Underdetermination in Quantum Physics
- or: how to conceive unconceived alternatives?
Markus Aspelmeyer
Faculty of Physics, University of Vienna
3 roads towards unconceived alternatives
• Find experimental data that falsifies the theory
• Find hints that the theory is not complete
• Accept it (= find a new conceptual basis to go
beyond the existing theory)
„There is nothing new to
be discovered in physics
today […]“
„…only two little clouds
[…] on the blue sky of
physics […]“
1900
Lord Kelvin (1824-1907)
Two unresolved questions
Why the quantum ?
single-photon
source
„C
“
K
C
I
L
Why the classical ?
Schrödinger‘s cat IS alive…
Objective randomness: „Why the quantum?“
detector 1
beamsplitter
detector 2
Quantum theory does not provide
a cause for the individual result 
Objective randomness
“The Weakness of the Theory lies ... in
the Fact, that Time and Direction of the
Elementary Process are left to
„Chance“.”
A. Einstein, 1917 Z. Physik
Beyond Probabilities?
Quantum theory:
probabilistic predictions for individual events
Can one go beyond this?
Verschränkung / Entanglement
• non-separable quantum states
• state describes only joint correlations
• no information on individual subsystems
Erwin Schrödinger
Naturwissenschaften 23, 807 (1935)
Verschränkung / Entanglement
EPR
EPR(1935)
(1935)
„it
„itisispossible
possibletotoassign
assigntwo
twodifferent
differentwave
wavefunctions
functionstotothe
thesame
samereality“
reality“
Schrödinger
Schrödinger(1935)
(1935)
„Verschränkung
„Verschränkungder
derVoraussagen“
Voraussagen“(entanglement
(entanglementofofpredictions)
predictions)
„Verschränkung
„Verschränkungunseres
unseresWissens
Wissensum
umdie
diebeiden
beidenKörper“
Körper“(entanglement
(entanglementofofour
our
knowledge)
knowledge)
Psi-Funktionen
sich
• non-separable
quantum
states (tangled
Psi-Funktionenhaben
haben
sich„verheddert“
„verheddert“
(tangledup)
up)
„Verquickung“
der
Erwartungskataloge
(mixing
„Verquickung“
deronly
Erwartungskataloge
(mixingofofexpectation-catalogue)
expectation-catalogue)
• state
describes
joint correlations
•
„„Verschränkung“
Verschränkung“ 
Entanglement

no information onEntanglement
individual subsystems
Erwin Schrödinger
Naturwissenschaften 23, 807 (1935)
Beyond Probabilities?
Einstein, Podolsky, Rosen, Phys. Rev. 47, 777 (1935):
Measurements on entangled systems provide „elements of physical reality“
that are not contained in the quantum mechanical description
(=incompleteness)
Some (out of many) replies:
Bohr, Phys. Rev. 48, 696 (1935)
Peres, quant-ph 0310010 (2003)
Bell‘s Theorem / GHZ Theorem
J. S. Bell, Physics 1, 1 (1964)
Greenberger, Horne, Zeilinger (1989)
A) Predictions of quantum theory are correct
B) Realism:
The outcome of any measurement depends on
properties carried by the system prior to and
independent of the measurement
C) Locality:
The outcome of any meaurement is independent
of actions in space-like separated regions.
Bell’s
Bell’stheorem:
theorem:granted
grantedA),
A),either
eitherB)
B)or
orC)
C)or
orboth
bothfail
fail
experimentally testable using entangled particles
Alice
-1
1
1 2
1
Entangled
Source
Bob
2
-1
1
Bell‘s Theorem
Alice
-1
1 2
„Entangled“
Source
1
Bob
1 2
-1
1
A1=±1,
A2 = ±1
B1= ± 1,
B2 = ± 1
Correlation function: E21=p(A2B1=1)–p(A2B1=-1)
Local Realism:
E11+E12+E21-E22 ≤ 2
Quantum Mechanics:
Bell 1964, CHSH 1969, Bell 1971, CH 1974, GHZ 1989
2 2
Laser
BBO
Alice
Bob
Bell Experiments
PRL 28, 938 (1972)
Approx. 0.1 events per second
(1 nm bandwidth)
Bell Experiments
PRL 28, 938 (1972)
Other
Otherrelevant
relevantexperiments:
experiments:
Clauser
ClauserPRL
PRL36,
36,1223
1223(1976)
(1976)
Fry
Fry&&Thompson
ThompsonPRL
PRL37,
37,465
465(1976)
(1976)
Aspect
Aspectet
etal.,
al., PRL
PRL47,
47,460(1981)
460(1981)
Aspect
Aspectet
etal.,
al.,PRL
PRL49,
49,1804
1804(1984)
(1984)
Perrie
Perrieet
etal.,
al., PRL
PRL54,
54,1790
1790(1985)
(1985)
Weihs
Weihset
etal,
al,PRL
PRL81,
81,5039
5039(1998)
(1998)
Rowe
Roweet
etal.,
al.,Nature
Nature409,
409,791
791(2001)
(2001)
…
…
Approx. 0.1 events per second
(1 nm bandwidth)
Entanglement & Bell test over 144 km, Scheidl, Zeilinger et al. (2008)
Greenberger-Horne-Zeilinger (GHZ) Theorem
Elements of reality to x,y operations: Xi, Yi = ± 1
Correlations: Y1Y2X3=-1, Y1X2Y3=-1, X1Y2Y3=-1
Local realism:
Quantum physics:
X1X2X3 = -1
X1X2X3 = +1
Alice (1)
-1
Entangled
source
1 2
1
Bob (2)
1 2
1
1 2
A1=±1 XA
A2 = ±1  YA
-1
Claire (3)
1
-1
C1=±1 XC
C2 = ±1  YC
B1= ± 1  XB,
B2 = ± 1  YB
Greenberger, Horne, Zeilinger, in: Bell's Theorem, Quantum Theory, and Conceptions of the Universe (1989)
GHZ experiments
A consistent set
of elements of
reality is
IMPOSSIBLE for
GHZ states
Pan, Bouwmeester, Zeilinger, Nature 403, 515 (2000)
What is left?
Local
Localrealistic
realistictheories
theoriesare
areinconsistent
inconsistent
with
withpredictions
predictionsof
ofquantum
quantumtheory
theory
with
withexperimental
experimentalobservation
observation
Which assumption is wrong?

