Emergent

quantum

mechanics

John Preskill, Caltech

Breakthrough Prize Symposium

10 November 2014

Frontiers of Physics

short distance long distance complexity

Higgs boson

Neutrino masses

Supersymmetry

Quantum gravity

String theory

Large scale structure

Cosmic microwave

background

Dark matter

Dark energy

“More is different”

Many-body entanglement

Phases of quantum

matter

Quantum computing

WHAT’S INSIDE A BLACK HOLE?

“Testing quantum mechanics”

-- “Loophole free” Bell inequality experiments (photons).

-- “Cat states” (macroscopic superpositions).

-- Complex highly-entangled systems (toward “quantum

supremacy”).

( + )1

2

What is the alternative to quantum theory?

Who has the biggest cat?

238U, C60, spin squeezing, superconducting (flux qubits),

optomechanics, Bose-Einstein condensates … How to

compare?

( + )1

2

N⊗ N⊗

" " /meas

catiness N N N= ≈ (1 - )2

(how may spins we’d measure to collapse the superposition)

-- answer depends on choice of decomposition into subsystems.

-- catiness may depend on spatial separation, or masses.

-- we can’t compare “tests” of quantum theory using different platforms unless we know what we’re testing!

Emergent quantum mechanics?

“chaos”

standard

model

RG flow

UV

IR

-- What principles constrain the “chaos”?

-- Relax unitarity (and locality) in the UV?

-- Violation of unitarity, Lorentz invariance, gauge invariance relevant in the IR.

-- Nonunitary evolution implies energy nonconservation.

-- General covariance without energy conservation?

experiments

Metaphor I: Quantum error correction

physical

noise

logical

information

RG flow

UV

IR

-- Encode protected information in highly entangled states, so the information is well protected against environmental decoherence.

-- Dissipation needed to drain entropy introduced by noise. Nonunitary dynamics could provide the necessary dissipation.

-- “Eternal qubits,” engineered to have very long coherence times, might be realized fairly soon.

-- Either “topological codes” or a hierarchy of codes within codes.

Metaphor II: The leaky brane

-- overall conservation of energy and information.

-- but energy and information can leak from the brane into the bulk.

-- the effective theory on the brane is nonunitary and does not conserve energy.

-- coupling to gravity is consistent.

bulk

energy,

information

Principle of “anomaly inflow”: An effective theory in D dimensions may be inconsistent, but makes sense when realized at the boundary of a (D+1)-dimensional theory. (Cf. symmetry-protected topological phase of matter.)

Revisions in the principles of quantum theory should illuminate and/or be illuminated by deeper insights into quantum gravity. (Emergent quantum theory may require emergent dimensions.)

Local field theories

Path integral formulation of density operator evolution in a scalar field theory.

-- Completely positive map.-- Poincare invariant.

D. Poulin

exp( ( () ) $( , ))iS i O OSφ φ′ ′+−

evolution of ketevolution of bra

“dissipator”

Dissipator can be a high-dimension operator, irrelevant by power counting.

But lower-dimensional relevant operators are induced by renormalization unless forbidden by symmetries.

Lorentz-invariant fixed point is typically either infinite temperature (maximally mixed state) or zero temperature (vacuum). Zero temperature only if dissipator involves derivatives of fields.

(Small) violations of microcausality are generic.

We still don’t understand these theories, or how they flow.

Convergence

Invitation to reconsider possible deviations from standard quantum theory.

-- puzzles regarding the inside of black holes.

-- advancing technology for unprecedented experiments.

-- guidance from symmetry-protected phases.

-- inspiration from quantum error correction.

bulk

energy,

information

Reasonably likely outcome: deeper understanding of why quantum theory has to be as it is.

Possible (but not likely) outcome: viable models of emergent quantum theory … and perhaps experimentally testable predictions.