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Contexts, Systems and Modalities : a new ontology for Quantum Mechanics
Alexia Auffèves1 and Philippe Grangier2
1
Institut Néel, F38042 Grenoble, France
2 Institut
d’Optique, F91127 Palaiseau, France
Foundational Attitudes Toward
Quantum Mechanics : the lanscape
A Snapshot of Foundational Attitudes
Toward Quantum Mechanics
Maximilian Schlosshauer, Johannes
Kofler, Anton Zeilinger
Stud. Hist. Phil. Mod. Phys. 44, 222-230
(2013) arXiv:1301.1069 [quant-ph]
Poll at the conference
"Quantum Physics and the Nature of Reality"
Traunkirchen, Austria, July 2011
> 80 years after
the EPR-Bohr debate,
still quite a challenging
situation!
Sketch of the talk
Einstein and quantum physics
Albert Einstein is clearly a "founding father" of
quantum physics, but he is also the author of the
sharpest criticisms against it.
* A founding contribution (1905)
Light is made of quanta, lated named photons,
which have a well defined energy and
momentum. Nobel Prize 1921 (Millikan 1923).
* A fruitful objection (1935)
The quantum formalism allows for very peculiar situations when
one looks at pairs of entangled particles.
Spelled out in a famous article by Einstein, Podolsky, Rosen
(EPR) in 1935 : they propose a simple definition of reality and
locality, and conclude that the quantum formalism is "incomplete".
4
A debate for many decades
* EPR's conclusion : quantum mechanics is
incomplete (there is some "hidden information")
* Bohr disagrees, intense debate over many years
but not much attention from majority of physicists
• Quantum mechanics accumulates success:
•  Understanding nature: structure and properties of matter,
quantum theory of light, interactions between light and matter...
•  New concepts, and revolutionary inventions: transistor, laser…
•  No disagreement on the validity of quantum predictions, only
on its interpretation: debate considered as "philosophical".
The situation changed radically with Bell' theorem (1964)
and the acknowledgement of its importance (1969-82...).
5
Bell’s theorem in a nutshell...
+1
Entangled pair of photons
I
II
a ν
b
ν
2
1
λ
−1
S
+1
+1
λ
+1
−1
Consider local supplementary parameters theories (in
the spirit of Einstein’s ideas on EPR correlations):
Then the two photons of a same pair have a common property λ
A( λ ,a) = +1 or − 1
ρ( λ ) ≥ 0,
B( λ ,b) = +1 or − 1
∫ ρ(λ ) d λ = 1
Look at the polarization correlation coefficient E(a, b) = ( A B )av.λ
between the measurements results, then (Bell-CHSH inequalities) :
−2 ≤ S ≤ 2 with S = E(a,b) − E(a, b′ ) + E(a ′,b) + E(a ′, b′ )
a
But...
SQM = 2 2 = 2.828... > 2
b
Conflict !
a’
Experimental
b’ verdict ?
6
Four generations of experiments
Pioneers (1972-76): Berkeley, Harvard, Texas A&M
•  Convenient inequalities: CHSH (Clauser Horne Shimony Holt)
•  First results contradictory (Clauser = QM; Pipkin ≠ QM), but
clear trend in favour of Quantum mechanics (Clauser, Fry)
•  Significantly different from the ideal scheme
Experiments at Institut d’Optique (1977-82)
• A source of entangled photons of unprecedented efficiency
• Schemes closer and closer to the ideal GedankenExperiment
• Test of quantum non locality (relativistic separation)
Third generation experiments (1988-2014, many places...)
• New sources of entangled pairs
•  Separate closure of loopholes (improved locality, detection..)
• Entanglement at a large distance... towards Q. communications
Fourth generation experiments (2015 - ... )
•  Simultaneous closure of all loopholes (nearly ideal expts)
7
Experiment with variable polarizers
A. Aspect, Phys. Rev. D 14, 1944 (1976).
A( λ ,a,b)
Bell's locality hypothesis :
B( λ ,a,b)
ρ( λ ,a,b)
In an experiment with variable polarizers (switch faster than L / c),
results from relativistic causality (no faster than light influence) !
