1. Translations in Relative Locality
Niccolò Loret
with Giovanni Amelino-Camelia and Leonardo Barcaroli
Università “La Sapienza” Roma
XI School of Cosmology
17-22 September IESC, Cargese

2. THE LOCALIZATION PROBLEM
PLANCK LENGTH
κ-MINKOWSKI

3. κ-POINCARE' DEFORMED TRANSLATION GENERATORS COALGEBRIC SECTOR
DEFORMED SIMPLETIC SECTOR

4. BRONSTEIN-ZELMANOV-OKUN CUBE
General Relativity
Special Relativity
LOOPS
Quantum Field Theory
STRINGS
Quantum Gravity
BLACK
HOLE
THERMOD.
Newtonian Gravity
Galilean Relativity
Quantum Mechanics
Chandrasekhar Regime

5. RELATIVE LOCALITY LIMIT
WE STILL HAVE A DEFORMED MOMENTUM SPACE AT
BUT NO WEIRD PLANCK LENGTH EFFECTS RELATED TO SPACETIME QUANTIZATION
DINSTANT NONLOCALITIES
- What we really see in our telescopes and particle detectors are quanta arriving at different angles with different momenta and energies.
- As naive observers looking out at the world, and no less as particle physicists and astronomers, we are basically ”calorimeters” with clocks
SPACETIME IS AN INFERENCE THAT WE BUILD ON MOMENTUM SPACE

6. CURVED MOMENTUM SPACE
SPACETIME TRANSLATIONS AS THE ACTION OF TOTAL MOMENTUM ON COORDINATES
WE CAN EXPRESS NONLOCALITIES AS SOME SORT OF CURVATURE OF MOMENTUM SPACE:

7. WORDLINES IN RELATIVE LOCALITY
MOMENTUM-DEPENDENT COORDINATES

8. RAINBOW METRICS CAN WE FORMALIZE SUCH EFFECTS INTO A METRIC?
- We notice that a pointlike observer has to perform a translation in order to study the shape of the spacetime he is in
IN THE MINKOWSKIAN LIMIT FROM κ-POINCARE' MODEL WE OBTAIN:

9. PHENOMENOLOGY ? FOCUSING IN THE DE SITTER CASE
WE CAN EASELY CALCULATE THE RATIO BETWEEN THE OBSERVED WAVELENGTH IN ALICE AND BOB:

10. REFERENCES
[1] G.Amelino-Camelia, J.Lukierski, A.Nowicki, Act.Phys.Pol. 4, Vol 29 (1998)
[2] G.Amelino-Camelia, L.Freidel, J.Kowalski-Glikman, L.Smolin, Phys. Rev. D 84, (2011)
[3] J. Magueijo, L.Smolin, Class. Quantum Grav. 21, 1725 (2004)
[4] G.Amelino-Camelia, N.Loret, G.Rosati, Phys. Lett. B 700, (2011)
[5] G.Amelino-Camelia, N.Loret, G.Mandanici, F.Mercati, Int J. Mod. Phys. D 19, (2010)
[6] G.Amelino-Camelia, N.Loret, L.Barcaroli, in preparation
[1]G.Amelino-Camelia, J.Lukierski, A.Nowicki, Act.Phys.Pol. 4, Vol 29 (1998)
[2]G.Amelino-Camelia, L.Freidel, J.Kowalski-Glikman, L.Smolin, Phys. Rev. D 84, (2011)
[3]J. Magueijo, L.Smolin, Class. Quantum Grav. 21, 1725 (2004)
[4]G.Amelino-Camelia, N.Loret, G.Rosati, Phys. Lett. B 700, (2011)
[5]G.Amelino-Camelia, N.Loret, G.Mandanici, F.Mercati, Int J. Mod. Phys. D 19, (2010).
[6]G.Amelino-Camelia, N.Loret, L.Barcaroli, in preparation