Fluctuations of Light Velocity and the Origins of Electromagnetic Constants

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 9èmes Journées Phénomènes Ultra-rapides Université de Rouen 17-19 Octobre 2011

2. What is the physical origin of the electromagnetic constants c, e0 and m0 ? • c, e0 and m0 are considered to be fundamental constants • There is no physical mechanism explaining their origin and their observed values • They are assumed to be invariant in space and in time But are c, e0 and m0 really fundamental constants ? Or Do they originate from the properties of the quantum vacuum and its interactions with photon ?

3. Vacuum filled with continuously appearing and disappearing virtual fermions (f, f ) pairs ti = Life-time of the pair of type i Ni= Density of the pair si = Cross-section for a photon to be trapped Photon has an infinite « bare » velocity f f A possible mechanism giving a finite value to the speed of light M. Urban, F. Couchot, X. Sarazin, Preprint arXiv in preparation Photon propagation in vacuum = successive transient captures by virtual charged fermions Number of interactions on i-type pairs to cross L Mean time for a photon to cross L

4. Quantum vacuum filled with continuously appearing and disappearing virtual fermions (f,f) pairs An effective description of quantum vacuum where is the rest mass energy • Average energy of the pair: • Life-time of the pair: • Virtual pair densities are driven by the Pauli exclusion • Separation between the fermion and antifermion in a pair • Cross-section for a real photon to be trapped by a virtual pair (Thomson) KW is the main free parameter of our model

5. Calculation of the light velocity Fluctuations of Nstop  Fluctuations of the transit time With KW~32, our model predicts s0  50 as.m-1/2 Using our quantum vacuum description (previous slide) If we sum over all the types of fermions when KW  32

6. This description of quantum vacuum leads also to a physical origin of e0 and m0 with the right order of magnitude e0 = polarization of the virtual pairs m0 = magnetization of the virtual pairs

7. Vacuum Permittivity e0 E - + - + - + - + • 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 • t is larger for pairs aligned with E  POLARISATION • En moyennant sur  • En sommant sur l’ensemble des fermions • (3 familles) If KW  32 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 !!!

8. 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) If KW  32 Vacuum Permeability m0 I B = m0nI + m0M M = magnetization of the matter If matter is removed: B = m0nI  0 B The vacuum is paramagnetic

9. Comments • 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 • c2.m0.e0 =1 is obtained using a corpuscular model • Within this framework: e0, m0 and c are only observables of quantum vacuum • Two experimental predictions • 1) Statistical fluctuation of the propagation time of the photons in vacuum • 2) c will vary if the vacuum is modified by an external stress (SHADOK effect)

10. Measurements of possible fluctuations of c Pulsar ~kpc FWHM ~ ms GRB ~ 1-10 Gpc FWHM ~ 10 ms 100 fpc = 3 km FWHM ~ 6 fs Time Width rms (s) Vacuum Length L (pc) We can improve the sensitivity using femto laser

11. The FLOWER Setup The length of the cavity can be modified Input/output Hole COLA (LOMA) 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

12. Example with 5 round trips f2 f (rad) f1 f2 = 4p/5 f1 = 2p/5 General solution f = k.p / N N = number of round trips Length (m) of the Herriot cell RC = 1.8 m • 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 •  Thesystematic 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 s(Argon@1 atm, L=50m,l=80015nm) ~ 60 fs

13. Preliminary Tests in LOMA Here an example with 11 round trips Preliminar planar mirror  Dedicated high quality mirror with a hole has been purchased Gold metallic concave mirror already available “Ultra high” quality F = 15 cm

14. 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

15. Flower Phase 1 Herriot cell Lcell ~1.55 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 Flower Phase 2 With fastest femto laser: rms ~ 2 fs Improved accuracy of autocorrelation meas. ~ 0.5 fs (150 nm step) Better than GRB Similar to microburst from Crab pulsar s0 ~ 0.2 fs.m-1/2 This setup allows to measure the dispersion in gas with high accuracy  Test if any discontinuity or discrete properties of the photon propagation in vacuum

16. Super-Flower Herriot cell Lcell ~ 50 m (as CALVA in LAL Orsay) ~ 50 round trips  Can reach Lvacuum = 5 km Width (rms) of initial laser pulses sin~ 2 fs If s0 ~ 50 as.m-1/2, Lvacuum=5 km sout~ 4 fs sin~ 2 fs svacuum ~ 3.5 fs

17. Effet SHADOK Et si on pompait le vide ????

18. Effet SHADOK A pump laser, circularly polarized +1, with ultra high intensity, masks some virtual pairs Number of occupied pairs The idle pulse (circularly polarized +1) will move with a higher velocity c* The idle pulse, circularly polarized +1, moves with a velocity c Virtual fermion antifermion pair s= +1/2 s= -1/2

19. Effet SHADOK • Mercury Laser @ Livermore (LLNL) • 1 PW peak power: 15 J, 15 fs • 1023 W/cm2 maximum focused irradiance • 10 Hz repetition rate • l = 1 mm If focal spot ~ 1mm2  dc/c ~ 3.10-4 If the laser spots are focused along 1mm, it should creates an advance of the idle pulse of 1 fs

20. CONCLUSIONS • A mechanism has been proposed to give a finite value of the speed of light in agreement with the observed value • This quantum vacuum description gives also the origin of e0 and m0 • It leads to two experimental predictions - possible fluctuations of the transit time of photons of ~ 50 as.m-1/2 - a possible advance of a idle pulse of ~ 1 fs after having propagated 1 mm in a ultra high intensity pump laser • Ultra short femto lasers seem to be the ideal tool to perform these tests • Attosecond pulses for FLOWER ? Are FROG/RABBIT able to detect a time broadening of the XUV attosecond pulses ? (see S. De Rossi’s talk for geometric aberrations)

21. BACKUP

22. Création de paire Stop en Go g réel g réel g réel e- virtuel Paire disparaît g virtuel Coulombien e+ virtuel

23. s0 ~ 0.7 fs.m-1/2 st  10 ms Astrophysics Constraints Gamma Ray Burst Fermi observations: Only one “short” GRB with afterglow and redshift measurement GRB 090510 measured by Fermi g-ray Space Telescope Z = 0.9  dL = 1.8 1026 m

24. 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 MHz @ GHz  Requires Dedispersion Technique (computing) 1.368 GHz ~10 ms st  1 ms @ 5 GHz s0 ~ 0.2 fs.m-1/2

25. The proposed experiment is based on expertise gained from a collaboration with the LOMA In 2010-2011 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

26. 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

27. ~ fs.kpc1/2 Current theories of possible varying speed of light • Variation of c in space ? 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) • Chromatic dispersion of c ? Singularities in space-time at Planck scale ~ 10-35 m (MPlanck~1019 GeV) At this energy scale, the dispersion relation is not linear any more  c depends on the energy of the photon • G. Amelino, J. Ellis, et al., Nature 393, 763 (1998) • J. Ellis et al., Phys. Lett. B 665, 412 (2008) • Best experimental limits with Gamma-ray bursts: Abdo et al. Nature (2009) • Fluctuations of c ? • Light-cone fluctuations: quantum metric fluctuations from quantum gravity • H.Yu et L.H. Ford, Phys. Rev. D 60 084023 (1999)