problem with speculating that there are charged tachyons is the
assumption that it is ordinary charge, like that on an electron or a
proton.  But that is not a logical assumption.  Rather, the charge on
a tachyon would more likely be a superluminal analog of our version
of charge, and would therefore be just as undetectable as the
tachyon's mass, energy, momentum, etc.  Consequently, a breakthrough
in detecting an alternate-dimensional type of charge is needed, if we
want to relate tachyonic charge to bradyonic charge.


EOF
___________________________________________________________________
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I believe that Astrology will eventually be counted among the
sciences by the scientific community at some point in the future;
perhaps as a "soft" science, like psychology.
And I suggest that this will come about because physicists will
finally recognize that undetectable alternate-dimensional forces,
such as superluminal forces, establish connections of various kinds
between all objects in the Universe, and that some of those forces
constitute astrological influences, with observable effects on the
human psyche.

Knowing about tachyons, a proper understanding of which requires that
at least one set of alternate dimensions exist in the form of a
mathematically imaginary superluminal spacetime (corresponding to our
mathematically real spacetime), brings with it the implication that
astrological forces are actually tachyonic - which explains why such
forces cannot be detected using the kinds of particle-detection
instrumentation we currently have available.

But that is going to change, as follows.

Many physicists are already trumpeting the call to embrace alternate
dimensions as a way to explain things that the standard models of
particle physics and cosmology cannot address. Consider, for
instance, Harvard physics professor Lisa Randall, and her
article "The Case for Extra Dimensions" in the latest issue of
Physics Today magazine (July 2007, page 80), where she writes: "Extra
dimensions can have implications for the world we see, and they can
explain phenomena that seem utterly mysterious when viewed from the
perspective of a three-dimensional observer." [ Online, see:
www.physicstoday.org ]

Randall goes on to state flatly that the Large Hadron Collider,
scheduled for startup next year, will prove, within the next five
years, that there exists an extra dimension associated with gravity,
and which explains why gravity is the weakest of the four fundamental
forces (because it is very strong in an alternate-dimensional realm,
called a "brane", and dissipates most of its energy in that realm,
instead of in ours).

I personally contend that gravity too is faster-than-light, and is
therefore a tachyonic force, which hypothesis is actually consistent
with Randall's theory (she has published a book on her gravity
theory). And I predict that confirmation of Randall's ideas, by
experiments carried out with the Large Hadron Collider, will lead
physicists to the very same conclusion. They will be compelled to
admit that the search for the quanta of gravity and the search for
tachyons is one in the same search.

This, in turn, will lead to experimental proof for the existence of
tachyons, which will be accompanied or immediately followed by
empirical proof that many previously unexplained paranormal
phenomena, such as psychic ability and astrological forces (presently
discounted by most scientists), will find satisfying explanation when
Tachyonics (the study of tachyons) is employed to understand the
energies involved.

For more on tachyons and Tachyonics, go to
www.TachyonicsSociety.org

--- In TheAoISCT@yahoogroups.com, Jonesalonzo1@... wrote:
>
>
> Ahaz and Manasseh are false Thirteens in the zodiac from Abraham
to  Josiah.
> Then the true Thirteens appears as Hezekiah and Josiah, the
Reforming  Kings.
> And all three of these --- True Shepherd, Final Judge and
Reforming  King ---
> are summed up in the New Testament in the figure of Jesus Christ.
He  appears
> in the sequence after the False Thirteen, Judas Iscariot, the
Betrayer.
>
>
>
>
> I'm missing something here.  Weren't there 12 disciples?  So  how
does Judas
> qualify as number 13?  I think I might suggest  something.  It
could be that
> Judas let the devil come into him, so  actually the devil was the
13th member
> of the group.


In the Old Testament sequence (The Torah sequence)

0  1  2  3  4  12  5  6  9  7  8  11  13

starting with number One, the twelfth position is number Thirteen.

The Bible zodiacs are covered in the archives of the following forum:

      http://yahoogroups.com/group/Finnegans-Wake

Peter is number One among the disciples. That is why he is named

Peter,i.e. the rock and foundation (TAURUS 1, fixed earth).

Paul

To Kurt Richter

Thank you for responding to my post regarding the story-telling numbers.  I am
not competent to comment on Tachyonics,  but I would like to offer a general
view on a Unified Theory of Everything.

It is a  contradiction-in-terms. A theory is an articulation.  Articulation is a
function of Division, Duality (2). Unity (1) cannot be articulated. It can be
expressed, but not articulated. The search for a theory is thus futile. It is
only more going in the wrong direction, in the direction of division. Duality is
conflict, corruption. That is why the Bible  pictures the first division as the
conflict between the brothers Abel and Cain, which results in the first murder.
That is why higher mathematics produces nuclear weapons.

The Fall from a unified (1) to a divided (2) mind is followed by the birth (3)
of the dream-world, the Cancer-Capricorn Round, the illusory cycles from birth
(3) to cyclic End (8) and back to birth again. All articulated statements give
rise to their own opposite, their own contradiction. In the reunified mind
(stage Eleven, the new One, the new Unity) there is no attachment to theory.
Everything is spontaneous and not repeating. Everything is unknown.

I apologize for the deficiencies in my articulation. Thank you for listening.

Best wishes,
Paul Albertsen

__________________________________________________
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--- In TheAoISCT@yahoogroups.com, Jonesalonzo1@... wrote:
>
> ... hkurtrichter@... writes:
> I  believe that our emotions, our mind, and our life-force are all
> interrelated at the quantum level, just as you noted, but view them
> as  significantly different from each other.  ...
>
> Do you think there might be a different type of tachyon for each of
these (3?) fields?
>


Exactly.  And more!

Consider this.  Physicists know of at least four fundamental forces of
nature; gravity, electromagnetism, and the two nuclear forces.
Each of these forces involve fields of different kinds.

Gravity is a central force field, and I believe it is tachyonic in
nature.  I have a saying about it that I use rhetorically whenever I
get the chance.  I say:  "Gravity is faster-than-light, and is
therefore a tachyonic force".  By this I mean that gravity is mediated
by a special kind of tachyon (although mainstream science has it that
there is a spin-2 massless "graviton" traveling at lightspeed).
Then there are the electric and magnetic fields, involving photons, and
which, whcn acting together, comprise an electromagnetic field.
And, of course, there are the nuclear fields, of which the strong
nuclear force is described using fields involving virtual particles
called "gluons", which serve to bind protons and neutrons together in
the nucleus of an atom.

Now, if the implications of Einstein's theory of Special Relativity are
correct about the possible existence of at-least one superluminal
universe coexisting with our standard universe, then that opens up the
possibility of tachyonic analogs of all of these fields (except for
gravity, of course, which is already tachyonic).

Each of these fields naturally accomplishes something different.

So, it is not such a stretch to imagine that other types of tachyonic
fields exist, and that some of these explain certain aspects of our
human physiology, such as the life-force, our emotions, and the inner
workings of the human mind.

To:  Captain Jim,

Thank you for your comments.  Your participation is greatly
appreciated.  I would thus like to continue along these lines, and
respond a little to your post.

You Wrote:
That's an interesting premise... that astrology is linked to
tachyonics.  Astrology is based on a sort of "action at a distance"
principle... the idea that stars and planets billions of miles away
can have an almost instantaneous effect on people and things on earth
in general.  Maybe it isn't exactly instantaneous but just really,
really fast (ftl... like a tachyon).  Its interesting to note that
action at a distance is the phrase that is also used to describe
Newtonian gravity.  And gravity is also postulated to be the result
of tachyonic action.

My Response:
Actually, the concept of instantaneous action-at-a-distance for
gravity was not Newton's idea, and he disapproved of it.
It was the contention of another scientist named Cotes, whose
suggestion happened to become popular, and is still with us.
Newton himself believed in what you hinted; that gravity acts at a
distance, but not instantaneously (i.e., not with infinite speed).
He believed that there was indeed an agent of some kind, and that it
acts faster-than-light (though not infinitely so), yet he left the
question as to the true nature of this agent quite open to debate.
My thesis on gravity, which involves a special type of tachyon as the
gravitational-exchange particle, answers that question.
[ See "Tachyonic Gravity" at www.TachyonicsSociety.com ]

You Also Wrote:
As far as the idea of the seat of our emotions being tachyonic.  I'm
not so sure.  I think most of it is just simple biochemistry,
however, I'm not willing to rule out that some component of our
nervous system might be influenced by quantum effects.  And quantum
effects are, again thought to be the result of tachyonic activity.
So while I don't see emotions as purely the result of tachyons, they
could very well be a factor in the workings of them but I think
acting on an even more basic level than emotions.  They might be the
origin of our "soul".  Which brings us back to the idea that the soul
works or exists in some "astral" plane.  The connection of course is
the astral- part of astrology.

My Response:
Allow me to clarify.  By suggesting that the "seat" of our emotions
is tachyonic, I do not rule out the biochemical factors, and agree
largely with what you said.  Obviously, detectable external stimuli
will cause our emotions to change, but so will undetectable stimuli,
such as our thoughts.
When we hear an old song that brings up either happy or sad memories,
it can stir our emotions quite effectively. But what exactly is doing
the stirring?
I believe that our emotions, our mind, and our life-force are all
interrelated at the quantum level, just as you noted, but view them
as significantly different from each other.
The life-force, it seems to me, must be a tachyonic field that
permeates the entire universe, and our physical bodies are animated
by merely interacting with it.
Our minds also work because our physical brains interact with another
kind of tachyonic field, and our emotions have their field too.
In that sense, therefore, because tachyonic fields of any sort must
be represented as actual-imaginary fields, mathematically, then they
can logically be labeled as spiritual (astral) in nature.  Hence the
connection to astrological influences from the planets and stars;
assuming, of course, that celestial objects emit tachyonic radiation
of different kinds, in addition to detectable forms of radiation,
such as photons constituting electric and magnetic fields; the quanta
of gravity alreacy assumed to be a special type of tachyon [although
there is evidence that photons themselves have tachyonic substructure
(are made of very small tachyons)].
Put more broadly, Tachyonics allows us to postulate a superluminal
foundation for the observable universe.  That is, the ultimate
building-blocks for everything we know (whether you view such
constituents as string-like, as point-particles, or as something
else) are probably super-small tachyons.  And, therefore, many of the
interaction energies assocaited with life, the universe, and
everything, in addition to detectable energies, will necessarily be
tachyonic in nature.

--- In TheAoISCT@yahoogroups.com, "HKurtRichter" <hkurtrichter@...>
wrote:
>
> To:  Paul,
>
> Thank you for posting to The AoISCT message board.  I am pleased to
> allow you to present your ideas, which I find intersting, because I
> too incorporate Astrology into my world view.
>
> There is one thing I would like for you to comment on, however,
which
> I have not seen you do much of yet.  It is just this:
> Our primary supposition at The AoISCT Group is that Tachyonics (the
> study of tachyons) can be used to explain a variety of supernatural
> phenomena, including astrological influences.
>
> In particular, we hold that, in addition to gravitational,
electric,
> and magnetic fields, there are also tachyonic fields at work (i.e.,
> fields of energy in which the exchange-particles travel faster-than-
> light), and these perhaps have an even more profound affect on
human
> minds and emotions than do those "detectable" fields, which mainly
> influence our physical bodies (with indirect affects on our mental
> faculties), while superluminal fields can affect our minds and
> emotions quite directly; assuming, of course, that the life-force,
> the source of thoughts in our minds, and the seat of our emotions
are
> all themselves tachyonic in nature.
>
> I would very much like to see how you would go about incorporating
> Tachyonics into your theories, and how you would then relate your
> ideas specifically to Interdiscipline Synthesis Cosmology.
>
That's an interesting premise... that astrology is linked to
tachyonics.  Astrology is based on a sort of "action at a distance"
principle... the idea that stars and planets billions of miles away
can have an almost instantaneous effect on people and things on earth
in general.  Maybe it isn't exactly instantaneous but just really,
really fast (ftl... like a tachyon).  Its interesting to note that
action at a distance is the phrase that is also used to describe
Newtonian gravity.  And gravity is also postulated to be the result
of tachyonic action.  As far as the idea of the seat of our emotions
being tachyonic.  I'm not so sure.  I think most of it is just simple
biochemistry, however, I'm not willing to rule out that some
component of our nervous system might be influenced by quantum
effects.  And quantum effects are, again thought to be the result of
tachyonic activity.  So while I don't see emotions as purely the
result of tachyons, they could very well be a factor in the workings
of them but I think acting on an even more basic level than
emotions.  They might be the origin of our "soul".  Which brings us
back to the idea that the soul works or exists in some "astral"
plane.  The connection of course is the astral- part of astrology.

To:  Paul,

Thank you for posting to The AoISCT message board.  I am pleased to
allow you to present your ideas, which I find intersting, because I
too incorporate Astrology into my world view.

There is one thing I would like for you to comment on, however, which
I have not seen you do much of yet.  It is just this:
Our primary supposition at The AoISCT Group is that Tachyonics (the
study of tachyons) can be used to explain a variety of supernatural
phenomena, including astrological influences.

In particular, we hold that, in addition to gravitational, electric,
and magnetic fields, there are also tachyonic fields at work (i.e.,
fields of energy in which the exchange-particles travel faster-than-
light), and these perhaps have an even more profound affect on human
minds and emotions than do those "detectable" fields, which mainly
influence our physical bodies (with indirect affects on our mental
faculties), while superluminal fields can affect our minds and
emotions quite directly; assuming, of course, that the life-force,
the source of thoughts in our minds, and the seat of our emotions are
all themselves tachyonic in nature.

I would very much like to see how you would go about incorporating
Tachyonics into your theories, and how you would then relate your
ideas specifically to Interdiscipline Synthesis Cosmology.

(continued)

TWELVE  When we combine the numbers of a major pair of opposites in the basic
unit (1-4) --- the flow of Time (female 3) and the structure of Space (male 4)
--- we have their product as 3x4=12. Thus in this sequence, step number Twelve
is the entire time-space continuum, the Totality. And now, in the astrophysical
field, the expanding universe is filled by a uniform cloud of hydrogen atoms
(along with a small percentage of helium). We might refer to this as the
universal theater, where all the dramas of female (3) and male (4) of time and
space, and other opposites, will be played out. Nothing is yet actualized, but
everything is possible. It is like a fog, where any kind of shape might be
imagined, but nothing is ever defined.

The universal fog is unlimited, so this number Twelve is represented by PISCES,
the Fishes, for the ocean, as an image of infinite expanse, a Totality. And this
totality includes not only the past development of the universe, but all  future
growth as well.

As an example of Three (CANCER) and Four (LEO)  working together, consider the
flowing circulation of the blood, like a stream of running water (3) and the
pumping of the heart, with its Four-chambered  structure. The heartbeat is in
two parts, systole and diastole, suggesting the strong and weak sides of lame
Leo.

FIVE   The two focal points of the ellipse (4) now coalesce into a single point.
This causes the perimeter to become a Circle, and concentric circles. This
return to the pristine point of unity might be why stage Five is associated with
virginity, as VIRGO (5). That is only one way in which stage Five might be said
to look backward rather than forward. VIRGO is the last sign of the first half
of the standard zodiac. So as a minor End it is backward looking or at least
motionless. The motionless character is also indicated by Five being the Middle
number in the sequence we are using here (and the Bible uses).

      0   1   2   3   4   12   5   6   9   7   8   11   13

The middle looks neither forward nor backward, but is stationary, as is the
center of a circle. So in Genesis 49 Issachar (5) is described as "lying down",
i.e. motionless. And in the book of Joshua (5), Joshua conquers Jericho by 
leading a march around its perimeter, encircling it. In that book God makes the
sun and the moon stand still in the middle of the sky.

