On Bounds on aPossible Energy
Dependence of theSpeed of Light inVacuum

Jim Hinton!

!
Universityof Leicester!

Manel Martinez
ICRR SeminarthJuly 24 2018

Outline
1) Gravitation in the quantum regime ?
2) The measurement of Time of Flight3) Present situation4) Multi-messengers ?
5) Summary and Outlook
Thanks to G. Amelino-Camelia, M. Gaug, L. Nogues and E. Moretti1) Gravitation in thequantum regime?

As of today Quantum Gravity is just in our imagination !

Giovanni Amelino-Camelia, “Quantum Spacetime Phenomenology”, Living Reviews on Relativity 16 (2013) 5

As of today:
No consistent theory describing gravitation in the quantum
regimeAND
No direct experimental evidence calling for it…!
ALTHOUGH
Some important observations related to gravity remain
unexplained…
(dark matter, dark energy,…)Giovanni Amelino-Camelia

What is special about the Planck
Mass/Length/Time ?
- Introduced in 1906 by Max Planck as a combination of threefundamental constants:• h -> quantum world• c -> relativistic world• G -> gravitation… far, far away from our reach… !BUT…
• We can write for the dimensionless gravitational coupling(or fine structure constant):

showing that for m~Mpl gravitation becomes a strong interaction !
• At Epl the Compton wavelength of a particle =equals its gravitational radius (Schwarzschild radius) =So that the particle is trapped in its own gravitational field.

Gravity meets the Quantum world !

Giovanni Amelino-Camelia

When approaching the Planck Scale the fabricof space-time may become foamy andrelativistic symmetries may be deformed ordistorted (“violated”)

John Wheeler - 1955

Let me fly mi imagination…
Spacetime structure in vacuum
does carry energy (for instance
Gravitational Waves)
Energy fluctuations in the quantum
vacuum in gravitation may create
and annihilate spacetime topologicalstructures (blackholes, wormholes,..)

The speed of light in vacuum may
depend on its wavelength ?
=> That will break Lorenz Invariance !

What is Lorenz Invariance ?
• Lorentz transformations arise necessarily under the assumptions of:– Spatial and temporal homogeneity– Spatial isotropy– Equivalence principle (equivalence of inertial frames)– Pre-causality (time-ordering of two events along an observerworldline does not change in different systems of reference).
(see e.g. S. Sonego and M. Pin. J.Math.Phys. , 50:042902, 2009, arXiv:gr-qc/08121294)• Have to give up at least one of these axioms to obtain violation of LI.
• Lorentz invariance is a cornerstone of both the Standard Model andGeneral Relativity!
• Lorentz Invariance has been tested to extreme precision so far andno hint for LI violation has been found.

What is Lorenz Invariance ?
• Lorentz transformations arise necessarily under the assumptions of:– Spatial and temporal homogeneity– Spatial isotropy– Equivalence principle (equivalence of inertial frames)– Pre-causality (time-ordering of two events along an observerworldline does not change in different systems of reference).
(see e.g. S. Sonego and M. Pin. J.Math.Phys. , 50:042902, 2009, arXiv:gr-qc/08121294)• Have to give up at least one of these axioms to obtain violation of LI.
• Lorentz invariance is a cornerstone of both the Standard Model andGeneral Relativity!
• Lorentz Invariance has been tested to extreme precision so far andno hint for LI violation has been found.

Lorenz Invariance Violation andQuantum Gravity
Direct quantization of General Relativity (GR) leads tonon-renormalizable Quantum Field Theory (QFT)• High energy LIV can regularize field theories• Some QG models with LIV:
● Wraped brane worlds. One model in P.Horawa (arXiv:0812.4287)● Loop quantum gravity . C.Rovelli (arXiv:gr-qc/9710008)● Effective Field Theories. Overview in R.Bluhm (arXiv:hep-ph/0506054)• Some QG models without LIV:
● String theory with Lorentz-covariant dynamics. A.Kostelecky (Phys. Rev.
Lett. 63)

●Doubly Special Relativity (DSR) G.Amelino-Camelia (arXiv:hep-th/0012238)

Lorenz Invariance Violation andQuantum Gravity• Other hints:– Discretization of space-time destroys spatial and temporalhomogeneity (through appearance of virtual black holes).
– There exists a (non-local, cosmological) distinguished reference frame:
the Cosmic Microwave Background.
– Analogue frameworks within Bose-Einstein Condensates display
effective (acoustic) LI at low energies which “break” at higher energies.