 Not possible with massive polarizer
 Possible with optical switches
a’
C1
PM
b’
ν1
S
a
ν2
C2
PM
b
Counters
Switches C1 and
C2 redirects light
• either towards
polarizer a or a'
• either towards
polarizer b or b'
Equivalent to
polarizers switching
on both sides !
8
Orsay’s source of pairs of
entangled photons (1980-82)
1
J
=
0
D
y
e
la
se
r
K
r
io
n
la
se
r
2
551 nm
ν
1
+
1
2
−
{ x, x
+ σ − ,σ +
+ y, y
}
}
J
=
1
t
r
=
5
ns
ν
2
423 nm
J
=
0
=
{ σ ,σ
Emission of two
entangled
photons by an
atomic cascade.
* Laser-induced two-photon
excitation of a cascade in a
Calcium 40 atomic beam.
 100 detected pairs per second
1% precision for 100 s counting
9
Experimental results
A. Aspect, P. Grangier, G. Roger, PRL 49, 91 (1982)
A. Aspect, J. Dalibard, G. Roger, PRL 49, 1804 (1982)
a’
C1
PM
ν1
S
ν2
a
C2
"Static polarizers" :
* violation by 40 st. dev.
within a few minutes
b’
PM
b
N(a,b) , N(a, b′ )
N(a ′,b) , N(a ′, b′ )
"Moving polarizers" :
* reduced signal
* data accumulation for
several hours
* switching uncorrelated
but not fully random
... but convincing results :
* Bell’s inequalities violated by 6 standard deviations.
* Each measurement space-like separated
from setting of distant polarizer
-> Einstein’s causality enforced
* Remaining "loopholes" : low efficiency, imperfect switching
10
:
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!
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t
B. Hensen et al., Nature 526, 682 (2015).
o
p
y
“Loophole-free Bell Inequality Violation Using
h
s
’
l
Electron Spins Separated by 1.3 Kilometres,”
Bel
M. Giustina et al., Phys. Rev. Lett. 115, 250401 (2015).
“Significant-Loophole-Free Test of
Bell's Theorem with Entangled Photons,”
L. K. Shalm et al., Phys. Rev. Lett. 115, 250402 (2015).
“Strong Loophole-Free Test of Local Realism,”
(...).
“Can Quantum-Mechanical Description of
Physical Reality be Considered Complete?”
A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47, 777 (1935) :
« One would not arrive at our conclusion by insisting that if the quantities P and Q
cannot be both simultaneously predicted, then they are not simultaneously real. This
would make the reality of P and Q (in the second system) depend upon the process of
measurement carried out on the first system, which does not disturb the second system
in any way. No reasonable definition of reality could be expected to permit this. »
N. Bohr, Phys. Rev. 48, 696 (1935) :
« EPR's criterion of physical reality contains an ambiguity in the meaning of "without in
any way disturbing a system". Of course there is no mechanical disturbance of the
system under investigation, but there is an influence on the very conditions which
define the possible types of predictions regarding the future behavior of the system.
These conditions constitute an inherent element of the description of any
phenomenon to which the term "physical reality" can be properly attached. »
What are these « very conditions » required by Bohr to speak
about the physical reality of quantum phenomena ?
Philosophical standpoint
Many physicists (including me) will support Physical Realism, understood as :
The purpose of physics is to study entities of the natural world, existing independently
from any particular observer's perception, and obeying universal and intelligible rules.
Many physicists (inc. me) look at certain and reproducible events as real, so we like :
If, without in any way disturbing a system, we can predict with certainty (i.e., with
probability equal to unity) the value of a physical quantity, then there exists an element
of physical reality corresponding to this physical quantity.
but Bell tests show that this view does not work as such... so don't forget Bohr :
The very conditions which define the possible types of predictions regarding the future
behavior of the system constitute an inherent element of the description of any
phenomenon to which the term "physical reality" can be properly attached.