Further, the circle rotates around one of its diameters to become a Sphere. So
stage Five has two geometrical figures of movement.

Number Five is the first Sum in the sequence. (Number Four might better be
regarded as a doubling of the same number. And Three is not Two plus One because
One is unity, and there is nothing else to add it to.). So the first Sum is
2+3=5. Thus the summarizing, comprehensive work of VIRGO, shaping and arranging
everything in its proper order in the universal theater. (As a similar but
fictional summation or Summa, compare the "Comedia" of Dante. And for his
historical position as VIRGO, see "Great Cycles of History", Age of PISCES, Era
of VIRGO.)

      http://geocities.com/zreunion/Cycles.html

In terms of astrophysics, the all-encompassing concentric circles, suggest a
Summation of everything. Thus this is the stage in which all the matter in the
universal theater is differentiated and defined. Gravity pulls groups of atoms
together into galaxies and stars and planets. And in the stars, all the heavier
elements are formed. Also in this step the chemical compounds are formed. So
this is a stage of tremendous labor, fitting the VIRGO reputation for tireless
work. And as the two focal points of the ellipse coalesced, we might say that
the matter of the universe coalesces in this stage to form the catalog of
heavenly bodies. As the previous stage was likened to a universal theater, in
this present step Five all the furniture of the theater is shaped and is
arranged in its proper place in the all-encompassing design. So the stage is
set. The astrophysical, preparatory steps are complete. In the second half of
the sequence we will enter the realm of the Biosphere.

SIX     Life. Now, into the universal theater is introduced the cast of
characters. The living ones are all based on the cell. There are two geometrical
figures-of-movement in this stage: The Sphere is carried over from the previous
step. But now it looks forward, so to speak, rather than backward,as (LIBRA 6)
is the beginning of the second half of the standard zodiac. And it looks forward
to the second figure derived from the circle: the Helix. As the helix turns
around its perimeter, while moving forward into the third dimension, it might be
called the "discovery figure" of three dimensions.

Apparently all forms of cellular life, from the amoeba to human beings, are
based on the DNA molecule. And the shape of that molecule, as recently
discovered, is a double Helix.

Number Six is derived here as 3+3 or Three on each side. With Three on each side
there is a Balance.But as the swinging arc of that step is always in motion, the
is also the potential for imbalance. We cannot have Balance with out its
opposite being possible. Thus this stage is likened to the balance scales,
LIBRA, and specifically the balance scales of Justice.

This balance step is the stage of Compromise, of diplomacy.

NINE     Death. Number Nine is Three squared, or the first higher "power" of
Three. And as Three is relatively incoherent, the power of incoherence is
Disintegration. But such decay frees
life from old forms and prepares the way to new growth. Nine is out of place in
the sequence, perhaps in order to directly oppose TAURUS (1) unity, where Place
is all-important. SCORPIO opposes Taurus in the standard zodiac. In the Bible,
this is the stage of Satan, the great Serpent. And a serpent is a great
swallower, as is death. This is the stage of the Antagonist, the Rebel.

The "geometrical" figure of Nine, SCORPIO, is the Vortex, which is derived from
the helix of stage Six, producing a spinning funnel-shape. This can appear as a
whirlpool, and as a destructive tornado, a "twister". Thus where Libra (6) tends
toward compromise, SCORPIO is the step of uncompromising Commitment, to one side
or the other, war. In the Bible, stage Nine is represented by Saul, the
rebellious king, always having his spear at his side, like a scorpion's sting.

The three preceding stages can also represent the three faces of the Great
Mother Goddess, Cancer (3)  who gives birth to all things:

VIRGO  (5)  the virgin              For example, Greek Artemis (Latin Diana)
LIBRA   (6)  the sexual partner, nubile woman         Aphrodite (Venus)
SCORPIO (9)  the  hag, witch                                Hecate

The Moon and Time also have three phases.

                                      (to be continued)

Paul Albertsen

__________________________________________________
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(continued)

SEVEN        Growth resumes, but in place of cellular growth (stage 6) there is
now Social growth. And in a human context, the height of social growth is
Civilization, with its institutions:  governmental, economic, religious,
scientific, artistic, educational, etc. In the geometrical sequence, we might
think of this as a multitude of expanding spheres, which expansion makes
civilizations imperialistic, encroaching on one an- other's territory.

Seven is derived as 3+4, making it the second and last Sum in the sequence. It
is also the largest sum and the sum of female-male, time-space, so SAGITTARIUS
is associated with large size, ripeness, maturity and winning at contests,
complete development, classics. The emblem of this sign is an archer, shooting
an arrow upward and forward, indicating the Aspiration to higher things that is
associated with this sign. And as it is also concerned with bringing youth to
maturity, this the sign of the Teacher.

EIGHT     Expanding spheres (stage 8) tend to expand against each other, thus
creating lines of Limitation between them. These boundary lines move back and
forth as one sphere expands (7) and the other contracts (8). An example is the
Millenia-long conflict between Western Civilization and Middle Eastern
Civilization. It began around 700 B.C. between the Greeks and the Phoenicians.
And it continued between the Greeks and the Persian Empire, until the latter was
conquered by Alexander. That conquest initiated a thousand year occupation of
Middle Eastern territory by the Greeks and then the Romans. So the line of
limitation between the two civilizations was shifted far to the east.

The occupation was ended by the rise of Islam, under which banners the middle
easterners counter-attacked, regaining lost territory and more. The line of
limitation between the two was shifted into the West, into Spain, and under the
Ottoman Turks, it was shifted into and over Anatolia. The western Crusaders made
a short-lived attempt to counter-attack, but their success was only brief. The
Ottoman Empire then expanded over the Balkans , westward all the way to Budapest
at one time.

Eight is a double Four. As four was the stage of Structure, Eight is a double,
or intensified structure. We might call it Inner Structure. Thus the interest of
CAPRICORN (8) in finding out the inner-structure of things, by Study. Examples
are delving into the inner structure of the atom in physics, and into the inner
structure of the cell in biology. And it might be congruent with this to think
of the geometrical figure of stage Eight as contracting spheres.

The emblem for this stage is a mountain goat with a fish's rear body, suggesting
the upper and lower Limitations of earth-bound life. And another major
limitation is here reached. A movement began with stage Three, the opposite
sign, CANCER. That sign of birth, after the duality of the preceding GEMINI,
gave birth to the whole world of duality-opposition. But in duality, everything
that begins must have an end. And CAPRICORN (8) is the limit or end of what
began in stage Three. From birth (3) to end (8) and back to birth again. This is
thus a Cyclic end, recycling over and over and over again. And everything in it
is based on the ambiguity of two points (GEMINI (2), which keep changing by
reversing polarity. There is thus an implicit illusory quality to the
CANCER-CAPRICORN Round. Everything is changing and there is no permanent
identity. It is the stuff that dreams are made of. And the recirculating cycles
keep repeating over and over again. As the American playwright
Eugene O'Neil said despairingly (and not quite correctly), "There is no present,
no future. There is only the past, repeating over and over and over again". It
is from this Dream Round that some people aspire to escape, to awake.

The Archer's arrow (7) aspiring to go beyond the repeating Round, falls short.
In a dualistic world, what goes up must come down. That is another Limit which
is reached here.

The rhythm of expansion-contraction, expansion (7)-contraction (8) sets up a
back-and-forth swinging between the two polarities, a tide-like alternation that
reminds us of the swinging arc of CANCER (3). So from stage Eight (8) CAPRICORN,
we suddenly find ourselves back at stage Three again. And we are about to be
born into another Round of the repeating dream cycle. In the End (8) there is
only new beginning.

And the universe itself is said to be in a rhythm of expansion and contraction.

TEN     Ten is not counted, because it is Zero again.

ELEVEN     As we have seen cellular life (6) and social life, Civilization (7)
we now consider Individual life (11).  But it is a particular form of individual
life that is meant. It is the individual who goes beyond the contradictions of
Duality, beyond the tempting allure of the Dream Round (3-8). He or she is
detached from the apparent reality of existence. As Eleven is the new One, the
individual finds reunion, the new Unity. For example, in the Bible, Joseph
presides over a great reunion of his family. And he is "set apart from his
brothers", i.e. a unique individual. He is number Eleven among the brothers in
Genesis 49.

As Joseph was morally incorruptible, another figure is raised again from the
corruption of death, apparently to physical incorruption. That is Lazarus, who's
story is presented in chapter Eleven of the gospel of John. We might cite two
more examples: John the Baptist takes the place of Malachi, "My messenger" the
last book in the Old Testament. Malachi is number Eleven among the minor
prophets. And Elijah and Elisha are two men in one spirit, representing the
function of this stage to reconcile opposites. When they first meet, the younger
man (Elisha) is plowing with twelve pair of oxen. He sacrifices one pair,
leaving Eleven. They occupy position number Eleven in the zodiac from Abraham
(1) to King Josiah (13). And they reappear in the Bible's last book, the book of
"Revelation", as the Two Witnesses --- in chapter Eleven.

But few people attain this degree of reconciliation. Most fall far short, so far
as falling into the condition of fallen (divided) man and woman, LEO (4) and
CANCER (3). An example of this short-coming is the tale of Samson and Delilah,
locked in their fatal embrace. He is identified as LEO by fighting with a lion,
and she as CANCER by coming from a river valley (flow, running water). They
occupy place number Eleven in the book of Judges. Another example is found in
the Grail-story, "Parzifal", where Gawan fights with a lion, in chapter Eleven.
The true AQUARIAN in "Parzifal" is apparently his brother Feirefiz who learns to
see the Grail. He, "stayed (at the Grail castle) for Eleven days, and departed
on the twelfth". In this sequence, Eleven is the twelfth number.

            0  1  2  3  4  12  5  6  9  7  8  11  13

We might call that the Torah sequence.

Eleven is the new One, but unlike the first unity (1) Eleven is not followed by
Division (2). Hence it remains together, incorruptible in a way.

The zodiac sign of this stage is AQUARIUS, the water carrier. The air is the
carrier of water that evaporates from the sea, evaporation thus representing
detachment, refinement. The emblem or glyph for AQUARIUS is the Human Being.

THIRTEEN     Thirteen is Beyond the universe of Twelve, as Zero is Before it.
They share the same sign, ARIES, the Ram. We might show this stage in a
quotation from the beginning of the gospel of John, with a suggested
translation:

       In the beginning was the Original Intelligence (Greek: Logos). And the
Original Intelligence was
       with God. It was of the same nature as God. By it were all things made ...
And it came and lives
      among us.

There are two ARIES (13), a false on and a true one. For example, in Genesis 49
the list of brothers concludes with Benjamin. As Aries the Ram he should be the
leader of his sheep ,his flock. But instead he is described as, "a ravening
wolf". He is a false shepherd, a false ARIES (13). The true Thirteen appears in
the next book (Exodus) as Moses, the good shepherd who leads his flock to the
promised land. He is the true ARIES (13).

Again we might cite the two tales of false Levites that concludes the Book of
Judges.They are false Thirteens. the true Thirteen appears in the next book as
Samuel, the Final Judge.

Ahaz and Manasseh are false Thirteens in the zodiac from Abraham to Josiah. Then
the true Thirteens appears as Hezekiah and Josiah, the Reforming Kings. And all
three of these --- True Shepherd, Final Judge and Reforming King --- are summed
up in the New Testament in the figure of Jesus Christ. He appears in the
sequence after the False Thirteen, Judas Iscariot, the Betrayer.

Jesus Christ, as the Original Intelligence, enters the fallen , divided, world
of the CANCER---CAPRICORN Round. And he takes upon himself the most conspicuous
role, the sacrificial king LEO (4) in order to encourage people to leave the
fallen, divided, world, to awaken from the dream.

Paul Albertsen.

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Cosmology by the Numbers II

(continued)

Six       LIBRA   Life.   In keeping with the geometric sequence, we can say
that our recent scientific discoveries indicate that Life is based on the DNA
molecule. And the shape of that molecule is a double Helix. The Helix is one of
the two geometric figures of LIBRA (6) The other one is the Sphere, carried over
from the previous stage (5). Both are formed from the circle of Virgo (5). The
sphere is formed by spinning the circle around a diameter, and the Helix by
spinning around the perimeter while extruding that perimeter out into the third
dimension, a coil shape.. Unlike the spinning sphere, which keeps going over the
same ground, the helix doesn't repeat, but keeps discovering new territory. This
fits the position of Libra (6) as the Beginning of the second half of the
zodiac. So stage Five (Virgo) being the end of the first half, looks backward,
and the sphere there looks back to the concentric circles. But the sphere of
Libra (6) looks forward, to the Helix. So as
  stage Five was one of recapitulation and summary, stage Six is one of  forward
movement and discovery.

Thus as Virgo (5) in the "Iliad" was set in the motionless scene of Troy, Libra
(6) in the "Odyssey" is an ongoing adventure. But it apparently has to overcome
Virgo (5) first. So the "Odyssey" begins with Odysseus and his men bottled up in
the cave of the giant Cyclops, in a condition of motionless stagnation. And the
Cyclops has a single circular eye, in the middle of its face. Odysseus manages
to destroy the Cyclops eye, thus metaphorically defeating Virgo (5) so that
movement can start again. And that new movement consists of the Achaeans
escaping from the Cyclops cave by clinging beneath the bellies of sheep, as the
now-blind giant lets the sheep out of the cave, feeling their backs as they
pass. So we have an image of Rebirth, a Libran renaissance overcoming the
stagnation of Virgo.

And the same theme ends the book. In Odysseus' absence, his palace has been
occupied by suitors for the hand of his wife, since she is apparently a widow.
They do nothing but hang around, in a situation of Virgoan stagnation. And his
wife, Penelope puts them off by saying that she must first weave a funeral
shroud, which she patiently works at by day, and undoes her work at night, so
that it will never be finished. She thus represents the tireless work of Virgo.
But when Odysseus returns, he kills the suitors and saves his wife from her
patient labors.

In between that opening and closing of the book, we hear the tale of the Trojan
horse, from which the Greeks emerge in another example of rebirth, thus
fortifying the Libra theme of the book.

For the position of the "Iliad" and "Odyssey"  in time, see, "Great Cycles of 
History":

                         http://geocities.com/zreunion/Cycles.html

Just as there were Three phases to Time (Cancer 3) and Four directions to Space
(Leo 4) so there are Six directions to the three dimensional stage Six,
front-back, left-right and up-down.


Nine   SCORPIO   Death. Growth (6) changes into decay and disintegration (9). 
But that is necessary, in the dualistic pulse of things, for growth to resume
and continue. Decay and disintegration produce fertile ground for the future.
Thus in FW, chapter seven, Shem takes the role of Scorpio (9) and is described
in consistently negative terms---until the very end of the chapter, where in a
reversal of opposites, the life-force ("lifewand") is with him instead of with
his brother Shaun.

Seven  SAGITTARIUS  Now growth resumes, in the form of human societies and
cultures, Cellular life (6) is replaced by Social life (7). And in the human
context, the height of social life is Civilization,  with its institutions:
economic, educational, religious. Number Seven is the largest Sum in the
sequence (3+4=7) so Sagittarius is associated with large size and completeness,
and with winning at contests. The name means the Archer, who is depicted as
firing an arrow forward and upward, indicating the Aspiration to higher things.
But being still within the dualistic world of opposites, everything that goes up
must come down. So the Archer's aspirations meet with Limitation in the next
stage.

We might say that the geometric figure of stage Seven is a multitude of
expanding spheres, each one representing a civilization or institution.
Civilization is inherently expansive, imperialistic.

