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Overview of Tachyons
by
H.K. Richter
According to Einstein’s theory of Special Relativity, the mass m of a moving particle is given by a formula that can be denoted; m = mo/[{1-[(v/c)^2]}^(1/2)] , where mo is the rest-mass, v is the velocity, and c is lightspeed (~ 186,000 mi/sec); as viewed from our everyday (i.e. standard) frame of reference. (Serway, 1124) Obviously, there are three solutions with respect to the value of v; (1) v is less than c, which ensures that m is a real quantity, (2) v = c, so that m = 0 (the case for massless photons), and (3) v is greater than c, making m an imaginary quantity (due to the presence of the square-root of a negative number). (Lerner, 1246) This third possibility implies the existence of particles with reversed causality (negative time), 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 negative energy and/or momentum as calculated from a standard reference frame, and, as the given equation shows, it would take an infinite amount of energy to slow a tachyon down to lightspeed (due to the reversed causality) [just as it would take an inifinite amount of energy to accelerate a real mass up to lightspeed].
This does not, however, definitively prohibit the existence of tachyons (as Einstein himself is said to have assumed), since it is quite possible that just as many tachyons of various kinds were created by the Big Bang as were the fundamental particles we have discovered so far. 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 imagine the generation of certain infinite-speed and/or very-high-speed tachyons by means of various sublight (tardyonic) particle interactions, because such tachyons would be so easy to create.
There is also evidence that we exist in a universe that is actually embedded in an infinite multitude of alternative, or “parallel", universes. That is, the known universe may abide in a super-dimensional reality, which thus allows that there exists at least one tachyonic analog of the known universe (the one predicted by Special Relativity). (Kane, 13)
There is today much theoretical work being done on the subject of tachyons. For more information, the reader is encouraged to do a Google search using the key-word “tachyons”, which brings up a large number of sites.
Example of Preferred Site:
Text References:
Feinberg, G. “Particles That Go Faster Than Light”, Sci. Am., Feb. ‘70; pp.69-77.
Kane, G.L. “Experimental Evidence for More Dimensions ...”, Physics Today, May, 1998; 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.
For those who demand 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;
L = [e^(-T)][1+ T + (dT)^2] ,
where e is the base of natural logs, the d indicates a partial differential, and other energies (potential, thermal, etc.) are zero.
Should such a tachyon be viewed as amenable to the influence of a field of force, then the tachyon's associated potential energy U can be defined in terms of a scalar potential function p; U = -(p^2){log[(p^2)/e]} , and the Lagrangian becomes;
L = [e^(-T)][1 + T + (dT)^2] - (p^2){log[(p^2)/e]} .
Reference:
For an overview of Lagrangian functions, go to
In his website, http://users.primushost.com/~ewall, E.L. Wall provides a rather convincing model of subatomic interactions involving tachyons, and which he reports is consistent with experiment. [Wall's book, The Physics of Tachyons, is available from Hadronic Press; I-57485-001-6.] Therein, tachyons are absorbed by various known particles, which scenario brings with it the possibility that tachyons can also be released (emitted) in reverse processes; implying a mechanism by which tachyons can be produced by ordinary matter. It remains, of course, for physicists to test Wall's model.
One tachyon that physicists may already have detected, however (in an indirect fashion) could, in fact, be the neutrino. Calculations involving the energy spectrum of the electrons in certain low-energy beta-decay experiments have yielded a negative value for the square of the associated neutrino's mass; which means the neutrino's rest-mass is imaginary. And, as it cannot be firmly established that neutrinos travel only at or below lightspeed (it has merely been assumed that this is so, up to now), then there is no physical reason to insist that neutrinos cannot travel faster-than-light. We could object on the grounds that causality would be violated, but then we must maintain (and, therefore, be able to prove) that some "law" of the non-violation of causality is not just a rule devised by Man, to satisfy the demands of Man's dogma, but is a mandate strictly adhered to by Mother Nature -- who often has quite contrary ideas of her own, despite what physicists may prefer.
Reference:
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The ultimate conclusion, from obvious patterns of plausible inference that can be gleaned from all of this, is that gravity is caused by certain types of tachyons, with the neutrino as an example. Indeed, the idea that gravity is faster than light has been put forth by a number of respected scientists, who have based their suggestions on sound theoretical formalisms. Given a valid Lagrangian for a tachyon that explains gravity (and from which we can derive a Hamiltonian that can be used to establish a quantum field theory of its interactions), along with the stated means of the generation of tachyons (with the elusive neutrino as the first example of such tachyons to actually be detected), we are presented with a scenario in which gravity can finally be unified empirically, at the quantum level, with the other fundamental forces of nature.
For more on this, click the link labeled "More ..." below, and after considering that page, click the link "Application to Gravity", read the refresher on gravity (if needed), then click the link indicating "More ..." at the bottom of that page. An explanation is given as to how tachyons can be used as the quanta of gravity; enabling gravity to be unified with the other forces in a guage-field setting.
Reference:
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Copyright 2003, H.K. Richter
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