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

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