Eight    CAPRICORN  The cyclic End of the repeating Round, from birth (3) to end
(8) and back to birth again. Our expanding spheres encounter one another, and
their mutual pressure produces lines of Limitation. These lines shift
back-and-forth with time as one or another of a competing pair gains ascendancy.
An example might be the line of contact and competition between Western
civilization and Middle-eastern civilization. Their conflict began around 700
B.C. between the Greeks and the Phoenicians. It continued between the Greeks and
the Persians, until Alexander defeated the Persian Empire, leading to a thousand
year occupation of most of Middle-eastern Civilization by the West. That
occupation reached its limit when the new religion of Islam inspired
Middle-easterners to reclaim their native territory and expnnd to Spain The West
counter-attacked briefly in the Crusades, but the Ottoman Turks soon recaptured
all of Anatolia, and conquered much of the Balkans. The next
  pushing of the line of limitation began with Napoleon invading Egypt, followed
by the British and the Americans in various places. Now the Middle-eastern
Civilization is trying to regain the initiative and push the line of mutual
limitation back into the West.

The same sort of interplay can be found institutionally between various
religious bodies. Two examples are Protest-Catholic and Sunni-Shiite, waging
chronic hostilities against each other. And of course the scientists tell us
that the universe itself is in a rhythm of unimaginably long expansions and
contractions.

When we consider this oscillation of expansion-contraction. expansion
(7)-contraction (8) it swings back-and-forth like the tides. It fits right into
the pendulum-like ebb and flow, and we find ourselves back at Cancer (3) again,
about to be born into another cycle of "riverrun".

Eleven  AQUARIUS  The aim of the Archer (7) is achieved. Duality is finally
overcome in Reunification. The opposites are resolved. No Self, no Other. The
opposition between the one and the many becomes the paradox of both the one and
the many at once. "Either-Or" becomes "Both-And". This is the new Unity, and
thus inarticulate. So it is difficult to say anything about it, because language
is dualistic. But let's see what others have said".

"You must exterra acquarate to interirrigate all the arkypelicans."

That is from the Wake in the last chapter's zodiac, position number Eleven.You
must evaporate to irrigate all the islands (archipelagos). And you must purify
to integrate all the fallen, divided men and women. "Arky": Noah's ark (4)
fallen man, and the mother pelican, who was reputed to make blood flow from her
own breast to feed her young: Cancer (3) fallen women. Evaporation purifies
water in this stage of Aquarius (11) the new One, called the "Water Carrier"
because the air holds all the evaporated water. And detachment from the
dream-world of the Round purifies the human individual.

But this paradoxical integration of the one and the many is difficult to
achieve. Most people remain caught up in the non-stop imagery of the
Cancer-Capricorn Cycle. So in dealing with stage number Eleven (the new One)
there is an established practice of presenting not Eleven, but the fallen Three
and Four (Cancer and Leo). A famous Biblical example of this is in position
Eleven in the book of Judges. There we find Samson and Delilah locked in their
fatal embrace. He is identified as Leo (4) by fighting with a lion, and she as
Cancer (3) by coming from a river valley.

The same picture is shown in "Parzifal" where Gawan fights with a lion, in
chapter Eleven.

Similarly in FW the Mookse and the Gripes are the strong and weak sides of Leo,
and the Gropes represents Cancer as well. They appear in chapter six, question
Eleven. Then in chapter Eleven, most of the story is taken up with Noah (4) and
the killing of the Russian general, another sacrificial king (4). But Aquarius
is represented positively in stanzas covering numbers One through Five, with a
refrain of lifting-up
and "waters parted from the sea", i.e. evaporation.

And there are a few places in the Bible where a positive Aquarian appears. The
first is Joseph, in position number Eleven among the brothers in Genesis 49. He
is separate from his brothers, unique. He resists temptation and presides over a
great Reunion, reunification, of his family.

Then there are Elijah and Elisha, two men in one spirit. When they first meet,
the younger man is plowing with twelve pair of oxen. He sacrifices one pair,
leaving Eleven. And John the Baptist, a unique individual. He is number Eleven
by taking the place of Malachi, who is number Eleven among the minor prophets.


Thirteen  ARIES  The original intelligence. What shall we say  that which is of
the same nature as "nothing", Aries (0) ? Perhaps we can offer a translation of
the opening of the gospel of John:

"In the beginning was the original intelligence. (Greek:Logos). And the original
intelligence was with God.
And it was of the same nature as God. By it were all things made.....And it came
to live among us."

Paul Albertsen



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In the best of the Grail stories --- "Parzifal" by Wolfram von Eschenbach (c.
1210 A.D.)---there is a numerical structure to the work, a structure that is
also used in the Bible. What follows is an attempt to apply that same structure,
a sequence of numbers, to the origin and development of the universe.

"Recounting" can mean counting again or telling a story. And "tell" can also
mean counting or telling a story. Can the story of the Universe be told from
counting  a sequence of numbers? And at the same time is the ancient Zodiac
involved in this? Suppose we start the count at Zero and see what happens.

ZERO     "Nothing". But then there is an event --- shall we call it the Big
Bang? And that "Nothing"---"explodes" to become Something. We might equate that
sudden rush of activity with the first sign of the zodiac, with ARIES the Ram,
always driving forward, having no place to stop.

ONE     "Something". The first substantial number. But what that something is we
cannot say, because in Unity (1) their is no identity, no articulate speech. We
might however associate this stage with the first figure of Geometry, the single
Point. Does that Something exist? It cannot be said, because to say yes or no
would be to engage in duality (2) opposition, which stage has not yet arrived.
So whatever we say about this stage is a dualistic approximation of unity (1).

This stage where everything is in a single point should not be imagined as all
the matter of the universe being compressed into a tiny space, because as yet
there is no matter, no time or space. There is just pure energy in a
dimensionless situation.

One being the first substantial number, this stage has the character of
solidity, like a rock and foundation. Hence the classification of this step as
"fixed earth", and its analogy to a Bull: TAURUS. And just as the previous stage
was the first Start, this, being the first Place (point) is also the first Stop.
And to indicate how the numbers spontaneously give rise to stories, the Bible
calls this first place the garden of Eden, where Adam-and-Eve live in unity (1)
until their Fall into Division (2).

In astrophysics this is called the stage of "perfect symmetry" where everything
is the same as everything else.

TWO     Division, opposition, conflict. The single point divides into opposite
poles. Now there is contrast, hence identity "A" is "A" by virtue of being "Not
B". Now articulation is possible. And the identities that appear are sub-atomic
particles, the best known being perhaps the Quarks. They are the basic building
blocks of matter, and occur only in pairs, polar opposites..So this stage of
division is represented as GEMINI the Twins The name "quark" was taken from the
book "Finnegans Wake" by James Joyce, a book which is based on the same
numerical-geometrical sequence as is followed here..

In the Bible Genesis story Two is counted in the persons of the brothers Abel
and Cain, a pair of opposites in conflict. Cain kills his brother, indicating
the nature of the fallen (divided) world as a place of conflict and
contradiction.

The geometrical figure for stage Two is the straight line between the opposite
poles.


THREE    As the young universe continues to expand, lowering both temperature
and pressure, the quarks bond together to form hadrons, such as the proton and
the neutron. These are the future atomic nuclei. And their bondage will last for
all time. This stage might be regarded as the beginning of Time also in another
way. The state of matter there is a Plasma, which has been described as a
nuclear soup, which apparently is a flowing condition. This situation is also
found in the geometrical figure for step Three. A third point appears,
oscillating between the two polar opposites. Its path is a curve. But this
bending arc has no fixed path, as there is no dimensional context in which to
fix its route. So its course is unpredictable and infinitely variable,
suggesting a Flow, which we might liken to the flow of Time. And to the
back-and-forth swinging of the tides.

As it moves both forward and backward, the path of stage Three resembles an
animal that walks both forward and backward, the crab. And it lives in the tidal
zone, the most fertile part of the sea.. So this part of the zodiac is called
CANCER, the Crab.

Following Unity (1) and Duality (2) Three is the stage of Multiplicity.
Unlimited multiplicity can also be read as Fertility, which combined with the
flowing nature of this step, make it the stage of the Female archetype. She is
often thought of as the Great Goddess, for example Inanna, Ishtar, Astarte,
Isis, Demeter, Cybelle.  And unlimited multiplicity can seem like a flood after
the restriction of duality. Indeed that is how Genesis portrays it, as the
world-wide Flood, where breeding pairs of all animals were saved.

This stage (3) is "Ruled" by the Moon, the ruler of the tides. The Moon has
three phases --- waxing, full and waning, just as there are three phases to
Time, past, present and future.

FOUR   Now the swinging arc of Stage Three fixes its path in one direction and
swings all the way around to form an orbit. As the two opposing points of step
Two are still present to serve as focal points, the new orbit is an Ellipse.
With its two axes at right angles to each other, and its fixed perimeter, this
is the first Structure of the sequence. And it corresponds to atomic structure.
As the universe continues to expand and temperature and pressure are lowered,
electrons are able to stay in orbit around protons, forming Hydrogen. This is
also the stage of the appearance of the structure of Space, which allows photons
to move freely about, thus permitting the advent of Light. But if the structure
of the ellipse is any guide, it would appear that this first structure of space
is somehow only two dimensional.

In the Bible story Noah builds the world's first structure, the Ark, and thus
overcomes the flood. He restores coherence to the world after the flood. But
then he gets drunk, losing his coherence. He falls from his strong side onto his
weak side, limping, as it were.
As the two axes of the ellipse might also be called "legs", one long and one
short, it suggests a limp. Or considering it as one leg, alternately long and
short, it is clear why this is the stage of the Male principle. And if there is
any humor in this, it was in the plan from the beginning.

The male archetype was often represented in the ancient pagan religion as the
divine and sacrificial King, consort of the Goddess. Such kings or gods were
Gilgamesh, Tammuz, Osiris, Dionysus, Oedipus. And inherently the king or god is
lame. Such lameness takes many forms. For example King Gilgamesh and Enkidu are
related as the strong and weak sides of LEO (4). That polarity is sometimes
reversed.  Osiris is lame in that he is missing a "leg", his penis. And King
Oedipus is lame since childhood.

This stage of light is ruled by the Sun, whose color and radiance are resembled
by the male lion. So this is the stage of LEO (4).

And that forms our initial unit, Unity (1) Division, opposition (2)
Multiplicity, Female, Time (3) Male, Space. (4).The next step begins to produce
numbers as combinations of the basic unit.

                                         (to be continued)

Paul Albertsen



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All readers here are invited to participate.

Tiwari on Tachyons

A commentary on S.C. Tiwari's book,
Superluminal Phenomena in Modern Perspective.


Book Title: Superluminal Phenomena in Modern Perspective
Subtitle: Faster-than-Light Signals: Myth or Reality?
Author: Suresh C. Tiwari
Publisher: Rinton Press

Reviewer:
H. Kurt Richter
Founder, The Tachyonics Society of America
www.TachyonicsSociety.com


Positive Promotional Review -

Dr. Suresh C. Tiwari, a physicist, of the Institute of Natural
Philosophy in Varanasi, India, authored the book Superluminal
Phenomena in Modern Perspective, subtitiled "Faster-Than-Light
Signals: Myth or Reality?".  It was published by Rinton Press,
headquartered in Princeton, NJ, in 2003.

After reading the book entirely, and studying several chapters in-
depth, I can honestly say that I remain very impressed. The huge
amount of research and deep analysis Dr. Tiwari has done, just to be
able to write such a book, comes through heroically, and I would
contend that it stands as a timely addition to the literature on
superluminal phenomena.  I recommend the book to physics and
mathematics students, physics teachers, and others involved in
research on superluminal phenomena, and who seek an insightful review
of the current state of affairs in this area of theoretical and
applied physics, along with a comprehensive list of the most
important print sources on the subject.

The book was well-planned; starting with an introductory chapter
containing interesting historical information, and an impressive
discussion of the variability of natural constants. This is followed
by a chapter on the fundamental concepts Tiwari considers essential
for an accurate understanding of superluminal phenomena (an extremely
enlightening chapter), in which he takes great pains to point out -
and clear up - a number of misconceptions that plague the topic.

The next six chapters can be read independently of each other, and
are entitled, respectively; Superluminal Propagation of
Electromagnetic Waves, Tachyons, Quantum Nonlocality, Quantum
Information Science, Astrophysical Observations, and Cosmology.

In the final chapter, Tiwari summarizes the information in the rest
of the book, then presents his recommendations on revisions to
theories and concepts associated with the basic science. Of special
interest is his suggestion that researchers should focus more on the
meaning of time, since time is not yet sufficiently well understood.
And because the very definition of velocity depends on a specificaton
of a time parameter (velocity is the rate of change in distance with
respect to time), then the progress of research into superluminal
phenomena is hampered by the fact that we do not have an adequately
empirical or philosophically satisfying explanation of time -
which, in turn, raises epistomological concerns relative to the
conceptual aspects of all such research efforts, and therefore of
many fundamental notions in physics.

More to the point, Tiwari is calling for a re-examination of the
relationship between space and time, proposing his own "Space-Time
Interaction Hypothesis"; a re-examination that would result in a new
understanding of reality, including a revolutionary reformulation of
inarguably the two most important theories in modern physics; Special
Relativity and Quantum Mechanics.

The book is available online at www.RintonPress.com
In book-stores, order ISBN 1-58949-037-1.


Critical Review -


Overview:

In what follows, it may appear, at first, that I am giving negative
comments, but readers are asked to endure the next few paragraphs
before drawing any conclusions. I am aware that first impressions
are said to be the most important, but I am bound by honesty to be as
open as possible about the book I am commenting on, before someone
buys it based solely upon the foregoing promotional review.

Dr. Suresh C. Tiwari is a physicist from India, and the founder of
the Institute of Natural Philosophy in Varanasi. The English version
of his book, Superluminal Phenomena in Modern Perspective, was
published in 2003 by Rinton Press, headquartered in Princeton, NJ,
although Dr. Tiwari himself was born, raised, and educated in India.
Consequently, it seems that Tiwari, as we all naturally do, thinks in
his native tongue, and for that reason the English edition contains a
number of, shall we say, grammatical anomolies, when taken from a
critical English mindset. It is obvious, though, even upon casual
inspection of the book, that it is the publisher who is at fault in
that respect.

I would, in fact, charge that Rinton has done Tiwari something of a
serious disservice, in that the book's English grammer is in dire
need of editing (apparently, none was done), the spacing of the
lettering is mangled in far too many places (the typesetters must
have been intoxicated), and the binding is of rather low quality,
despite the whopping price-tag (nearly $80, if ordered online).

Nevertheless, once you get past these deficiencies, recognize that
they are not of Tiwari's doing, and that the printing/publishing
decision-making behind the book was out of his control (apparently,
he had to sign all rights over to Rinton, to get them to publish it),
it becomes clear that the research Tiwari has done is important.
[Note: I would suggest familiarity with mathematics and/or physics to
the level of a Bachelor's Degree, or higher, for a proper
understanding of the book.]

As to the cost, for those on a budget, instead of buying, I suggest
borrowing through the Library Loan Program at your nearest/favorite
public, college, or university library.

The book is worthwhile reading straight through, to get a sense both
of the historical foundations of the topic and the current trends in
the field, but, for scientists needing a compendium of new research
and/or experimental avenues to consider, the book is repleat with
mention of many unanswered questions, old and new debates, and
numerous technical directions waiting to be pursued.

I especially recommend Chapter 2, on fundamental concepts, to
graduate students looking for a concise explanation of the physics
one needs to embark upon advanced investigations into the phenomena.


