beyond the planck scale - instytut fizyki teoretycznejplanckscale/lectures/5-friday/1... · ·...
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Beyond the Planck scale
Steven B. Giddings
UCSB and CERN
The Planck Scale -- XXV Max Born Symposium
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Suggestion: focus on the Planck scale may be misleading
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Suggestion: focus on the Planck scale may be misleading
CM breaks down; what new physics?
Atom
“classical instability paradox”possible theoretical analogy:
electron
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Suggestion: focus on the Planck scale may be misleading
CM breaks down; what new physics?
Atom
“classical instability paradox”possible theoretical analogy:
electron
Experiment guided the resolution: 1) a different scale 2) new principles (QM)(a0)
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Plan:
1) Review arguments(If you see a better alternative, tell me)
2) Summarize some ongoing work on the problem
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A complete theory of quantum gravity should describe (or avoid) ultraplanckian collisions
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A complete theory of quantum gravity should describe (or avoid) ultraplanckian collisions
The reason:e!
Boost to E !Mp
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A complete theory of quantum gravity should describe (or avoid) ultraplanckian collisions
The reason:e!
Boost to E !Mp
Just need: 1) Lorentz invariance
2) very weak notion of locality
(LI violation might postpone...)
e+
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In TeV-scale gravity models, even
at LHC!
(A review: arXiv:0709.1107)
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E !Mp : dynamics
• Control impact parameter b -- wavepackets
• Large E: semiclassical picture
• Classically, produce black hole, + radiation
• Quantum corrections: Hawking radiation
“BH”
!
(Indeed, LI doesn’t avoid, if form BHs other ways)6
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So, confront information paradox:
Hawking, updated: nice slice argument
Locality:
|!NS! " "out = Trin|!NS!#!NS |
! information lost
(Hawking, 1976)
nice slice
SBH = !Tr (!out ln !out) " ABH
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The problem is, QM is remarkably robust:
Banks, Peskin, Susskind (1984):
Such breakdown of QM! Massive E nonconservation
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The problem is, QM is remarkably robust:
Banks, Peskin, Susskind (1984):
Such breakdown of QM! Massive E nonconservation
Info storage in remnants?
Let’s try to keep unitarity!!
Infinite species
Infinite production instabilities
(See e.g. hep-th/9310101, hep-th/9412159)
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So, keeping Lorentz invariance and quantum mechanics apparently tells us to revisit locality:
RS ! (GDM)1/(D!3)
On scale :
By a time:
! ! RSSBH
(Page, hep-th/9306083)
>>> lp
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CM breaks down here
QM takes over here
(CM irrelevant)
Atom
a0
The atomic analogy:
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The atomic analogy:
Black hole
Suggestion: take literally -- new principles at
LQFT breaks down here
“QG” becomes important here?
RS
RS
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What does string theory say?
Hints(?) at a solution:
Idea: “holography:”
D-dim. grav ! (D-1) non-grav unitary thy
(AdS/CFT)
But ...
microstate counting, etc.
addresses nonrenormaliziblity
extendedness/nonlocality
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2) The problem appears intrinsically nonperturbative
1 + O!"
RS(E)b
#2(D!3)$
1) No apparent role for string extendednessSBG, hep-th/0604072SBG, Gross, Maharana, arXiv:0705.1816
(unitarity a more critical issue than renormalizability ?)
“different time scales”
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3) Microstate counting: not far from BPS (Schwarzschild)
4) Holographic “duals”don’t clearly contain sufficient information
- A test: recover the flat space S-matrix
Limited progress: Gary, SBG, Penedones arXiv:0903.4437
Potential obstacles: Gary, SBG arXiv:0904.3544
(And such strong holography seems possibly overoptimistic)
Whether or not strings the solution ...
- No understanding of local observables!
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Questions to answer:
1) Where does local QFT fail? Correspondence boundary
2) What is the mechanism?
3) What physical/mathematical framework replaces QFT, and how might locality emerge from it in
familiar contexts?
what is wrong with nice slice argument?
how does it preserve unitarity?
how to preserve consistency/causality?
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1) Where fails:
Breakdown of classical mechanics:
!x!p = 1 (phase space)
2) Mechanism: classical phase space
quantum wavefunction
3) Framework: Hilbert space; Schrodinger/Heisenberg mechanics
(correspondence boundary)
wave behavior of matter
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Some possible proposals for a correspondence boundary for gravity:
planckian curvature: R < M2P
string uncertainty principle: !X ! 1!p
+ !!!p
modified dispersion: p < Mp
1 particle}holographic (information)
bounds:multiparticleS ! A/4GN
(Veneziano/Gross)
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CM: x(t) , p(t)
validitydynamical descript.
!x!p > 1
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CM: x(t) , p(t)
validity
QFT +GR:
!x,p!y,q|0!(min uncertainty wavepackets)
dynamical descript.
!x!p > 1
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CM: x(t) , p(t)
validity
QFT +GR:
!x,p!y,q|0!(min uncertainty wavepackets)
dynamical descript.
|x! y|D!3 > G|p + q|
!x!p > 1
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CM: x(t) , p(t)
validity
QFT +GR:
!x,p!y,q|0!(min uncertainty wavepackets)
dynamical descript.
|x! y|D!3 > G|p + q|
!x!p > 1
(generalizations: N-particle; dS)
“locality bound”SBG & Lippert;hep-th/0605196; hep-th/0606146
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Correspondingly, mechanism:“delocalization w.r.t. semiclassical geometry, intrinsic to unitary dynamics of nonperturbative gravity”
contrast with: extended strings (or branes)(correspondingly, clear distinction between “string uncertainty principle” and the locality bound)
~ “nonlocality principle”
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- high-energy scattering
How do we probe/quantify locality?
