1. Tachyon – Faster than light particles 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

2. Overview  Background – the idea  Concept – Theory  Problems – Antitelephone  Research – Discovery?  Conclusion

3. 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

4. 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

6. 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

7. 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

8.  In timelike space, E and p are proportional  In spacelike, as p increase E decrease

9. 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

10. 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

11. Using tachyons – Dave At t=1.5s Dave sends message Because of time dilation, t=1.3 for Jason Not surprising because of relativity

12. Using tachyons – Jason Because of tachyons’ speed, Jason receives message before seeing Dave sending it

13. Using tachyons – Jason Say Jason sends a message back

14. Using tachyons - Dave He receives the Jason’s message before sending the first message!

15. 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

16. 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

17. 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

18. 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

19. 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

20. Resources  http://en.wikipedia.org/wiki/Tachyon http://en.wikipedia.org/wiki/Tachyon  http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachy ons.html http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachy ons.html  http://scienceworld.wolfram.com/physics/Tachyon.html http://scienceworld.wolfram.com/physics/Tachyon.html  http://io9.com/5846519/do-faster-than-light-neutrinos-let-you- change-the-past http://io9.com/5846519/do-faster-than-light-neutrinos-let-you- change-the-past  http://scienceworld.wolfram.com/physics/X-Wave.html http://scienceworld.wolfram.com/physics/X-Wave.html