Quantum gravity phenomenology in an emergent spacetime: concepts, constraints and speculations. Fourth Meeting on Constrained Dynamics and Quantum Gravity Cala Gonone (Sardinia, Italy). September 12-16, 2005. Stefano Liberati SISSA/INFN Trieste.
Fourth Meeting on
Constrained Dynamics and Quantum Gravity
Cala Gonone (Sardinia, Italy). September 12-16, 2005
T. Jacobson, SL, D. Mattingly:PRD 66, 081302 (2002); PRD 67, 124011-12 (2003)
T. Jacobson, SL, D. Mattingly:Nature 424, 1019 (2003)
T. Jacobson, SL, D. Mattingly, F. Stecker:PRL 93 (2004) 021101
T. Jacobson, SL, D. Mattingly: astro-ph/0505267, Annals of Phys. Special Issue Jan 2006
Old “dogma” we cannot access any quantum gravity effect…
In recent years several ideas about sub-Planckian consequences of QG physics have been explored: e.g. Extra dimensions effects on gravity at sub millimeter scales, TeV BH at LHC, violations of spacetime symmetries…
Idea: LI linked to scale-free spacetime -> unbounded boosts expose ultra-short distances…
Suggestions for Lorentz violation come from:
Very different approaches but common prediction of
modified dispersion relations for elementary particles
Almost all of the above cited framework do lead to modified dispersion relations that can be cast in this form
If we presume that any Lorentz violation is associated with quantum gravity and we violate only boost symmetry
(no violation of rotational symmetry)
Note: (1,2) are dimensionless coefficients which must be necessarily small -> standard conjecture
1(/M)+1, 2(/M) with 1 and with <<M
where is some particle physics mass scale
This assures that at low p the LIV are small and that at high p the highest order ones pn with n 3 are dominant…
See e.g. D. Mattingly, “Modern tests of Lorentz invariance,”
Liv. Rev. Rel. [arXiv:gr-qc/0502097].Theoretical Frameworks for LV
Real LIV with a preferred frame
Apparent LIV with an extended SR
(i.e. possibly a new special relativity with two invariant scales: c and lp)
Spacetime foam leading to stochastic Lorentz violations
Renormalizable, or higher dimension operators
EFT, non-renormalizable ops,
(all op. of mass dimension> 4)
Mainly astrophysical constraints
Extended Standard Model
Renormalizible ops. (lab constraints)
E.g. QED, dim 3,4 operators
E.g. QED, dim 5 operators
Time of fight: time delay in arrival of different colors
Birefringence: linear polarization direction is rotated
through a frequency dependent angle due to
different phase velocities of photons polarizations.
Amelino-Camelia, et al. Nature 393, 763 (1998)
LI synchrotron critical frequency:
T. Jacobson, SL, D. Mattingly
Nature 424, 1019 (2003)
There is now a maximum achievable synchrotron frequency max for ALL electrons!
Hence one gets a constraints by askingmax≥ (max)observed
The range of available energies of the incoming particles for which the reactions happens is changed.
Lower threshold can be shifted and upper thresholds can be introduced
Pair production can happen with asymmetric distribution
of the final momenta
If LI holds there is never an upper threshold
However the presence of different coefficients for different particles allows Ei to intersect two or more times Ef switching on and off the reaction!
Sufficient condition for asymmetric Threshold.
Since the sixties it is well-known that the universe is opaque to protons (and other nuclei) on cosmological distances via the interactions
In this way, the initial proton energy is degraded with an attenuation length of about 50 Mpc.
Since plausible astrophysical sources for UHE particles (like AGNs) are located at distances larger than 50-100 Mpc, one expects the so-called Greisen-Zatsepin-Kuzmin (GZK) cutoff in the cosmic ray flux at the energy given by
Constraint from photon-pion production
p+ CMB p+0if GZK confirmed
The range of p,for n = 3 dispersion modifications where the GZK cutoff is between 21019 eV and 71019 eV:
constraints of order 10-11 on both p,
Constraint from absence of proton vacuum Cherenkovp+ p+
pand are in multiples of 10-10
(Jacobson, SL, Mattingly: PRD 2003)
In 2004 Gagnon and Moore performed analysis taking into account the partonic structure founding same orders of magnitude for the constraints
Let’s consider all the Lorentz-violating dimension 5 terms (n=3 LIV in dispersion relation) that are quadratic in fields, gauge & rotation invariant, not reducible to lower order terms (Myers-Pospelov, 2003). For E»m
Warning: All these LIV terms also violate CPT
electron helicities have independent LIV coefficients
photon helicities have opposite LIV coefficients
u= unit timelike 4-vector that fix the preferred system of reference
Moreover electron and positron have inverted and opposite positive and negatives helicities LIV coefficients (JLMS, 2003).
