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  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   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
Copenhagen
De Broglie-Bohm
Many worlds
Objective collapse
Micro world
not real
non-realistic
(mathematical tool)
Macro world
Nature of theory /
randomness
Collapse?
depends on
experiment
probabilistic /
irreducible
yes, due to
measurement
real
(guiding field)
realistic
realistic
deterministic /
“reducible”
no, measurement
reveals ignorance
universal: real
(many branches)
universal:
realistic
universal:
realistic
deterministic /
“irreducible”
no, branching (due
to decoherence)
depends (start with
Copenh. or Bohm)
depends
realistic
depends /
depends
objective collapse
of the wavefunction
Measurement problem
Copenhagen
De Broglie-Bohm
Many worlds
Objective collapse
Proponents
Critics
pseudo problem: measurement is a
primitive of the theory
measurement must be a physical process;
Heisenberg cut; realism given up
does not appear; particles have
deterministic trajectories
the theory is non-local, preferred frame
necessary, unobservable/hidden properties
solved: all measurement results are
realized; always unitary evolution
preferred basis problem; what is the
nature of (unobservable) alternate realities?
objective collapse solves the
measurement problem
change of quantum mechanical laws;
ad hoc; problem with energy conservation