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Spooky action at distance also for neutral kaons? What has CP violation to do with nonlocality? by Beatrix C. Hiesmayr Faculty of Physics University of Vienna Austria Physics Particle Physics Quantum Theory Discrete 2008, Beatrix C. Hiesmayr What does Particle Physics teach us about QM? ... a lot!! Is there nonlocality also in high energy systems? Are Bell inequalities violated? Particle physics? photons, atoms, single neutrons, ... Spooky action at distance also for neutral kaons? Discrete 2008, Beatrix C. Hiesmayr The EPR scenario Antisymmetric Bell state: 12 l 1 2 1 2 1 2 1 2 1 2 0 H K B I l 1 0 l 0 l l l 1 l 0 r V l r r K V 0 0 r ... photon B II 0 B0 l l r ... kaon ... B-meson r l r r ... spin 1/2 K0 r B ... qubit H l K 0 r r r ... single neutron in interferometer Discrete 2008, Beatrix C. Hiesmayr The EPR scenario 1935: Einstein-Podolsky-Rosen-PARADOX Completeness of the theory: “Every element of the physical reality must have a counterpart in the theory” Quantum theory is not complete! Discrete 2008, Beatrix C. Hiesmayr What are Bell inequalities? No spooky action at distance! realism locality free will Local realistic theories: Quantum Mechanics: P (a , b) P (a , c ) P (c , b) inequalities for probabilities always satisfied! quantum mechanical probabilities may violate the inequalities! Experiment has to decide! Discrete 2008, Beatrix C. Hiesmayr Generalized Bell inequality for kaons Bertlmann, Hiesmayr, PRA 63 (2001) What can Alice & Bob measure? Are you in a certain quasispin kn or not? measurement device ta kn 1 n n 2 2 n K 0 n K 0 quasispin local realistic theories SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td ) E ( kn , t a ; km , t b ) E ( kn , t a ; km ' , t c ) E ( k n ' , t d ; k m , t b ) E ( k n ' , t d ; k m ' , t c ) 2 • vary in times • vary in quasi-spin • or both QM: S Photon 2 2 2.8 Discrete 2008, Beatrix C. Hiesmayr !?Nonlocality related to a symmetry violation?! Bell inequalities CP violation world anti-world Discrete 2008, Beatrix C. Hiesmayr CP violation K0 , K 0 2 , CP 1 3 CP 1 Experiment: 1964 Christensen, Cronin, Fitch and Turlay KS KL 1 2 (1 | |2 ) 1 2 (1 | |2 ) { K1 K 2 } 103 { K 2 K1 } CP violation Leptonic charge asymmetry: ( K L l l ) ( K L l l ) 3 ( 3 . 27 0 . 12 ) 10 ( K L l l ) ( K L l l ) Discrete 2008, Beatrix C. Hiesmayr Generalized Bell inequality for kaons (I) SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td ) E ( kn , t a ; km , t b ) E ( kn , t a ; km ' , t c ) E ( k n ' , t d ; k m , t b ) E ( k n ' , t d ; k m ' , t c ) 2 I. Vary in quasi-spin: kn K S , km K k n' k m ' K 1 0 0 ?! CP violation related to nonlocality !? •Bertlmann, Grimus, Hiesmayr,PRA (2001) •Hiesmayr, Found. of Phys. Lett (2001) 0 0 0 Leptonic charge asymmetry: ( K L l l ) ( K L l l ) (3.27 0.12) 103 ( K L l l ) ( K L l l ) Discrete 2008, Beatrix C. Hiesmayr Generalized Bell inequality for kaons (II) SCHSH (kn , km , kn' , km ' ; ta , tb , tc , td ) E ( kn , t a ; km , t b ) E ( kn , t a ; km ' , t c ) E ( k n ' , t d ; k m , t b ) E ( k n ' , t d ; k m ' , t c ) 2 II. Vary in time: kn km k n' k m ' K 0 0 0 E ( K , ta ; K , tb ) cos m(ta tb ) e ( ta tb ) S Photon 2 2 2.8 Violation! Kaons? •Bertlmann, Bramon, Garbarino, Hiesmayr, Phys. Lett. A (2004) •Bertlmann, Hiesmayr, Phys. Rev. A (2001) S Kaon ( t a , t b , t c , t d ) 2 NO violation! Strangeness oscillation/decay: x m 2m 1 S PROPOSITION: The CHSH-inequality