The Concept of Tachyons:

In the chapter entitled "Fundamental Concepts", Tiwari references
Albert Einstein's 1905 paper on Special Relativity (published in
Germany), and Einstein's book, The Meaning of Relativity, first
published in 1922. He gives a brief explanation of the Special
Theory of Relativity (STR), based on those works, and as part of that
explanation asserts that "it is only the constancy of the velocity of
light that is crucial in STR", and that "whether it has to be a
limiting velocity is unimportant." (p.29)

He also points to a book by the knighted Cambridge University
professor Sir Arthur S. Eddington, entitled The Mathematical Theory
of Special Relativity (Cambridge U. Press, 2nd ed., 1924), which
Tiwari presents as containing perhaps the first example in the
literature of a discussion on the STR-related possibility of the
existence of faster-than-light (FTL) particles (i.e., tachyons).

Now, many sources state that Arnold Sommerfeld was the first
physicist to seriously consider the existence of FTL particles that
resemble tachyons, prior to Einstein's 1905 paper. However, Tiwari
points out that G.L. LeSage (of Geneva), in 1782, was the very first
in the literature to publish the suggestion of FTL particles,
referred to as "ultra-mundane corpuscles", in an attempt to explain,
in a mechanical theory, Newton's formula for gravity [although it is
said elsewhere that LeSage, in 1758, based the now defunct theory of
what came to be called "LeSage Gravity" on the then unpublished work
(completed in 1690) of the French mathematician N.F. de Duillier].
(p.6) Thus, it appears that Sommerfeld was not the first to
contemplate FTL particles, and that Eddington was actually the first
to recognize that Einstein's STR implied their existence.

In his own book, at the beginning of Chapter 4, entitled "Tachyons",
Tiwari refers to Eddington once more, and says that, while Eddington
admitted that FTL particles are "not forbidden" by STR, Sir
Eddington "discards them on physical grounds" (p.103), maintaining
that, because the lightspeed constant, c, acts as a type of spacetime
barrier (a universal speed-limit, as it were), such particles cannot
exist. (p.34) Of course, no doubt due to Eddington's prominance,
that view prevailed among physicists for decades, and is still very
much with us (to some extent), although most physicists today
recognize that this particular assertion on Eddington's part must be
viewed as an out-dated assumption.

Tiwari cites the 1962 article in the American Journal of Physics
(number 30, page 718), entitled "Meta-Relativity", by O.M.P.
Bilaniuk, V.K. Deshpande, and E.C.G. Sudarshan, which proposed the
existence of FTL particles (later named "tachyons"), and which showed
that, despite the fact that c is a limiting velocity, STR does not
actually forbid the existence of FTL particles, and that "no physical
principles are violated" by the possible existence of such
particles. (p.103) [The name "tachyon" was coined by the physicist
Gerald Feinberg, some years later.]

Tiwari goes on to restate the well-known equations for the
relativistic scalar energy E and relativistic vectorial momentum P
for any given particle, which equations I denote here as follows;
E = m(c^2) / [(1 - [(v/c)^2])^(1/2)] ,
P = mV / [(1 - [(v/c)^2])^(1/2)] ,
where m is the particle's rest-mass, and V is its vectorial
velocity; |V| = v . (p.106)
These quantities are related according to the following formula;
E^2 = (pc)^2 + [m(c^2)}^2 .
This is referred to as the "energy-momentum relation",
where p = |P| .

Obviously, there are three types of particles implied by realtivity
operator, 1/[(1 - [(v/c)^2])^(1/2)], in the formulas for E and P.
First, if v < c, then the denominator is a real number, so that E, P,
and m are all real, although m is also required to be nonzero. We
call such particles "tardyons", from the Latin "tardus",
meaning "slow", although "bradyon", from Greek "bradys" (with the
same meaning), is also widely used.
Second, if v = c, then the denominator is zero, making E and P
infinite unless we assert that "m" is zero (which effectively cancels-
out the infinity). This, of course, is the case for massless
photons, and similar particles, for which the energy and momentum are
defined in terms of frequency and/or wavelength;
E = hf = pc , so that p = hf/c = E/c , with h = pw ,
where f is frequency, p is scalar momentum, w is wavelength, and h is
Planck's constant (~ 6.6 x 10^-34 Joule-seconds).
We call such particles "luxons", from Latin "lux", meaning "light".
Finally, if v > c, then the denominator becomes an imaginary number,
which implies that the rest-mass, m, is imaginary, although it too
must be nonzero, and we can still regard E and P as real, except that
they will be negative real, if we regard the E and P for bradyons as
positive real.

Clearly, there is no requirement from these formulas that the only
way to create a tachyon is to accelerate a bradyon past the
lightspeed barrier. The equations simply imply the existence of all
three types of particles - bradyons, luxons, and tachyons.

Furthermore, though Tiwari does not say this (it is my own
contention), while the ratio v/c in the denominator works out to show
that it would take an infinite amount of energy to accelearte a
bradyon up to lightspeed (and, likweise, an infinite amount of energy
to slow a tardyon down to lightspeed), there is no inharent
prohibition against interactions between all three types of
particles.

Now, a negative energy for tachyons means, for instance, that they
will actually speed-up as they lose energy, as viewed from a standard
(bradyonic) reference-frame. Infinite speed is the tachyon's zero-
energy level, as we see them from ordinary spacetime. And any causal
difficulty we encounter in this understanding can be solved simply by
specifying the reference-frame from which a tachyon is observed.

If necessary, we can apply what is called the "reinterpretation
principle", as suggested by Bilaniuk and Sudarshan in 1969, which I
paraphrase as follows; for any observer viewing negative energy
tachyons traveling backward in time, there can be specified another
frame of reference from which an observer views the same particles as
positive energy tachyons traveling forward in time.

In other words, it is all relative to your frame of reference. An
observer in a standard frame views a tachyon as exhibiting reversed
causality, compared to his own, but an observer in a superluminal
frame would see the tachyon as exhbiting normal causality, and would
regard the other observer as exhibiting reversed causality. (p.107)

In this context, Tiwari also mentions that there are at-least two
categorizations of tachyons, based on velocity, corresponding to the
two categorizations of bradyons; those moving, and those at rest.
Below, I present a personal understanding of this issue (based on
Tiwari's text, p.108)

A bradyon, for instance, will be considered "at rest" if it has zero
velocity measured from a frame that is also at rest with respect to
the bradyon. But a nonzero velocity measured from a standard frame
can imply one of two equivalent conditions; either the bradyon is
moving with respect to the frame from which it is being observed, or
the bradyon is still at rest (relative to another frame) and the
observer's frame is moving (relative to the resting bradyon).

This implies that there is no truly absolute-zero velocity,
anywhere. All velocities are relative, in reality, including all
zero velocities.

By the same token, while a tachyon can be considered "at rest" in a
given frame, the corresponding zero-reference for a tachyon is
infinite velocity, as viewed from a standard frame. But there is no
absolute-infinite velocity for a tachyon either, because it is just
as relative as the bradyon's zero velocity.

We therefore have two kinds of zero velocity; one is absolute, and
must therefore be considered a purely non-physical notion, so that it
is useless with respect to practical physics applications, while the
other is relative, and is the only zero velocity that has usefulness
in physics, as indicative of a zero-reference, or starting-point, for
an associated nonzero velocity. Correspondingly, we also have two
kinds of infinite velocity; one is absolute, so that it too has no
usefulness for physics applications, while the other is relative, and
is thus a valid reference-velocity for certain tachyons (in analogy,
and opposite, to a zero-velocity reference for bradyons).

Here, Tiwari reports that relative infinite-velocity tachyons are
lebeled "transcendental" tachyons by the above noted authors. Such
tachyons can be used to specify rest-frames for non-transcendental
tachyons, but otherwise have limited importance.


Objections to Tachyons:

Tiwari next cites what he takes as the two main objections to the
existence of tachyons, appearing in discussions published in Physics
Today magazine in 1969. There was the contention that the notion of
imaginary mass for tachyons raises questions about how the General
Theory of Relativity (GTR) can be applied to them, so as to gain an
adequate understanding of the role that inertia and gravitational
mass play in tachyonic frames of reference. That is, the assumption
was that only detectable changes in energy and momentum would be
observable for tachyons, and the notion of the tachyon will therefore
remain a mere theoretical curiosity as long as we do not know
anything about how tachyons interact with ordinary matter and with
gravity. The other objection was that the existence of tachyons
would violate the "principle" of causality. (p.109)

However, Tiwari does not provide resolutions to these objections,
presenting the issues as unresolved. On the other hand, he does
suggest that a better understanding of the issues would result from a
better understanding of how time is involved; more specifically, the
time ordering of events.

He states: "Anyone who thinks deeply on the meaning of time-ordering
inevitably arrives at the conclusion that dynamical laws, whether
classical or quantum, have built in time-symmetry, and do not provide
us a direction of time." Noting also that Newton's absolute time was
a metaphysical concept, he says: "Einstein adopts a measurement
convention for the 'relative time' of Newton by employing constancy
of the velocity of light as a standard. Past and future ordering of
events makes physical sense only if the relativistic time is seen in
the context of time-elapse of the absolute time."
Also: "Relativistic paradoxes and contrived arguments to save the
causality principle result from treating the relative time defined by
Einstein's convention as the true time." What exactly then, he seems
to be asking, is this "true time"? (p.113)

As an alternative, Tiwari says that, instead of assuming that the
velocity of light is the fundamental consideration, we should regard
time as the fundamental consideration, and, after mentioning the
Planck length and the Planck time, he holds that there must be
an "absolute time interval," which could be the Planck time, of
course, although he unexpectedly asserts that the Planck length could
not then be used to establish a corresponding absolute length scale.

With that, Tiwari nevertheless suggests that, using his approach, "a
range of speeds, less than or greater than c, is possible", and that
the principle of causality "retains its key position", in the
resulting framework, although "the meaning of mass (real or
imaginary) for any object has to be understood afresh."

This last point, despite any first impression it may convey, does not
pose a threat to Tiwari's approach, because mass is not measureable
anyway. Tthe weight of an object is measureable, for instance, from
which we calculate the mass, but the mass itself is not directly
measureable. (p.109-113)

By the way, Tiwari does go into "tachyonic effects in gravity and
superstrings", but provides only an overview of what is already
known, and other than his suggestion that we pay more attention to
time does not give any original means of resolving the given
objections. Rather, he feels that superstring theory will possibly
provide answers at some point in the future.


The Search for Tachyons:

Under the sub-heading "Experimental Searches" (p.115), Tiwari starts
the topic by mentioning a few seemingly serious attempts to detect
tachyons, noting that: "The first experimental investigation by T.
Alvager and P. Erman was based on the suggestion that tachyons might
be present in beta decay. Presence of a charged tachyon in a strong
radioactive beta source was searched during the years 1963-65, but in
vain." His citation is a 1969 article in Physics Today magazine, in
which Bilaniuk and Sudarshan discuss these series of experiments.
[See: Physics Today, 22(5) (1969).]

However, I found more details in an obscure archived paper* by
Sudarshan, in which it is stated: "The simplest method of
identification of a tachyon is to measure its energy and momentum and
verify that the momentum is larger than the energy; equivalently one
may measure the velocity directly by a time of flight method. The
first method has already been employed by T. Alvager and P. Erman who
used a magnetic deflection in a double focussing beta spectrometer to
select the momentum of the particles, and a semiconductor counter to
measure the energy. They concluded that in Thulium 170 there were
less than 10^-4 tachyons per electron, if at all." [Citation: Nobel
Institute Report (1966).]
Now, Tiwari next writes: "Another experiment was based on detecting
Cherenkov radiation emitted by charged tachyons. In the experiment
carried out by Alvager and Kreisler gamma rays from a 5-millicurie
cesium-134 radioactive source collide with lead. A strong electric
field is applied to this presumed source of tachyons so that emission
of Cherenkov radiation is detectable; but the results were
negative." [Citation: T. Alvager and M.N. Kreisler, Phys.Rev. #171,
year 1968, page 1357.]
But Sudarshan, citing the 1962 American Journal of Physics
article "Meta-Relativity", by Bilaniuk, Deshpande, and himself,
correctly points out: "Both of these experiments presume that the
tachyons are electrically charged; if the tachyons are neutral, both
the experiments must give negative answers." [Citation: Am. J.
Phys. #30, page 718 (1962).]
* Paper; The Nature of Faster-Than-Light Particles and Their
Interactions, by E.C.G. Sudarshan (of the University of Texas at
Austin). Sub-topic; Methods of Experimental Detection of Tachyons.
This paper is labeled; ARKIV FOR FYSIK Band 39 nr 40. I obtained it
online by a Google search using the keyword "T. Alvager".

In my opinion, while the literature abounds with physicists who tout
these results as suggesting that tachyons do not exist, what the
experiments actually show, and only show, is that tachyons are either
electrically neutral, or, if any of them are charged, they simply do
not possess the kind of electric charge that we are used to dealing
with (i.e., that we can detect), and that even this is true only
within the detection ranges established by the limits of the
experiments.
It is more likely, given what we know about tachyons theoretically,
that the assumption that any of them have a detectable form of
electric charge is not really a valid inferrence, and the null
results of the experiments just cited tend not to support the
contention that tachyons do not exist, but rather that it is not
logical to demand that this assumption must be an "a priori"
requirement.
Because of the alternate-dimensional nature of tachyons, any form of
electric charge that any of them might exhibit would probably be a
superluminal analog of what we know as electric charge. Hence, any
experiment designed to detect tachyons based on the idea that they
posses a standard form of electric charge is doomed to failure from
the outset. And this should have been recognized by theoretical
physicsts long before the said experiments were proposed.
So, it is difficult for me to believe that bias against the very
notion of the existence of tachyons was and is today not motivating
the researchers responsible for conducting such experiments, when the
researchers base the designs of their experiments on the initial
assumption that charged tachyons could possess the standard form of
electric charge; despite the obvious theoretical implication that
tachyonic charge is probably not at all like the standard type of
charge that we know.

In Sudarshan's 1969 paper, he suggested that "there are four
experimental methods of searching for tachyons which do not require
them to be charged particles." I quote as follows.
(a) Search for "decays in flight" of a stable particle:
If we find that a particle which is stable in its own rest frame
(like the proton) appears to decay in flight we can be sure that at
least one of the "decays" products is a tachyon.
(b) Large angle scattering:
If fast particles scatter through large angles with a pronounced
resonance in the invariant momentum transfer, a tachyon is being
emitted (or absorbed!).
(c) Poles in the scattering amplitudes:
If the scattering amplitude between two ordinary particles exhibits a
pole in the invariant momentum transfer variable for negative (space-
like) values we can conclude that a tachyon is being exchanged.
[Footnote: "For suitable kinematics the pole may appear in the
physical region; it is therefore desirable to have a tachyon with
width."]
(d) Effective mass plots:
The original method of identifying pion-pion resonances can be
adapted to the present case by plotting the effective 4-momentum
squared of a collection of pions with some of the pions in the
initial state and some in the final state. A peak in such an
effective squared mass plot at a negative value would be evidence for
a tachyon. One has to eliminate, in such an analysis, and purely
kinematic enhancements. [Here, for the said "original method",
Sudarshan cites an entry by himself, G. PINSKI, and K.T. MAHANTHAPPA,
in Proceedings from the Tenth International Conference on High Energy
Physics (Rochester, 1960).]

Sudarshan next states that: "All these methods presume that the
tachyon, whether it is charged or neutral, participates in strong
interactions. A fifth method which may be employed consists of a
search for the missing mass squared in a suitably selected set of
processes. In principle, missing mass spectroscopy can be used
independent of the strength of the interactions of tachyons."

Tiwari, in the chapter on tachyons, does not directly comment on the
four methods Sudarshan listed above, although he does cite Sudarshan
in many other places in his book, and, as of the time of publication
(2003), asserted that the missing mass method, along with all other
experiments based on the detection of Cherenkov radiation, as well as
searches associated with cosmic rays, had yielded no hard evidence
for the existence of tachyons. (p.115)

Researchers have, of course, calculated a negative value for the
squared rest-mass of the muon neutrino; implying that this type of
neutrino is a tachyon. However, Tiwari pointed out that, while
claims that this is evidence for the imaginary mass of neutrinos in
general, "such a claim is not supported by researches in neutrino
physics." Yet, Tiwari did not actually provide a citation that
contradicts the claim. And he admitted too that "the question
remains unsettled" (p.116); directing the reader to a summary of the
then "current status" on the subject. [Reference: V. Barger, D.
Marfatia, and K. Whisnant, Physical Review Letters #88, year 2002,
page 011302.] Unfortunately, the review article he suggests has
grown somewhat dated by now (as of early 2007). The most up-to-date
information on this topic can be found by doing a Google search using
the words "tachyons" and "muon neutrinos" in the same search phrase.

My take on all of this is that the searchers have been searching in
the wrong places, because of faulty initial assumptions. For
instance, all of the cited experiments relied on the assumption that
something unusual would be detectable using experimental equipment
and instruments that are used to study bradyons and luxons. But
trying to detect tachyons based on detectable electric charge,
particle decays, scattering angles, scattering amplitudes, missing
mass, or Cherenkov radiation presupposes that tachyons will behave in
ways that can be discerned from our bradyonic frame of reference.
Even the indication that the muon neutrino may have a negative
squared rest-mass, and documentable superluminal phenomena (such as
superluminal photonic tunnelling), seem to me to be revealing more
about the underlying nature of spacetime (that it is tachyonic),
rather than serving as dependable indicators of the existence of
various kinds of tachyons.

Clearly, as implied by the equations of Einstein's theory of Special
Relativity, all tachyons exist in an alternate-dimensional frame of
reference, as viewed from our natural bradyonic reference-frame.
Consequently, new research directions are needed. These will involve
new conceptualizations, new instrumentation, and new interpretations
of the data we collect in our experiments.

In that respect, I believe Tiwari is on the right track, in calling
for a re-examination of our definitions both of space and of time,
for the purpose of gaining a deeper understanding of nature, though
it will require a revision both of Special Relativity and of Quantum
Mechanics. However, I see that effort as only part of the overall
sea-change in our way of thinking; perhaps a key part, to be sure,
but not the whole story. In my estimation, the initial assumption
that will bring about the next great leap in our intellectual
development, though presently only an hypothesis, is that gravity is
tachyonic.

In other words, I suggest that the search for tachyons and the search
for the quanta of gravity are one in the same search. I also hold
that this realization, used to define the parameters on which
pertinant experiments are based, will yield breakthrough results in
the very near future.

Tiwari, of course, does not suggest this, and gives only a review of
what is presently understood about tachyonic effects in gravitational
fields, and tachyons arrising from superstring theories.


Gravity and Superstrings:

In the final portion of the chapter on tachyons, Tiwari
writes: "Recent advances in tachyon physics (in the theoretical
domain) originate in quantum electrodynamics in the presence of
gravity, and tachyons in superstring theories. Faster-than-light
photon propagation due to vacuum polarization effects in a background
gravitational field was discovered by Drummond and Hathrell in 1980
[Citation: Physical Review D, #22, page 343.]. On the other hand
tachyons have been known to arise from early times in bosonic
strings - both closed and open; their importance in recent years
has been due to the developments in the brane theory and non-
perturbative techniques in string theory."
Tiwari then explains superluminal photons (based on the given
citation), noting that the framework that results from combining
Quantum Electrodynamics (QED) and the Special Theory of Relativity
(STR) "has been very successful" at explaining the electromagnetic
interactions among subatomic particles, but that attempts to
incorporate the General Theory of Relativity (GTR) [i.e., the
curvature of spacetime caused by gravity], "is plaged by
insurmountable difficulties." (p.117)
Yet, after going into some of the details of the associated research,
which included the study of vacuum polarization subjected to the
curved geometry of GTR, Tiwari seems delighted to quote the said
researchers, summarizing their conclusions, as stating that "either
perturbative QED is inadequate as a theory when extended to a general-
relativistic background, or that photons indeed can travel faster-
than-light." [His apparent delight is explained as follows.]
Implications for cosmology theories are therefore profound, of which
Tiwari also points out: "That vacuum polarization leads to photon
velocity exceeding the velocity of light in the early times of the
evolution of the universe in a rather intriguing way agrees with the
time-varying velocity of light hypothesis in some models of
cosmology." And "we note that not just photons, neutrinos also
become superluminal ...". On the other hand, after labeling
superluminal photons as "quasi-photons", he cautions that such a
photon "should not be interpreted as a tachyon." (p.121) [Note that
part of Tiwari's suggestion that we re-evaluate our concept of time
depends on whether or not the lightspeed constant is a fixed constant
that does not vary with time. Hence his delight at experimental
support for the conclusion that photons can be made to travel FTL,
under a special, though repeatable, set of conditions.]

From there, Tiwari segways into string theory, noting that QED is a
point field-theory, in which the path of a particle establishes
a "world-line" in space, while strings are one-dimensional objects
that sweep out "world-sheets" as they move through space; thus
resulting in those branches of string theory called "brane theory"
(i.e., membrane theory) and its close but older relative "superstring
theory". He then gives a concise overview of the most important
aspects of string theory, and how tachyons are involved; noting here
that the dynamics of tachyons "may provide useful insight into non-
purturbative features of superstrings", leading to "an optimal
formulation of the theory." (p.121)

As for myself, I accept that string theories, especially their latest
incarnation, brane theory, provide a better understanding of nature
than can be had with quantum theory alone, but there is simply too
much empirical support for the point-particle descriptions associated
with subatomic interactions to completely abandon the point-particle
form of relativistic quantum-field theory altogether. It seems to me
that brane theory and quantum theory are actually compatible, if we
notice that they are distance specific. Quantum mechanics, for
instance, allows us to study subatomic particles down to distances on
the order of the Planck length, while brane theory lets us see what
spacetime is like at even smaller distances. The two scenarios need
not be at odds, nor should one be abandoned in favor of the other.
And, in that case, since brane theory involves an inharent prediction
of tachyonic objects (FTL strings), at sub-Planck-length distance
scales, and therefore begs for the acceptance of such objects by the
mainstream physics community, then these objects can and should
likewise be regarded as possibly manifesting themselves as point-like
tachyons at distances larger than the Planck length; as described by
the kinematic equations of STR.

Among those point-like tachyons, I am convinced, though Tiwari does
not mention the notion in his book, that there is one which explains
quantum gravity better than any other hypothetical particle suggested
to be responsible for the warping of space caused by gravity, as
described by the "field equations" of GTR - which tachyon I have
described thoroughly in my thesis on tachyonic gravity.
For a condensed version of my thesis, click "Tachyonic Gravity" at
www.TachyonicsSociety.com
I am, however, willing to concede that such tachyons may be string-
like (or, more correctly, may have string substructure), when viewed
at distance scales smaller than the Planck length.

Studying Tiwari's book has, in fact, done much to strengthen the
conviction that my thesis is valid, because I find in the book no
unbiased theory to refute it, and find therein, as well, a great
store of reliable information supporting the conclusion that
tachyons, of many kinds, probably do exist.

Based on that conviction, and on "faith" in the open-minded
researchers actively engaged in the investigation of superluminal
phenomena these days, I predict that a point-like tachyon will
be "discovered" within the next few months, and soon thereafter it
will be confirmed, beyond doubt, that what I have been saying all
along must be viewed as a scientific fact, instead of as a science-
fiction hypothesis;

gravity is faster-than-light, and is therefore a tachyonic force.

The Imagination Unit, Part 2

The Standard Imaginary Unit

As mentioned earlier,
the relativistic mass M of an ordinary particle in motion can be
related to the same particle's rest-mass, m, by the equation;

M  =  Rm  =  m / [(1 - [(v/c)^2])^(1/2)] .

Consider again a tachyon of mass tM, with correspondingly the same
amount of moving mass. The tachyonic mass, tM, can be represented by
describing it as an imaginary analog of M, written;
tM = -iM ,
where i is the standard imaginary-unit, defined;
i = (-1)^(1/2) , so that i^2 = -1 .

Note that the minus-sign accompanying i, in this definition of tM, is
absolutely mandatory for presenting a rigorous definition of tM.

In such cases, the imaginary-unit (i) is used in a purely algebraic
sense, as an operator that, when multiplied to a real number, is
understood - by convention - to imply that the given real number
is to be viewed as an imaginary number. To go any further on this
topic, however, it is necessary to lay some groundwork, so that later
statemements will be readily understood. [Readers sufficiently
familiar with the theory behind complex and imaginary numbers, as
presented below, may wish to proceed to the next post.]

The imaginary-unit comes about as a natural consequence of
considering certain numbers that cannot be categorized as "real".
For instance, no real number x is such that x^2 = -1.

We can, however, imagine another kind of number, i, defined
specifically as the square-root of -1, so that i^2 = -1.
Thus, if X is a positive real number, and we want to find the square-
root of its negative, then we can always write;
(-X)^(1/2) = [(-1)X]^(1/2) = ... = i[X^(1/2)] .
For example,
(-25)^(1/2) = [(-1)(25)]^(1/2) = [(-1)^(1/2)][25^(1/2)] = i5 .

Now, all of the sums of real and imaginary numbers form a set called
the "complex numbers", which, obviously, includes the set of all real
numbers and the set of all imaginary numbers.

To explain how complex numbers work, let x and y denote real
numbers. Then let iy denote an imaginary number, and let z denote
the sum of x and iy, according to the equation;
z = x + iy .

Here, z is a complex number, while x is referred to as the "real-
number part" or "real component" of z, and y is referred to as
the "imaginary-number part" or "imaginary component" of z.

We can also represent this using function notation, where Re is a
function of z that gives a real number, Re(z), and Im is a function
of z that gives an imaginary number, Im(z), defined;
z = x + iy = Re(z) + Im(z) ,
where Re(z) = x , and Im(z) = iy .

Consequently, if x is nonzero but iy = 0, then z is real.
On the other hand, if iy is nonzero but x = 0, then z is referred to
as a "pure imaginary".
Of course, whenever z = 0, then one of the following mutually
exclusive cases must be true;
Case 1: x = 0 and y = 0 simultaneously, or
Case 2: iy = -x , where x and y are each nonzero.

Interestingly, because complex numbers are essentially the same as
ordered pairs of numbers, then the following definitions hold for
almost all complex numbers.

The absolute-value |z| of a standard complex number z, and which
absolute-value is called the "modulus" of z, is a real number that
can be obtained using the Pythagorean theorem;
|z| = |x + iy| = [(x^2) + (y^2)]^(1/2) .
Letting z denote a complex number defined as a sum, so that
z = x + iy ,
and letting z* denote another complex number defined as the
corresponding difference, so that
z* = x - iy ,
where z* employs the same values of x and y as does z,
we say that z* is the "conjugate" of z.
The product of z and z* is the square of the modulus of z, according
to the following proof;
z*z = (x - iy)(x + iy) = (x^2) - xiy + xiy - [(iy)^2]
= (x^2) - [(-1)(y^2)] = (x^2) + (y^2) = |z|^2 .
The ratio, z/Z, of two complex numbers, z and Z, is a real number
obtained by multiplying the numerator and denominator by the
conjugate of the denominator, which is the same as dividing the
product Z*z by the squared modulus of Z, denoted;
z/Z = (Z*z)/(Z*Z) = (Z*z)/(|Z|^2) .

One tremendously useful application of complex numbers is their
appearance in the solutions to certain very important equations,
which should be covered briefly as follows.

An equation of the form
a(x^2) + bx + c = 0
is referred to as a "quadratic equation", in standard form, where x
is a variable, and a, b, and c are arbitrary constants.
Equations of this form are used to solve so many real-world problems
that a full accounting of them would fill an encyclopedia. So, we
need not go into numerous examples here, although at least one
example would perhaps be appropriate.

If, in the given equation, the constant "a" is half the acceleration
g due to gravity near the surface of the Earth, and "x" is changed to
time t, with "b" as the initial velocity v of a falling object,
dropped from an initial height H, reaching a lower height h in the
time t, and we let c = h - H (because we will need a negative
value for this difference, arrising from the fact that the height of
the object is decreasing), then we can write a quadratic equation in
standard form, as follows;
(1/2)g(t^2) + vt + (h - H) = 0 .
When rearranged to isolate h, this equation gives us the height, h,
after the time t has elapsed;
h = -(1/2)g(t^2) - vt + H .
This, then, is an excellent example of how quadratic equations crop
up in real-life situations; in this case, should we need to know the
height of a falling object at some time during its fall.

We move on to point out how complex numbers come into play in the
context of quadratics.

Again, let us assume that there is a quadratic equation in standard
form, denoted;
a(x^2) + bx + c = 0 ,
as described above.
Here, let
s = d^(1/2) ,
where
d = (b^2) - 4ac ,
to establish a convenient abbreviation.
Such an equation has a solution x that can be obtained as follows.
Possibility 1 is; x = (-b + s)/(2a) ,
Possibility 2 is; x = (-b - s)/(2a) ,
where s = d^(1/2) = [(b^2) - 4ac]^(1/2) .
The difference d, in the term s, is called the "discriminant" of the
quadratic equation, and, due simply to the fact that s is the square-
root of a difference, then it is sometimes allowed that s could be
the square-root of a negative number (i.e., the term s could be an
imaginary number).
In particular, if d is positive, then s is real, and therefore x
comes in two distinct and real versions, called the "roots" of the
quadratic equation, corresponding to "-b + s" and "-b - s" .
That is, if d is positive, then it is said that the quadratic
equation has "two distinct real roots".
However, if d = 0, then s = 0, so that
-b + s = -b - s = -b ,
and there is only one real root, called a "double root", because it
satisfies both possibilities given for x above.
Such a root is readily obtained by writing;
x = -b/(2a) .
Alternatively, if d is negative, then s is an imaginary number, and
the given quadratic equation has no real roots. In such cases, the
quadratic equation can be referred to as "irreducible", in venues
where only distinct real roots and/or double roots are considered.
Otherwise, for negative determinants, the possiblities for x can be
denoted as follows.
Possiblity 1 is; x = (-b + si)^(1/2) ,
Possibility 2 is; x = (-b - si)^(1/2) ,
where
si = [d^(1/2)][(-1)^(1/2)] = [(-1)d]^(1/2) = (-d)^(1/2) .
This shows how the imaginary-unit, i, can be introduced in the
context of quadratic equations.

The invention of complex numbers, which hinge on the notion of
imaginary numbers, the basic understanding of which, in turn, is made
clear by the definition and applications of the standard imaginary-
unit, i, has provided us with very useful mathematical tools; for
example, in providing various means of solving quadratic equations
that have negative determinants.

Algebraically, of course, complex numbers obey a special set of
rules, as follows.
Let A, B, C, and D denote real numbers.
Then the following relationships hold true.

A + Bi = C + Di if and only if A = C and D = B .

(A + Bi) + (C + Di) = (A + C) + (B + D)i .

(A + Bi) - (C + Di) = (A - C) + (B - D)i .

(A + Bi)(C + Di) = (AC - BD) + (AD + BC)i .

