Tiwari on Tachyons

A commentary on S.C. Tiwari's book,
Superluminal Phenomena in Modern Perspective,
from Rinton Press (2003).


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.