Locality? (non-local realistic theories)

Realism? (local non-realistic theories)

Locality and realism? (non-local non-realistic theories)
Beyond Bell: Leggett‘s incompatibility theorem
Alice
-1
1 2
„Entangled“
Source
1
A1=±1,
A2 = ±1
Bob
1 2
-1
1
„geisterhafte Fernwirkung“
B1= ± 1,
B2 = ± 1
(A)
(A)Measurement
Measurementoutcomes
outcomesare
aredetermined
determinedby
bypre-existing
pre-existing
properties
propertiesof
ofparticles
particlesindependent
independentof
ofthe
themeasurement
measurement(realism).
(realism).
(B)
(B)Physical
Physicalstates
statesare
arestatistical
statisticalmixtures
mixturesof
ofsubensembles
subensembleswith
with
definite
definitepolarisation
polarisation
(C)
(C)polarisation
polarisationisisdefined
definedsuch
suchthat
thatexpectation
expectationvalues
valuestaken
takenfor
for
each
eachsubensemble
subensembleobey
obeyMalus’
Malus’Law.
Law.
A.J. Leggett, Found Phys. 33, 1469 (2003)
Gröblacher, Paterek, Kaltenbaek, Brukner, Zukowski, Aspelmeyer, Zeilinger (2007)
Beyond Bell: Leggett‘s incompatibility theorem
A. J. Leggett, Found. Phys.33, 1469 (2003)
Wu & Shaknow (1950), Kocher & Commins (1967)
CHSH (1969), Freedman & Clauser (1972)
Leggett (2003), Gröblacher et al. (2007)
Bell’s theorem:
local realistic theories are at variance with observable quantum phenomena
Leggett’s theorem:
a broad class of non-local realistic theories (crypto-nonlocal) are at variance with
observable quantum phenomena
Gröblacher, Paterek, Kaltenbaek, Brukner, Zukowski,
Aspelmeyer, Zeilinger, Nature 446, 871 (2007)
Beyond Bell: Leggett‘s incompatibility theorem
A. J. Leggett, Found. Phys.33, 1469 (2003)
Wu & Shaknow (1950), Kocher & Commins (1967)
CHSH (1969), Freedman & Clauser (1972)
Leggett (2003), Gröblacher et al. (2007)
Bell’s theorem:
local realistic theories are at variance with observable quantum phenomena
Leggett’s theorem:
a broad class of non-local realistic theories (crypto-nonlocal) are at variance with
observable quantum phenomena
Gröblacher, Paterek, Kaltenbaek, Brukner, Zukowski,
Aspelmeyer, Zeilinger, Nature 446, 871 (2007)
Why the classical?
The challenge(s) of macroscopic systems
Schrödinger‘s Cat: The Measurement Problem
E. Schrödinger, Naturwissenschaften 23, 52 ff. (1935)
single-photon
source
Schrödinger’s Cat = Entanglement involving macroscopically distinct states
should be possible for arbitrarily large systems
A mechanical cat? Schrödinger‘s mirrors
x ~ F / k
What is „the classical“?
Does it exist BY PRINCIPLE (=beyond quantum theory)
or for all practical purposes (FAPP)?
“new physics”
(Penrose, GRWP,
Karolyhazy, Diosi, ...)?
y”
t
i
s
s
ce
e
n
l
’s
ca
i
n
g
e
o
g
l
“
ha
n
e
p
(Co en cut,
gold ty, ...)?
xi
e
l
p
com
“st
dec anda
rd
ohe
(qu rence
dar antum ”
wi n
ism
)?
(c) Oppenheim
Schrödinger‘s Cat: The Dilemma
Why is it problematic?
Against intuition I: For certain „states“ in nature we tend to believe that
they are dichotomic and mutually exclusive (they either „ARE“ or „ARE
NOT“)
Against intuition II: The „reincarnation beamsplitter“ or the „arrow of
time“ argument… i.e. for some states in nature we tend to believe that
they are „irreversible“ (e.g. ‚click in a detector‘or death‘)
Ad II: The arrow of time problem
How to observe the (macroscopic) superposition state?
 measurement in „correct“ basis = re-coherence at a beamsplitter

