Q2CIII, 10 july 2008

the “Quantum Gravity problem” and the type of “Quantum Gravity Phenomenology” it can motivate

genuine Planck-scale sensitivity is achievable

difficult phenomenology but the Planck scale often providesassociated “target sensitivities”, and this can in some cases be usedto strengthen proposals of fundamental-physics experiments in space(“we shall improve the limits by 2 or 3 orders of magnitude” “we shall improve the limits to the level needed to probe Planck scale”)

Planck-scale physics in spaceGiovanni AMELINO-CAMELIAUniv. of Rome “LA SAPIENZA”

GAC,”Fundamental physics in space: a quantum-gravity perspective”, GenRelGrav36(2004)539-560 [needs updating]

●Quantum Mechanics and GR are very successful in their respective domains of typical applicability, but inconsistencies are unavoidable if we combine them naively in theanalysis of situations in which they both should be relevant: there should be a “quantum gravity”, i.e. some nontrivial “unification” of QM and GR

● most robust “theoretical evidence” on the quantum-gravity realm: Planck-scale nonlocality; Planck-scale spacetime quantization (discretization, noncommutativity, fuzziness); …………

Planck scale Ep 1028eV (Planck length Lp1/Ep 10-35m)

2

•violations of Poincarè/Lorentz symmetry •spacetime fuzziness •some implications for the Equivalence Principle

•decoherence

•...............

The fact that such striking effects would be plausible (though not necessary) at the Planck scale has been acknowledge for decades now,but for a long time it was thought that the smallness of the effects(due to the smallness of the Planck length) would bean unsurmountable difficulty for experimental tests

in most approaches to this “QG problem” spacetime ends upbeing described by a nonclassical (“quantum”) geometry, with some nonlocality,spacetime fuzziness, spacetime noncommutativity,and this can indeed lead to striking consequences, including

Effects of spacetime quantization should be small but striking!!!

3

we have robust evidence that something new must be there at the Planck scale….some authors would argue that quantum-gravity effectscould show up already at a lower scale, but nobody will argue against the claim that something new must be there by the time we get to the Planck scale….so we better sharpen our tools for the Planck scale!!

also because there may well be nothing (of quantum-gravity relevance) below the Planck scale:

ELEP;MW EGUTEP

e.g. scenarios with large extra space dimensions

we should “walk the plank”:c

Kifune, Astr.Journ.Lett.(1999)GAC+Piran, PhysRevD(2001)GAC,Nature(2000)

imagine space is discrete with lattice scale the Planck length, then naturally you end up with something like

then compute the threshold energy requirement for photopion production

p +γCMBR => p+πwith this modified dispersion relation and one finds a shift of the threshold,

which implies an observably large shift of the “GZK scale” for the cosmic-ray spectrum

In which sense we have “proven sensitivity to effects introduced genuinely at the Planck scale”?

m2 + p2 E2 -E4/Ep2

0,

2

30,

, #2 th

p

thprotQGth

k

E

kmmk

O(1)

see,e.g.,t’Hooft, CQG(1996)

correction important already when Ep2 (kth,0 ) 4/(mprotm )

*following this line of analysis (and data recently gathered at the Pierre Augercosmic-ray observatory) we are now close to establishing as a scientific factthat rigid Planck-scale discretizations of spacetime are not allowed

*so we do have, at least in some cases, a chance to probe effects introduced genuinely at the Planck scale

* and this “threshold-anomaly analyses” provide examples of how wrongthe naive “Yang-Mills integrated-out-gauge-bosons intuition”is about the magnitude of Planck-scale-induced effects can be:

“must require Planckian energies” requires large boosts (even at relatively “low” energies)!!

