Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
François Hénault Institut de Planétologie et d’Astrophysique de Grenoble Université Joseph Fourier Centre National de la Recherche Scientifique BP 53, 38041 Grenoble – France
Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Plan of the presentation
• Part 1 Semi-classical, heuristic interpretation of modern J. Bell’s experiments • Part 2 A quick look behind – Revisiting the Science story
Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
2
Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Sketch of modern Bell's experiments Y -Z
Detector D2+
Detector D2-
β
Polarizing beamsplitter PBS2
X
Entangled photons generator
α Exciting photons generator Detector D1-
Polarizing beamsplitter PBS1
Detector D1+
Z
• Measure correlations between the four detectors when varying PBS angles α and β Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Semi-classical interpretation • Assume a “hidden rule” stating that photon polarization states are opposite at their creation. Orientations of linearly polarized photons n°1 and 2 are [ λ, -λ] • Complies with the conservation law of cinematic momentum Y
Y
β
β α’
λ
λ α
α
X -λ λ
β’ λ’
Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
4
Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Equivalence with Quantum Physics • Joint detection probabilities between couples of detectors: 2
2π
[D1+, D2+]
P+ + =
∫ cos(α − λ ) cos(β − λ ) dλ
2π
= cos 2 (α − β ) / 4
0 2π
[D1-, D2-]
P− − =
∫ sin (α − λ ) sin (β − λ ) dλ 2π
2
= cos 2 (α − β ) / 4
0 2
2π
[D1+, D2-]
P+ − =
∫ cos(α − λ ) sin (β − λ ) dλ
2π
= sin 2 (α − β ) / 4
0 2
2π
[D1-, D2+]
P− + =
∫ sin (α − λ ) cos(β − λ ) dλ
2π
= sin 2 (α − β ) / 4
0
• Correlation coefficient:
E(α, β ) =
P+ + + P− − − P+ − − P− + P+ + + P− − + P+ − + P− +
= cos 2 (α − β )
• Complies with Quantum Physics – Allows violation of Bell's inequalities Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Are Bell’s inequalities applicable here? • Bell’s inequalities writes: - 2 ≤ S(α, β, α' , β' ) = E (α, β ) − E (α, β' ) + E (α' , β ) + E (α' , β' )
≤ +2
• No reason that λ stays common for each couple (α,β) and (α’, β’) because measurements are not simultaneous Y Y β
β α’
λ
λ α
α
X -λ λ
β’ λ’
Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
The EPR paradox (1/2) •
A. Einstein, B. Podolsky, N. Rosen, "Can Quantum-Mechanical description of physical reality be considered complete ?," Physical Review vol. 47, p. 777-780 (1935)
•
Definitions: – Physical reality: A parameter measurable from an experimental apparatus without disturbing it, and predictable by a physical theory – Completeness: A theory taking into account all elements of physical reality
•
Quantum Mechanics are based on Heisenberg’s Uncertainty Principle. Do they give a complete view of physical reality ? 1) If No, a more complete theory may exist 2) If Yes, we must accept the Uncertainty Principle and sacrifice our usual understanding of objective physical reality
•
To decide between hypotheses n°1 and 2, EPR descri bed a Gedanken experiment
Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
The EPR paradox (2/2) •
• • • • •
A. Einstein, B. Podolsky, N. Rosen, "Can Quantum-Mechanical description of physical reality be considered complete ?," Physical Review vol. 47, p. 777-780 (1935)
The EPR Gedanken experiment is based on intricated particles – Not necessarily photons It shows that some elements of physical reality (here the position and momentum of particles) can be determined simultaneously This contradicts hypothesis n°2, hence only hypoth esis n°1 is valid and Quantum Mechanics are not complete It finally seems that the main purpose of EPR was to defeat the Uncertainty Principle Additional remarks: – The paper strictly follows the formalism of Quantum Mechanics – No "modern" considerations about causality, non-locality, propagation of information faster than the speed of light, or hidden variables
Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Answer from N. Bohr •
N. Bohr, “Can Quantum-Mechanical description of physical reality be considered complete?,” Physical Review vol. 48, p. 696-702 (1935)
• EPR paradox was not the first attack against the Uncertainty Principle • In his answer, N. Bohr essentially discusses two previous Einstein’s ‘s Gedanken experiments involving photons only • He also suggests that intricated particles should be considered as a single global system instead of two independent systems ( Non locality ?) “Recoiling slits” Solvay conf. 1927
“Photon box” Solvay conf. 1930
∆x ∆p ≥ h/2π
∆E ∆t ≥ h/2π
Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
D. Bohm's interpretation •
D. Bohm, Y. Aharonov, “Discussion of experimental proof for the paradox of Einstein, Rosen and Podolsky,” Physical Review vol. 108, p. 1070-1076 (1957)
• New interpretation of the EPR paradox, based on contemporary quantum formalism • Measurements performed on spinned atoms should be equivalent to those of position and momentum of particles • No instantaneous “hidden interaction” between atoms can exist – This would violate the laws of special relativity • Spinned atoms experiment could be simplified by measuring correlations between polarizations of intricated photons • NOTA: In earlier papers (1952), Bohm firstly mentioned the possibility of “hidden variables”. But he abandoned this idea in his 1957 paper Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Bell's inequalities •
J. Bell, “On the Einstein Podolsky Rosen paradox,” Physics vol. 1, p. 195-200 (1964)
• Following Bohm’s ideas, Bell evoked experiments based on spinned particles – not photons – and Stern-Gerlach magnets detectors • There exists a huge quantity of Bell's inequalities. Here we used the Clauser, Horne, Shimony and Holt (CHSH) form: - 2 ≤ S(α, β, α' , β') = E(α, β ) − E(α, β') + E(α' , β ) + E(α' , β') ≤ + 2
• CHSH finally defined modern setups for testing Bell’s inequalities from photon polarization states, and four different polarizer angles • Later, the violation of Bell’s inequalities was experimentally demonstrated by Aspect et al, Weihs et al, and followers • This is currently considered as the ultimate proof of Quantum Physics completeness, but… Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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Can violations of Bell’s inequalities be considered as the final proof of quantum physics ?
Conclusion • We proposed a semi-classical model explaining the violation of Bell’s inequalities in modern experiments based on photons polarization • But these experiments do not seem to respect the original spirit of EPR paper, that consists in measuring position and momentum of any type of particle • The EPR paradox should be considered as the 3rd and last attack from Einstein against Heisenberg’s Uncertainty Principle • A final proof of the completeness of quantum physics theory remains to be demonstrated Conf. 8832 – The Nature of Light: What are Photons? V
San Diego, 08-28-13
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