The Measurement Problem

Quantum Foundations Seminar

Max Planck Institute of Quantum Optics

Munich, December 12th 2011

Johannes Kofler

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 mechanicsand 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-realisticrandomness: 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 through a guiding equation:

• Measurement: just reveals pre-existing propertiesno 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 collapsebranching into different real worlds (due to decoherence)

• Properties: at universal level: realistic & localno counterfactual definitenesssame 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 problemQuantum Darwinism: pointer states & einselection (interaction Hamiltonians)

• Effects of decoherence can be suppressed in well-controlled experimentsMacroscopic superpositions not forbidden in principle

• Important for the quantum-to-classical transitionImportant 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 10–7 m and rate per particle 10–16 s–1

Decay rate for N particles: N

• 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

Wavefunction Micro world Macro worldNature of theory /

randomnessCollapse?

Copenhagennot real

(mathematical tool)non-realistic

depends on experiment

probabilistic / irreducible

yes, due to measurement

De Broglie-Bohmreal

(guiding field)realistic realistic

deterministic / “reducible”

no, measurement reveals ignorance

Many worldsuniversal: real

(many branches)universal: realistic

universal: realistic

deterministic / “irreducible”

no, branching (due to decoherence)

Objective collapsedepends (start with Copenh. or Bohm)

depends realisticdepends /depends

objective collapse of the wavefunction

Measurement problem

Proponents Critics

Copenhagenpseudo problem: measurement is a

primitive of the theorymeasurement must be a physical process;

Heisenberg cut; realism given up

De Broglie-Bohmdoes not appear; particles have

deterministic trajectoriesthe theory is non-local, preferred frame

necessary, unobservable/hidden properties

Many worldssolved: all measurement results are

realized; always unitary evolutionpreferred basis problem; what is the

nature of (unobservable) alternate realities?

Objective collapseobjective collapse solves the

measurement problemchange of quantum mechanical laws;

ad hoc; problem with energy conservation