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Too Beautiful Not to be True: The Hidden Logic of Quantum Mechanics Avshalom C. Elitzur Copyleft Permission is granted to everyone to copy and/or use this work or any part of it. Abandon hope all ye who enter here Dante Determinism Objectivity Locality Schrödinger © Jie Qi crest trough “in phase” crest constructive interference trough crest trough “out of phase” crest trough destructive interference The Double-Slit Experiment (Courtesy of Tel-Aviv Municipality) Constructive Destructive Constructive interference Proof: Light=Waves Interference of water waves Interference of light waves The Mach-Zehnder Interferometer: • Photon is emitted and split into two • Reflected back (notice phase shift upon reflection!) • One half split again • Second half split again (at the same time) • Destructive Interference on detector D • Constructive Interference on detector C • All light reaches detector C. detectors C D half-silvered mirrors solid mirrors light source Confused? Don’t worry: It will soon get much worse. Interference occurs with single Can we outsmart the “which path” uncertainty? 1. Photons 2. Electrons Interference 3. Neutrons 0% 100% 4. Atoms 5. Molecules 6. … 0 1 1 0 50% Can we outsmart the “which path” uncertainty? Interference 0% 100% 50% Can we outsmart the “which path” uncertainty? 50% 50% 50% Can we outsmart the “which path” uncertainty? 50% 50% 50% Can we outsmart the “which path” uncertainty? Interference 0% 100% Meet the Uncertainty h Principle: xp 2 Interference 0% 100% Heisenberg position unknown ? ? Meet the Uncertainty h Principle: xp 2 Interference 0% 100% momentum lost Heisenberg position known Can we outsmart the “which path” uncertainty? No, but Nam et Ipsa Ignorantia Scientia Potestas Est* *Knowledge Ignorance begets power Interaction-Free Measurement: The Elitzur-Vaidman (1993) Bomb-Testing Experiment 1. Photon emitted 2. Split 3. No Boom 4. Remaining wave splits 5. “Forbidden” detector D clicks D C A New Monster is Born What was I thinking… © Ted Dawson The Einstein-Podolsky-Rosen Experiment Classical analogue: Two coins ? ? The Einstein-Podolsky-Rosen Experiment Quantum version: Two particles The Einstein-Podolsky-Rosen Experiment Quantum version: Two particles Or Bell’s Test for Particle Telepathy: 3 Possible Questions, 2 Possible Answers 1. Is your spin “up” in the α direction? 50% “Yes” , 50% “No” 2. Is your spin “up” in the β direction? 50% “Yes” , 50% “No” 3. Is your spin “up” in the γ direction? 50% “Yes” , 50% “No” Overall: 100% correlations for same-question pairs but 50% correlations for different-question pairs! pre-established agreement would give higher correlations! “Telepathy” between particles proved A quantum dynasty Bohm Aharonov Vaidman Elitzur Dolev Bell’s Test for Particle Liar Telepathy: The Elitzur-Dolev Quantum Paradox: 3Replacing Possible Questions, 2 Possible Answers Bell’s Third Question 1. Is your spin “up” in the α direction? 50% “Yes” , 50% “No” 2. Is your spin “up” in the β direction? 50% “Yes” , 50% “No” youspin entangled other particle? 3. Are Is your “up” in with the γ the direction? 50% “Yes” , 50% “No” The Quantum Liar Paradox 1 A1* A2 A1 A2 * 2 • Two excited atoms A1 and A2 reside in cavities facing a beam-splitter • One detector clicks, source of the photon uncertain • Thereby entangling the two atoms • An orthogonal measurement to excited/ground is introduced • EPR • Bell-inequality violated • The liar paradox all over again The Quantum Liar Paradox – One atom is found to be excited, which seems to indicate that it emitted no photon. – Hence, it could not interact with the other atom and should not be entangled with it. – But, by violating Bell’s inequality, its “having preserved its photon” is due to entanglement with the other atom! Which is equivalent to saying THIS SENTENCE HAS NEVER BEEN WRITTEN :-) Большая Советская Энциклопедия Lavrentiy Beria History, The Soviet Encyclopedia’s Version When the “hero of the people” former KGB head is shot as a traitor, you take back old volumes of the encyclopedia, take out the pages of the entry “Beria” and replace them with “Bering.” Our Relativistic Quantum Model Could Nature be similarly reiterating a process’s evolution at the quantum level? References Dolev, S., & Elitzur, A.C. (2001) Non-sequential behavior of the wavefunction. http://arxiv.org/PS_cache/quant-ph/pdf/0102/0102109v1.pdf Elitzur, A.C., & Dolev, S (2006) Multiple interaction-free measurement as a challenge to the transactional interpretation of quantum mechanics. In Sheehan, D. [Ed.] Frontiers of Time: Retrocausation – Experiment and Theory. AIP Conference Proceedings, 863, 27-44. Elitzur, A.C., & Dolev, S (2007) The inexhaustible source of insights revealed by every photon. Proceedings of SPIE Volume 6664: The Nature of Light: What Are Photons?, C. Roychoudhuri, A.F. Kracklauer, & K. Creath, Eds, 666402-666413. http://a-c-elitzur.co.il/uploads/articlesdocs/photon5(2).pdf What a pity to die at the dawn of relativity! (Herman Minkowski, 1909)