Knowing (from experiment) whether GQ is Lorentz invariant
or not, is a fundamental ingredient to select theories.
see e.g. S. Liberati, Tests of Lorentz invariance: a 2013 update. Classical and Quantum Gravity, 30(13):133001, 2013 (arXiv:1304.5795v3)
and D. Mattingly. Modern Tests of Lorentz Invariance. Living Reviews in Relativity, 8:5, 2005 (arXiv:gr-qc/0502097)

How to test it ?
• LIV extensions of the standard model (SME)
lead to a modified dispersion relation:
222

E = p + m + f ( p; ξ / M Pl )where
* f ( p; ξ / M Pl ) is a function of dimension (mass)2 ,* MPl the Planck mass (1.21019 GeV) and* ξ a coupling parameter (naturally of order 1).

Modified dispersion relations◦ In low-energy limit, f ( p; ξ / M Pl )expanded:can be(3)ξf ( p; ξ / M Pl ) ≈ EPlξ i(1) pi + ξ ij(2) pi p j + ijk pi p j p k +…
EPl

◦ Assuming non-violation of rotational symmetry:
(3)
(4)
ξξ
f ( p; ξ / M Pl ) ≈ EPlξ (1) p + ξ (2) p 2 +p3 + 2 p(4) +…
EPl
E Plaffectlow-energy physics

affecthigh-energy physics

Modified dispersion relations◦ In low-energy limit, f ( p; ξ / M Pl )expanded:can be(3)ξf ( p; ξ / M Pl ) ≈ EPlξ i(1) pi + ξ ij(2) pi p j + ijk pi p j p k +…
EPl

◦ Assuming non-violation of rotational symmetry:
(3)
(4)
ξξ
f ( p; ξ / M Pl ) ≈ EPlξ (1) p + ξ (2) p 2 +p3 + 2 p(4) +…
EPl
E Plviolate CPT

Modified dispersion relations◦ In low-energy limit, f ( p; ξ / M Pl )expanded:can be(3)ξf ( p; ξ / M Pl ) ≈ EPlξ i(1) pi + ξ ij(2) pi p j + ijk pi p j p k +…
EPl

◦ Assuming non-violation of rotational symmetry:
(3)
(4)
ξ
ξ
f ( p; ξ / M Pl ) ≈ EPlξ (1) p + ξ (2) p 2 +p3 + 2 p(4) +…
EPl
E Pl

birefringence(R. C. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211601 (2003), arXiv:hep-ph/0301124)

Terrestrial experiments: LE tests
It is well tested that nature is Lorentz Invariant well below the Planck scale. For this reason,
looking for LIV deviation at low energy (ξ(1) and ξ(2) terms) require experiments with very
high precision.
Penning traps: Change in cyclotron motion and Larmor precession of a charged
particle confined for long time. Limits in R.K. Mittleman et al (Phys. Rev. Lett. 83, 2116)● Clock comparison: Differences in the frequencies of clocks (co-local atomictransitions) over long periods of time. O.Bertolami et al (arXiv:hep-ph/0412289)● Cavity experiments: Variation of the cavity resonance frequency with spaceorientation. Some limits in G. Amelino-Camelia (arXiv:gr-qc/0501053)● Neutral mesons: Test sidereal variations and other orientation effects on massdiference of K0 eigen-states. Some limits in De Angelis et al. (Nuovo Cim., C034N3:323,2011)● Spin polarized torsion balances: Orientation dependence of a spin polarization
generated by a specific pattern of magnets. Time-like limits on ξ(2) of O(10-29).
M.Smiciklas et al (arXiv:1106.0738)
A detailed review on these experiments and more can be found at: D.Mattingly (arXiv:gr-qc/0502097)●

Astrophysical experiments: HE tests
To constrain the ξ(3) and ξ(4) terms, much higher energy is required, notreachable by experiments at Earth. High and Very High Energy astrophysics
are playing an important role in this field.
● Vacuum birefringence: Change in polarization angles with energy anddistance provoking decrease in polarization degree. L.Maccione et al(arXiv:0809.0220)● Threshold reactions: LIV-allowed and LIV-modified reactions.
T.Jacobson et al (arXiv:hep-ph/0209264)○ Photon-pair creation.
○ Gamma-ray decays.
● Synchrotron radiation: changes in the expected frequency forSynchrotron emission due to LIV presence. Study for Crab Nebula inT.Jacobson et al (arXiv:astro-ph/0212190).
● Photon Time of Flight: Energy and distance dependence of the photon
speed. Kinematical approach.