„alive“
p=1
BS
BS

„dead“
BS
BS
alive / p = 1
The resurrection beamsplitter !!??
Bell II? An incompatbility theorem for Macro-Realism
Macrorealism = The conjecture that at some level of physics quantum
superpositions of macroscopically distinct states do not exist
An incompatibility theorem?
A) Quantum Theory is correct
For all macrorealsitic
theories
Violated by QM
B) A macroscopic object with several possible macroscopically distinct states is,
at any time, always in one of these states (macrorealism)
C) It is possible to determine in which state the system is without in any way
disturbing the system or its dynamics (non-invasive measurability)
Leggett-Garg: Provided A) is correct, either B) or C) have to be wrong
experimentally testable bound for correlations
Collapse by nonlinearity?
Nonlinear extensions of the Schrödinger equation could generate a „collapse“ (BBM 1976)
Experimental test via diffraction of neutrons (GKZ 1981)  falsification of BBM
Bialynicki-Birula, Mycielski, Ann. Phys. 100, 62 (1976)
Shimony, PRA 20, 394 (1979)
Gähler, Klein, Zeilinger, PRA 23, 1611 (1981)
Also: nonlinearities are
•inconsistent with 2nd law (Peres) and
•can allow for signaling (Weinberg, Gisin)
Collapse by gravity?
Karolhyhazy (1960s)
Diosi (1980s)
Penrose (1980s)…
Marshall, Simon, Penrose,
Bouwmeester, PRL 91, 130401 (2003)
also: A.D. Armour, M.P.
Blencowe, and K. Schwab,
PRL 88, 148301 (2002.)
R. Penrose, in:
Quantum
[Un]Speakables,
Springer 2001
number of particles in experiment
Current Experiments
100000
E. Schrödinger, August 1952
10000
1000
C60 Arndt et al.
100
TPP Hackermüller et al
10
1
1950
1960
1970
1980
Year
1990
2000
2010
Message of the quantum: Another unconceived alternative…
What are the foundational principles of the existing theory?
What does it tell us about nature?
What exists?
Registered events
What are the fundamental buiding blocks of the world?
Information on probabilities about possible measurement
outcomes
Why quantum theory?
Because it is a necessary framework for a theory „about
observation“
“Lieber Schrödinger!
Du bist faktisch der einzige Mensch, mit dem ich mich
wirklich gern auseinandersetze. [...] Dabei sind wir in der
Auffassung des zu erwartenden Weges schärfste
Gegensätze.
[...]”
Albert Einstein to Erwin Schrödinger, 8.8.1935
Einstein‘s gun powder & Schrödinger‘s cat
“Das System sei eine Substanz in einem chemisch labilen
Gleichgewicht, etwa ein Haufen Schiesspulver, der sich
durch innere Kräfte entzünden kann [...] . Im Anfang
charakterisiert die -Funktion einen hinreichend genau
definierten Zustand. Deine Gleichung sorgt aber dafür,
dass dies nach Verlauf eines Jahres gar nicht mehr der Fall
ist. Die -Funktion beschreibt dann vielmehr eine Art
Gemisch von noch nicht und von bereits explodiertem
System. Durch keine Interpretationskunst kann diese Funktion zu einer adäquaten Beschreibung eines
wirklichen Sachverhaltes gemacht werden; in Wahrheit gibt
es eben zwischen explodiert und nicht-explodiert kein
Zwischending
Albert Einstein to Erwin Schrödinger, 8.8.1935
[...]”