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Quantum Mechanics, Locality and Realism (an amateur perspective) Marco G. Giammarchi – Infn Milano

Quantum Mechanics, Locality and Realism (an amateur perspective) Marco G. Giammarchi – Infn Milano. Quantum Mechanics as an abstract theory The Bohr-Einstein debate about Quantum Mechanics The EPR statement Bell’s Inequality: Locality and Realism Classical-Quantum boundary

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Quantum Mechanics, Locality and Realism (an amateur perspective) Marco G. Giammarchi – Infn Milano

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  1. Quantum Mechanics, Locality and Realism(an amateur perspective)Marco G. Giammarchi – Infn Milano Quantum Mechanics as an abstract theory The Bohr-Einstein debate about Quantum Mechanics The EPR statement Bell’s Inequality: Locality and Realism Classical-Quantum boundary Recent developments E. Schroedinger A. Einstein J. S. Bell A. Aspect W. Heisenberg LNGS - 28 June 2012

  2. Quantum Mechanics as an abstract theory • Quantum era was opened in 1900 (Planck’s Law) • Problems with the classical theory of matter (blackbody radiation, specific heat of solids, stability of atomic systems) • Early Quantum Physics (Bohr model) as a quantized classical theory Still correspondence between the objects of the theory and the physical concepts • Quantum Mechanics (end of 20’s) is an abstract theory • Amazingly succesful (currently, clearly “the best” theory. Actually a meta-theory) • Relativistic version could be produced (that predicted antimatter, actually discovered just after the prediction). LNGS - 28 June 2012

  3. Postulates of Quantum Mechanics Physical System  Hilbert Space with an inner product Physical States  Vectors in the (separable) Hilbert Space Hilbert Space of composite systems  Tensor Product of Hilbert Spaces of the subsystems Physical quantities  Self-adjont operators in the Hilbert Space No trivial correspondence between the objects of the theory and the physical concepts Physical Symmetries  (Anti)Unitary operators acting on Hilbert vectors (states) Some counter-intuitive characteristics: An intrinsically probabilistic theory The Heisenberg Uncertainty Principle LNGS - 28 June 2012

  4. Five Great Problems in Theoretical Physics (According to Lee Smolin) The problem of quantum gravity: Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature. The foundational problems of quantum mechanics: Resolve the problems in the foundations of quantum mechanics, either by making sense of the theory as it stands or by inventing a new theory that does make sense. The unification of particles and forces: Determine whether or not the various particles and forces can be unified in a theory that explains them all as manifestations of a single, fundamental entity. The tuning problem: Explain how the values of the free constants in the standard model of particle physics are chosen in nature. The problem of cosmological mysteries: Explain dark matter and dark energy. Or, if they don't exist, determine how and why gravity is modified on large scales. More generally, explain why the constants of the standard model of cosmology, including the dark energy, have the values they do. LNGS - 28 June 2012

  5. The Bohr-Einstein debate about Quantum Mechanics • A double shock to Albert Einstein: • Introduction of matrix formulation of Quantum Mechanics (W. Heisenberg), with no spacetime elements • Introduction of the probabilistic interpretation (M. Born) • A Einstein: “God does not play dice” • This was ok for Niels Bohr who strengthened the role of the (classical) observer: • Principle of Complementarity: Objects governed by quantum mechanics, when measured, give results that depend inherently upon the type of measuring device used • Einstein criticism: first phase: • Gedanken experiments to show that Uncertainty Principles can be violated • (measuring device had an absolute role) • Bohr’s anwers always included treatment of the measuring device LNGS - 28 June 2012

  6. About coherent superpositions Physical meaning of a "coherent superposition"? Any superposition of states is a possible state Young's hole experiment Interference fringes Addition of the probability amplitudes of each path Signature of a coherent superposition = interference fringes Quantum phase of the superposition = phase of the fringes LNGS - 28 June 2012