2) The measurement ofTime of FlightPhoton Time of Flight
From the modified photon dispersion relation, we can derive a velocity

If n > 2, the velocity is energy dependent and the difference of arrivaltimes (ΔT) of 2 photons (E1 and E2)can be expressed, as function of
their travelling time (T) asIf the traveling time is larger, that is, the source is distant, the LIVeffect is amplified. So we should focus on n=3 and n=4.

Photon Time of Flightsourceobserver

ELE
EHE

Δt

Ingredients needed• Fast flaring source (clock tick)• At the highest possible distance (cumulativedelay effect)• With the highest possible energy (energy scale
determines Effective QG scale tested)Which tool ?: Cherenkov telescopes !
●Very good time resolution●Distant sources.

●Very high energy●Highest energies gamma-ray detectors:○○○○

MAGIC (2 telescopes, Spain)
H.E.S.S. (5 telescopes, Namibia)
VERITAS (4 telescopes, Arizona)
Upcoming CTA (2 arrays of telescopes,Spain and Chile) More info in M.Actis et al(arXiv:1008.3703)

Image of MAGIC-I

Sensitivities for different sourcesCaveats- VHE gamma rays are absorbed by pair production with
the EBL photons -> trade-off between d and E.
- Acceleration mechanisms may produce sourcedependent intrinsic delays -> combine different source
types and at different distances.
- No light-curve model -> complex flares that require
cumbersome statistics treatment

ToF: Extracting LIV from data

Pair View

Peak comparison

Computation of spectral lags
between pairs of photons ina data set. The distributionof the spectral lags is used
to estimate the LIVparameter.

Comparison of the time
distribution peaks ofsubsets of a same data set
with different energy
ranges.

●●Application of themethod to GRBs inV.Vasileiou et al (arXiv:1305.3463)

28

Whipple, Fermi,H.E.S.S. andapplication of themethod to CrabPulsar in M.Gaug et al(arXiv:1709.00346)

ToF: Extracting LIV from data

Dispersion cancellation

Maximum Likelihood

LIV makes the time
distribution smoother,
injecting inverse LIV
effect, we try to recover
the sharpness of the time
distribution. Several waysof applying this idea.

Maximization of the Likelihood
function, created by the PDFs ofevery events. The PDFs iscreated by a model that makes
maximum use of the informationand contains several parameter,
the LIV one among them.

●One version of themethod in M.Danielet al (arXiv:1204.2205)●29

Explanation of the methodin M.Martinez et al (arXiv:0803.2120),application to Pulsar inM.Gaug et al (arXiv:1709.00346)

Method: time-lag maximum
likelihood analysis
reconstructed energy
true energy (unknown)

True energy distribution(No absorption, noexperiment effects)

Detector efficiency intime and energy(Collection Area)

Relation between Es andE. Detector effect.

Event time distribution
at the source (Beforepropagation effects)

M. Martinez and M.Errando Astropart.Phys.31:226,2009

3) Present situation

Main ToF measurements- First astrophysical limit on ξ(3) was obtained from the Crab Pulsar (opticaldata)! (Warner & Nather, Nature, 222 (1969) 157)
- Greatly improved with EGRET data from the Crab Pulsar (up to 2 GeV) (Kaaret,A&A 345 (1999) L32)
- Simple limit from WHIPPLE using a Mrk421 flare (Biller et al.,Phys Rev.Lett 89(1999) 2108)- Rapid flares of Mrk501 detected with MAGIC (Albert et al., PhLB 668 (2008)253) and PKS2155 detected by H.E.S.S. (Abramowski et al., Aph 34 (2011) 738)- Current best limits from Fermi-LAT using GRBs (specially GRB090510)(Vasileiou et al. Phys. Rev. D 87 (2013) 122001)-Crab pulsar analysis beyond 400 GeV by MAGIC (Ahnen et al., ApJS 232(2017) 9)