Could all these statements be made compatible together ?
We will propose an answer later, but remember:
Sir Arthur Conan Doyle (1920's) : Once you eliminate the impossible,
whatever remains, no matter how improbable, must be the truth.
Sketch of the talk
Classical Physics :
Systems and Properties
Classical physics :
* A « System » is an entity of the natural world that can be isolated well enough to
carry physical properties with definite values, such as mass, charge, position...
* Such properties are measured by using devices external to the system, and
attributed to the system itself: a particle « has » a mass, a position, a velocity...
* Strictly speaking one should say: ..when it is measured by this given apparatus.
The complete specification of this apparatus will be called a « Context » , but it can
be forgotten in classical physics, only the results of the measurement matter.
* Once measured, the properties are « known », they can be measured repeatedly,
and the results can be predicted with certainty, taking into account the dynamical
evolution of the system : the properties « belong » to the system (ID card).
Quantum Physics :
Systems, Contexts, and Modalities
Quantum physics :
* A « System » is an entity of the natural world that can be isolated well enough
to carry properties with definite values, such as mass, charge, position...
* Such properties are measured by using devices external to the system, and the
complete specification of the measurement apparatus will be called a « Context »
* Once measured, the values of the properties can be measured repeatedly,
and the results can be predicted with certainty, in a given context.
* The set of definite (fully predictable) values of the physical properties
belongs jointly to the system and the context, and it will be called a modality.
*What is « real » is the combination of Context, System and Modality (CSM)
Usual langage (classical...) : a photon « has » a polarization oriented at 45°
CSM : the photon (system) is transmitted with certainty (modality)
through a polarizer oriented at 45° (context)
Ultimate reality
Observer
Context
System
Ultimate reality
Observer
Context
System
Ultimate reality
Observer
Context
System
Classical ontology :
the observer can know the "real"
physical properties of the system,
and the context is only used as an
auxiliary tool for measurements.
Usual quantum ontology : through
successive "entangling" interactions
and unitary evolution, the system
will include the context, and also
(ultimately ) the observer.
CSM ontology : the context appears
always between the system and the
observer, and definite values of the
relevant physical properties
(modalities) are attributed jointly to
the system and the context.
Element of physical reality vs modality
If, without in any way disturbing a system neither changing the context,
we can predict with certainty (i.e., with probability equal to unity) the
value of a physical quantity, then there exists an element physical reality
corresponding to this physical quantity. It is called a modality.
* This approach agrees with the « very conditions »
required by Bohr to make and to check
definite and reproducible predictions
(i.e. with objectivity, taken as contextual).
Ultimate reality
Observer
* However it also implies a boundary between
a quantum system and a classical context
(sometimes called « shifty split » in a deprecating sense).
Context
System
* The « split » is not a problem for CSM, because a modality is defined in terms
of both the system and the context, and the system cannot include the context.
« Quantum mechanics can explain anything, but not everything »
A. Peres and W. H. Zurek, Am. J. Phys. 50, 807 (1982)
The Quantization Principle
Now we have a good physical definition of a quantum state / modality , but what
prevents to have a unique context where all modalities would be defined ?
1. Within a given context, the modalities are mutually exclusive, i.e. if one of
them is true (realized), the other ones are wrong (not realized). In a
different context, there will be a different set of mutually exclusive modalities.
2. Modalities taken from two different contexts are generally « non mutually
exclusive », or « incompatible », i.e. if one one of them is true, one cannot tell
whether the other ones are true or wrong. Incompatible modalities are « nonclassical » : classically, it should be possible to distinguish them by making
more measurements, i.e. by extending the context.
3. Quantization principle : the number N of mutually exclusive modalities is
a property of the quantum system, and it is independant of the context.
Example of polarized photons
context
«x»
context
«+»
smoking
2 exclusive
modalities
woman
man
non smoking
1. context
«+»
2. context
«x»
3. context
«+»
Select
woman
Select
smoking woman
Select
man ? yes !