  7. Einstein versus the Uncertainty Principle : We picture the double slit as a coherent superposition of amplitudes on screen 2. Any experiment designed to evidence the corpuscolar part of the process (detection on b,c of the passing particle) would destroy the interference pattern No “welcher weg” information. • Einstein: when the particle goes through S1, it will receive an impulse along x • Mesure the recoil along x of the S1 screen • Use momentum conservation • Then the Vx of the particle is known • The momentum information can be used to know which path the particle has travelled without disrupting the interferecence pattern! Uncertainty Principle is violated (positions and velocity can be known, and the resulting interference pattern comes from a statistical mixture (since we know, event by event, the path chosen by the particle) LNGS - 28 June 2012

  8. Bohr response includes the measuring device as a quantum object: An extremely precise determination of the velocity of the screen S1 along x, involves some uncertainty on the x position of the screen itself. The uncertainty on the x position of S1 will change the path difference between the two paths a-b-d and a-c-d therefore washing away the interference patter on the screen F. During the Einstein-Bohr debate, Einstein considered physical quantities (and their interrelations) as existent without necessarily referring to the measurement process (REALISTIC approach). Bohr always considered the result of an experiment, including the role played by the measuring device (POSITIVISTIC approach) LNGS - 28 June 2012 LNGS - 28 June 2012

  9. The EPR statement The the famous EPR (Einstein, Podolsky, Rosen) 1935 paper it is shown that a consequence of Quantum Mechanics is the existence of long-distance correlations (Entanglement). According to Einstein this was the proof that Quantum Mechanics is (probabilistic because) incomplete. A complete theory would then contain elements that could explain the entanglement in a causal (deterministic) way. Einstein’s ideas (and personality) greatly influenced David Bohm, who built up a non-local theory based on the concept of pilot waves (Bohmian Mechanics) Real path Bohm, David (1952). "A suggested Interpretation of the Quantum Theory in Terms of Hidden Variables, I and II, Physical Review 85. Pilotwaves The particle will go through one single well defined slit but the (instantaneous, superluminal) pilot wave will “inform” the particle of the existence of the second slit. “Spooky action at a distance” LNGS - 28 June 2012

  10. The general idea of the EPR statement: If one considers the dissociation of a molecule : B A Suppose I measure σ(x;A)  by momentum conservation σ(x;B) is known Suppose I measure σ(y;A)  by momentum conservation σ(y;B) is known Suppose I measure σ(z;A)  by momentum conservation σ(z;B) is known σ(x,y,z;B) (all the components) is an element of reality (which can be measured without perturbing the system) But Quantum Mechanics allows to specify only a component (and the modulus square) of the B spin  Quantum Mechanis is an incomplete theory ! LNGS - 28 June 2012

  11. Bell’s Inequality: Locality and Realism After the EPR debate there was still hope that a local realistic theory (based perhaps on hidden variables) could be the ultimate theory of the micro-world ! A theory with hidden variables perhaps could be local (non-Bohmian, no spooky action at a distance) and deterministic A general criteron to confront Quantum Mechanics with a local realistic theory 1964, John Stewart Bell "On the Einstein Podolsky Rosen paradox" Bell demonstrated that local realism yields predictions that are in contradictions with Quantum Mechanics (and measurements) LNGS - 28 June 2012

  12. Bell’s Inequality (minimal version) A set of elements Three dichotomic variables (trivially true) Summing up: In the macroworld that seems obvious, but what if a is + polarization of a photon along axis a and a-bar is the negative polarization along the same axis? LNGS - 28 June 2012

  13. The study of correlated photons: same-angle polarimetry (J. Baggot – The meaning of Quantum Theory) source A B Orientation a Orientation a PA1 -- + h v h v -- + PA2 Initial state vector: (symmetric when A ↔ B) Measurement Eigenstates: PA1 PA2 • + + • + - • + • - - LNGS - 28 June 2012

  14. Now, express the state vector (in the base of circular polarizazion state) in the base of measurement (linear polarization) eigenstates: Probabilities of results: Using the conversion between linear and circular polarization eigenstates: LNGS - 28 June 2012