GRB090510 (Fermi)
z = 0.9

Fermi Collaboration Nature 462 (2009) 331-334

Mrk 501 (MAGIC)z = 0.034

PKS2155 (H.E.S.S.)z = 0.12
Phys. Rev. Lett. 101 (2008)

200-800 GeV>800 GeV
Phys. Lett. B 668 (2008) 25334

Crab Pulsar (MAGIC)d = 2.2 Kpc

MAGIC Coll, ApJS 232 (2017) 9)

Current ToF limits

Next steps for IACTs
Until not long ago:●●●Every experiment working individually.
Data is private.
Getting LIV bound with only the source observedby the instrument.

Now: the LIV Consortium (H.E.S.S. + MAGIC +VERITAS)
●
●
●
●
●
●
●
●

Joined efforts to study LIV.
MoU agreement to share published data andInstrument Response Functions.
LIV ToF analysis with a combination of different
types of sources from different experiments.
First results presented at ICRC 2017, in Korea.
L.Nogués et al (arXiv:1710.08342)
List of sources growing with publications.
Redshift study.
Combined Likelihood method.
Preparations and predictions for CTA.

4) Multi-messenger ?

GW170817/GRB170817A

GW170817/GRB170817A• Binary NeutronStar merger
detected by
LIGO-Virgo.
• Follow up by~70 ground- andspace- based
observatories.
PRL.119 161101 (2017)
ApJL 848: L12 (2017)

Follow upGamma ray

Binary properties from GW detection

Quantum regime ?
- Extremelly high energy > 0.025 MSun
BUT
- Max Frequency ~ 500 Hz⇒ Wavelength ~ 600 KmMacroscopic (classical) World !

Constraint on the GW speed

… and LIV (EM sector)- Given the long wavelength of GW, in spite of the hugeenergy released, it is not really exploring the quantum regime=> assume vGW = c- LIV test sensitivity limited by:* Relatively short distance ( ~ 40 Mpc => z ~0.01 )* Relatively low energy ( ~ 200 KeV ) -> Fermi GBM=> not competitive at all with current bounds:
EQG1 ~ 5 x 1011 GeV
EQG2 ~ 1 x 104 GeV

Current ToF limits

IceCube-170922A/TXS0506+056

IceCube-170922A/TXS0506+056• HE neutrino
associated (3 sigma)
with Blazar.
• Follow up by ~ 15
ground- and spacebased observatories.
Science 361, eaat1378 (2018)

IceCube-170922A/TXS0506+056• Very Large neutrino energy ~290 TeV
neutrinos have mass but at that energy -> v/c ~ 1 – 0.5 x 10-31• Large gamma energy, up to ~ 500 GeV• Large source distance z=0.3365 +- 0.0010

but-

The neutrino emission was not “simultaneous” with the emission ofgammas=> no useful LIV constraintFollow up

Lightcurve and spectrum
Sept 22ndOct 3-4th5) Summary andOutlook

● Measuring a possible Energy Dependence of the Speed of Light in

Vacuum is important because it may pinpoint LIV due to the quantum
structure of spacetime (Quantum Gravity).
● Effects are expected to be tiny O(E/EPL) but at our reach with gamma

ray detectors (satellites + ground-based)=> We can measure delays of seconds in distances of hundreds ofmillions light years=> huge step forward !
● Present bound on a linear realisation of LIV already above EPL but

measurements should continue.
● Bounds on a (more theoretically favoured) quadratic realisation of LIV

still far away from EPL but…

flares keep coming and sensitivity keeps growing !

Long “monster” Mrk421 2014 MAGIC flare
Change of wobble
Observation pause
due to extension
decision-ON events: 12994
ON above 4 TeV: 122
OFF events: 1550
Energy: 100 - 51000 GeV
Number of wobbles: 13
Original analysis: Mireia
Extension: 3.5h

●Analysis rather complex and still ongoing (Leyre Nogues
PhD Thesis – Nov 2018), but bounds may sizably improvecurrent ones (linear and quadratic).

●And if PeV gammas detected (in CTA or, for instance,
using Very-Large Zenith Angle observations) bounds inquadratic term could improve by up to 4 orders ofmagnitude.

STAY tuned !
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