The Tachyonics Society of America
Dedicated to the Study of Tachyons

We study Tachyons, engage in the scientific endeavor of Tachyonics, and strive to understand all Superluminal Phenomena in an empirical fashion.  You are welcome.

This site is for open publishing of research on tachyons.  Submit comments, articles, and article ideas by e-mail to
Tachyons Overview                                                                                   By Harrison Kurt Richter, Founder.  

According to Einstein’s theory of Special Relativity, the mass  m  of a moving particle is given by the following equation;

in standard mathematical form.  In basic keyboarding symbols, this is;
m  =  mo / [ {1- [(v/c)^2] }^(1/2) ] ,
where mo is the rest-mass, v is the velocity of the particle, and c is lightspeed (~186,000 mi/sec),
as viewed from a standard reference frame (coordinate system). (Serway, 1124)
Note that this formula involves the Relativity Operator, 1/[{1 - [(v/c)^2]}^(1/2)], which has a radical in the denominator.

Obviously, there are three cases with respect to the velocity, v;
(1) v < c, making  m  real, where time is positive, in which case the particle is called a “bradyon”,
(2) v = c, where  m = 0 , which is the case for massless photons, also called “luxons”, and
(3) v > c, making  m  an imaginary quantity, due to the presence of a negative under a radical in the denominator of the formula for  m , and where time is negative, as viewed from a standard or "bradyonic " reference-frame.  (Lerner, 1246)

This third possibility implies the existence of particles with reversed causality (negative time), and which always travel faster than light. Named the “tachyon” by physicist Gerald Feinberg in 1967 (Feinberg, 69) [though first proposed by O.M.P. Bilaniuk, V.K. Deshpande, and E.C.G. Sudarshan, in 1962], such a particle would also exhibit complex energy and/or momentum as calculated from a bradyonic frame, and, as evaluation of the given equation shows, it would take an infinite amount of energy to slow a tachyon down to lightspeed -- just as it would take infinite energy to accelerate a bradyon up to lightspeed.

That does not, however, prohibit the existence of tachyons (as Einstein himself is said to have assumed), since it is possible that just as many tachyons of various kinds were created during the first phases of the Big Bang that initiated the visible universe as were all the bradyons and luxons we know about today. What is more, since an infinite speed is the tachyon’s zero-energy level, then it is not outside the bounds of plausible inference to suggest the possible generation of certain infinite-speed and/or very-high-speed tachyons by means of bradyonic interactions, because such tachyons would be so very easy to create.

And there is evidence that we exist in a universe that is embedded in an infinite multitude of alternate universes; meaning, the visible universe probably abides in a super-dimensional collection of universes called the “Multiverse”, which thus allows that there exists at least one superluminal analog of the known visible universe (as implied by the Light Cone of Special Relativity). (Kane, 13)

Indeed, ancient thinkers (Vedic seers, the Taoists, Mayans, and many others) long ago held that our world is super-dimensional in nature, so modern science has now come full circle, in also recognizing this fact. The development of M-Theory, for instance, depends on the concept of the Multiverse.  And there is today much theoretical and experimental work being done on the subject of tachyons, and on experimental investigations into other superluminal phenomena.

For more, see:
Internet Search Terms: “tachyons”, “tachyonics”, “superluminal”.

Print References:
Feinberg, G. “Particles That Go Faster Than Light”, Sci. Am., Feb. ‘70; pp.69-77.
Kane, G.L. “Evidence for More Dimensions”, Physics Today, May ‘98; pp. 13-15.
Lerner, R.G. & Trigg, G.L. Ency. of Physics, 2nd Ed. VCH Publishers, '91.
Serway, R.A. Physics for Scientists and Engineers, 3rd Ed. Harcourt Brace, '92.

