faster than light

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…