4 classical cases :
smoking man
smoking woman
non smoking man
non smoking woman
Classical conclusion:
Half of smoking women
are actually men !
Why nonsense ?
Because « smoking »
and « woman » are
non-exclusive modalities
(cannot be combined)
Usual langage (classical...) : the photon « has » a polarization oriented at 45°
CSM : the photon (system) is transmitted with certainty (modality)
through a polarizer oriented at 45° (context)
Why probabilities ?
The quantization principle implies that one must use probabilities !
Let us consider one system and two contexts C and C', with N modalities { bn }in
context C, and N modalities { bm’ } in context C’, where n and m go from 1 to N.
Combining the incompatible modalities bn and bm’ in a single context with 2N
modalities is forbidden by the quantization principle, like knowing with certainty
whether a photon will be transmitted or reflected both through a polarizer oriented
at 0°, and through a polarizer oriented at 45°, in conflict with N = 2.
Therefore the only relevant question that can be answered by the theory is:
if the initial modality is bn in context C, what is the probability for obtaining
modality bm’ in context C’ , if a measurement is performed in context C' ?
Probabilities are not related to any "ignorance", but to the ontology of the theory :
there is no "global context" where all modalities can be made mutually exclusive.
Sketch of the talk
From Einstein, Podolsky and Rosen to Bell's inequalities
Source S emitting pairs
of photons "1" and "2" in the quantum state :
(| x1 x2 > + | y1 y2 >)/√2
Entangled state !
« Hidden variables » or « supplementary parameters » denoted λ, with a normalized statistical distribution ρ(λ) :
ε1 = ± 1, ε2 = ± 1, E(θ1, θ2) =
then :
∑
ε1 ε2
∫ dλ ρ (λ)
= 1
∫ dλ ρ (λ) ε1 ε2 p(ε1 | λ, θ1) p(ε2 | λ, θ2)
-2≤S≤2
with :
S = E(θ1, θ2) + E(θ'1, θ2) + E(θ'1, θ'2)
E(θ1, θ'2)
locality /
freedom
of choice
One can get SQM = 2√2 => Conflict => Experiments => QM wins ! Modalities from entanglement
Alice
Singlet state: one modality,
among 4 mutually exclusive ones
Context 1+2
Bob
System 1+2
1/ Before measuring on one side, the ensemble of two particles has a modality,
i.e. it has definite predictable properties (e.g., it is in a singlet state : total spin = 0).
* However, it is impossible to attribute definite predictable properties (a modality) to
each of the particles taken separately (different contexts, incompatible modalities).
* Therefore the "local hidden variables" λ cannot be defined, and thus Bell's
inequalities cannot be demonstrated ! End of the story ?
* No ! because then, how to explain the correlations ? (classically, if there are
no properties "carried" by each subsystem, there are also no correlations).
Modalities from entanglement
Alice
Singlet state: one modality,
among 4 mutually exclusive ones
Context 1+2
Bob
System 1+2
Context 1
System 1
Alice
Bob
Alice and Bob make
measurements: one modality,
among 4 mutually exclusive
ones, incompatible with the
previous one: probabilities !
Context 2
System 2
Modalities from entanglement
Alice
Singlet state: one modality,
among 4 mutually exclusive ones
Bob
Context 1+2
System 1+2
Context 1
System 1
Alice
System 1
in Context 2
Bob
System 2
in Context 1
Context 2
System 2
2/ After measuring on one side (by Alice), what happens on Bob’s side ?
Just nothing ! But Alice can predict Bob’s state with certainty, in her context
Alice has the context, and Bob has the system, and both are needed !
They can be combined as a modality only in their common future.
