faster than light
TRANSCRIPT
FASTER THAN C ? INFORMATION
He is gaining on
me
DEBANUJ
ATOMS
LIGHT
LORENTZ MODEL
ATOM
LORENTZ MODEL
ELECTRON
NUCLEUS
small
Damped Harmonic Oscillator
LORENTZ MODEL
where
Solution :
LORENTZ MODELUsing Maxwell’s Equations :
Refractive index is a function of frequency!!
• PHASE VELOCITY : Rate at which the phase of the wave
propagates in space.
VELOCITY OF LIGHT
PHASE VELOCITY
Any waveform can be decomposed as a weighted sum of different monochromatic
components
VELOCITY OF LIGHT
• GROUP VELOCITY : Different monochromatic components travel
at different phase velocities and the velocity of the maximum of the pulse is called group velocity.
VELOCITY OF LIGHT
GROUP VELOCITY
VELOCITY OF LIGHTGroup velocity is given by :
SLOW AND FAST LIGHT
By changing group velocity
can be made anything from negative infinity to infinity
SLOW AND FAST LIGHTNEGATIVE GROUP VELOCITY?
WHAT? THE PULSE LEAVES BEFORE ENTERING??
CAUSALITY ???
THE BOSS IS NOT HAPPY !
CAUSALITY ???
FABIENNEGUESTS
CAUSALITY ???
FABIENNE
FABIEN
V= 0.75 c
x
t
t’X’
(0,0)
(0,0)
Boundary of light cone
v1=c
v2=2cNegative time
CAUSALITY ???
BUT IS GROUP VELOCITY WELL DEFINED IN SPACE
AND TIME?
PULSE DISTORTIONNormalized field amplitude in a dispersive medium is governed by :
Where U(z,T)is the normalized amplitude of the electric field in the dispersive medium.
1
PULSE DISTORTIONTo solve the PDE Fourier Transform methodcan be used :
Substituting in 1 :
2
PULSE DISTORTIONSolving 2 :
Frequency dependence in phase
Pulse gets distorted! Group velocity does not make sense
INFORMATION IN A PULSE
(1868-1951)
Arnold SommerfeldIn 1907, predicted that the front of a step modulated pulse always propagates with a velocity of c irrespective of the dispersion of the medium.
Velocity of front = c
front
INFORMATION IN A PULSELater investigations in this field report that information is stored only in points of a pulse that are non-analytic. (Parker et al, Optics Communications , 229(2004), 23-27)
I is the total amount of differential information. p(x) is anyarbitrary continuously varying function of space. R denotes the residues of the function.
INFORMATION IN A PULSE
c
Non-analytic points propagate with velocity=c.
EXPERIMENTAL SETUP
K-vapour was used to create anomalous dispersionAnd achieve superluminal group velocity.
RESULTS
Information is detected later for the advanced pulse.
MODEL
Comparison of delay with a theoretical model basedOn Maxwell’s equations.
CALCULATION
where
L is the length of the cellvi is information velocity
Delta t is detection latency
small
CALCULATION
Using vi vac = c
SUMMARYInformation cannot travel faster than the vacuum speed
of light.
So forget about changing the past…
Be in the present…
And decorate the future…