1. Fuzzy quantum space-time phenomenology
Giovanni Amelino-Camelia
Dip. Fisica Universita’ La Sapienza
Fabrizio Fiore
Osservatorio Astronomico di Roma

2. Summary Context High-z QSOs: QST probes? HST observations
Ground based Adaptive Optic observations
Constraints to QST scenarios, present and future

3. CONTEXT Quantum space-time problem Several formalisms
No observational support so far, due to the small value of Planck length/time, despite the fact that Planck effect can cumulate when propagated on Cosmological distances/times
Limits on quantum space-time effects of the order of Planck mass on some candidate QST scenarios, obtained by Fermi observations of single photons from GRBs

4. CONTEXT
Fermi limits are for systematic effect: in-vacuo dispersion of light
The case of the short GRB090510
Some issues with limits from single photons detections

5. CONTEXT
Systematic effects of in-vacuo dispersion are found in several models for quantum-gravity/quantum-spacetime, but they are not generic
Some models do not have systematic in-vacuo dispersion but still have “fuzziness” (non-systematic effects)
One can also have both systematic and non-systematic effects within the same model
Fuzzy photon arrival times
Fuzzy distances

6. QST with QSOs
Quantum space-time scenarios predict a degradation of the diffraction images of distant sources (GAC ,2001,2003, Ragazzoni+ 2003, Ng+2003, Steinbring 2007, Tamburini+ 2011)
From fuzzy distances to phase shifts
The first naïve approach prompted tests using HST observations of distant QSOs: Phase shift of light propagated over long distance

7. Ideal distant, bright, point like sources
Why QSOs?
Extremely luminous (up to 1048 egs/s) cosmic sources found up to z~7 (baby Universe, first 600 Myr)
Bright optical/NIR sources
Compact sources (typical sizes <10 pc, both continuum and broad emission lines)
Big contrast with their host galaxies (1000 or even more)
Ideal distant, bright, point like sources

8. Fuzzy QST ΔLmin=a0(lp/L)α
Time cannot be measured with uncertaintly < tP~5.4×10-44 s
ΔLmin=a0(lp/L)α
ΔLmin=a0lp(L/lp)1-α Lieu+2003 GAC+1999,2001,2002
Cumulative factor Cα=(ΔL/Δλ) i.e. how Planck scale effects are amplificated traveling a distance L
Since Δλ=a0lp(λ/lp)1-α Cα=(L/λ)1-α
for incoherent fluctuations Ng+2003

9. Fuzzy QST
Consider the phase of light of wavelength λ traveling a distance L
The phase is continuously subject to incoherent QST fluctuations
Ng+2003
Considering Cosmological redshift Steinbring 2007

10. QST with QSOs
Use of diffraction as interferometry effect by a telescope dish of diameter D. An error on the phase of a wave-front translate in an error ΔL on the distance of the light source. This will translate in an apparent angular shift Δθ Ragazzoni+2003
Phase shifts cause a drop of the Strehl ratio: image peak/diffration spike of unaberrated telescope

11. Strehl ratio The case of an extended source, the galaxy Mkr231
S=image peak/unaberrated telescope
Unaberrated telescope,
point source
PSF
Galaxy profile

12. QST with QSOs
PSF
QSOs
Tamburini+ 2011
Steinbring 2007

13. LBT AO observations of QSOs
SDSS J z=3.340
AO star 11.6”, Seeing ”
[HB89] z=2.365, radio loud
AO star 21”, Seeing ”

14. QST with QSOs Δφ(λ,D,S)=λ∕D√ln(S)
Δφ(0.75,2.4,0.83)=1.5×10-7rad (HST I band)
Δφ(2.2,8.2,0.6)=1.9×10-7rad (LBT K) present observations
Δφ(1.2,8.2,0.5)=1.2×10-7rad (LBT J) feasible right now
Δφ(0.75,8.2,0.4)=8×10-8 rad LBT SHARK and forerunner, I band,
Δφ(0.75,23,0.4)=3×10-8 rad LIVE, LBT Interferometer visible extension, I band, ~2020)
Δφ(1.2,40,0.7)=3×10-8 rad E-ELT Y/J, Mikado, ~2025)

15. Why LBT? The best adaptive optic system so far on 8m class telescope!
Extremely good Strehl ratio at NIR wavelengths (>0.9)
Good Strehl ratio at optical wavelength ( )
Binocular telescope, 23m baseline.
LBT deformable secondary mirror:
0.9m diameter 400 actuators working at kHz frequencies to correct wave-front errors due to atmosphere disturbances

16. QST with QSOs
Limits to QST models Tamburini+2011
How reliable are these limits? Are QST scenario truly exluded from the HST data?

17. Fuzzy QST: a more rigorous approach
On very general grounds one can conclude that spacetime fuzziness should produce a minimum uncertainty for lengths of form
Studies done so far claim they tested directly  but a «minimum-uncertainty principle» could not be tested using particles of specific type and energy!!! Assumption so far was that the same δL should apply at all energies for photons, but this assumption is unjustified….may well lead to overestimating the effects of spacetime fuzziness on low-energy particles

18. QST with QSOs Counter-example: a case with produces
in combination with the Heisenberg Uncertainty principle

19. QST with QSOs: Conclusions
This recently-found counter-example shows that the significance of limits on spacetime fuzziness from QSOs has been largely overestimated.
On the other hand it is difficult to gauge the possible admissible range of strengths of the effects of spacetime fuzziness on the basis of the single phenomenological model we recently understood
Improving limits on fuzziness with QSOs deserves attention
AO observations of high-z QSOs look promising to search for new physics on scales not accessible to HST (or most other ground based systems).