  15. Expectation values So, doing the joint measurement means: The expectation value of the measurement: Since A fully correlated measurement LNGS - 28 June 2012

  16. When the polarizers have different angles: source A B Orientation a Orientation b v Rotated with respect to PA1 v’ v h’ PA1 -- + h v h’ v’ -- + b-a h PA2 Initial state vector: (symmetric when A ↔ B) Measurement Eigenstates: PA1 PA2 • + + • + - • + • - - LNGS - 28 June 2012

  17. Now, express the state vector (in the base of circular polarizazion state) in the base of measurement (linear polarization) eigenstates: The coefficients are: Therefore the decomposition of the wave function: LNGS - 28 June 2012

  18. Probabilities for the joint results: Expectation of the a,b correlation: LNGS - 28 June 2012

  19. Quantum mechanical correlation ! The predictions of Quantum Mechanics are based on the properties of a two-particle state vecotr which, before collapsing into one of the measurement eigenstates is “delocalized” over the whole experimental arrangement. The two particles are in effect, always “in contact” prior to measurement and can therefore exhibit a degree of correlation that is impossible for two Einstein separable particles LNGS - 28 June 2012

  20. Quantum correlations and Bell’s Inequality These quantum correlation violate Bell’s Inequality. Let us in fact make the 3 following set of measurements: LNGS - 28 June 2012

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  22. What does it mean? Violation of Bell’s Inequality has been demonstrated in thousands of experiments (the first being the Aspect 1982 experiment) Between the assumptions of Bell’s Inequality there is the idea that physical quantities in the microwolrd exist before being measured (realism). This disagrees with the experiments. Quantum Mechanics (Copenhagen interpretation): we cannot talk about “real” quantities. We can only talk about quantities being measured. The observer is part of the physical system and there is no sharp subject/object separation. A little epistemological price to pay in order to use the most powerful physical theory ever invented (actually a meta-theory) Alternative (still alive): Bohmian Mechanics (with non-local pilot waves) LNGS - 28 June 2012

  23. Since old things are always new: Copenhagen interpretation (Bohr formulation) A quantum phenomenon comprises both the “observed” quantum system and the classical measuring apparata. It does not make any sense to speak about the quantum system in itself without specifying the measuring process (It is senseless to assign simultaneously complimentary attributes – like x,p – since they cannot be measured at the same time) The wave function is a representation of the quantum system An experimental prediction that surpasses the limitations of the theory is not possible in principle LNGS - 28 June 2012

  24. Entanglement Coherent superposition for a bipartite system "Entangled state" = non factorisable state No system is in a definite state Quantum correlations Violation of Bell's inequalities Correlations in all the basis V V The two photons form an EPR-pair H H S Anticorrelation

  25. Classical-Quantum Boundary How comes that a quantum system generates at the macroscopic level (on statistical ensembles) the classical probabilistic additive behaviour ? Decoherence A loss ofcoherenceof the phaseanglesbetween the componentsof a system in quantum superposition Decoherencehas the appearanceof a wavefunctioncollapse Itoccurswhen a system (irreversibly) interactswith the environment Itis the candidate theorytodeterminehowclassicalbehavioremergesfrom a quantum startingpoint LNGS - 28 June 2012

  26. Letus start withanentangled state, a system and a detector …andbuild up the density matrix A non unitaryevolutionprocessthatwillcanceloff-diagonal (phasedependent) terms Decoherence can be interpreted as classical coefficients LNGS - 28 June 2012

  27. The Schrödinger-cat paradox Entanglement of a microscopic system with a macroscopic one Atwo-level atomand acatin a box Total correlation The cat "measures" the atomic state Linear evolution The system form an EPR pair Quantum correlations Atom projected on |e>+|g> Cat projected on |dead>+|alive> Macroscopic state superposition

  28. Decoherence A macroscopic object interacts with its environment and gets entangled with it Coherent superposition (dead> and |alive>) Decoherence Statistical mixture (|dead> or |alive>) Classical correlations in the « natural » basis No interference between macroscopic states

  29. Classical Correlations Quantum Correlations LNGS - 28 June 2012

  30. The quantum-classical boundary Microscopic object Environment -3 parts -2 time scales Mesoscopicobject -Continuous monitoring of the environment -No entanglement -  ’Classical’ behavior -Entanglement -« Schrödinger cat » states -Quantum behavior Classical world Quantum world Continuous parameter to explore the quantum-classical boundary?

