Macroscopic Realism Emerging from Quantum Physics

Johannes Kofler and Časlav Brukner

15th UK and European Meeting on the Foundations of Physics

University of Leeds, United Kingdom, March 2007

Faculty of PhysicsUniversity of Vienna, Austria

Institute for Quantum Optics and Quantum InformationAustrian Academy of Sciences

Classical versus Quantum

Phase space

Continuity

Newton’s laws

Local Realism

Macrorealism

Determinism

- Does this mean that the classical world is substantially different from the quantum world?

Hilbert space

Events, ”Clicks”

Schrödinger + Projection

Violation of Local Realism

Violation of Macrorealism

Randomness

- When and how do physical systems stop to behave quantumly and begin to behave classically?

Macrorealism

[Leggett–Garg (1985)]

Macrorealism per se “A macroscopic object, which has available to it two or more macroscopically distinct states, is at any given time in a definite one of those states.”

Non-invasive measurability “It is possible in principle to determine which of these states the system is in without any effect on the state itself or on the subsequent system dynamics.”

t = 0

t

t1 t2

Q(t1) Q(t2)

Quantity: Q

Temporal correlations

All macrorealistic theories fulfill the

Leggett–Garg inequality

t = 0

t

t1 t2 t3 t4

t

Violation no objective properties prior to and independent of measurements

When is macrorealism violated?

1/2

Spin-1/2

Classical Spin

classical+1

–1

Evolution Observable

Violation of macrorealism

precession around x

Macrorealism

for

Spin-j precession in magnetic field

Violation of macrorealism for arbitrarily large spins j

(totally mixed state!)

Shown for local realism [Mermin, Peres]

Parity of eigenvalue m of Jz measurement

Violation of macrorealism for macroscopically large spins?

classical limit

j

Coherent spin state (t = 0):

exact measurement

fuzzy measurement

fuzzy measurement & limit of large spins

This is (continuous and non-invasive) classical physics of a rotated classical spin vector!

The quantum-to-classical transition

Classical limit:Ensemble of classical spins with probability distribution g

Transition to Classicality: General state

General density matrix:

f can be negative!

Quantum

Hamilton operator:

Probability for result m:

Classical

Probability to detect in a slot:

g is non-negative!

Hamilton function:

Superposition versus Mixture

Coarse-graining Coarse-graining

Neighbouring slots(many slots)

Parity measurement(only two slots)

Violation of Macrorealism Classical Physics

1 3 5 7 ...

2 4 6 8 ...

Slot 1 (odd) Slot 2 (even)

No macrorealismdespite of coarse-graining

Unitary time evolution Ut

Ut is „non-classical“: It acts non-collectively only on two non-neighbouring sub-spaces

- Violation of macrorealism because of the „cosine-law“

- Coarse-graining does not help as j and –j are well separated

Quantum Physics Discrete Classical Physics(macrorealism)

Classical Physics(macrorealism)

inaccurate measurements

limit of large spinslimit of large spins

Macro Quantum Physics(no macrorealism)

macroscopic objects

macroscopic objects

Relation Quantum-Classical

1. Classical physics emerges from quantum laws under the restriction of coarse-grained measurements, not alone through the limit of large quantum numbers.

2. Conceptually different from decoherence. Not dynamical, puts the stress on observability and works also for fully isolated systems.

3. As the resources in the world are limited, there is a fundamental limit for observability of quantum phenomena (even if there is no such limit for the validity of quantum theory itself).

quant-ph/0609079

New Scientist (March 17, 2007)

Conclusions