The term ‘tachyon’ was coined by Gerald Feinberg in 1967, following a 1962 paper[i] that discussed the possibility of objects existing whose velocity exceeded the speed of light[ii].  Despite the enthusiasm of the New Age industry and Star Trek fans, no conclusive evidence for the existence of tachyons has been offered, and there are a number of theoretical objections to their existence.  This report will examine the theoretical nature of tachyons, their possible interaction with ordinary manner, and attempts to determine their actual existence.

One of the key postulates of Einstein’s Special Theory of Relativity is that nothing can travel faster than the speed of light.  Although e=mc² is famous for relating energy to mass, it is a special case (here the velocity is zero – so called rest mass) of the more general equation: $latex E=\frac{mc^{2}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}&bg=000000&fg=ffffff&s=4$[iii] Equation 1 The mass of the object defined in equation 1 is at that objects given energy level - “as judged from a co-ordinate system moving with the body”[iv].  However, as velocity increases through the absorption of energy, so to does mass (by a factor of E₀/c^{2 [v])}, requiring more energy to reach higher speeds, and thus creating a greater mass.  As velocity  approaches the speed of light, mass approaches infinity, presenting a barrier to obtaining the speed of light that cannot be crossed. Whilst this barrier appears to end all possibility of faster-than-light (FTL) velocities, it makes the assumption that the starting velocity of the object is less than the speed of light (subluminal).  Tachyons overcome this barrier by always having a velocity greater than the speed of light (superluminal). The major argument supporting the existence of tachyons is that they do not breach Einstein’s Special Theory of Relativity.  Referring again to Equation 1, if velocity v exceeds the speed of light c, then the denominator of this equation is the square root of a negative number – a so-called imaginary number (denoted by the term i).  A real number divided by an imaginary number is an imaginary number, which means that for an object with superluminal velocity, its mass is imaginary.  An object with an imaginary mass moving superluminally has a real (measurable) energy, and does not breach Special Relativity.