- local observables
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How do we probe/quantify locality?
- local observables
- high-energy scattering
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Asymptotically flat space:
Investigate general properties of scattering, consistent with unitary quantum evolution, basic features of gravity
The gravitational S-matrix
SBG and Srednicki arXiv:0711.5012 SBG and Porto, WIP
e.g: locality polynomiality?
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T (s, t) = (const)E4!D"!
l=0
(l + !)C!l (cos ")
"e2i"l(s)!2#l(s) ! 1
#
! =D ! 3
2
PW expansion:scattering:
A. Can infer features of , in “weak gravity” regime (large impact param. -- Born, eikonal)
!l !l
2! 2
B. Ansatz for BH region
!l !S(E, l)
4(Bekenstein-Hawking entropy - approx. thermal description)
l ! ERS(E) = L
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Features:
- significant indications, amplitudes not polynomial:
plausibly associated w/ lack of usual locality?T (s, t) ! es!t"
!BH ! [RS(E)]D!2(related: viol. of Froissart, eg )
- interesting constraints from crossing
(not “too” nonlocal)
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This is “outside” (asymptotic) viewpoint. To discuss “inside,” need local observables~
Indeed, locality - QFT:
[O(x),O(y)] = 0 , (x! y)2 > 0
Diff invariance ! None in gravity!
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Likely resolution: Relational approach:“proto-local observables”
see: SBG, Marolf, Hartle; Gary & SBG: 2d, concrete
Basic idea: O =!
d4x!"gB(x)O(x)
!B(x)" = b(x)
for appropriate background: !O" # O(x0)
localization relative to background
But: - localization only approximate
- must include background/observer24
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In the inside perspective, can find flaw in nice slice
argument, and see where Hawking went wrong ?
Some thoughts: Sharp computation of hep-th/0606146
SBH
requires fine-grained, local |!!NS
Two potential obstacles:
1) observ. background !large mods. to
2) backreaction of fluctuations
|!!NS
!large mods. to |!!NS
Both by !Page ! RSSBH
(literal CM/QM analogy may be another out...)25
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- Apparent signals of perturbative breakdown; proposed resolution of information paradox
- Non-pert. completion would be required to describe information “relay”/ restore unitarity
- Interestingly, there are parallel arguments in dS,
Nice slices
suggesting LQFT incomplete after ! ! RdSSdS
(Likely related argument: Arkani-Hamed et al arXiv:0704.1814)
but, a clue ...
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Work w/ Marolf on dS, etc. arXiv:0705.1178, and WIP x2
R4dSeSdS
- More general limitations on local QFT for volumes >
- Investigation of proto-local observables in dS
deal w/ constraints, linearization stability
- Measurement for protolocal observables
In general, expect similar considerations to possibly be important in cosmology
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To sum up, should be probing limits of local quantum field theory description, likely on scales ! lP
“unitarity restored at price of locality”
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To sum up, should be probing limits of local quantum field theory description, likely on scales ! lP
How to progress?
( How to invent QM w/out experiment?)~
One small step: what is a general enough quantum-mechanical framework to incorporate these ideas?
More general than “generalized QM”
arXiv:0711.0757
“unitarity restored at price of locality”
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Thought experiments, pursuing a consistent quantum description of
- high energy scattering
- observables
- cosmology
and eliminating superfluous concepts
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How can we have a theory w/ features of gravity:
2) Quantum mechanical
1) Consistent ( causal)~
3) Nonlocal
4) Nearly-local(i.e. behaves locally in usual low-energy circumstances)
A highly non-trivial set of conditions to satisfy!
Might this help guide us to such a “Non-Local (but Nearly-Local) Mechanics”?
} essential tension
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Backups
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Tidal string excitation
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Q1: understand diffractive excitation
Picture:hep-th/0604072;arXiv:0705.1816 w/ Gross and Maharana
asymptotic excitation Aichelburg-Sexl
“tidal excitation”
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Trapped surface
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Trapped surface
Black hole
Different timescales
No role for extendedness?
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Phase diagram
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ln(E)
ln(b)
2D ! 4
lnE
consider strings, or more generally
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ln(E)
ln(b)
2D ! 4
lnE
1D ! 3
lnE
lsstrings
ECMs
consider strings, or more generally
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2D ! 2
lnE
“diffractive excitation”
ln(E)
ln(b)
2D ! 4
lnE
1D ! 3
lnE
lsstrings
ECMs
consider strings, or more generally
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ln(E)
ln(b) Born scattering
2D ! 4
lnE
Eikonal scatterin
g
2D ! 2
lnE
Tidal string excitation
1D ! 3
lnE
Strong gravityls
strings
ECMs
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Locality bd
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Other versions of the locality bound:
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Other versions of the locality bound:
Measurement limit: !t(!x)D!3 ! G!
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Other versions of the locality bound:
Measurement limit: !t(!x)D!3 ! G!
N-particle: !x1,p1 · · · !xN ,pN |0!
Max|xi ! xj |D!3 < G|!
i
Pi|not good for
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Other versions of the locality bound:
Measurement limit: !t(!x)D!3 ! G!
N-particle: !x1,p1 · · · !xN ,pN |0!
Max|xi ! xj |D!3 < G|!
i
Pi|not good for
de Sitter: see SBG and Marolf, arXiv:0705.1178
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