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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 : n o i ! s e u l l c b a n o n c e t n e l u b e a r d a i o ) v m a s i n l u a e t r u l b a c l o u l f ( e s r e a s e C h 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....