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Constraints on photon velocities! Subir Sarkar ! Rudolf Peierls Centre for ! Theoretical Physics OPERA versus Maxwell and Einstein, King’s College London, 23 Nov 2011! The first demonstration that the speed of light is finite came from observations of Jupiter’s moons (Galileo, Roemer, Huygens, Halley) “For it is now certain from the phenomenon of jupiter's satellites, confirmed by the observations of different astronomers, that light is Propagated in succession, and requires about seven or eight minutes to travel from the Sun to the Earth”. Isaac Newton, Opticks (1704) The first accurate measurement of the speed of light was also from astronomical observations of the aberration of starlight by Bradley (1729)! … he obtained 304000 km/s (within 1.4% of correct value) but did not give an error estimate! It was not until a century later that speed of light was measured in a terrestrial experiment (Fizeau, Foucalt, Cornu, Michelson …) This is of course the cornerstone of special relativity ! … is there any need to test Lorentz invariance further? Bronshtein’s ‘cube of theories’! Matvei Petrovich Bronshtein (1906-38)! Progress in Astronomical Sciences (Gostekhizdat, Moscow, 1933), Vol. 3, p. 3! … see also Gamov, Ivanenko & Landau, Zh. Russ. Fiz.-Khim. O-va., Chast Fiz. 60, 13 (1928)! Why quantize gravity?! ! Nevertheless, due to the inner atomic movement of electrons, atoms would have to radiate not only electromagnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics but also the new theory of gravitation. ! A. Einstein! Preussische Akademie Sitzungsberichte (1916)! The road to quantum gravity! Canonical ! Construct a quantum theory in which Hilbert space carries a representation of the operators corresponding to the full metric (or some function) without the background metric being fixed …! (Bergmann, Dirac, … Peres, Arnowitt, Deser, Misner, Ashtekar, Rovelli, Smolin, …)! Covariant ! Construct a quantum field theory of the fluctuations of the metric over a flat Minkowski space (or other background metric space) …! (Rosenfeld, Fierz, Pauli, … DeWitt, Feynman … t Hooft, Veltman, Deser, van Nieuwenhuizen …)! No hard predictions … but general expectation of LI violation at the quantum gravity scale Is this observationally testable? We proposed deformed dispersion relation which preserves the O(3) subgroup of SO(3, 1):! Assuming that the Hamiltonian eqn. of motion is still valid, this gives: ⇒ time delays increasing with energy: Meanwhile some γ-ray astronomers were interested in our proposal …! γ-ray bursts are the most powerful explosions in the universe, radiating as much energy in a few seconds to minutes as ! our Sun will do in its entire ~10 billion year lifetime Norris, Scargle, Bonnell [astro-ph/9912136] ! ⇒ z = 0.903 This test was done 10 years later … but no anomalous dispersion seen! [Nature 462 (2009)331]! Implies a ‘conservative’ bound on the anomalous dispersion energy scale of 1.2 x 1019 GeV FERMI light curve for GRB 080916C (z = 4.35 ± 0.15) ! The bulk of the emission of the second peak is moving toward later times as the energy increases! ! The arrival time of the 13.22+0.70-1.54 GeV photon relative to T0 ! (t = 16.54 s) is a conservative upper limit on its Δt relative to MeV photons and implies a lower limit:! MQG >1.3x1018 GeV ! Science 323 (2009)1688! Even higher energy photons with time structure are available …! Active galactic nuclei TeV γ-rays have been seen from several AGN by ground-based Atmospheric Cherenkov Telescopes … occasionally there are ‘flares’ presumably due to instabilities in the accretion of matter by the central supermassive black hole! Last month, the MAGIC gamma-ray telescope collaboration based on La Palma in the Canary islands announced that they had measured a 4-minute time difference between the arrival time of high and low-energy gamma rays released at the same time in a flare from the Markarian 501 galaxy, some half a billion light years away. According to Einstein’s theory of special relativity, both sets of photons should have arrived simultaneously, and the team is controversially …. New Scientist, 29 April 2007 ! Inferred time delay of 0.03 s/GeV from observed dispersion of photons from Mrk 501 (d ~ 150 Mpc)! [Phys. Lett. B668 (2008) 253]! ⇒ MQG = 0.47+0.31-0.13 x 1018 GeV! … if no intrinsic source dispersion!! However subsequently HESS has observed a flare in another AGN! with no observable time delay between low and high energy photons PRL 101 (2008) 170402! A recent reanalysis puts the 90% CL bound: MQG > 2.1 x 1018 GeV! [arXiv:1101.3652] Ellis & Mavromatos, arXiv:1111.1178 Presently all experiments consistent with belief that photons of all energies travel in vacuum at the speed of light (future test with CTA) Summary! The quantum-gravitational ground state may spontaneously violate Lorentz invariance! If such effects are of O(E2/MP) then will observe anomalous dispersion of high energy photons from pulsed distant sources (AGN, GRBs, pulsars) ! … there are tantalising indications for such effects in current data, which motivate further tests e.g. with CTA! Theorists should make explicit predictions for observables .. and suggest new ways in which Planck scale effects can be tested by experiment! But for the moment Einstein rules OK!!