A Tachyon Legrangian From Open-String Theory

For those who want to see a Lagrangian for the tachyon, an example can be found in Open String Theory, in which a Lagrangian density L can be given in terms of the kinetic energy T for a free (unbound) tachyon; 

in standard differential form. But in keyboarding symbols, this is;
L = (e^T)[1+ T + (d T)^2] ,
where e is the base of natural logarithms, the d denotes the partial differential, and other energies (potential, thermal, etc.) are zero. However, should such a tachyon be amenable to the influence of an externally applied field of force, then the tachyon's potential energy U can be defined in terms of a scalar potential function p, according to the formula;
U = -(p^2){ [log[ (p^2)/e ] } ,
so the Lagrangian then becomes;
L = (e^T)[1+ T + (d T)^2] - (p^2){ [log[ (p^2)/e ] } .

Bradyons May Have Tachyonic Substructure

One tachyon that physicists may have detected, in an indirect fashion, could be the neutrino. Calculations involving the energy spectrum of electrons in certain low-energy beta-decay experiments have yielded a negative value for the square of the associated neutrino's mass; making the neutrino’s rest-mass imaginary. And, as it cannot be firmly established that neutrinos travel only at/below lightspeed (it had merely been assumed that this was so), then there is no valid reason to insist that neutrinos cannot travel faster-than-light, and there is now mounting evidence that they can and often do travel at superluminal rates, under the right conditions.

More likely, instead of being a tachyon, however, it is possible that neutrinos, and perhaps all bradyons, have tachyonic substructures. And, in that case, we may conjecture that such substructures are associated with some superluminal superstructure that wholly pervades the visible universe. This would, in fact, go a long way towards explaining such enigmatic phenomena as superluminal photonic tunneling, quantum non-locality, superluminal motions in quasars, and a number of other pertinent experiments and astronomical observations.

Some individuals object to idea of tachyons on the grounds that their existence would violate causality, but then they must maintain that some "law" of the non-violation of causality is not just a rule devised by Man, to satisfy the limitations of the human imagination, but is a mandate strictly adhered to by Mother Nature -- who often has quite contrary ideas of her own, despite what men may prefer.

Comments and questions welcome. E-mail:

Definition of Richter's Tachyonics Operator 

Welcome to the official web-site of the Tachyonics Society of America. 
Note:  This site is new, and still under construction.  Content added frequently.   
And thank you for your interest in our work.    
Related Links

The Tachyonics Operator Explained      The complete treatise on Richter's Tachyonics Operator.

Richter’s Assertions on Tachyonic Gravity      Summary of Richter's conclusions on applying Tachyonics to gravity.

Superluminal Gravitation and the Linearized Wave Equation      Richter's thesis on Tachyonic gravity; introducing the GET particle.

Tachyonics Implies Unification      How the Tachyonics Operator unifies gravity with the other forces of nature, using the GET particle.

The GET Particle and Dark Energy      The gravitational exchange tachyon (the GET particle) explains astronomy's dark energy.

The GET Particle’s Path      Math on determining the experimentally testable path of a GET particle.

Latest Developments in Tachyonics                                                                Announcement from Harrison Kurt Richter

Confirmation has been obtained by me from a high-level AI research team (for the second time) on their interest in my mathematical invention, the Tachyonics Operator, for use in modeling consciousness and the subconscious in a manner that can be implemented with code and transfer-functions in an AI CPU (synthetic brain). 

The operator is used to generate a superluminal number-system, which is then used for writing algorithms that model the concsious and subconscious activity of the human brain as interaction of the gray-matter with an invisible but ubiquitous superluminal energy field pervading the visible universe.

Learn about my new operator at the "New Math" and "Velocity Spectrum" pages on this site (or at the above links).

The said research is proprietary, but the math they are looking at is open-source information.  I mention this here in hopes that other researchers will consider my ideas, so one firm will not corner the market on utilizing the concept.

Updates will be posted as they arise.  And thank you for your interest.

Comments and inquiries welcome:
I'm also on Facebook:  Harrison Kurt Richter, in Asheville, NC.
 Interdiscipline Synthesis Cosmology
Applying tachyonics to experimental science.