Crab nebula (and other SNR) well explained by synchrotron self-Compton (SSC) model:1. Electrons are accelerated to very high energies at pulsar2. High energy electrons emit synchrotron radiation3. High energy electrons undergo inverse Compton with synchrotron ambient photons
From Aharonian and Atoyan, astro-ph/9803091
We shall assume SSC correct and use Crab observation to constrain LV.
Crab alone provides three of the best constraints. We use:
T. Jacobson, SL, D. Mattingly: invariance,” Annals of Phys. Special Issue Jan 2006Constraints for EFT with O(E/M) LIV
TOF: ||0(100) from MeV emission GRB
Birefringence:||10-4 from UV light of radio galaxies (Gleiser and Kozameh, 2002)
Using the Crab nebula we infer:
-decay: for ||10-4 implies || 0.2
from 50 TeV gamma rays from Crab nebula
Inverse Compton Cherenkov: at least one of 10-2 from inferred presence of 50 TeV electrons
Synchrotron: at least one of -10-8
Synch-Cherenkov: for any particle with satisfying synchrotron bound the energy should not be so high to radiate vacuum Cherenkov
Renormalization group arguments might suggest that lower powers of momentum in
will be suppressed by lower powers of M so that n≥3 terms will be further suppressed w.r.t. n≤2 ones. I.e. one could have that
Alternatively one can see that even if one postulates classically a dispersion relation with only terms (n)pnMn-2 with n3 and (n)O(1) then radiative (loop) corrections involving this term will generate terms of the form (n)p2+(n)p M which are unacceptable observationally (Collins et al. 2004).
This need not be the case if a symmetry or other mechanism protects the lower dimensions operators from violations of Lorentz symmetry.
Idea: SUSY protect dim<5 operators but SUSY is broken…
Can we get some hint of how things might work using some toy model?
The propagations of quantum excitations in a BEC system simulates that of a scalar field on a curved spacetime with an energy dependent metric. In particular adopting the eikonal approximation the dispersion relation for the BEC quasi-particles is
This dispersion relation (already found by Bogoliubov in 1947) actually interpolates between two different regimes depending on the value of the fluctuations wavelength|k|with respect to the “acoustic Planck wavelength”C=h/(2mc)=px
with x healing length=1/(8a)1/2
So we see that analogue gravity via BEC reproduces that kind of LIV that people has conjectured in quantum gravity phenomenology…
Unfortunately the 1-BEC system just discussed is not enough complex to discuss the most pressing issues in quantum gravity phenomenology
In factin order to “see” a modification of the coefficient of k2 in the dispersion relation one needs at least two particles
So what we need is an analogue model which has at least two kind of quasiparticles which “feel” the same effective geometry at low energies and show LIV in the dispersion relations at high energies
Fortunately we have such a model:
a system of two coupled BEC
This system reproduces a QFT in a spacetime with two scalar fields,
one massive the other massless.
As such this is an ideal system for reproducing the salient features of the situations studied in quantum gravity phenomenology…
Separately each BEC as a dispersion relation of the form
When one switched the laser coupling on, at low frequencies
one can tune the system so to have a common speed of light and gets
12k12, 12k12+m2(cs=1) [Note that the mass is generated via the coupling]
What happens if one looks at the behaviour at high energies?
Will the Lorentz violation remain at order k4 or a naturalness problem will arise?
See Silke Weinfurtner’s talk later…
For GRB we need anyway
Probably new advances will require better understanding of the astrophysics
Better understanding of the naturalness problem could tell us something important about EFT in an emergent spacetime…