Download Constraints on photon velocities! Subir Sarkar OPERA versus Maxwell and Einstein

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!!