Tachyon – Faster Than Light Particles
Background
Tachyon comes from the Greek word ταχύς or tachys, meaning swift, quick, fast, or
rapid. It is a hypothetical particle that always moves faster than or as fast as light. The first
theoretical prepositions for tachyons were made by George Sudarshan in 1962 however the
name tachyon was coined later in 1967 by Gerald Feinberg. Tachyons are known to not agree
with known laws of physics. If they exist, then a tachyonic antitelephone could be built to carry
information faster than light. This leads to a violation of causality and hence why most physicists
think that tachyons cannot exist. The idea is however, justifiable to some extent through
calculations using verified laws of physics.
Idea of faster than light particles
The concept was discussed by Deshpande, Bilaniuk, and Sudarshan in their paper in
1962. They offered a suggestion that something can travel faster than light, despite the speed of
light being the maximum speed for massless particles. Later in 1969, Sudarshan and Bilaniuk
wrote “Possibility of Faster-Than-Light Particles” where they propose particles with negative
squared mass.
The paper can be summarized in some major steps. First, we shall draw a graph with
momentum (p) on the x-axis, and energy (E) on the y-axis. Then we draw the "light cone" – two
lines with the equations E = ±p. This divides our 1+1 dimensional space-time into two regions.
Above and below are the "timelike" quadrants, and to the left and right are the "spacelike"
quadrants. This is shown in a 3-dimensional diagram below.
Diagram 1
We know from fundamental relativity that E² = m² + p². In diagram 1, the surface that
bounds the cones is where energy is equal to the momentum of the particle only; there is no
component of the energy that exists from mass. Massless particles called luxons travel along the
line equation. As far as we know, only photons are massless and thus, its energy comes solely
from its velocity. Photons should therefore have the highest possible velocity in this universe.
Everything with mass called bradyons will have fall inside the light cones. The plane formed by
the axes is our present and we will move through the future light cone. The origin of the graph is
point (p,E)=(0,m) where m is the rest mass.
Another relativistic equation that we know is E = m[1−(v/c)²]−½ . If tachyons exist, they
will have v > c which would make E imaginary. So we choose to have m imaginary instead and
E is real negative E² − p² = m² < 0 or p² − E² = M² where M is real. This equation brings about a
hyperbola that branches sideways from the graph we drew earlier. We call this region spacelike
while our region of existence is timelike.
Diagram 2
From the 2-dimensional diagram above, we can readily observe that tachyons accelerate
(p goes up) if they lose energy (E goes down). Furthermore, a zero-energy tachyon is
"transcendent", or moves infinitely fast. This gives rise to some problems.
Problems
Cherenkov radiation is radiation caused by charged particles that travel faster than the
speed of the produced electromagnetic radiation travelling in the immediate medium. An
example will be underwater nuclear reactors. The speed of light in water is 0.75c. Particles can
be accelerated past this speed although still less than c in the generators and so a soft blue glow
is given out through the radiation.
If charged tachyons move faster than light in vacuum, then they should produce
Cherenkov radiation. This would lower their energy. However, recall that the momentum of
tachyons increases as the energy decreases. This would cause them to accelerate more and hold
even more energy. In other words, charged tachyons would probably lead to a runaway reaction
releasing an arbitrarily large amount of energy.
Another problem as stated in the beginning is the possibility of a tachyonic antitelephone
to transmit signals faster than the speed of light, thus leaving our timelike dimension. We
imagine Jason and Dave sending each other messages,
Say due to their distance, light would take about 1 second to
travel from Dave to Jason and vice versa. Because they used
tachyons, they both receive their message in 0.25 second of it
being sent. This causes no apparent issue. Now we imagine
them moving away from each other at a speed of 1/2c.
Diagram 3
Say at t=1.5 Dave sends a message to Jason. Due to this time
dilation, Jason receives it at t=1.3. This is not too surprising.
However if we observe Jason’s point of view, it gets interesting.
Diagram 4
Due to slower light, Jason sees that Dave sent the message at
t=1.7. But he receives it at t=1.3 if we recall earlier. So he receives
the message before Dave sends it. Say Jason sends a message back
to Dave. And say the message is “Do not send me a message.”
