Tachyons, Time Travel, and Paradoxes

Tachyons are faster than light particles. Are such things possible and if so, are there odd effects which may arise because of them? Here, we consider experiments, paradoxes, and possible ways out.


Acausal Signals

For the signal which travels from P to Q, there may be issues for a moving observer, even if the observers moves with v < c. The black line marks the curve vt = ct' and the magenta line marks the line of simultaneity (the x'-axis). Note that the signal is sent at time ct = ct' = 0, but is received at time ct' <0 ===> it is received before it is sent. This leads to issues. This effect leads to the Anti-Telephone, and to the Tolman Paradoxes (causality issues). Anti-telephone messages are theoretically possible, but people cannot travel backward in time.


    Tachyons

    In Special Relativity, because we require that the laws of physics are of the same form and that the speed of light is the same for all observers in inertial frames, the energy and momentum of particles must have different forms than which you are familiar. To the left is shown the energy of a particlein free space in Special Relativity. You are more familar with the form

    E = 0.5 mv2 + mc2

    Actually we don't usually add the rest mass energy because in classical physics we can't tap this energy and so we just usually redefine the energy as E' = E + mc2. For v > c, the radical leads to an imaginary number. In order for the energy to be real, this means that the rest mass of a tachyon must be imaginary!


    Cosmic Ray Showers

    Primary cosmic rays produce extensive air showers when they strike nuclei in our upper atmosphere. In such interactions produce tachyons, we expect that they would arrive at the ground before the shower particles. After an early possible detection by Ashton et al. (1977), no subsequent work has produced a positive result.


Cerenkov Radiation

In a medium, such as water where the index of refraction is n > 1, a beam of light travels with speed v = c/n < c. In this medium, if a charged particle can travel faster than c/n, it will emit Cerenkov radiation (much as a supersonic jet produces a sonic boom). In the panel to left, the faint blue glow in the reactor is Cerenkov radiation. The Japanese Super-K neutrino detector on the Cerenkov effect to detect neutrinos. High energy neutrinos scatter and produce high energy muons and electrons which travel faster than c/n leading to Cerenkov radiation (see panel to the right). If charged tachyons exist, then they would produce Cerenkov radiation in vacuum, losing energy and speeding up!


    Neutrinos

    Neutrinos are ghost-like sub-nuclear particles. Until the last decade, neutrinos were generally assumed to be massless and to thus travel at the speed of light. However, with the resolution of the Solar Neutrino Problem wherein neutrinos may change form as they travel through the Sun, it is clear that neutrinos are not massless and so do not have to travel at the speed of light. Tritium beta-decay experiments are consistent with m2 < 0 or that m is imaginary. The MINOS experiment (from Fermi-lab to the Candian border) measures the differences between the squares of the muon and tau neutrino masses. They do not claim that m2 is negative, they measure the difference between m2; and their results are consistent with v < c, but v > c could sneak in under the error.