  31. Microscopic object (S) Environment (E) Mesoscopicobject (D) Now let us entangle the quantum system/detector wavefunction with the environment: When the states of the environment corresponding to the different states of the detector are orthogonal, the density matrix that describes the system-detector combination is obtained by tracing over the environment degrees of freedom: LNGS - 28 June 2012

  32. A modelofDecoherence Quantum system in interaction with the environment • Collectionofharmonicoscillators ? • A quantum field ? Environment ? A degree of arbitrariness here ! In a popular model a particle with position x and a potential One can demonstrate that in the high-T limit, the evolution of the density matrix is governed by the Master Equation: LNGS - 28 June 2012

  33. The Master Equation usual Hamiltonian term Frictional term (relaxation) Decoherence term The decoherencetermtendsto wash awayoff-diagonaltermsresponsiblefor quantum correlationofspatiallyseparatedwavepackets LNGS - 28 June 2012

  34. Howdoesit work? Let us start with a 2-gaussian wavepacket The matrix density features peaks that are on the x,x’ diagonal and peaks that are off-diagonal (which contains the quantum phases information) LNGS - 28 June 2012

  35. The effect of Is negligible for the on-diagonal terms while for the off-diagonal term it will give a decay rate : For a macroscopic object the decoherence time is many orders of magnitude smaller than the relaxation time. E.g. for m=1 g, T=300 K, separation of 1 cm : LNGS - 28 June 2012

  36. Recent Developments: long distance correlations Long distance correlations in quantum criptography La Palma – Tenerife 144 km PRL 98 (2007) 010504 Recent Developments: attosecond quantum interference Interference in the time-energy domain: the role of slits is being played by windows in time of attosecond duration (F. Lindner et al., PRL 95 (2005) 040401). LNGS - 28 June 2012

  37. Recent Developments: from elementary particles to big molecules Interference patterns in double-slit experiments with massive particles (de Broglie waves interference) In contrast to classical physics quantum interference can be observed when single particle arrive at the detector one-by-one Matter waves interference observed for : • Electrons, e.g. C. Johnsson, Z. Phys. 161 (1961) 454 • Neutrons, e.g. A. Zeilinger et al., Rev. Mod. Phys. 60 (1988) 1067. • Atoms, e.g. Phys. Rev. Lett. 61 (1988) 1580, Phys. Rev. Lett. 66 (1991) 2689. • Molecules, e.g. Science 266 (1994) 1345, Nature 41 (1999) 682, Science 331 (2011) 892. Nanofabrication and nanoimaging techniques allowed to study quantum interference patterns with molecules up to ≈ 1000 AMU e.g. Nature Nanotechnology (2012) doi10.1038/nnano.2012.34 LNGS - 28 June 2012

  38. Another Quantum-Classical boundary: particle size Particle “wavelength” Particle “size” In the normal situation for a particle POINTLIKE If the particle is a macromolecule New regime being explored where LNGS - 28 June 2012

  39. Fullerene experiment: Quantum interferometry experimental study of decoherence LNGS - 28 June 2012

  40. Conclusion (or beginning?) Quantum Mechanics : best theory ever in terms of numerical predictions Copenhagen Interpretation : (among other things) no sharp separation between observer and quantum system Entanglement at long distance Entanglement and classical size Alternative approach (Bohmian): non local. Still viable. Classical-Quantum boundary: decoherence as the candidate theory How can a theory that can account with precision for almost everything we can measure still be deemed lacking? The only “failure” of quantum theory is its inability to provide a natural framework that can accomodate our prejudices about the workings of the universe (W.H. Zurek). Or the workings of “us and the universe”. LNGS - 28 June 2012

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