Diagram 5
For Jason, again his message takes 0.25s to reach Dave.
Diagram 6
Dave will receive the message even before he sent out the first message. And what if he decides
to not send that message now? This is how tachyons is believed to be able to affect the past.
Diagram 7
Research
Tachyons can be assigned normal properties of matter like the spin as well as an
antiparticle, the antitachyon. Some modern presentations of tachyons have amazingly allowed
tachyons to have real mass. This allows and perhaps requires tachyons to be studied in the
quantum field where the arbitrarily large energy problem can possibly be solved by considering
the spontaneous tachyon-antitachyon pairs which renders the vacuum unstable. Research was
also done using the Klein-Gordon equation and Maxwell equation. We might obtain | p | ≥ | E |,
in which case E is real and we get solutions that look like waves whose crests move along at the
rate | p/E | ≥ 1, that is, moving no slower than the speed of light. We might also obtain | p | < | E
|, in which case E is imaginary and we get solutions that look like waves that amplify
exponentially as time passes.
Tachyons are not completely invisible or undetectable due to the difference in dimension.
We can possibly produce them in a nuclear reaction. If they are charged then we can detect the
Cherenkov radiation produce as the tachyons speed away faster and faster. It has been suggested
that tachyons can be produced from high-energy particle collisions. This called for the
observation of cosmic rays where tachyons might result.
Referring back to Einstein’s theory that the fastest speed a particle can travel is the speed
of light, the theory does not prevent apparent velocities from exceeding c. For example, phase
velocity and group velocity of a wave may exceed the speed of light, but no energy or
information actually travels faster than c. This does not violate causality and is obtained by
solving the Maxwell equation. Some of the solutions are waves called X waves. This therefore
gives hope for a loophole to the theory such that tachyons or any other superluminal phenomena
may exist.
In 1985, Chodos and others proposed neutrinos as tachyonic particles in their paper The
Neutrino as a Tachyon. The model uses the Lorentz invariance as in the Standard-Model
Extension where neutrinos experience Lorentz-violating oscillations and can travel faster than
light at high energies. This proposal was strongly criticized.
In 1973, researchers Philip Crough and Roger Clay identified a putative superluminal
particle in an air shower using a large collection of particle detectors. However, the results has
not been reproduced. Recently in September 2009, a collaboration between CERN in Geneva,
Switzerland, and the Laboratori Nazionali del Gran Sasso (LNGS) in Gran Sasso, Italy claimed
to have detected muon neutrinos travelling at superluminal speeds in Oscillation Project with
Emulsion-tRacking Apparatus (OPERA). OPERA researchers however discovered later in 2012
that the result was caused by a loose fiber optic cable connecting a GPS receiver to an electronic
card in a computer. Further investigations and experiment repetition showed that the speed of
neutrinos are consistent with the speed of light.
Conclusion
Theoretically on paper, tachyons might still exist since modern calculations hint us of
tachyons. If somehow the ability of the particles to travel faster than the speed of light does not
violate causality, then the restriction still holds. Or perhaps Einstein was wrong? Maybe there is
no limit – at least not the speed of light – to the speed at which particles can travel. Science itself
grows from the improvement of theories and laws. But will the existence of tachyons therefore
finally allow us to make use of time travel? It is a very interesting opportunity yet scary at the
same time. The theory of tachyons certainly raises many questions and it almost seems certain
that it is futile. However, I as well as other hopeful scientists are still interested in tachyons.
Resources http://en.wikipedia.org/wiki/Tachyon
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html
http://scienceworld.wolfram.com/physics/Tachyon.html
http://scienceworld.wolfram.com/physics/X-Wave.html
http://io9.com/5846519/do-faster-than-light-neutrinos-let-you-change-thepast http://journals.aps.org/pr/abstract/10.1103/PhysRev.159.1089
http://www.uam.es/personal_pdi/ciencias/jcuevas/Teaching/Taquiones.pdf
http://en.wikipedia.org/wiki/Cherenkov_radiation
http://en.wikipedia.org/wiki/Tachyonic_field
http://en.wikipedia.org/wiki/Lorentz_covariance
http://en.wikipedia.org/wiki/OPERA_experiment
http://en.wikipedia.org/wiki/Standard-Model_Extension