The Measurement Problem

Johannes Kofler

Quantum Foundations Seminar Max Planck Institute of Quantum Optics Munich, December 12th 2011 The measurement problem

Different aspects:

• How does the wavefunction collapse occur? Does it even occur at all? • How does one know whether something is a system or a measurement apparatus? When does one apply the Schrödinger equation (continuous and deterministic evolution) and when the projection postulate (discontinuous and probabilistic)? • How real is the wavefunction? Does the measurement only reveal pre-existing properties or “create reality”? Is quantum randomness reducible or irreducible? • Are there macroscopic superposition states (Schrödinger cats)? Where is the border between quantum mechanics and classical physics? The Kopenhagen interpretation

• Wavefunction: mathematical tool, “catalogue of knowledge” (Schrödinger) not a description of objective reality • Measurement: leads to collapse of the wavefunction (Born rule) • Properties: wavefunction: non-realistic randomness: irreducible • “Heisenberg cut” between system and apparatus: “[T]here arises the necessity to draw a clear dividing line in the description of atomic processes, between the measuring apparatus of the observer which is described in classical concepts, and the object under observation, whose behavior is represented by a wave function.” (Heisenberg) • Classical physics as limiting case and as requirement: “It is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms.” (Bohr) “I am unable to prove mathematically that the condition of irreversibility would suffice to define a classical approximation, but I feel confident it is a necessary condition.” (von Weizsäcker) The Kopenhagen interpretation

Many modern variants:

• Based on decoherence: Consistent histories: wavefunction collapse substituted by decoherence (Omnès, Hartle, Gell-Mann, Griffiths) • Information theoretic: Clifton, Bub, Halvorson: no signaling, no broadcasting, no bit commitment Caves, Fuchs, Schack: “quantum Bayesianism”, degrees of belief Brukner, Zeilinger: an elementary system carries one bit of information De Broglie–Bohm interpretation

• Wavefunction: “quantum field” or “guiding potential” or “pilot wave” evolves according to Schrödinger equation

• In addition: actual configuration of particle positions Qk (hidden variables) • Velocities are determined by the wavefunction ψ through a guiding equation:

• Measurement: just reveals pre-existing properties no collapse • Properties: wavefunction: real, deterministic evolution (trajectories) randomness: reducible (ignorance of initial conditions, equilibirum hypothesis) non-local (non Lorentz-invariant, preferred frame) same predictions as standard quantum mechanics • No backaction: “[T]he Schrödinger equation for the quantum field does not have sources, nor does it have any other way by which the field could be directly affected by the condition of the particles.” (Bohm and Hiley) De Broglie–Bohm interpretation

• Trajectories in the double slit experiment

Source: http://commons.wikimedia.org/wiki/File:Doppelspalt.svg Many worlds (Everett) interpretation

• Wavefunction: universal wavefunction has objective reality • Measurement: no collapse branching into different real worlds (due to decoherence) • Properties: at universal level: realistic & local no counterfactual definiteness same predictions as standard quantum mechanics • Problem of preferred basis: Why does Schrödinger’s cat branch into |alive〉 or |dead〉 and not into |alive〉+|dead〉 or |alive〉–|dead〉?

Source: http://en.wikipedia.org/wiki/File:MWI_Schrodingers_cat.png Many worlds (Everett) interpretation

• Problem of interpreting probabilities: “The measure of existence of a world quantifies its ability to interfere with other worlds in a gedanken experiment.” (Vaidman) • Claim (Deutsch and others): Many-worlds interpretation is testable against Copenhagen interpretation by showing interference of different worlds (undoing a detection process) • However: In Copenhagen the border between quantum and classical is not the same as between microscopic and macroscopic (Bohr-Einstein Solvay debates) Decoherence

• Loss of coherence due to interaction of a system with its environment • Solves a weak form of the measurement problem: Explains why off-diagonal terms of density matrices vanish rapidly

→

• Does not answer the strong form: How and why a particular result is realized in a measurement • Preferred-basis problem Quantum Darwinism: pointer states & einselection (interaction Hamiltonians) • Effects of decoherence can be suppressed in well-controlled experiments Macroscopic superpositions not forbidden in principle • Important for the quantum-to-classical transition Important for the many-worlds-interpretation (branching) Important for the consistent histories interpretation (“Copenhagen without collapse”) Objective collapse models

• Phenomenological theories Alter the laws of quantum physics

• Avoid superpositions of macroscopically distinct states Create objective reality at the macroscopic level

• Properties: quantum mechanical at microlevel classical on the macrolevel objective collapse of the wavefunction in principle experimentally testable

• Examples: GRW, Penrose, and others Ghirardi, Rimini, Weber (GRW)

• Non-quantum mechanical background noise leads to spontaneous localization Schrödinger equation gets supplemented by a stochastic non-linear term

• 2 free parameters: distance σ ∼ 10–7 m and rate per particle λ ∼ 10–16 s–1 Decay rate for N particles: N λ

• Pearle: relativistic generalization (GRWP)

• Problem: energy conservation, “tails” Penrose

• Gravitational collapse • Consider two distinct states of a massive object

• Which ∂/∂t operator should one take for the superposition

• ∂/∂t operator is linked to classical space-time of different branches • Approximate identification between space-times

• Error corresponds to uncertainty in energy: gravitational self energy ∆EG of the difference between the mass distributions as a measure • Heisenberg uncertainty leads to lifetime of the superposition: Summary

Nature of theory / Wavefunction Micro world Macro world Collapse? randomness

not real depends on probabilistic / yes, due to Copenhagen non-realistic (mathematical tool) experiment irreducible measurement real deterministic / no, measurement De Broglie-Bohm realistic realistic (guiding field) “reducible” reveals ignorance universal: real universal: universal: deterministic / no, branching (due Many worlds (many branches) realistic realistic “irreducible” to decoherence) depends (start with depends / objective collapse Objective collapse depends realistic Copenh. or Bohm) depends of the wavefunction

Measurement problem Proponents Critics

pseudo problem: measurement is a measurement must be a physical process; Copenhagen primitive of the theory Heisenberg cut; realism given up does not appear; particles have the theory is non-local, preferred frame De Broglie-Bohm deterministic trajectories necessary, unobservable/hidden properties solved: all measurement results are preferred basis problem; what is the Many worlds realized; always unitary evolution nature of (unobservable) alternate realities? objective collapse solves the change of quantum mechanical laws; Objective collapse measurement problem ad hoc; problem with energy conservation