1. FLOWER Fluctuations of the Light velOcity WhatEver the Reason
François Couchot, Xavier Sarazin, Marcel Urban
LAL Orsay
Jérome Degert, Eric Freysz, Jean Oberlé, Marc Tondusson
LOMA, Bordeaux
Presented by Xavier Sarazin
Conseil Scientifique du LAL
28 juin 2011
CS du LAL 28/06/2011

2. Is the speed of light a fundamental constant ?
Three types of possible effects
Time-variation of c c(t)
Chromatic dispersion of c c(E)
 c depends on the energy of the photon
Fluctuation of c sc
 c is constant in average but possible stochastic fluctuations around c
CS du LAL 28/06/2011

3. Time-variation of c Variation of c in space
- Initially formulated by Einstein
The constancy of the velocity of light can be maintained only insofar as one restricts oneself
to spatio-temporal regions of constant gravitational potential (Ann. Physik 38 (1912) 1059)
- Proposed as an analogy to General Relativity
GR  Refractive index of vacuum modified by gravitational field
Curvature and Delay due to varying index in space
Eddington 1920
Felice 1971
Evans, Nandi and Islam 1996
Variation of c in time ?
- A possible way to explain the apparent Dark Energy
J. Barrow and J. Magueijo, APJ, 532 (2000)
CS du LAL 28/06/2011

4. Chromatic dispersion of c
Singularities in space-time at Planck scale ~ m (MPlanck~1019 GeV)
At this energy scale, the dispersion relation is not linear any more
 The vacuum refractive index depends upon the energy of the photon
 c depends on the energy of the photon c(E)
G. Amelino, J. Ellis, et al., Nature 393, 763 (1998)
J. Ellis, N. E. Mavromatos and D. V. Nanopoulos, Gen. Rel. and Grav., 32, (2000),
J. Ellis, N. E. Mavromatos and D. V. Nanopoulos, Phys. Lett. B 665, 412 (2008)
Figure of merit to constrain this model is (L/Dt)×DE
 Best experimental limits with Gamma-ray bursts
Abdo et al, Nature, 2009
CS du LAL 28/06/2011

5. Fluctuations of c
Correlated to any discontinuity or discrete properties of the photon propagation in vacuum.
 Leads to fluctuations of the transit time of photons
Light-cone fluctuations (quantum metric fluctuation from quantum gravity)
H.Yu et L.H. Ford, Phys. Rev. D (1999)
~ fs.kpc1/2
Corpuscular model of photon propagation
M. Urban, F. Couchot et X. Sarazin arXiv:
CS du LAL 28/06/2011

6. A coherent corpuscular model of quantum vacuum
to explain the three electromagnetic constants e0, m0 and c ?
Preprint arXiv:
New hypothesis in this model (compare to standard QED):
Average energy of the pair:
Life-time of the pair:
Minimum Distance between fermions in the same spin-state:
 Density
(Two f-f spin combinations)
CS du LAL 28/06/2011

7. In our model: virtual pairs f f bear a mean electric dipole
Vacuum Permittivity e0 + - E
Polarisation P of the molecules by the field E
 opposite charges on the dielectric plates
 Voltage decreases  C is increased
With vacuum: e  0  e = e0 !!!
In our model: virtual pairs f f bear a mean electric dipole
The virtual pairs are polarized, BUT only during their life-time t
t depends on the coupling energy of the pair to the field E
En moyennant sur 
En sommant sur l’ensemble des fermions
(3 familles)
CS du LAL 28/06/2011

8. The vacuum is paramagnetic
Vacuum Permeability m0 I
B = m0nI + m0M
M = magnetization of the matter
If matter is removed: B = m0nI  0 B
The vacuum is paramagnetic
In our model of vacuum: m0 originates from the magnetization of the virtual pairs
Virtual fermion pair has a magnetic moment:
It is aligned during its life-time t
t depends on the coupling energy of the pair to the field E
En moyennant sur 
En sommant sur l’ensemble des fermions
(3 familles)
CS du LAL 28/06/2011

9. If we sum over all the types of fermions
Light velocity
Photon propagation = successive interactions and transient captures by virtual particles
Cross-section for photon capture s
(Thomson)
 Number of interactions to cross L: Ncol = N × s × L
 Transit time of a photon to cross L: t = Ncol × t
If we sum over all the types of fermions
Fluctuations of Ncol  Fluctuations of the transit time
Our model predicts
CS du LAL 28/06/2011

