Macroscopic Realism Emerging from Quantum Physics

1
Macroscopic Realism Emerging from Quantum Physics
Faculty of Physics University of Vienna, Austria
Institute for Quantum Optics and Quantum
Information Austrian Academy of Sciences

• Johannes Kofler and Caslav Brukner
• 15th UK and European Meeting on the Foundations
  of Physics
• University of Leeds, United Kingdom, March 2007

2
Classical versus Quantum
Phase space Continuity Newtons laws Local
Realism Macrorealism Determinism
Hilbert space Events, Clicks Schrödinger
Projection Violation of Local Realism Violation
of Macrorealism Randomness
- Does this mean that the classical world is
substantially different from the quantum world?
- When and how do physical systems stop to behave
quantumly and begin to behave classically?
3
Macrorealism
LeggettGarg (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.
Q(t1)
Q(t2)
t
t1
t2
t 0
4
?t
Dichotomic quantity Q Temporal
correlations All macrorealistic theories
fulfill the LeggettGarg inequality
t 0
t
t1
t2
t3
t4
Violation ? no objective properties prior to
and independent of measurements
5
When is macrorealism violated?
Spin-1/2
Evolution Observable
1/2

Violation of macrorealism
Classical Spin
precession around x
1
classical
Macrorealism
1
6
Violation of macrorealism for macroscopically
large spins?
Spin-j precession in magnetic field
(totally mixed state!)
j
Parity of eigenvalue m of Jz measurement
classical limit
Violation of macrorealism for arbitrarily large
spins j
Shown for local realism Mermin, Peres
7
The quantum-to-classical transition
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!
8
Transition to Classicality General state
Quantum
Classical
General density matrix
Probability to detect in a slot
f can be negative!
?
Probability for result m
g is non-negative!
Hamilton operator
Hamilton function
Classical limit Ensemble of classical spins with
probability distribution g
9
Superposition versus Mixture
10
Coarse-graining ? Coarse-graining
Neighbouring slots (many slots)
Parity measurement (only two slots)
1 3 5 7 ...
2 4 6 8 ...
Slot 1 (odd)
Slot 2 (even)
Violation of Macrorealism
Classical Physics
11
No macrorealism despite of coarse-graining
Unitary time evolution Ut

• Ut 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

12
Relation Quantum-Classical
inaccurate measurements
Discrete Classical Physics (macrorealism)
Quantum Physics
macroscopic objects
macroscopic objects
limit of large spins
limit of large spins
Classical Physics (macrorealism)
Macro Quantum Physics (no macrorealism)
13
Conclusions

• Classical physics emerges from quantum laws under
  the restriction of coarse-grained measurements,
  not alone through the limit of large quantum
  numbers.
• Conceptually different from decoherence. Not
  dynamical, puts the stress on observability and
  works also for fully isolated systems.
• 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/0609079
• New Scientist (March 17, 2007)