1. Faculty of Physics University of Vienna, Austria Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences Macroscopic Realism Emerging from Quantum Physics Johannes Koflerand Časlav Brukner 15th UK and European Meeting on the Foundations of Physics University of Leeds, United Kingdom, March 2007

2. Classical versus Quantum Phase space Continuity Newton’s laws Local Realism Macrorealism Determinism Hilbert space Events, ”Clicks” Schrödinger + Projection Violation of Local Realism Violation of Macrorealism Randomness - Does this mean that the classical world is substantially different from the quantum world? - When and how do physical systems stop to behave quantumly and begin to behave classically?

3. 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.” Q(t1) Q(t2) t t1 t2 t = 0

4. t Quantity: Q Temporal correlations All macrorealistic theories fulfill the Leggett–Garg inequality t = 0 t t1 t2 t3 t4 Violation  no objective properties prior to and independent of measurements

5. for When is macrorealism violated? Spin-1/2 Evolution Observable 1/2 Violation of macrorealism Classical Spin precession around x +1 classical Macrorealism –1

6. Violation of macrorealism for macroscopically large spins? Spin-j precession in magnetic field (totally mixed state!) j Parity of eigenvalue m of Jzmeasurement classical limit Violation of macrorealism for arbitrarily large spins j Shown for local realism [Mermin, Peres]

7. The quantum-to-classical transition 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!

8. Transition to Classicality: General state Quantum Classical Probability to detect in a slot: General density matrix: f can be negative!  Probability for result m: g is non-negative! Hamilton operator: Hamilton function: Classical limit: Ensemble of classical spins with probability distribution g

9. Superposition versus Mixture

10. Coarse-graining  Coarse-graining Parity measurement (only two slots) Neighbouring slots (many slots) 1 3 5 7 ... 2 4 6 8 ... Slot 1 (odd) Slot 2 (even) Violation of Macrorealism Classical Physics

11. No macrorealism despite 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

12. Relation Quantum-Classical inaccurate measurements Discrete Classical Physics (macrorealism) Quantum Physics macroscopic objects macroscopic objects limit of large spins limit of large spins Macro Quantum Physics (no macrorealism) Classical Physics (macrorealism)

13. Conclusions • Classical physics emerges from quantum lawsunder the restriction of coarse-grained measurements, not alone through the limit of large quantum numbers. • Conceptually different from decoherence. Not dynamical, puts the stress on observability and works also for fully isolated systems. • As the resources in the world are limited, there is a fundamental limit for observabilityof quantum phenomena (even if there is no such limit for the validity of quantum theory itself). quant-ph/0609079 New Scientist (March 17, 2007)