10. We never found any other calculation/derivation of m0, e0 or c
Comments
The experimental values of m0, e0 and c constrains our model and its “fudge” factors
We were really excited to find that similar ideas (but different mechanism) have been proposed recently by G. Leuchs, A.S. Villar and L.L. Sanchez-Soto where they also derive e0 and m0
G. Leuchs et al. Appl. Phys. B 100 (2010) 9-13
We never found any other calculation/derivation of m0, e0 or c
Within this framework: e0 m0 and c are only observables of quantum vacuum
 They can vary if the vacuum is modified by an external stress
 new predictions ?
High fields E,B: one expects variation of c stronger than QED predictions
See current tests LNCM Toulouse (Rikken) and LCAR Toulouse (Rizzo)
mumesic atoms : one expects short distance deviations to standard r~200fm
See LKB (Indelicato) and anomaly of energy level in muonic Hydrogen
CS du LAL 28/06/2011

11. Measurements of possible fluctuations of c
At least two approaches predict fluctuations of c
At Planck scale from quantum gravity
~ 0.1 – 1 fs.m1/2 from corpuscular photon propagation
In any case, we think that it is a fundamental test of physics
The experimental way to test fluctuations is to measure a possible time broadening Dt of a light pulse travelling a distance L of vacuum
Fluctuations vary as
The figure of merit is
There is today no existing experimental limit !!!
So we did the job ourself…
CS du LAL 28/06/2011

12. Astrophysics Constraints Gamma Ray Burst
Fermi observations: Only one “short” GRB with afterglow and redshift measurement
GRB measured by Fermi g-ray Space Telescope
Z = 0.9  dL = m
st  10 ms
s0 ~ fs.m-1/2
CS du LAL 28/06/2011

13. Strong Dispersion ~ 1 ms / 6 MHz @ GHz
Astrophysics Constraints
Millisecond pulsars
1.428 GHz
Very short pulses observed from the crab pulsar with Arecibo Radio Telescope (0.1 – few GHz)
Crossley et al., Astrophys. J. , 722 (2010) 1908
Strong Dispersion ~ 1 ms / 6 GHz
 Requires Dedispersion Technique (computing)
1.368 GHz
~10 ms
st  1 ms @ 5 GHz
s0 ~ fs.m-1/2
CS du LAL 28/06/2011

14. We can improve the sensitivity using femto laser
GRB ~ 1-10 Gpc
st ~ 1-10 ms
Time Width rms (s)
Pulsar ~kpc
st ~ ms
10 fpc = 300 m
st ~ 4 fs
Vacuum Length
L (pc)
CS du LAL 28/06/2011

15. The FLOWER Setup The length of the cavity can be modified
Input/output Hole
Ti:Sapphire
Pulsed Laser
10 nJ / pulse
Dt0 (rms) ~ 20 fs
Dl (rms) ~ 15 nm
Primary
pulse
Concave Mirror M2
Planar Mirror M1
RC = 1.8 m
The number of round trips
can be modified
Motor
stage
Non linear
crystal
Diode M
Intensity Autocorrelation
CS du LAL 28/06/2011

16. The number of round trips can be modified
 Allow measurements of different vacuum path lengths Lvacuum
For a given number of round trips, the length of the cavity can be modified
 The systematic due to possible mirror dispersions can be separately measured
We will first validate and calibrate the setup by filling the Herriot cell with a gas
 chromatic dispersion atm, L=50m,l=80015nm) ~ 60 fs
f1 = 2p/5
f2 = 4p/5
General solution
f = k.p / N
N = number of round trips
RC = 1.8 m
Length (m) of the Herriot cell
f (rad) f1 f2
Example with 5 round trips
CS du LAL 28/06/2011

17. Preliminary Tests in LOMA
Here an example with 11 round trips
Gold metallic concave mirror already available
“Ultra high” quality
F = 15 cm
Preliminar planar mirror
 Dedicated high quality mirror with a hole will be purchased next month
CS du LAL 28/06/2011

18. Preliminary simulation for 21 round trips and RC = 1.8 m
Stable solution for f = 16p/21 and L = 1.56 m
By construction: the outgoing beam is similar to the incoming beam
With the available gold concave mirror, we can already reach a vacuum path length
Lvacuum = 2×21×1.56 = 65.5 meters
CS du LAL 28/06/2011

19. using the autocorrelation technique
The proposed experiment is based on expertise gained from a collaboration with the LOMA
In we have performed a series of dispersion measurements in SiO2
using the autocorrelation technique
COLA Platform: tuned pulsed laser (OPG/OPA) to generate frequencies around the minimum SiO2 dispersion l=1272 nm
Suprasil-311 from Hereaus,
High uniformity and purity
Dn/n ~ 10-6
SiO2 Rod L=20cm
Ti:Sapphire Laser
OPA l generator
Dt0 (rms) ~ 25 fs
Dl (rms) ~ 20 nm
Primary
pulse
Intensity Autocorrelation
Motorstage
Non linear
crystal
Diode
CS du LAL 28/06/2011

