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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
THE LOCALIZATION PROBLEM
PLANCK LENGTH
κ-MINKOWSKI
κ-POINCARE'
DEFORMED TRANSLATION GENERATORS
COALGEBRIC SECTOR
DEFORMED SIMPLETIC
SECTOR
BRONSTEIN-ZELMANOV-OKUN CUBE
1/c
General
Relativity
Special
Relativity
Quantum
Field
Theory
STRINGS
Galilean
Relativity
Quantum
Mechanics
ℏ
B
L
A
C
K
H
O
L
E
Quantum Gravity
T
H
E
R
M
O
D.
Newtonian
Gravity
Chandrasekhar
Regime
G
RELATIVE LOCALITY LIMIT
WE STILL HAVE A
DEFORMED MOMENTUM
SPACE AT
DINSTANT NONLOCALITIES
BUT NO WEIRD PLANCK
LENGTH EFFECTS RELATED TO
SPACETIME QUANTIZATION
- 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
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:
WORDLINES IN RELATIVE LOCALITY
MOMENTUM-DEPENDENT COORDINATES
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:
PHENOMENOLOGY ?
FOCUSING IN THE DE SITTER CASE
WE CAN EASELY CALCULATE THE RATIO BETWEEN THE OBSERVED
WAVELENGTH IN ALICE AND BOB:
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, 084010 (2011)
[3] J. Magueijo, L.Smolin, Class. Quantum Grav. 21, 1725 (2004)
[4] G.Amelino-Camelia, N.Loret, G.Rosati, Phys. Lett. B 700, 150156 (2011)
[5] G.Amelino-Camelia, N.Loret, G.Mandanici, F.Mercati, Int J. Mod.
Phys. D 19, 2385-2392 (2010)
[6] G.Amelino-Camelia, N.Loret, L.Barcaroli, in preparation