Bell's hypothesis vs modalities:
where is the trick ? « Hidden variables » or « supplementary parameters » denoted λ, with a normalized statistical distribution ρ(λ) :
For Alice and Bob :
∫ dλ ρ (λ)
= 1
p(ε1, ε2 | λ, θ1, θ2) = p(ε1 | λ, θ1) p(ε2 | λ, θ2)
Initial modality denoted µ (fixed value), then new modality νA|B or νB|A (after one measurement)
(remember : modality = pure state, but belongs to the system and the context)
For Alice :
p(ε1, ε2 | µ, θ1, θ2)
= p(ε1 | µ, θ1) p(ε2 | µ, θ2, ε1, θ1)
= p(ε1 | µ, θ1) p(ε2 | θ2, νB|A [µ, ε1, θ1])
For Bob :
p(ε1, ε2 | µ, θ1, θ2) = p(ε2 | µ, θ2) p(ε1 | θ1, µ, ε2, θ2)
= p(ε2 | µ, θ2) p(ε1 | θ1, νA|B [µ, ε2, θ2])
* These equations obviously agree with QM, for any µ
* Sounds like "instantaneous reduction of the wave packet", but nothing at all
happens at Bob's site: the modality is defined locally at Alice's site, knowing µ.
Bell's hypothesis vs modalities:
where is the trick ? « Hidden variables » or « supplementary parameters » denoted λ, with a normalized statistical distribution ρ(λ) :
For Alice and Bob :
∫ dλ ρ (λ)
= 1
p(ε1, ε2 | λ, θ1, θ2) = p(ε1 | λ, θ1) p(ε2 | λ, θ2)
Initial modality denoted µ (fixed value), then new modality νA|B or νB|A (after one measurement)
(remember : modality = pure state, but belongs to the system and the context)
For Alice :
p(ε1, ε2 | µ, θ1, θ2)
= p(ε1 | µ, θ1) p(ε2 | µ, θ2, ε1, θ1)
= p(ε1 | µ, θ1) p(ε2 | θ2, νB|A [µ, ε1, θ1])
For Bob :
p(ε1, ε2 | µ, θ1, θ2) = p(ε2 | µ, θ2) p(ε1 | θ1, µ, ε2, θ2)
= p(ε2 | µ, θ2) p(ε1 | θ1, νA|B [µ, ε2, θ2])
* Two different "realities" for Alice and Bob ? No, a modality is a certainty in a
given context, but modalities in different contexts are related probabilistically.
* Second part of the formulas: same as changing context for a single photon.
Did we reach the objective ?
* A modality is a real physical phenomenon which requires a system and a
context to be defined. Given that, the ultimate origin of the quantum behaviour
is quantization (Rovelli, Zeilinger...), and quantum theory is universal.
Philosophical options...
Hard subjectivist ("crazy bayesian")
-  how certain are you that you are certain ?
-  a probability assignment is not a fact (Caves, Fuchs and Schack...)
- the fact : it is possible to design a set of measurements so that if you perform it
again and again on the same system it will give again and again the same result.
In such a case we tell that the system is in a well defined modality / quantum state.
Hard realist ("deceived lover of hidden variables")
- a state corresponds to a set of elements of physical reality (= the results can be
predicted with certainty and measured without changing in any way the system).
- the fact : reality is ok, but it must be attributed jointly to the context and the
system; then a modality is a quite acceptable element of physical reality
Philosophical options...
Hard platonist ("mathematical objects do exist")
-  a vector in an Hilbert space is not a mathematical tool, but a definition of reality
-  unitarity of evolution is basic, the observed classical world must "emerge" from it
- the fact : manipulating vectors (projectors) in an Hilbert space is the quantum
way to calculate probabilities, it is not a "reality". The "reality" is the modality,
i.e. the set of values of physical properties that you will obtain again and again
by performing measurements on the same system in the same context.
Super-hard platonist ("mathematical objects exist physically")
-  nothing else than | ψ ⟩ exist (within a universal | ψ ⟩ )
-  the many-world picture must be understood "ontologically"
- the fact : same as above, but not recognized as a fact : the only "facts" are about
| ψ ⟩ itself, so there is no way to agree (physical realism is gone).
Thank you for your attention !
Alexia Auffèves
Quantum physics
Grenoble, France
Nayla Farouki
Philosophy, epistemology
Grenoble, France
Thank you to Franck Laloë, Anthony Leverrier, François Dubois....