20.  Results in agreement with expected values at the level of 10-5
First direct measurement of group index (pulse velocity) with very high accuracy ~ 10-5
 Results in agreement with expected values at the level of 10-5
(102 – 103 better than previous measurements)
Dispersion measurement by intensity correlation
With SIO2, we are dominated by chromatic dispersion which limits the systematic uncertainty to s0 ~ 20 fs.m-1/2
It demonstrates the high sensitivity and high precision of that technique
Accuracy of the pulse width (rms) measurement ~ 2 fs
(It might be sligthly improved with a pure pulse directly from the oscillator)
Optics Publication in preparation
It must be much simpler with vacuum because the chromatic dispersion is null
CS du LAL 28/06/2011

21. Equipment already funded
Flower Phase 1
Equipment already funded
Herriot cell Lcell < 1.8 m
Can reach at least Lvacuum = 65 m with 21 round trips
Width (rms) of COLA laser pulses ~ 20 fs
Accuracy autocorrelation measurement ~ 2 fs (width rms)
Expected sensitivity of vacuum fluctuations: s0 ~ 1 fs.m-1/2
With new femto laser: rms ~ 5 fs
~ 40 round trips
Improved accuracy of autocorrelation meas. ~ 0.5 fs (150 nm step)
Better than GRB
Similar to microburst from Crab pulsar
s0 ~ fs.m-1/2
CS du LAL 28/06/2011

22. Extra gains in senstivity
Super-Flower ?
Herriot cell Lcell ~ 50 m (as CALVA)
~ 50 round trips
 Can reach Lvacuum = 5 km
Width (rms) of initial laser pulses ~ 1 fs
Autocorrelation accuracy ~ 0.1 fs (30 nm)
Expected sensitivity of vacuum fluctuations: s0 ~ fs.m-1/2
CS du LAL 28/06/2011

23. Participation physicists 2011-2012
LOMA: Jérôme Degert 25%
Eric Freysz (25%)
Jean Oberlé (25%)
Marc Tondusson (25%)
LAL: François Couchot (70%)
Xavier Sarazin (50%)
Marcel Urban (100%)
Equipment
Laser and room on optical table available for full time in LOMA (COLA)
Optical elements and autocorrelators available in LOMA
Flat mirror and extra elements will be purchased next months by LAL and LOMA
Funding for 2011
GRAM Funding for 2011: 1500 euros
LAL funding for 2011: 3000 euros
LOMA similar contribution
Request for 2012
Travel: 7 keuros
We plan to submit a proposal to ANR 2012 and GRAM 2012
We plan to propose a thesis
CS du LAL 28/06/2011

24. CONCLUSIONS
The measurement of possible fluctuation of c (fluctuation of the transit time of photons) is a fundamental test in physics
With FLOWER Phase-1 ( ) we can achieve stringent limits (s0~ 0.2 fs.m-1/2) with a relative simple setup
 the equipments are available or already funded
 perfect setup to study all the systematics and artefacts
Our model of vacuum predicts other effects
Variation of c with strong E,B fields (see QED)
Variation of the Coulomb law in short distance (see mumesic atoms)
 We have started discussions with LKB (Paris) and LCAR (Toulouse)
Travel budget required for 2012
CS du LAL 28/06/2011

25. GRAM (Gravitation, References, Astronomie, Metrologie)
Action Spécifique crée par l’INSU début 2010
Appel d’offre 2011: financement du projet FLOWER de 1500 euros
Avis du Conseil Scientifique
Il a été décidé que votre demande concerne les thématiques du GRAM et qu'un financement est a terme envisageable
Il apparait dans votre demande qu'une telle analyse est en cours (analyse théorique détaillée de l'exactitude attendue pour l'expérience et de sa comparaison à d'autre expériences, notamment astrophysiques recherchant les mêmes effets) et le CS du GRAM vous encourage vivement à la mener à terme et de la publier. A cette fin une somme de 1500 € vous est accordée pour couvrir les missions associées à cette activité théorique.
Le CS du GRAM vous encourage à re-soumettre une demande expérimentale lors des prochains appels d'offres, dès lors que l'analyse théorique déboucherait sur une comparaison favorable avec les autres expériences dans le même domaine. Une éventuelle future demande devant être examinée dans les contraintes budgétaires et programmatiques de l'appel d'offre en question, le présent texte ne présume pas d'un engagement du GRAM concernant ces futures demandes. Pour le CS du GRAM : Peter Wolf et Gilles Métris
CS du LAL 28/06/2011