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CS du LAL 28/06/20111 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

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CS du LAL 28/06/20112 Time-variation of c c(t) Is the speed of light a fundamental constant ? Three types of possible effects Fluctuation of c c c is constant in average but possible stochastic fluctuations around c Chromatic dispersion of c c(E) c depends on the energy of the photon

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CS du LAL 28/06/20113 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) Time-variation of c

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CS du LAL 28/06/20114 Singularities in space-time at Planck scale ~ 10 m (M Planck ~10 19 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) Chromatic dispersion of c Figure of merit to constrain this model is (L/ t)× E Best experimental limits with Gamma-ray bursts 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) Abdo et al, Nature, 2009

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CS du LAL 28/06/20115 Light-cone fluctuations (quantum metric fluctuation from quantum gravity) H.Yu et L.H. Ford, Phys. Rev. D (1999) Correlated to any discontinuity or discrete properties of the photon propagation in vacuum. Leads to fluctuations of the transit time of photons Corpuscular model of photon propagation M. Urban, F. Couchot et X. Sarazin arXiv: Fluctuations of c ~ fs.kpc 1/2

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CS du LAL 28/06/20116 A coherent corpuscular model of quantum vacuum to explain the three electromagnetic constants 0, 0 and c ? Preprint arXiv: 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) New hypothesis in this model (compare to standard QED):

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CS du LAL 28/06/20117 Vacuum Permittivity 0 Polarisation P of the molecules by the field E opposite charges on the dielectric plates Voltage decreases C is increased + E With vacuum: 0 = 0 !!! In our model: virtual pairs f f bear a mean electric dipole The virtual pairs are polarized, BUT only during their life-time depends on the coupling energy of the pair to the field E En moyennant sur En sommant sur lensemble des fermions (3 familles)

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CS du LAL 28/06/20118 Vacuum Permeability 0 I B B = 0 nI + 0 M M = magnetization of the matter If matter is removed: B = 0 nI 0 In our model of vacuum: 0 originates from the magnetization of the virtual pairs The vacuum is paramagnetic Virtual fermion pair has a magnetic moment: It is aligned during its life-time depends on the coupling energy of the pair to the field E En moyennant sur En sommant sur lensemble des fermions (3 familles)

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CS du LAL 28/06/20119 Light velocity Transit time of a photon to cross L: t = N col × Fluctuations of N col Fluctuations of the transit time Number of interactions to cross L: N col = N × × L Cross-section for photon capture Photon propagation = successive interactions and transient captures by virtual particles If we sum over all the types of fermions Our model predicts (Thomson)

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CS du LAL 28/06/ 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 0 and 0 G. Leuchs et al. Appl. Phys. B 100 (2010) 9-13 We never found any other calculation/derivation of 0, 0 or c Within this framework: 0 0 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 Comments The experimental values of 0, 0 and c constrains our model and its fudge factors

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

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CS du LAL 28/06/ Astrophysics ConstraintsGamma Ray Burst Fermi observations: Only one short GRB with afterglow and redshift measurement GRB measured by Fermi -ray Space Telescope Z = 0.9 d L = m t 10 ms 0 ~ 0.7 fs.m -1/2

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CS du LAL 28/06/ Astrophysics ConstraintsMillisecond pulsars Strong Dispersion ~ 1 ms / 6 GHz Very short pulses observed from the crab pulsar with Arecibo Radio Telescope (0.1 – few GHz) Requires Dedispersion Technique (computing) Crossley et al., Astrophys. J., 722 (2010) GHz GHz ~10 ms 0 ~ 0.2 fs.m -1/2 t 1 5 GHz

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

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CS du LAL 28/06/ The FLOWER Setup Primary pulse Ti:Sapphire Pulsed Laser 10 nJ / pulse t 0 (rms) ~ 20 fs (rms) ~ 15 nm Motor stage Diode Non linear crystal Intensity Autocorrelation R C = 1.8 m Concave Mirror M2 Planar Mirror M1 M The length of the cavity can be modified The number of round trips can be modified Input/output Hole

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CS du LAL 28/06/ The number of round trips can be modified Allow measurements of different vacuum path lengths L vacuum 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, =800 15nm) ~ 60 fs General solution = k. / N N = number of round trips R C = 1.8 m Length (m) of the Herriot cell (rad) Example with 5 round trips

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

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CS du LAL 28/06/ Preliminary simulation for 21 round trips and R C = 1.8 m Stable solution for = 16 /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 L vacuum = 2×21×1.56 = 65.5 meters

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CS du LAL 28/06/ In we have performed a series of dispersion measurements in SiO2 using the autocorrelation technique The proposed experiment is based on expertise gained from a collaboration with the LOMA Suprasil-311 from Hereaus, High uniformity and purity n/n ~ COLA Platform: tuned pulsed laser (OPG/OPA) to generate frequencies around the minimum SiO 2 dispersion =1272 nm Primary pulse Ti:Sapphire Laser OPA generator t 0 (rms) ~ 25 fs (rms) ~ 20 nm Motorstage Diode Non linear crystal Intensity Autocorrelation SiO2 Rod L=20cm

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CS du LAL 28/06/ With SIO2, we are dominated by chromatic dispersion which limits the systematic uncertainty to 0 ~ 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 First direct measurement of group index (pulse velocity) with very high accuracy ~ 10 Results in agreement with expected values at the level of 10 (10 2 – 10 3 better than previous measurements) Dispersion measurement by intensity correlation

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CS du LAL 28/06/ Flower Phase Herriot cell L cell < 1.8 m Can reach at least L vacuum = 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: 0 ~ 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) 0 ~ 0.2 fs.m 1/2 Better than GRB Similar to microburst from Crab pulsar Equipment already funded

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CS du LAL 28/06/ Extra gains in senstivity Super-Flower ? Herriot cell L cell ~ 50 m (as CALVA) ~ 50 round trips Can reach L vacuum = 5 km Expected sensitivity of vacuum fluctuations: 0 ~ 0.02 fs.m 1/2 Width (rms) of initial laser pulses ~ 1 fs Autocorrelation accuracy ~ 0.1 fs (30 nm)

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CS du LAL 28/06/ 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 Participation physicists 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

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CS du LAL 28/06/ 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 ( 0 ~ 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 CONCLUSIONS

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CS du LAL 28/06/ 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 GRAM (Gravitation, References, Astronomie, Metrologie) Action Spécifique crée par lINSU début 2010 Appel doffre 2011: financement du projet FLOWER de 1500 euros Avis du Conseil Scientifique

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