This is all well and good, but both physicists and mathematicians are unable to define what constitutes an imaginary mass, and what the properties of such an object would be.  One property that would characterise tachyons would be that losses of energy would increase velocity, whilst increases in energy would decrease it.  This is the opposite of what occurs with ordinary matter.  Hence, as a tachyon gains energy, it approaches the speed of light (from above), requiring more and more energy to reach the speed of light, and thus facing the same barrier to crossing the speed of light as normal matter.  Because tachyons can never go slower than the speed of light, they can never be at rest, and therefore, their rest mass m, which is imaginary, is never reached, potentially providing a theoretical loophole.  A similar argument is used for designating the zero mass of a photon. More disconcertingly, tachyons appear to have the potential to breach causality, by being able to travel faster than light.  Any number of scenarios have been suggested to show how the ability for particles to travel superluminally would lead to logical absurdities, the so-called “Tachyonic Antitelephone”[vi] being a famous example.  Whilst we are not suggesting that tachyons can be used to build spaceships to travel back in time, their potential as a communication medium (just like electromagnetic radiation) introduces such scenarios.  A possible barrier is discussed later in this report. To discover tachyons, we would need to observe a physical reaction (most likely at the particle level) that could only be explained by tachyons.  To date, with a small number of possible exceptions, such evidence has not emerged.  In one instance, a cosmic ray particle appeared to reach the Earth before a photon[vii], but such a one-off observation cannot be considered as conclusive. If a tachyon were to cause a particle reaction with a known particle, one could attempt to measure the rest mass of the tachyon by determining the missing energy and missing momentum of the mystery particle, and using this to calculate the square of the missing mass via: $latex m^{2}c^{4}= E^{2} -(pc)^{2}&bg=000000&fg=ffffff&s=4$[viii] Ignoring the c⁴ on the LHS, we are looking for a reaction where m² < 0.  To date, no such reactions have been observed One possible tell-tale sign would be Cherenkov radiation.  This is a form of radiation given off by charged particles moving at velocities exceeding the speed of light in the medium that the particle is travelling through.  Because tachyons are always moving faster that the speed of light, they should always be emitting Cherenkov radiation, which radiates at a specific angle to the particle trajectory[ix].  A further effect of tachyons emitting Cherenkov radiation would be the loss of energy triggering an increase in velocity, which would trigger an increase in energy loss, “leading to a runaway reaction and the release of an arbitrarily large amount of energy”[x]. The fact that no evidence of such radiation or energy releases has been identified leads to the conclusion that tachyons, if they exist, are not charged, and most likely do not readily interact with normal matter.  Whilst some theories suggest that they do not interact with normal matter at all, this would make them virtually undetectable, and move them to the “realms of the metaphysical”[xi]. A particle that does have the properties of being electrically neutral, and not readily interacting with matter is the neutrino (whose existence, like the tachyon’s, was once only in the realms of theory), and there have been several attempts to identify this particle as a tachyon candidate.  Although recent experimental results strongly point towards the neutrino possessing mass[xii], it has not been confirmed whether this mass is positive.  More specifically, the mechanisms used to extrapolate neutrino mass revolve around energy profiles, and deal with the square of mass[xiii].  Some results have given this mass squared as negative, indicating a possible imaginary mass. Neutrinos are created in a number of atomic reactions, such as the fusion mechanisms that power stars.  Another reaction that produces a neutrino (and the reaction that first lead to it being postulated) is the decay of neutrons.  Outside an atomic nucleus, a neutron has a half-life of about 10.3 minutes.  A neutron decays into a proton, an electron, and a neutrino (actually an anti-neutrino)[xiv].  Because a neutron has greater mass than a proton and electron, the anti-neutrino appears to have positive mass (conservation of energy).  However, some theories propose that at high energy levels, a proton will beta-decay into a neutron, an electron and a neutrino[xv].  For such a reaction to have energy conservation, the mass of the neutrino must be negative (in the rest frame of the proton[xvi]). The proposed energy levels for proton decay are far in excess of those that can be generated using Earth-based equipment.  However, cosmic rays have much greater energy levels, and their interactions with Earth’s upper atmosphere can be examined for evidence of proton decay.  One key piece of evidence (although certainly not conclusive) is a shift in the “cosmic ray spectrum”.  The spectrum plots the quantity of cosmic rays (flux) against their energy level, shown in Fig. 1.  A power law relationship exists, but there is a noticeable[xvii] change in the gradient of the function at energy levels of about 10¹⁵ electron volts – referred to as the ‘knee’. Fig. 1 – The Cosmic Ray Spectrum[xviii] Some researchers have proposed that the ‘knee’ is the result of proton decay at high energy levels, with such decay providing possible evidence for the existence of tachyons.  However, other less esoteric explanations for the data exist, and applying Ocham’s razor, seem to rule against the cosmic ray spectrum as indirect evidence of tachyons. What would be more compelling would be physical evidence of proton decay, which primarily refers to neutrons.  As neutrons have a short half life, the discovery of neutrons in the energy spectrum just above the predicted energy levels for proton decay would be encouraging (neutrons at much higher energy levels may be present due to relativistic effects on their speed, and hence half-life).  Some observations from the cosmic ray source Cygnus X3 in the 1970’s and 80’s showed the just such a neutron ‘spike’, but more recent data, using more sensitive instruments has failed to reproduce this. Whilst the evidence is sketchy and inconclusive for neutrinos (or any other particle) to be tachyons, their general use as a breach of causality (and the paradoxes it presents) has been questioned based on some subtle implications of quantum theory, whereby “localized tachyon disturbances are subluminal and superluminal disturbances are non-local”[xix] (meaning you can’t create it and send it, you can only do one or the other).  A further difficulty is that experimental data supporting neutrinos as tachyon candidates show velocities only slightly greater the speed of light, limiting use for circumventing the directional restriction of time[xx]. Although a number of interesting observations have been linked to the possible existence of tachyons, they remain to most physicists in the realm of thought experiments – consistent with the equations, but having a low likelihood of being discovered even if they were to exist.  However, with some serious arguments being put forward for neutrinos as tachyon candidates[xxi], and neutrinos being a major research attraction in the field of particle physics and astronomy, further information is likely to emerge in the future that will either dismiss them as candidates, or indeed show that some things can travel faster than light.

[i] Bilaniuk, Deshpande, Sudarshan, American Journal of Physics 30 (1962) p.718 [ii] http://www.physics.gmu.edu/~e-physics/bob/t.htm [iii] Einstein, A. “Relativity.  The Special and General Theory”, p.50, Three Rivers Press, 1961 [iv] Einstein, et al p.53 [v] Einstein, et al p.52 [vi] Benford, Gregory A., D. L. Book, and W. A. Newcomb. "The Tachyonic Antitelephone", Physical Review D, 2, Number 2 (15 July 1970), pp. 263-265 [vii] http://www.physics.gmu.edu/~e-physics/bob/h.htm [viii] Sartori, L., “Understanding Relativity”, p229, University Of California Press, 1996 and http://www.physics.gmu.edu/~e-physics/bob/h.htm [ix] http://rd11.web.cern.ch/RD11/rkb/PH14pp/node26.html [x] http://www.angelfire.com/on2/daviddarling/tachyon.htm [xi] http://www.physics.gmu.edu/~e-physics/bob/h.htm [xii] http://www.sns.ias.edu/~jnb/ [xiii] http://www.sns.ias.edu/~jnb/ [xiv] http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html [xv] http://xxx.lanl.gov/abs/astro-ph/9812336 [xvi] http://www.physics.gmu.edu/~e-physics/bob/y.htm [xvii] The change is actually quite slight, but the data is sufficiently robust to acknowledge it as a definite trend shift - http://imagine.gsfc.nasa.gov/docs/features/topics/snr_group/cr-knee.html [xviii] http://imagine.gsfc.nasa.gov/docs/features/topics/snr_group/cr-knee.html [xix] http://www.ibiblio.org/lunar/school/library/tachyons.html [xx] http://xxx.lanl.gov/abs/astro-ph/9812336 [xxi] http://xxx.lanl.gov/abs/astro-ph/9812336