6

many QG theorists would favour a picture in which the world lines of particles are “fuzzy” with fuzziness at scales of Planck-length magnitude per Planck time interval

and a simple-minded but effective way to give a first crude estimate of the size of this effect could rely on a picture in which particles still propagate in a classical geometry but their trajectory is affected by stochasticity at the level of Planck-length-size fluctuations with Planck-time frequency

naive intuition: study of this effect requires operating an interferometerat the huge Planck frequency (1044Hz)

Another case of wrong intuition

7

2)(

ffS

TfSdfL )(2

But if indeed the particles random walk with Planck-length fluctuations occurring each Planck time then we should expect the characteristic random-walk power spectrum which insteads is mostly low-frequency

GAC, Nature 398(1999)Ng+VanDam, FoundPhys(2000)GAC,PhysRevD(2000)GAC,Nature410(2001)Schiller et al, PhysRevD(2004)

8

*

*

Quantum Gravity?

also see GAC+Lämmerzahl, ClassicalQuantGrav(2004) [for in-vacuo dispersion]

model too crude….but naivety of “Planck-frequency expectation‘‘ robustly exposed…

should be increasingly important as we

gain access to lower and lower frequencies….GAC, Nature 398(1999)216Ng+VanDam, FoundPhys(2000)GAC,Nature410(2001)

wavelength-dependent speed for photons

GAC+Ellis+Mavromatos+Nanopoulos+Sarkar, Nature393(1998) Schaefer, PhysRevLett82(1999)Gambini+Pullin, PhysRevD59(1999) v = 1- η E/Ep

dE

dp

since this needs sharp time resolution, long distances travelled and(possibly) particles of high energy, gamma-ray bursts: - travel distances of order 1010 light years - microbursts within a burst can have duration 10-3 seconds - relatively large E (10 MeV... 100 MeV...possibly a few GeV...) GLAST numbers work out to provide sensitivity to ||1 (e.g. BATSE at ||10-3)

This would mean that two (nearly-)simultaneously-emitted photons would reach the Earth with a relative time-of-arrival difference of t = T η E/Ep where T is the overall time travelled

(N.B.: focusing here on linear effect but quadratic effect within reach applying the same strategy to some UHE neutrino observations)

an example where the numbers work out just perfectlyfor a “Planck-scale target sensitivity”:GLAST and Planck-scale-induced in-vacuo dispersion

Jacob+Piran,NaturePhysics3(2007)GAC, Nature Physics 3(2007)

from modified dispersion relation

*ability to manipulate atoms (often improved in space environment) is likely to be next opportunity….

*GLAST collaboration well aware; dedicated analyses planned

*most EUSO colleagues are aware

Planck-scale physics in space: already a reality

*spacetime fuzziness analysis also relevant for LISA, but I am not informed of any dedicated plans

11

= ?

example: atom recoil studies:atom absorbs a photon with frequency tuned on resonance, gets in an excited level and recoils, then a photon with a doppler-shifted frequency ’ deexcites the atom, inducing stimulated emission

a calculation for “deformed Lorentz symmetry”:-modify Lorentz symmetry via some Planck-scale effects, but introduce mathematics (Hopf algebra) to preserve equivalence of inertial frames

GAC, PhysLettB(2001) Magueijo+Smolin, PhysRevLett(2002)GAC,Nature(2002)

12

for m124GeV and 352 THz (Caesium, D2 line)F. Mercati

Doppler effect not fully understood from a“deformed-symmetry” perspective , but for some scenarios preliminary result is

GAC+Lämmerzahl

AFTER: even general (rather formal) QG reviews acknowledge importance of QGphenomenologyfor the overall development of QG

BEFORE: even Isham in his reviews only includes 3 lines on “experimental tests” just to argue that it could not possibly be done

Summary: “target sensitivity” and other features render Planck-scalephenomenology well suited for proposals of “fund phys in space”

QGphenomenology madesignificant progress in just a few years

Isham, “Structural issues in quantum gravity”, Proc. of General Relativity and Gravitation 1995

“Are we at dawn of Quantum-Gravity Phenomenology” GAC,@Karpacz1999,Lect.NotesPhys.541,1

Rovelli, gr-qc0006061 Carlip, Rept.Prog.Phys.64,885 Smolin, hep-th0408048

and it appears likely that, now that finally awareness of the futility of the pursuit of a “theory of everything” is spreading, efforts in the QGphenomenology direction will further increase

GAC,Nature408,661-664(2000)

Einstein’s utopia of a theory of everything:“I would like to state a theorem…: there are no arbitrary constants ... that is to say, Nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur”