There was a young lady named Bright,
Whose speed was far faster than light.
She went out one day,
In a relative way,
And returned the previous night!
— Reginald Buller
Tachyon – Faster
than light particles
Overview

Background – the idea

Concept – Theory

Problems – Antitelephone

Research – Discovery?

Conclusion
Background

ταχύς or tachys, meaning "swift, quick, fast, rapid“coined by Gerald
Feinberg

Theoretical propositions of Tachyons by George Sudarshan in 1962

Not consistent with the known laws of physics

Could be used to build a tachyonic antitelephone – violate
causality
The Idea

1967 – Gerald Feinberg in "On the possibility of faster-than-light
particles"

Quanta of a quantum field with negative squared mass (complex
mass)

Draw Energy and momentum graph

Draw “light cone” – lines with E = ±p
The Idea - Relativity

Fundamental relativity fact E² − p² = m²; simplify c=1

Any particle with mass m falls in this hyperbola

Massless particles have E² = p² and move on the cone

Point (0,m) is when particles are at rest
The Idea – Relativity

Another relativistic equation E = m[1−(v/c)²]−½

Tachyons would have v>c

E is imaginary!

Take m to be imaginary, E is negative real

E² − p² = m² < 0

Hyperbola branching sideways

In timelike space, E and p are
proportional

In spacelike, as p increase E
decrease
Problems – Large energy

Increase in p leads to decrease in E which leads to increase in p

If charged tachyons move at v>c, they produce Cherenkov
radiation

Causes them to lose energy

p increases even more!

Also, minimum v=c
Problems – antitelephone paradox

Since tachyons’ v>c, they seemingly can travel
back in time

Send messages to the past by using tachyons as
information carrier

Imagine Dave and Jason moving away from
each other at speed close to c

Diagram for using normal carriers
Using tachyons –
Dave
At t=1.5s Dave sends message
Because of time dilation, t=1.3 for Jason
Not surprising because of relativity
Using tachyons –
Jason
Because of tachyons’ speed, Jason receives message
before seeing Dave sending it
Using tachyons –
Jason
Say Jason sends a message back
Using tachyons Dave
He receives the Jason’s message before sending the first
message!
Research

Can be assigned normal matter properties like spin

Modern presentations allows tachyons to have mass

Could be produced from high-energy particle collisions

Search tachyons in cosmic rays

1973 - Philip Crough and Roger Clay identified a
putative superluminal particle in an air shower

Results were never reproduced
Research – not impossible?

Einstein’s theory does not prevent apparent v>c

E.g. phase velocity and group velocity of a wave may exceed
the speed of light, but no energy or information actually travels
faster than c

Can obtain superluminal solutions to Maxwell equation

Do not violate causality because wavefronts travel within c
Research

1985 – Chodos et al. proposed neutrinos as tachyonic

Modeled using Lorentz invariance

Neutrinos experience Lorentz-violating oscillations and can travel
faster than light at high energies

Strongly criticized
Research – discovery?

September 2011

Oscillation Project with Emulsion-tRacking Apparatus (OPERA)
observed muon neutrinos travelling at v>c

Repeated experiments concluded this was an error in
Conclusion

Theoretically, tachyons might still be probable

Modern calculations still hint probability

Not a popular idea because of Einstein’s theory

Does not stop some scientists from searching for it

Real or not, it is very interesting
Resources

http://en.wikipedia.org/wiki/Tachyon

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachy
ons.html

http://scienceworld.wolfram.com/physics/Tachyon.html

http://io9.com/5846519/do-faster-than-light-neutrinos-let-youchange-the-past

http://scienceworld.wolfram.com/physics/X-Wave.html