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Observables, gravitational dressing, and obstructions to locality and subsystems

Jul 4, 2016

16 pages

Published in:

Phys.Rev.D 94 (2016) 10, 104038

Published: Nov 14, 2016

e-Print:

1607.01025 [hep-th]

DOI:

10.1103/PhysRevD.94.104038

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Abstract: (APS)

Quantum field theory—our basic framework for describing all nongravitational physics—conflicts with general relativity: the latter precludes the standard definition of the former’s essential principle of locality, in terms of commuting local observables. We examine this conflict more carefully, by investigating implications of gauge (diffeomorphism) invariance for observables in gravity. We prove a dressing theorem, showing that any operator with nonzero Poincaré charges, and in particular any compactly supported operator, in flat-spacetime quantum field theory must be gravitationally dressed once coupled to gravity, i.e., it must depend on the metric at arbitrarily long distances, and we put lower bounds on this nonlocal dependence. This departure from standard locality occurs in the most severe way possible: in perturbation theory about flat spacetime, at leading order in Newton’s constant. The physical observables in a gravitational theory therefore do not organize themselves into local commuting subalgebras: the principle of locality must apparently be reformulated or abandoned, and in fact we lack a clear definition of the coarser and more basic notion of a quantum subsystem of the Universe. We discuss relational approaches to locality based on diffeomorphism-invariant nonlocal operators, and reinforce arguments that any such locality is state-dependent and approximate. We also find limitations to the utility of bilocal diffeomorphism-invariant operators that are considered in cosmological contexts. An appendix provides a concise review of the canonical covariant formalism for gravity, instrumental in the discussion of Poincaré charges and their associated long-range fields.

Note:

19 pages, latex. v2: small wording changes/improvements; matches version to appear in Phys Rev D

gravitation
field theory
general relativity
diffeomorphism
Poincare

References(45)

Figures(0)

[1]

Local quantum physics: Fields, particles, algebras

R. Haag
(
- Hamburg U.
)

- Berlin, Germany: Springer (1992) 356 p. (Texts and monographs in physics)

[2]

Hilbert space structure in quantum gravity: an algebraic perspective

Steven B. Giddings
(
- UC, Santa Barbara
)

- JHEP 12 (2015) 099
•
e-Print:
- 1503.08207
•
DOI:
- 10.1007/JHEP12(2015)099

[3]

Diffeomorphism-invariant observables and their nonlocal algebra

William Donnelly
(
- UC, Santa Barbara
)
,
Steven B. Giddings
(
- UC, Santa Barbara and
- Santa Barbara, KITP
)

- Phys.Rev.D 93 (2016) 2, 024030,
- Phys.Rev.D 94 (2016) 2, 029903 (erratum)
•
e-Print:
- 1507.07921
•
DOI:
- 10.1103/PhysRevD.93.024030

[4]

Gravitational observables and local symmetries

C.G. Torre
(
- Utah State U.
)

- Phys.Rev.D 48 (1993) R2373-R2376
•
e-Print:
- gr-qc/9306030
•
DOI:
- 10.1103/PhysRevD.48.R2373

[5]

Observables in effective gravity

Steven B. Giddings
(
- UC, Santa Barbara
)
,
Donald Marolf
(
- UC, Santa Barbara
)
,
James B. Hartle
(
- UC, Santa Barbara
)

- Phys.Rev.D 74 (2006) 064018
•
e-Print:
- hep-th/0512200
•
DOI:
- 10.1103/PhysRevD.74.064018

[6]

The Quantization of geometry

B.S. DeWitt

[7]

Quantum observables and recollapsing dynamics

Donald Marolf
(
- Penn State U.
)

- Class.Quant.Grav. 12 (1995) 1199-1220
•
e-Print:
- gr-qc/9404053
•
DOI:
- 10.1088/0264-9381/12/5/011

[8]

Les invariants de courbure de l’espace de Riemann a quatre dimensions

J. Géhéniau
,
R. Debever

[9]

Les quatorze invariants de courbure de l’espace Riemannien a quatre dimensions

J. Géhéniau
,
R. Debever

- Helv.Phys.Acta Suppl. 4 (1956) 101-105

[10]

