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-you change-the-past http://scienceworld.wolfram.com/physics/X-Wave.html