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 Physics University of Vienna, Austria Institute for Quantum Optics and Quantum Information Austrian 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 t1t1 t2t2 Q(t1)Q(t1)Q(t2)Q(t2)

Dichotomic quantity: Q Temporal correlations All macrorealistic theories fulfill the Leggett–Garg inequality t = 0 t t1t1 t2t2 t3t3 t4t4 t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 J z 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 MacrorealismClassical Physics Slot 1 (odd)Slot 2 (even)

No macrorealism despite of coarse-graining Unitary time evolution U t U t 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 spins Macro Quantum Physics (no macrorealism) 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/ New Scientist (March 17, 2007) Conclusions