is violated iff x>2 for kaons or for other mesons x>2.6. B-mesons: x=0.77 D-meson: x<0.03 Bs-mesons: x>20.6 Discrete 2008, Beatrix C. Hiesmayr Bell-CHSH forkaons kaons Bell-CHSHtype type inequality inequality for Bertlmann, Hiesmayr, PRA 63 (2001) 0 0 0 0 SCHSH ( K , K , K , K ; t a , t b , t c , t d ) 0 0 0 0 0 0 0 0 E ( K , ta ; K , tb ) E ( K , ta ; K , tc ) E ( K , t d ; K , t b ) E ( K , t d ; K , t c ) 2 Is it really not possible to distinguish E ( K , t ; K , t ) cos m(t t ) e between local realistic theories and quantum mechanics for neutral kaons in Photons: S 2 2 a2.8direct Violation! experiment? 0 0 a ( ta tb ) b a b Photon Kaons? S Kaon You have to be •Bertlmann, Bramon, Garbarino, Hiesmayr, ( t a , t b , t c , t d ) 2 NO violation! Phys. Lett. A (2004) more tricky! •Bertlmann, Hiesmayr, Phys. Rev. A (2001) Strangeness oscillation/decay: x m 2m 1 S PROPOSITION: The CHSH-inequality is violated iff x>2 for kaons or for other mesons x>2.6. B-mesons: x=0.77 D-meson: x<0.03 Bs-mesons: x>20.6 Discrete 2008, Beatrix C. Hiesmayr Bell inequality sensitive to strangeness violated? Hiesmayr, Eur. Phys. J. C (2007) 0 0 0 0 local realistic theories SCHSH ( K , K , K , K ; t a , t b , t c , t d ) 0 0 0 0 0 0 0 0 E ( K , ta ; K , tb ) E ( K , ta ; K , tc ) E ( K , t d ; K , t b ) E ( K , t d ; K , t c ) 2 Can we violate the BI for a certain initial state and if, what is the maximum value? Arbitrary initial state: r1e i K S K S r2e i K S K L r3e i K L K S r4e i K L K L 1 Expectation value: 2 3 4 Discrete 2008, Beatrix C. Hiesmayr Bell inequality sensitive to strangeness violated? Can we violate the BI for a certain initial state and if, what is the maximum value? Hiesmayr, Eur. Phys. J. C (2007) YES!! The maximal violation is obtained for a non-maximal entangled state Smax 2.15 A. DiDomenico A. Go Discrete 2008, Beatrix C. Hiesmayr Different view on CP violation (1) Hiesmayr, Huber Phys. Lett. A (2007) Bohr’s principle of complementarity: Quantum systems possess properties that are equally real but mutually exclusive! wave-particle duality Interferometric duality: The observation of an interference pattern and the adquisition of which-way information are mutually exclusive! predictability= a priori which-way knowledge P pure state: equality 2 21 V0 Greenberger,Yasin (1988); Englert (1996) fringe visibility Discrete 2008, Beatrix C. Hiesmayr Different view on CP violation (2) Hiesmayr, Huber Phys. Lett. A (2007) predictability= a priori which-way knowledge pure state: equality 2 2 P V 1 fringe visibility=interference1 contrast Kaon in time: K (t ) 0 short-lived state N 2p e S 2 t imS t KS e long-lived state L t imL 2 t KL Bramon,Garbarino, Hiesmayr, Phys. Rev. (2004) P ( K S (t ) ) V ( K S (t ) ) 1 2 1 2 e S t K S 2 eS t K S 2 2 1 „A kaon is a kind of double slit“ CP violation shifts obtainable information to different aspects of reality! Discrete 2008, Beatrix C. Hiesmayr Summary/Outlook: • CP violation implies nonlocality • CP violation shifts obtainable information to different aspects of reality • kaons provide a ``dynamical´´ nonlocality • nonlocality and entanglement are different quantum features for quantum particles with more degrees of freedom Hiesmayr, Huber, Spengler; in preparation direct experimental test of BI are highly desired! (open: if non—maximal entangled states can be produced in experiment) Outlook: BI with regenerators: A. DiDomenico A. Go Testable BI for DAPHNE (Frascati,Rom)?