Construction of a Complete Set of Independent Observables in the General Theory of Relativity

Arthur Komar

- Phys.Rev. 111 (1958) 4, 1182
•
DOI:
- 10.1103/PhysRev.111.1182

[11]

Poisson brackets between locally defined observables in general relativity

Peter G. Bergmann
(
- Syracuse U.
)
,
Arthur B. Komar
(
- Syracuse U.
)

- Phys.Rev.Lett. 4 (1960) 432-433
•
DOI:
- 10.1103/PhysRevLett.4.432

[12]

Local subsystems in gauge theory and gravity

- JHEP 09 (2016) 102
•
e-Print:
- 1601.04744
•
DOI:
- 10.1007/JHEP09(2016)102

[13]

Gauge invariant formulation of quantum electrodynamics

Paul A.M. Dirac
(
- Cambridge U.
)

- Can.J.Phys. 33 (1955) 650
•
DOI:
- 10.1139/p55-081

[14]

Einstein's theory in a three-dimensional space-time

- Gen.Rel.Grav. 16 (1984) 751-775
•
DOI:
- 10.1007/BF00762914

[15]

Role of Surface Integrals in the Hamiltonian Formulation of General Relativity

- Annals Phys. 88 (1974) 286
•
DOI:
- 10.1016/0003-4916(74)90404-7

[16]

Simplicial quantum gravity

H.W. Hamber

[17]

Invariant correlations in simplicial gravity

Herbert W. Hamber
(
- UC, Irvine
)

- Phys.Rev.D 50 (1994) 3932-3941
•
e-Print:
- hep-th/9311024
•
DOI:
- 10.1103/PhysRevD.50.3932

[18]

Quantum geometry of 2-D gravity coupled to unitary matter

Jan Ambjorn
(
- Bohr Inst.
)
,
K.N. Anagnostopoulos
(
- Bohr Inst.
)

- Nucl.Phys.B 497 (1997) 445-478
•
e-Print:
- hep-lat/9701006
•
DOI:
- 10.1016/S0550-3213(97)00259-9

[19]

On the Proof of the positive mass conjecture in general relativity

- Commun.Math.Phys. 65 (1979) 45-76
•
DOI:
- 10.1007/BF01940959

[20]

A Simple Proof of the Positive Energy Theorem

Edward Witten
(
- Princeton U.
)

- Commun.Math.Phys. 80 (1981) 381,
- Commun. Math. Phys. 80 ( 1981) 381-402
•
DOI:
- 10.1007/BF01208277

[21]

Combing gravitational hair in 2 + 1 dimensions

William Donnelly
(
- UC, Santa Barbara
)
,
Donald Marolf
(
- UC, Santa Barbara
)
,
Eric Mintun
(
- UC, Santa Barbara
)

- Class.Quant.Grav. 33 (2016) 2, 025010
•
e-Print:
- 1510.00672
•
DOI:
- 10.1088/0264-9381/33/2/025010

[22]

Comments on Microcausality, Chaos, and Gravitational Observables

Donald Marolf
(
- UC, Santa Barbara
)

- Class.Quant.Grav. 32 (2015) 24, 245003
•
e-Print:
- 1508.00939
•
DOI:
- 10.1088/0264-9381/32/24/245003

[23]

Relational observables in 2-D quantum gravity

Mirah Gary
(
- UC, Santa Barbara
)
,
Steven B. Giddings
(
- UC, Santa Barbara and
- Santa Barbara, KITP
)

- Phys.Rev.D 75 (2007) 104007
•
e-Print:
- hep-th/0612191
•
DOI:
- 10.1103/PhysRevD.75.104007

[24]

Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture

Daniel Harlow
(
- Harvard U. (main)
)

- JHEP 01 (2016) 122
•
e-Print:
- 1510.07911
•
DOI:
- 10.1007/JHEP01(2016)122

[25]

Emergence of helicity +- 2 modes (gravitons) from qbit models

Zheng-Cheng Gu
(
- MIT, LNS
)
,
Xiao-Gang Wen
(
- MIT, LNS
)

- Nucl.Phys.B 863 (2012) 90-129
•
e-Print:
- 0907.1203
•
DOI:
- 10.1016/j.nuclphysb.2012.05.010

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