(A + Bi)/(C + Di) = [(AC + BD)/[(C^2) + (D^2)]]
+ [(BC - AD)/[(C^2) + (D^2)]]i .

Graphically, we have yet another set of rules; as follows.

Consider the standard x,y-plane, and let an ordinary point P be
plotted on the plane;
P = (x,y) .
If we change y to yi, so that the y-axis becomes an imaginary axis,
then P becomes the point indicated by plotting the complex number z
as a point in this plane, so that
z = (x,yi) .
That is, a complex number z, defined by the formula denoted;
z = x + yi = (x,yi) ,
can be represented by a point in a plane that is formed by using the
real and imaginary number-lines as the coordinate axes for the plane.
Such a plane is called the "complex plane", and, with respect to this
plane, the complex number z can always be denoted by the ordered-pair
(x,yi).

Now, because complex numbers are actually ordered-pairs of numbers,
then they can also be used to represent vectors in the plane.
And here is how that is done.
If we stipulate that the point z is at the location indicated by the
arrow of a directed line-segment from the origin O to z, within the
complex plane, then the modulus |z| of z can be interpreted as the
magnitude of a vector represented by this directed line-segment;
explained as follows.

Let "r" denote the magnitude (length) of the vector, and let "a"
indicate the angle the vector makes with the x-axis. Then r is
defined formally;
r = |z| = ((x^2) + [(yi)^2])^(1/2)
= [(x^2) + (-1)(y^2)]^(1/2) = [(x^2) - (y^2)]^(1/2) ,
and we can specify z using the two variables, r and a, called "polar
coordinates", so that
z = x + yi = (x,yi) = (r,a) .
In that case, knowing (from trigonometry) that "r" and "a" are
related to x and y in the standard plane by the identities;
x = r(cosa) and y = r(sina) ,
we can, by substitution, determine a trigonometric representation of
z, with respect to the complex plane, and write;
z = r[(cosa) + i(sina)] ,
which is called the "polar form" of the complex number z.

We must remember, of course, that r is also the modulus of z.

Further, angle "a" is commonly referred to as the "amplitude" of z.

Another useful application of the imaginary-unit is in the
representation of sinusoidal waves; explained as follows.

Consider the graph of a sine-wave in the x,y-plane, with a period T
and wavelength L, and where the sine-wave is pictured as propagating
along the x-axis to the right, so that y is the amplitude of the wave
(its distance above or below the x-axis) at a given instant of time
t, making "y" a function f both of x and of t, denoted;
y = f(x,t) .
If v is the speed of the wave, then the frequency F, period T, and
wavelength L are related using the following formula;
F = 1/T = v/L .

Here, let A be a constant, called the "central maximum", which is the
maximum value of y.
Since a sine-wave can be used to represent a steady oscillation, a
perfect circular orbit, or other such harmonic motion, then we can
introduce another constant K of the motion, called the "wave number",
and relate it to the value of Pi (approximated as 3.14), so that
2(Pi) corresponds exactly to one cycle, according to the formula;
K = 2(Pi)L = 2(Pi)/(Tv) .

Now, any central maximum A approaching the y-axis from the left will
be located a distance D (on the x-axis) from the y-axis, at time t.
However, since the values of K and of D always vary proportionally
with respect to each other, then D can be obtained by introducing a
quantity k, referred to as the "phase constant", the "phase delay",
or simply the "phase", and by defining D as the ratio of k over K,
denoted;
D = k/K .
Then the sine-wave can be represented "on paper" by plotting the
following formula graphically;
y = f(x,t) = A cos[K(x - vt) + k] .

On the other hand, since uniform circular motion can be represented
as the number of radians swept-out per unit time, using the angular
frequency w, defined;
w = 2(pi)F = Kv ,
so that
K(x - vt) = Kx - Kvt = Kx - wt ,
then, alternatively, we can also write;
y = A cos(Kx - wt + k) .

Unfortunately, dealing with sinusoidal waves using trigonometric
functions can get tedious. The more efficient way to do the same
thing is to convert to complex notation, as follows.

From trigonometry, we have the following relationship, using the base
e of natural logarithms;
e^(iV) = cos(V) + i[sin(V)] ,
for any arbitrary or "dummy" variable V.
Thus, letting
V = Kx - wt + k ,
we can write;
e^[i(Kx - wt + k)] = cos(Kx - wt + k) + i[sin(Kx - wt + k)]
where the real (Re) and imaginary (Im) components can be defined;
cos(Kx - wt + k) = Re(e^[i(Kx - wt + k)]) , and
i[sin(Kx - wt + k)] = Im(e^[i(Kx - wt + k)]) .
Suppose, however, that only the real component is needed, or,
otherwise, the imaginary component is zero. Then we can define y
using only the real component, as follows;
y = A cos(Kx - wt + k) = Re(Ae^[i(Kx - wt + k)]) .
Next, we can introduce a new funtion y', defined;
y' = A[e^(ik)]e^[i(Kx - wt)] = A'e^[i(Kx - wt)] ,
where
A' = Ae^(ik) ,
so that the phase k can be temporarily "absorbed" into a more compact
representation, wherein the real component is denoted;
y = Re(y') .
This sort of representation makes for a much faster form of notation
when many waves are to be handled (which is a common task in physics
and engineering). It is referred to as "complex notation", and is
used primarily because it is quicker and easier to deal with
exponents than to manipulate sine and cosine functions. And it has
been explained here as another example of how the standard imaginary-
unit, i, has practical applications in real-world situations.

Having learned something about imaginary numbers, we can proceed to
the introduction of a new imaginary-unit; one that implies a wholly
new kind of operation.

[Continued in next post.]

The Imagination Unit

or

How to Describe Things Made of Tachyons



A Representations Theory by H. Kurt Richter



Part 1


About Tachyons

Because of certain implications of Einstein's theory of Special
Relativity, some physicists have predicted the existence of particles
that always travel faster-than-light (FTL).
Here is one way that this prediction comes about.
Consider an ordinary object at rest; for example, a basketball at
rest on a basketball court.
It has a rest-energy E and a rest-mass m, related by the well-known
equation E = m(c^2) ,
where c is the lightspeed constant (approximately 3 x 10^8
meters/second).

Suppose now that we roll the basketball across the court; setting it
in motion with respect to the the stationary floor of the court. It
can then be viewed as existing in a different frame of reference,
local to itself; one that is moving relative to the stationary frame
of the floor.

To relate these frames, we apply certain transformation equations;
explained as follows.

Orient a set of Cartesian coordinate axes so that the ball's center-
of-gravity starts at the origin O, fixed relative to the floor, where
we will begin counting the time t at t = 0, and the ball's center-of-
gravity, with a mere push, can be made to move in the positive x-
direction at a constant velocity v, without obstruction, so that the
values of y and z are always zero.

Next, let x, y, and z denote the spatial parameters, and t the time
parameter, for the stationary reference-frame, but let x', y', z',
and t' denote the corresponding respective parameters for the moving
reference-frame (the one moving with the ball), and where the x-axis
and the x'-axis lie on the same infinitely-long line in space. Then
the two reference-frames will be related according to the following
formulas, referred to as the "Lorentz transformations";
x' = R(x - vt) ,
x = R(x' + vt') ,
y' = y ,
z' = z ,
t' = R(t - [vx/(c^2)]) ,
t = R(t' + [vx'/(c^2)] ,
where R is an operator that allows us to calculate the relative value
of a quantity for a moving object from the corrresponding value taken
while the object is at rest. To explain rather briefly, the operator
R is a multiplicative operator that involves the ratio of velocity v
over the lightspeed constant c, and it can be defined;
R = 1/[(1 - [(v/c)^2])^(1/2)] = (1 - [(v/c)^2])^(-1/2) .

Since Einstein made extensive use of the Lorentz transformations in
his theory of Special Relativity, involving the operator R, then R
can be called the "Relativity Operator".

Here, if M denotes the basketball's moving mass, and m is its rest-
mass, then we have;
M = mR = m[(1 - [(v/c)^2])^(-1/2)] .
Notice therefore that, because the ratio v/c is under a square-root
symbol, then there is only one relationship between v and c that
makes sense for a real basketball; v must be less than c.

Suppose now, however, that we let M denote the mass of a real or a
virtual subatomic particle instead of a basketball. Then there are
three fundamental cases for M:
(1) v < c makes R real, which means that M is a real-valued non-zero
quantity.
This is the case for all subatomic particles with positive rest-mass
(electrons, protons, etc.).
(2) v = c makes R undefined, because, by convention, the square-root
of zero is zero, but the inverse of zero is undefined (or else it is
infinity). This is the case for massless photons.
(3) v > c makes R imaginary, which means that M is an imaginary
quantity.
This is the case for particles with negative rest-mass (particles
that travel FTL).

All of the subatomic particles cataloged by physicists as having
mass, as far as we can tell, have positive rest-mass, including real
and virtual paticles with measureable or calculable rest-mass. The
scalar energy E and vectorial momentum P are both defined using the
rest-mass m;
E = R[m(c^2)] and P = R(mV) ,
where V is vectorial velocity, defined; | V | = v .

Of note is the fact that the second case, for massless photons,
actually works-out to make R an infinity if we embrace the
mathematical convention that the inverse of 0 is infinity;
1/0 = infinity .
This occurs because, here v = c, so that
R = 1/[(1 - [(v/c)^2])^(1/2)] = 1/ [(1 - (1^2))^(1/2))]
= 1/[(1 - 1)^(1/2)] = 1/[0^(1/2)] = 1/0 .
Alternatively, yet remaining mathematically rigorous, we can say
instead that the inverse of 0 is undefined, and maintain that the
rest-mass of a photon is 0; which means that all photons are massless
particles, made entirely of energy.  [Note:  If mass is 0, then the
relativistic formula for mass gives the ratio 0/0, which is just 0;
i.e., the infinity implied by R gets canceled-out.]

Particles with negative rest-mass that always travel FTL are
called "tachyons". They will have reversed causality (negative
time), as compared to that of ordinary massive particles and/or
massless photons, and their rest-mass is both imaginary and
negative. But we will delve into this case in Part 3, and in much
greater detail than has been provided for the other two cases
above.

Notice, as well, that the relativity operator, R, dictates what
happens when you try to accelerate a real mass up to lightspeed.
It works-out that M approaches infinity as v approaches c.
In other words, it would take an infinite amount of energy to
accelerate a real mass up to lightspeed.
And because we do not have access to infinite amounts of energy, and
we do not observe infinite energy expended anywhere in the universe
at large, then the lightspeed constant represents a kind of universal
speed-limit. It is, by all accounts, a spacetime barrier.

Thus, many physicists have assumed (logically) that nothing "real"
exists on the other side of c.
Unfortunately, this has also caused some to conclude that tachyons
cannot be created, not even by a Big Bang like the one that initiated
our universe. Hence, some of these scientists insist that tachyons
do not exist, although that claim has yet to be proven conclusively,
and is not justfied by logical inferrence (it amounts to a personal
preference in the interpretation of Einstein's theory of Special
Relativity, not a mathematically rigorous interpretation).

To be clear, the relativity operator, R, does not suggest that
nothing FTL can exist at all. It does indicate that it would take
infinite amount of energy to accelarate a real mass up to c (because
of the ratio v/c), but it does not forbid objects that already travel
at FTL speeds from existing on the other side of c. Nor is it
necessary to get tachyons by accelerating real masses to and beyond
c. In the cosmological Big Bang idea called "Inflation Theory", it is
proposed that there was a brief period of superluminal expansion of
all the energy associated with the first moments of the Big Bang, and
it is therefore entirely possible that many particles of various kind
were created that retained the superluminal velocities of the
energies out of which they were formed at that time.  Furthermore,
because of its reversed causality, a tachyon's energy decreases as
its velocity increases, with its zero-energy state at infinite speed,
so it is reasonable to think that higher-speed tachyons were easily
created, because the required energy would be so low.

Also, while we depict tachyons as having imaginary mass
mathematically, we must remember that words
like "imaginary", "abstract", and other terms employed by
mathematicians, in math contexts, are labels for different types of
numbers, chosen to distinguish between those numbers. But such
labels do not necessarily imply that the numbers do not exist.
So, to label a tachyon's mass as "imaginary" does not imply non-
existence - because we are using the mathematical meaning of the
word "imaginary", not its common literary meaning.

Interestingly, the standard imaginary-unit, i, can be defined in
terms of two well-known irrational transcendental numbers. One of
these is the value of Pi, which is the ratio of the circumference
over the diameter of any size perfect circle, and is often given the
approximate value of 3.14. The other is the base e of natural
logarithms, defined as the limit as n approaches infinity of the n-th
power of the sum of 1 and 1/n, for any integer n. It is also defined
as the following expansion;
e = 1 + 1/n! + 1/2! + 1/3! + ... + 1/n! + ... ,
which is commonly approximated as 2.72.
The relationship between i, Pi, and e is that i equals ln(-1) divided
by Pi, denoted;
i = (-1)^(1/2) = [ln(-1)]/(Pi) ,
where ln(-1) is the logarithm, to base e, of negative unity.

Now, Pi is referred to as "irrational" and "transcendental" because
its decimal expansion is non-recurring and infinite. In fact, to
date, though computers have been used to calculate its value to
several million decimal places, we have yet to find its final digit.
And likewise, the base e of natural logarithms is labeled using the
same terminology, for the very same reasons.

Thus, because an imaginary number can always be represented as the
product of i and any real number, we can state that all imaginary
numbers can be defined in terms of these two irrational
transcendental numbers - although no-one would insist that Pi or e
do not actually exist.

Consequently, just because we think of tachyons as imaginary
particles, theoretically speaking, this does not mean that they
cannot or do not exist, somewhere.

To understand how tachyons work, be aware that it would take an
infinite amount of energy to slow a tachyon down to c, just as it
would take an infinite amount of energy to speed a tardyon (slower-
than-light particle) up to c.

By the way, tardyons are also referred to as "bradyons", from the
Greek word "bradus", meaning "slow".  In this context, then, we can
refer to massless particles (such as photons of light) as "luxons".

Consider the emission of a bradyon from some composite body, and
suppose that we have taken a high-speed video of the event.  Next,
imagine the emission of a tachyonic analog of the bradyon.
If we could "see" the emission of the tachyon, as viewed from our
ordinary (bradyonic) frame of reference, it would look as if the
tachyon came from infinity and was absorbed by the body.
In other words, viewing a video of the emission of tachyonic analogs
of bradyons, it would practically look as if we were running the
video of the ordinary process in reverse.

For a more in-depth explanation of tachyons, click "Tachyons" at
www.TachyonicsSociety.com, or, for a long list of sources, do a
Google search using the keyword "tachyon".

In what follows, a non-standard method of representing tachyons is
provided, where yet another operator - a new kind of imaginary-
unit, inspired by the standard imaginary-unit, i - will be used to
imply a transformation across the lightspeed barrier. However,
because this operator is based on the standard imaginary-unit, it is
best, for the broadest understanding of this new operator, to explain
in sufficient detail the standard imaginary-unit first.


More to come.

[Note:  This is a re-post of a previously posted article.]

While reading S.C. Tiwari's book, Superluminal Phenomena in Modern
Perspective (Rinton Press) [www.RintonPress.com/books/tiwari.html],
and recognizing that Dr. Tiwari has done a tremendous amount of
research on tachyons, I noticed that he attributes the first mention
of any kind of object resembling faster-than-light (FTL) particles
(not yet named "tachyons") to a mathematician named Le Sage, who is
alleged to have come up with the idea that "corpuscles" traveling FTL
could be used to explain Classical gravitaton (in Tiwari's book, see
page 6, Chapter 1, in Section 1.1, entitled "Historical Note").
There is some debate, however, on whether Le Sage or a Frenchman
named de Dullier originated the theory called "Le Sage gravity".

