faster than light

29
FASTER THAN C ? INFORMATIO N He is gaining on me DEBAN UJ

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Page 1: Faster than light

FASTER THAN C ? INFORMATION

He is gaining on

me

DEBANUJ

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ATOMS

LIGHT

LORENTZ MODEL

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ATOM

LORENTZ MODEL

ELECTRON

NUCLEUS

small

Damped Harmonic Oscillator

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LORENTZ MODEL

where

Solution :

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LORENTZ MODELUsing Maxwell’s Equations :

Refractive index is a function of frequency!!

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• PHASE VELOCITY : Rate at which the phase of the wave

propagates in space.

VELOCITY OF LIGHT

PHASE VELOCITY

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Any waveform can be decomposed as a weighted sum of different monochromatic

components

VELOCITY OF LIGHT

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• 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

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VELOCITY OF LIGHTGroup velocity is given by :

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SLOW AND FAST LIGHT

By changing group velocity

can be made anything from negative infinity to infinity

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SLOW AND FAST LIGHTNEGATIVE GROUP VELOCITY?

WHAT? THE PULSE LEAVES BEFORE ENTERING??

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CAUSALITY ???

THE BOSS IS NOT HAPPY !

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CAUSALITY ???

FABIENNEGUESTS

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CAUSALITY ???

FABIENNE

FABIEN

V= 0.75 c

x

t

t’X’

(0,0)

(0,0)

Boundary of light cone

v1=c

v2=2cNegative time

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CAUSALITY ???

BUT IS GROUP VELOCITY WELL DEFINED IN SPACE

AND TIME?

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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

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PULSE DISTORTIONTo solve the PDE Fourier Transform methodcan be used :

Substituting in 1 :

2

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PULSE DISTORTIONSolving 2 :

Frequency dependence in phase

Pulse gets distorted! Group velocity does not make sense

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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

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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.

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INFORMATION IN A PULSE

c

Non-analytic points propagate with velocity=c.

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EXPERIMENTAL SETUP

K-vapour was used to create anomalous dispersionAnd achieve superluminal group velocity.

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RESULTS

Information is detected later for the advanced pulse.

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MODEL

Comparison of delay with a theoretical model basedOn Maxwell’s equations.

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CALCULATION

where

L is the length of the cellvi is information velocity

Delta t is detection latency

small

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CALCULATION

Using vi vac = c

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SUMMARYInformation cannot travel faster than the vacuum speed

of light.

So forget about changing the past…

Be in the present…

And decorate the future…

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