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**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

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**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

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**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

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**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

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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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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=80015nm) ~ 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

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**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

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**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

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**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

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** 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

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**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

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**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

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**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

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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

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**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

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