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Letting Go of Spacetime

A short talk on why quantum gravity should make us suspicious of locality as a fundamental principle of physics.

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Letting Go of Spacetime:
Lessons for
Quantum Foundations
from Quantum Gravity
Sean Carroll
Caltech &
Santa Fe Institute
Radcliffe Institute Workshop:
The Bridge between
Quantum Theory and Reality
January 2021
Senses of Locality
Measurement locality: measurement outcomes
are independent of events outside the light cone.
Ontological locality –
Dynamical locality:
[no]
[unclear]
[probably not]
[probably not
even that]
Strong form: local beables.
Weak form:
Causality in QFT: operators
commute at spacelike
separation,
What is that supposed to
mean when we sum
over spacetime metrics?
x
t
Path integral:
Without a single classical metric, distances and
times are only approximate notions (at best).
Locality is tricky in quantum gravity
The Holographic Principle:
degrees of freedom aren’t
distributed locally in space
Von Neumann entropy:
Counting degrees of freedom:
QFT: of a region is infinite, and scales like volume.
QG: is finite, and scales like area ( ).
Holographic principle: we can think of quantum
information as “living on” the boundary of a region.
Horizon Complementarity:
degrees of freedom don’t even
have an objective “location”
infalling observer: local
quantum field theory
external observer: degrees of freedom
spread holographically across horizon
Thus: there’s no such thing as “where the information is.”
Motivation: reconciling unitary evolution with
empirical success of local QFT.
Field theory/Gravity duality:
“space” isn’t uniquely defined
Quantum
theory
Classical
theory 1
Classical
theory 2
Duality: two classical
theories with the
same “quantization.”
AdS/CFT: duality between an
N-dimensional field theory
and an (N+1)-dimensional
theory with gravity.
Local operators on one side
are non-local on the other.

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Letting Go of Spacetime

  • 1. Letting Go of Spacetime: Lessons for Quantum Foundations from Quantum Gravity Sean Carroll Caltech & Santa Fe Institute Radcliffe Institute Workshop: The Bridge between Quantum Theory and Reality January 2021
  • 2. Senses of Locality Measurement locality: measurement outcomes are independent of events outside the light cone. Ontological locality – Dynamical locality: [no] [unclear] [probably not] [probably not even that] Strong form: local beables. Weak form:
  • 3. Causality in QFT: operators commute at spacelike separation, What is that supposed to mean when we sum over spacetime metrics? x t Path integral: Without a single classical metric, distances and times are only approximate notions (at best). Locality is tricky in quantum gravity
  • 4. The Holographic Principle: degrees of freedom aren’t distributed locally in space Von Neumann entropy: Counting degrees of freedom: QFT: of a region is infinite, and scales like volume. QG: is finite, and scales like area ( ). Holographic principle: we can think of quantum information as “living on” the boundary of a region.
  • 5. Horizon Complementarity: degrees of freedom don’t even have an objective “location” infalling observer: local quantum field theory external observer: degrees of freedom spread holographically across horizon Thus: there’s no such thing as “where the information is.” Motivation: reconciling unitary evolution with empirical success of local QFT.
  • 6. Field theory/Gravity duality: “space” isn’t uniquely defined Quantum theory Classical theory 1 Classical theory 2 Duality: two classical theories with the same “quantization.” AdS/CFT: duality between an N-dimensional field theory and an (N+1)-dimensional theory with gravity. Local operators on one side are non-local on the other.
  • 7. Wormholes? The black-hole information puzzle has led to a resurgence of interest in wormholes, in two different contexts: • Real but microscopic wormholes relating entangled particles inside & outside the BH (ER=EPR). • Imaginary “Euclidean” wormholes used in the gravitational path integral to calculate properties of Hawking radiation. A modern version of “quantum foam.” [Quanta]
  • 8. Don’t build ontologies relying on a unique, well-defined concept of “spacetime.” Do think about why spacetime and locality are such approximately-good ideas. Do think about how to develop vague ideas from physics (holography, complementarity, wormholes) into sharper, more well-defined concepts. Potential lessons