Here's the scoop on Le Sage's theory of gravitation (mostly cut-and-
pasted from Wikipedia, but with some editing of my own).

In 1690 Nicolas Fatio de Duillier of France, and in 1782 Georges-
Louis Le Sage of Geneva, proposed independently a kinetic theory for
gravity, which offered an explanation for Newton's force equation.
However, because Fatio's work was not widely known and remained
unpublished for a long time, it was Le Sage's exposition of the
theory that became popular, and which also became the subject of
renewed interest in the late nineteenth century when it was studied
in the context of the then newly discovered kinetic theory of gases.

By the early twentieth century, the theory was generally considered
discredited, most notably due to issues raised by James Clerk Maxwell
and Henri Poincare.  Today, while Le Sage's theory is still studied
by some researchers (such as physics historians), it is not regarded
as a viable theory within the mainstream scientific community.

Referred to as "LeSage gravity", the idea is that the universe is
filled with "mundane courpuscles" that travel faster-than-light in
all directions; imparting the same amount of collisional force from
every direction on every isolated object.  But when two objects are
fairly close to one another, they get shielded by each other, so that
there is less force on the sides that face each other, which results
in the forces on the unshielded sides pushing the objects towards
each other; the total amount of force given by Newton's formula.

With the advent of Maxwell's objections, and the success of his
equations explaining electromagnetism (and since no "mundane
corpuscles" had ever been observed), Le Sage gravity lost out to the
assumption that there was instead a gravitational field, and that it
was analogous to the electromagnetic field, except that instead of a
dipole field (having two poles, each on opposite ends of a central
axis), gravity was rather a quadrupole field (having two sets of such
poles, and therefore two central axes, oriented at right angles to
each other).  This, indeed, remains the assumption among many modern
researchers, of how quantum gravity works; despite the fact that
there is no unbiased experimental justification for it.

For the complete Wikipedia reference, go to
http://en.wikipedia.org/wiki/Le_Sage's_theory_of_gravitation

I find it intersting, in any case, that one of the first explanations
of Newtonian gravity involving particles suggests particles traveling
faster-than-light, which, by the way, was compatible with Newton's
own vision of how the gravitational force was imparted.  And this
appears to be the first suggestion on the possible existence of
faster-than-light particles altogether.

Newton, by the way, did not originate, nor endorse, the concept of
instantaneous "action at a distance" that came to be attached to his
formulation of gravity (first by an Englishman named Cotes, then by
nearly everyone else), and which implies an infinite-speed mediator.
To the contrary, he believed in an aether that pervades all of space,
and that an "agent" of some kind, propagating through the aether with
a finite speed, was the mediator of the force (although Newton also
did not take a stance on exactly how fast this agent acted).

It is interesting to note that Einstein's understanding of gravity,
the theory of General Relativity (GR), did not dismiss Newtonian
gravity, but incorporates it as a special case.  In fact, GR retains
Newton's universal gravity constant (~6.67x10^-11 N m^2 / kg^2), and
is reported in many sources (and confirmed simply by doing the math)
to be equivalent to Newton's gravity at what is called the "weak
field limit" of GR.  And, though others (starting with Lorentz) set
the speed of gravity at the speed of light, c, based on the fact that
the electromagnetic field propogates at c (and most scientists were
assuming that gravity was analgous to electromagnetism, which made no
sense if gravity was instantaneous), this notion remains attached to
the pseudo-Riemannian equations of GR in many people's minds, despite
not formally being required in Einstein's original formulation of GR.

Since I have developed an hypothesis that certain special kinds of
tachyons can be used to explain quantum gravity, then I looked into
Le Sage's theory, but found it unsatisfactory.  Clearly, he was on
the right track.  But without a knowledge of Einstein's Relativity or
of Quantum Theory, he did the best he could.  However, I also find
unacceptable the long-standing assertion that gravity is a quadrupole
analog of electromagnetism, mediated by a spin-2 massless "graviton".

I am of the opinion that the type of tachyon I describe in my thesis
on gravity explains quantum gravity in a way that is compatible both
with GR and with Newton's vision, that it fits with all uncorrupted
experimental data we have on gravity (and better than any other kind
of exchange-particle so-far proposed for gravity), and that it is
also an empirically valid force mediator, which I contend is soon to
be proven beyond doubt experimentally.  [Indeed, sometime this year.]

For a brief version of my thesis, click "Tachyonic Gravity", at
www.TachyonicsSociety.com

And, for an overview of the latest experimental efforts focusing on
determining the most accurate theory of quantum gravity, see Lee
Smolin's article "Quantum Gravity Faces Reality", in the November
2006 issue of Physics Today magazine, page 44.

Stay tuned.

I recently obtained a copy of S.C. Tiwari's book,
Superluminal Phenomena in Modern Perspectives.

It was rather expensive, and the publisher, Rinton Press,
has done Dr. Tiwari a serious disservice with respect to the
overall quality of the first printing, because the book
contains a large number of typesetting and editing errors;
a situation I did not expect to see, considering the price.
[I ordered it online, at www.RintonPress.com, and paid $78,
by credit-card, plus $6 shipping. But it arrived in 3 days.]

However, Dr.Tiwari's accomplishment comes through anyway, and
is worth examining in great detail.  The blurb on the back of
the book is absolutely true.  It is a "comprehensive review" of
the literature on superluminal phenomena, including "balanced
critique with open mind" of the many theories and concepts most
associated with such phenomena.  And it provides "delineation
of deep physical insights" on the topic. It is indeed a "unique
endeavor", covering the "whole spectrum" of information on the
phenomena, in a single book.

I recommend the work to anyone interested in gaining a deep
understanding of all superluminal phenomena, and who seeks an
extensive ready-made list of print references on the subject.

For students and researchers with limited budgets, I suggest
obtaining the book using the Library Loan Program supported by
most public, college, and university libraries.

Once I have studied the book sufficiently to have committed the
information on tachyons to memory, I intend to post a detailed
review on this message board, and at my main web-site.

Stay tuned.

--- In TheAoISCT@yahoogroups.com, "captjim" <Jonesalonzo1@...> wrote:
>
> I'm not completely sure I understand.  Are you saying that Feinberg
> actually plagerized Sudarshan's work, - or could this be a case where
> two researchers came to the same independant conclusions and one was
> just published earlier than the other?
>

I stated that Feinberg "stole" the concept of the FTL particles which
he named "tachyons" from Sudarshan and his collaborators, without
giving them "proper" credit for being the first to publish the notion
in formal peer-reviewed physics language.  But I based my comment on
the information in the web-site I cited earlier; maintained by the
University of Texas at Austin (UoT@A).

That is, I am not making a charge of plagiarism, because I do not have
the authority to do so, but UoT@A is clearly stating that it happened,
and I believe them (because I, long ago, read the material in question,
and recall the similiarities in what was said in the two sources; the
1962 Journal article and Feinberg's 1967 Review article).  But readers
can judge for themselves by looking up the articles in the periodical
archives of their nearest university library.

It would not be the first time a scientist has presented the ideas of
someone else as his own, and gotten away with it.  And it has certainly
not been the last.  Are you surprised?

But to be kind to the late professor Feinberg, he did indeed coin the
name "tachyon", and that, apparently, is what has caused many to credit
him with devising the first physics representation of FTL particles.
And to be honest about Sudarshan, the idea of FTL particles had been in
the minds of theorists and science-fiction writers for decades.
It is just that the trio of Sudarshan, Deshpande, and Bilaniuk were the
first physicsts to seriously suggest the existence of FTL particles, in
the literature; complete with the first proper representations theory.
Their only discernable mistake, it seems to me, was in not giving their
hypothetical FTL particles a name with the "-on" suffix.

Hence, score one particle-naming publicity coup for Feinberg.

I'm not completely sure I understand.  Are you saying that Feinberg
actually plagerized Sudarshan's work, - or could this be a case where
two researchers came to the same independant conclusions and one was
just published earlier than the other?

It is commonly stated by U.S. physicists that Gerald Feinberg, of
Columbia University, originated the concept of the faster-than-light
particles he named "tachyons", but that is not correct.  Here, for
the reader's edification, is the truth of the matter.

Exerpt from online article "Theory of Tachyons: Faster than Light
Propagation", about E.C. George Sudarshan, Professor of Physics,
University of Texas at Austin.
____________

In the summer of 1958 when Sudarshan was at the University of
Rochester, someone asked him about what happens to energy and
momentum when a particle travels faster than light.
Sudarshan saw that energy and momentum could be made real by taking
rest mass to be imaginary for such particles.
The second difficulty of the apparent traveling "backward in time" of
such a particle was solved by the interchange of the emission and
absorption of the particle. Along with a graduate student, V. K.
Deshpande, Sudarshan wrote a short paper and sent it to Physical
Review Letters. It came back from a referee who rejected it, saying
it was incorrect. Sudarshan requested a second referee who said that
the results of the paper were correct, but it was all well known!
A third referee stated that he had "read both the previous referee
reports and he agreed with both of them"!
About two years later, after Sudarshan joined the University of
Rochester faculty, his colleague O.M.P. Bilaniuk offered to rewrite
the paper and get it published. He did it and they published it in
American Journal of Physics. It attracted a lot of attention and
several letters to Physics Today.

To make a quantum theory one had to quantize a scalar field with
imaginary mass. Dhar and Sudarshan completed this in the spring of
1968. (By this time Feinberg at Columbia published a paper with all
Sudarshan's results, without acknowledgement to him).
Feinberg's work contained essential inconsistencies, but it supplied
the name "tachyon" for these particles. Arons and Sudarshan corrected
the mistakes in Feinberg's work and carried out the correct
quantization of tachyons.

The quantum theory of tachyons contained the reinterpretation
principle; and they could have either spin 0 or "continous spin" and
could obey either Bose or Fermi statistics.
The quantum field theory leads to a tachyon cloud of virtual
particles coupled to a tachyon field.
Tachyons could manifest themselves as resonances in momentum transfer
in particle collisions. Various other aspects are treated in other
papers including many by Recami.
To date, no tachyons have been detected. However, tachyons arise
naturally in string theories but are suppressed or ignored.  ...

____________


Note that there are a significant number of important print sources
cited at the end of the above online article, which can be found at
http://www.ph.utexas.edu/fogs/sudarshan_tachyons.html

For more on Professor Sudarshan's accomplishments, go to
http://www.ph.utexas.edu/fogs/index.html

The foregoing information was copied and pasted without the
permission of the originators.
It was gleaned from an online Symposium, from the University of Texas
at Austin, entitled
"Sudarshan: Seven Science Quests".
The URL is as follows;
http://www.ph.utexas.edu/fogs/symposium/index.html

Readers here are invited to post comments, as desired.

Announcing a new affiliated TSoA discussion-group on Yahoo!

We have established a new discussion-group site labeled
"The TSoA Council on Superluminality" (TheTSoACoS).

The URL is;
http://tech.groups.yahoo.com/group/TheTSoACoS

The TSoACoS Group (pronounced as the "sacs" group) is an all-
encompassing Coterie of The Tachyonics Society of America.

The new group site was set-up to allow individuals whose interests
include all the topics of all three of the other Coterie of The TSoA to
post comments on a new message-board.

The stated purpose of the new group is to study the "epistemology" of
superluminality, Tachyonics, and FTL technologies.  Epistemology, in
general, is the branch of philosophy that deals with the origins, the
essential nature, and the ultimate limits of knowledge.  In this
context, however, it is the knowledge of superluminal phenomena,
tachyons, and FTL science that we are concerned with.

Of course, this means that any comment suitable for posting on the
message-board of any one of the other Coterie is available for
mirroring on the new board, and there subject to a broader-ranging
discussion than would ordinarily be considered on-topic within the
originating Coterie.

Feel free to post any comments you wish on the new message-board.

--- In TheAoISCT@yahoogroups.com, "captjim" <Jonesalonzo1@...> wrote:
>
> Well, I've seen nothing so far that contradicts your superluminal
> gravity ideas.  I've just recently started reading this thread but
> all I could see is that Merlin thinks you don't have the credentials
> to be credible.  I say, that that your titles have nothing to do
> with whether your ideas are true or not.  I say, stick to the ideas.
> Comment on those.  The closest he's come to addressing the real issues
> in the few posts I've read is to say that you don't have a good
> enough mathematical formulation for him to take the ideas seriously.
> He references a website which shows the type of math he expects to
> see.  This would be great if, like the theories on the site, a
> number of mathematicians from a number of disciplines had worked on
> the problem over a number of years.  Unfortunately, you are
> pretty much working alone and have only so far just scratched the
> surface of what potential there is in this theory.  Merlin might
> have a valid point though, that you need better math attached to your
> theory but you never claimed otherwise.
>

Thank you for your encouragement.  The only thing I would rephrase, and
it is a minor point, is in your last sentence.  I would say that the
term "better math" is a little too subjective.

What is better math?  I take it you meant "more elaborate math".

Merlin's notion of "better math" would be more advanced math, I guess,
but he failed to notice that no more advanced math is needed for my
thesis on tachyonic gravity.  In fact, although I did not state it in
my thesis, I have spent many years studying all of the most advanced
math on gravity and tachyons around, and I have, on paper, many more
elaborate schemes that could be published.  But they are redundant,
because they are all based on the math that I presented in my thesis.

There is indeed much more that can and should be done, but there must
also be a fundamental set of initial assumptions and an elementary
foundation for the concept that I presented.  And that was the overall
purpose of the way in which the thesis was written  -  for without such
a foundation we have nothing to build on for more advanced work.

My goal, then, was to get the ball rolling on the idea of tachyonic
gravity, the way I have described it.  So, my feeling is that, because
I have only a limited amount of time and resources to spend on it, I
need HELP with it, not condemnation FOR it.

I would much rather that someone at Merlin's level of accademic success
take hold of my ideas and turn them into something more significant
than I can do on my own.  And there are such scientists out there, who
are actually doing similar things in their own way.  A particularly
good example is Dr. S.C. Tiwari, who wrote the book Superluminal
Phenomenon in Modern Perspective (from Rinton Press), and with whom I
correspond with by e-mail on a semi-regular basis.  He has his books to
pursue, and therefore has told me he does not have time to work on my
ideas (although he does review my work), he gives me helpful advice,
instead of insulting remarks about my level of formal training.

Guys like Merlin have advanced math to work with in M-Theory and other
theoretical endeavors because, as you alluded to, those theories make
use of concepts that have been around for decades, and a great deal of
work has gone into the math and the science involved.  It is not fair,
therefore, that Merlin and his kind condemn new ideas like mine simply
because of vested interests in promoting some older ideas that the new
ideas may perhaps replace as the "next big thing" or important trend or
other popular movement in physics.

Notice that the String Theories, the forerunners of M-Theory, were once
held as outside the scope of "real" physics.  But that has changed, and
M-Theory, along with special applications of the several String Theory
concepts, are by far the areas of theoretical research concentrated on
by the vast majority of physics students and physics teachers today,
and serve as the primary motivation behind many experimental efforts
overseen by a number of highly-regarded and highly-paid physicists.

Hence the vested interests in such theories, and hence the tendency to
downplay alternative and/or competing theoretical ideas.

But there is growing interest in the investigation of superluminal
phenomenon in physics, and that will not go away, because it is most
certainly, more than anything else, the ultimate future of physics.

