The Measurement Problem Johannes Kofler Quantum Foundations Seminar Max Planck Institute of Quantum Optics Munich, December 12 th 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: Brukner, Zeilinger: quantum Bayesianism, degrees of belief 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 Q k (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 E G of the difference between the mass distributions as a measure Heisenberg uncertainty leads to lifetime of the superposition:
Summary Wavefunction Micro world Macro world Nature of theory / randomness Collapse? Copenhagen not real (mathematical tool) non-realistic depends on experiment probabilistic / irreducible yes, due to measurement De Broglie-Bohm real (guiding field) realistic realistic deterministic / reducible no, measurement reveals ignorance Many worlds universal: real (many branches) universal: realistic universal: realistic deterministic / irreducible no, branching (due to decoherence) Objective collapse depends (start with Copenh. or Bohm) depends realistic depends / depends objective collapse of the wavefunction Proponents Measurement problem Critics Copenhagen De Broglie-Bohm Many worlds Objective collapse pseudo problem: measurement is a primitive of the theory does not appear; particles have deterministic trajectories solved: all measurement results are realized; always unitary evolution objective collapse solves the measurement problem measurement must be a physical process; Heisenberg cut; realism given up the theory is non-local, preferred frame necessary, unobservable/hidden properties preferred basis problem; what is the nature of (unobservable) alternate realities? change of quantum mechanical laws; ad hoc; problem with energy conservation