Some will doubtless continue to call studies in superluminality and
Tachyonics useless exercises in science-fiction, even after empirical
evidence for the existence of tachyons starts coming in.  Indeed, that
will only reinforce the need for the new ideas to become more and more
popular, and thus more widely acknowledged, because the opposition will
come from people who will, as a consequence of their opposition, prove
themselves only the defenders of obsolete perceptions of reality.

What is more, it appears that such a day is coming sooner than I had
anticipated, even as late as two years ago, when I first setup my web
site; www.TachyonicsSociety.com.  I believe, in truth, that evidence
for the suggestion that gravity is faster-than-light will be announced
by experimentors whose credentials cannot be questioned within the next
few months.  Let's see if that actually happens, and discuss it here,
say about May or June of 2007.  What do you say?

Well, I've seen nothing so far that contradicts your superluminal
gravity ideas.  I've just recently started reading this thread but
all I could see is that Merlin thinks you don't have the credentials
to be credible.  I say, that that your titles have nothing to do
with whether your ideas are true or not.  I say, stick to the ideas.
Comment on those.  The closest he's come to addressing the real issues
in the few posts I've read is to say that you don't have a good
enough mathematical formulation for him to take the ideas seriously.
He references a website which shows the type of math he expects to
see.  This would be great if, like the theories on the site, a
number of mathematicians from a number of disciplines had worked on
the problem over a number of years.  Unfortunately, you are
pretty much working alone and have only so far just scratched the
surface of what potential there is in this theory.  Merlin might
have a valid point though, that you need better math attached to your
theory but you never claimed otherwise.

Counter-Responses, Section 6 (End of Part 5)

Merlin Wrote:
Kurt, you see me as so many others have in the past. You make the
(incorrect) assumption that I am a part of the establishment that
strives to keep new ideas out of the mainstream. I personally get
rather tired of that, but hey - it seems to come with the territory.
For the record, I did apologize (a couple of times) for being rude,
however, I do stick to my commentary as offered in refutation of the
facts you offered. That is how the scientific method works. Vetting
is supposed to occur so that errors do not creep into the science.
Like you, I would take it personally if someone were to find flaws in
my theories, however, I would not launch into a personal assination
attempt as you did. Instead, I would have "papered me to death" with
proof; that's how the process works. Just because you consider
yourself to be an outsider with radical views does not make you
immune to 100% of the scientific method. By avoiding the real
scientists (and the methods), you only isolate yourself further.
If you really are interested in finding out whether or not I
am "orthodox" in my study of the sciences, I suggest that you visit
here: Reality of our understanding.
<http://merlinsscience.0catch.com/Realitycheck.html> This is the site
where I "express myself" without having to worry about anything other
than speaking my piece; it's a work in progress.
By the way, Kurt, I am not a "One man show" either. I too have more
than just a handful of other experts in the fields relevant to my
areas of research working with (or for) me. I love to collaborate;
islands remain islands forever - even if bridges are built.

My Response:
I am reminded of a politician who engages in spin; such as when a
decades-long veteran of Washington politics claims to be
an "outsider".  Merlin likes to say that he does not promote
establishmentarian science, but, with the credentials he spouts, how
could he not?
He wrote:  "As a member of AIP  ...  I myself am a Fellow with honors
(in good standing) of the affiliates: APS (15 years), AAPT (17
years), AGU (8 years), AVS (9 years) & AAS (12 years). I also happen
to know that this lends absolutely nothing to your credentials;
unless you too are a Fellow w/honors. You see, I do fall into most of
the categories that you listed: Government researcher (former),
University Professor (currently) and Physicist (last 20 years), ..."
[Note:  AIP is the American Institute of Physics.  APS is the
American Physical Society.  AAPT is the American Association of
Physics Teachers.  AGU is the American Geophysical Union.  AVS is the
American Vacuum Society.  And AAS is the American Astronomical
Society.  Complete descriptions of these (among other) AIP affiliates
can be found by visiting www.aip.org.]
And yet, despite all of this, clearly showing that he has stature in,
and is "in good standing" with, the physics community, Merlin would
have us believe that he is not "part of the establishment that
strives to keep new ideas out of the mainstream".
Notice that he said "the" establishment instead of "an"
establishment.  This is a subtle hint that the establishment to which
he belongs is quite thoroughly populated by physicists who do, in
fact, tend to hinder the widespread acceptance of ideas that do not
fit well with their own ideas; most notably by keeping unwelcomed
unorthodox ideas out of mainstream physics publications (either with
the willing acquiessence of editors, or by applying coercive pressure
on them).
Fortunately, some in the physics community are coming to grips with
this sort of systemic foible, having been alarmed by the significant
numer of ethics scandals that did much to tarnish the image of
science in general, and desiring to mitigate such disrepute touching
their arena of the sciences.  Consequently, to their credit, Physics
Today magazine, for instance, has established itself among the few
publications keeping such issues in the minds of "real" physicists.
Allow me to quote one of Merlin's peers, from a commentary in the
Letters section of Physics Today of January 2006 (page 13).  W.W.
Carter writes:  "Editors of the principal journals reject manuscripts
that challenge prevailing theories or fall outside mainstream
research.  This practice eliminates new ideas in fundamental physics
and encourages routine articles in established fields.  The editors
protect themselves from many crackpot submissions, but also from the
few potentially great concepts.  An organization or journal that
screens original articles specifically to identify great ideas would
be a valuable asset."  Implying that no such organization or journal
presently exists!
Where Merlin and I part company, then, is that he is calling me
a "crackpot", while I am trying to suggest merely that my thesis is
a "potentially great" concept.  Yet, by his own admission, he views
my thesis as nonsense, and has posted arguments in support of his
position.  But, while decrying my ideas, he has made numerous
derogatory remarks against me personally.
I guess, however, if he is to be taken as a defender of the virtue of
mainstream thought in physics, that "vetting" and the "scientific
method" include insulting your opponent's intelligence.
On the other hand, readers who review the earlier messages in this
series of posts, and how all this got started, will be reminded that
it was Merlin who first launched an attack on me!   [Note that the
response I gave to a post he first submitted on the original thread
(by barging-in on a discussion between myself and another
participant), was only a disagreement, not an attack.  But Merlin
seems to have taken such offense that anyone would dare disagree with
him that he launched into a disrespectful and clearly vehement attack
on me as a person, with, it seems to me, my ideas as no more than a
platform upon which to stage the repeated firing-off of personal
insults.
I thus act in self-defense, against someone who obviously intends
harm to my reputation.
He is also accusing me of avoiding "real scientists".  But that is a
an outright lie.  I correspond with several real scientists by e-mail
on a regular basis, and often get encouragement from them, not
condemnation.
And I read copiously the work of many scientists from around the
globe.
I have visited Merlin's web-site too, but find there little in the
way of radical or even orginal ideas.
He reminds me likewise of string theorists, now working on M-Theory.
Once upon a time, their ideas were considered unorthodox.  But today,
they constitute the heart of mainstream efforts in theoretical
physics.  Yet, many still claim to promote unorthodox ideas!  Go
figure.

On 12-4-06, another participant on the forum expressed sympathy for
me, and also said:
'Good science should open doors to new possibilities, not close
them!'
In a reply to this, speaking of me, Merlin wrote:
'... there is nothing "good" to place us on a "new possibility" in
what he has been lecturing upon.'

My Response:
Like many overly self-centered scientists, Merlin states his opinion
as if it were an absolute fact.  Yet, I must admit that I too do
something similar, in my saying about gravity being a tachyonic
force.  [Indeed, I am so convinced of the hypothesis that gravity is
tachyonic that I routinely state my opinion bluntly that way.]
However, I always state that saying in a context in which it is
fairly clear that it is my personal conclusion; an opinion; a
possibility.  I have also always specifically made it clear that the
hypothesis and my thesis are mere science-fiction concepts, at this
time.  There may come a day when experimental evidence either proves
or disproves the hypothesis in an indisputible way, but that remains
to be seen (although I stand by the predictions I gave earlier).
The problem with this negative statement about my ideas by Merlin is
that he could not possibly know whether or not my ideas are good
enough to lead to useful new possibilities in our understanding of
pysical processes at some point in the future.
I must therefore say that time will tell, and I am hopeful that the
evidence will be in my favor.  In fact, I am quite confident that it
will be, because of the latest developments in detection technology,
and the growing interest in invetigating superluminal phenomenon in
physics  -  despite any objections Merlin may have of such efforts.
Let's give it a few months, and see what happens.


************


This ends my counter responses to Merlin's comments against me, as of
the date 12-13-06.
Stay tuned for more on the issues that have been raised in these
posts.

Counter Responses, Section 5

Merlin Wrote:
As for the "think-tank" - well, I encourage you to engage more "real
physicists" in your tank.

My Counter-Response:
OK.  But how many would Merlin suggest?  There are several who are
involved on an ongoing basis, and there has been some interest,
including a great deal of encouragement, by many others in the past
two years (since I started it).
Yet, in this case, I doubt the number of supportive scientists really
makes much difference to Merlin.  If it is any number short of a
plurality of all mainstream physicists in the world, I imagine Merlin
would say that we are all just a bunch of crackpots anyway, because
he obviously does not want to entertain even the hypothesis that
gravity could be faster-than-light.

Merlin Wrote:
... my favorite comment of all:
Kurt said, "As for the dispute between Merlin and myself, I believe I
have demonstrated in this thread that I am owed a sincere apology. "
I cannot even begin to comment on why anyone would think that an
apology would be warranted by the rebuttal above. No cogent argument
was achieved, and, after having read the entirety of the rebuttal -
my opinion remains unchanged. Wait a sec. - was that another bit of
shenanigans from you Kurt? I think it might have been... You
intimated that you managed to foil my critical dissection of your
theory by insinuating that an apology was warranted. By using your
logic, I could easily demand such an apology from you seeing as how
your rebuttal was even less compelling than your original argument.
Oh well, I guess we'll just have to agree to disagree. Good luck on
your quest for tachyonic gravity.

My Counter-Response:
What a conceited blow-hard!  My argument was quite "cogent".  And
his "critical dissection" of my theory on gravity (which is not a
theory, but a thesis; as I have, by now, pointed out far too many
times) was given not in the least in the form of constructive
criticism, but was plainly nothing short of a rather vehement and
extensive exercise in negative, even abusive, criticism.
And why, if I am such a nobody, so ignorant, lacking in sufficient
knowledge, with no compelling argument, does such a highly
experienced and impeccably-credentialed university professor, a
Fellow with honors of the American Institute of Physics, take the
time and trouble to offer such long-winded rebuttals to the ideas I
have published on the Internet?
Is it for my own good, as he suggests?  Or is it to prevent
unsuspecting readers from falling victim to my con, if that's what it
is?  Or is it rather to defend the integrity of the "scientific
method"?
Please.  Spare me the false heroism.
I am still owed an apology.
Yet, I will never get it, for there is something else at work here;
something unspoken, which I have only lately come to realize.  It is
something that Merlin has revealed about his motives in a number of
the Freudian slips that can be detected in his words.
From such hints I have finally concluded that it is not me personally
that Merlin disapproves of, nor does he really care how much or how
little I know.  It can only be the potential popularity of my ideas
that he fears.  And that fear has caused him to act out of all
proportion to the frivolity he attaches to the ideas.

Subsequently, Merlin Wrote:
... your "website's math" is not at all PROOF. For someone who claims
to be a "physicist", you should know that mathematical proofs look
absolutely nothing like what you are proposing at the tachyonics
website (yes - I did visit). I particularly liked the section where
you linked the readers to a different page due to the" limited
capabilities of the word processor used to write and publish this
article on the Internet, such symbols cannot be represented in a very
accurate way here."
... the fact that your entire 7-page thesis posted on AOL Hometown
display no "higher math" speaks volumes. Given that we are talking
about the interaction of theoretical particles outside of
relativistic bounds, I would have at least expected to see some math
similar to that of, something such as this.
<http://merlinsscience.0catch.com/YI.html>

My Response:
Here, once more, Merlin is attributing a position to me that I have
never taken.  Then he becomes derisive because I have not produced
what he already knew I have not produced before.  He seeks proof.
But I have never offered him or anyone else empirical proof of my
ideas.  There is what could be referred to as "circumstantial
evidence", for instance, for the existence of tachyons, and
convincing mathematical implications that gravity is tachyonic, but
there is no hard proof, much less any sort of evidence that someone
like Merlin will take as indisputable at this time; because, like the
vast majority of today's mainstream physicists, he seemingly does not
want tachyonic gravity to be true, no matter what!
And, due to the fact that he has already embraced a certain
conceptualization of how gravity works, sufficient to support his own
view of the way things are, I suspect that he will never acknowledge
the possibility that tachyonic gravity may be proven someday (despite
his preferences), and he will probably continue to deny even the
suggestion that gravity could be faster-than-light until some group
of physicists he cannot belittle comes along with the kind of proof
that he is demanding; at which, I further suspect, instead of
changing his mind, dismissing his previous views and taking as
scientific fact the proven case, he will, I now bet, experience
something like a nervous breakdown  -  because his world view, the
one he as been staking his reputation on, and teaching/preaching all
these years, along with that of many of his peers, will thereby have
been completely shattered!
There are, to be sure, ongoing experiments, and others which are
planned, that are recognized as the most advanced efforts at
determining the most accurate form of the quantum theory of gravity.
The top few were discussed recently in the article "Quantum Gravity
Faces Reality", by Lee Smolin, [of the Perimeter Institute for
Theoretical Physics (Waterloo, Ontario, Canada)], in Physics Today
magazine, the November 2006 issue, pages 44 - 48.
The blurb for the article reads:
"String theory is only one of many approaches to quantizing general
relativity.  Increasingly, all of those approaches will be judged by
how well they accord with experimental data."
I take such information very seriously, and try to keep abreast of
the latest developments.  Note too that several of the coming
experiments Smolin mentions could result in a re-examination of how
we represent quantum gravity, and I would go so far as to suggest
that this may very-well result in the conclusion that gravity is
superluminal in nature, and that its quanta could even be described
by the kind of tachyons I propose in my thesis.
I shall therefore go out on a limb here, and make the following
prediction, which Merlin can take as someday bringing to a close our
debate on whether or not my ideas are valid.  I predict that more
than one of these experiments (and others besides) will soon prove
beyond doubt that gravity is indeed tachyonic, and that this proof
will become undisputed no later than 50 years from now, but will be
embraced by the vast majority of physicists world-wide within the
next 5 years.  Yet, I am willing also to say that I believe these
experiments will start to be recognized by the experimentors as
leading them in that direction within the next few months!  [Some few
of which may even begin publishing their findings, in that regard, if
they are brave enough to do so.]
That should be soon enough for Merlin.
If, within the next few years, therefore, reports from the
researchers involved in at least two of the experiments mentioned in
Smolin's article do not state that the data being collected could be
interpreted as indicating a tachyonic representation format for the
most empirical quantum theory of gravity (even if my version of the
representation is not embraced), then I admit now that I have been
wrong about it all along.  But if those reports confirm instead that
what I have been saying is probably true (that gravity is tachyonic),
then that will prove that it was Merlin who was wrong, and that he
will indeed owe me a sincere apology.
But I conjecture on future events.  Let us return to the present.
To be as facetious as he, I am glad he "liked" it when I directed
readers at my site to another online source, due to the limits of my
software.  As I said before, I am not a wealthy man, and I do not
have unlimited resources with which to buy equipment.  I am a
moderate-income working-man, and devote my spare time to this
research as a hobby.  So, I can only afford to direct so much time
and money to it.  Thus, I simply have to do what I can with what I've
got, until I can afford to get something better.
And if that is not good enough for Merlin, well then all I can think
of to say to that is something politically incorrect.


More to come.