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By Yakir Aharonov
1 The makes use of of Paradox.1.1 Paradox in Physics.1.2 Errors.1.3 Gaps.1.4 Contradictions.1.5 evaluation of the Book.References.2 the right way to Weigh a Quantum.2.1 Why does the colour of the sunshine Change?2.2 Quanta.2.3 Uncertainty Relations.2.4 The Clock-in-the-Box Paradox.2.5 From Inconsistency to Incompleteness.References.3 Is Quantum thought Complete?3.1 The Einstein-Podolsky-Rosen Paradox.3.2 Polarized Photons.3.3 Quantum States and Observables.3.4 Bell's Inequality.3.5 Paradox and Beyond.References.4 levels and Gauges.4.1 Paradoxical Procedures.4.2 Classical and Quantum Phases.4.3 part Meets Gauge.4.4 The Aharonov-Bohm Effect.4.5 Quantum Consistency and the Aharonov-Bohm Effect.4.6 Flux Quantization.4.7 Magnetoresistance.4.8 Non-Abelian Phases.References.5 Modular Variables.5.1 A Lattice of Solenoids.5.2 Non-overlapping Wave Packets.5.3 Modular Momentum.5.4 The xmod, pmod Representation.5.5 Intimations of Nonlocality.References.6 Nonlocality and Causality.6.1 Causality and a Piston.6.2 Quantum results with no Classical Analogues.6.3 Modular Energy.6.4 Reconciling the Irreconcilable.References.7 Quantum Measurements.7.1 the speed Paradox.7.2 A Quantum dimension Paradigm.7.3 Quantum Measurements and Uncertainty Relations.7.4 Paradox Lost.References.8 dimension and Compensation.8.1 Paradox Regained.8.2 Compensating Forces.8.3 Quantum Measurements of Noncanonical Observables.8.4 Measuring the electrical Field.8.5 power and Time.References.9 Quantum Cats.9.1 Schr odinger's Cat.9.2 A Quantum Catalyst.9.3 Quantum Concatenations.9.4 A Quantum Catalog.References.10 A Quantum Arrow of Time?10.1 A Quantum Card Trick.10.2 Time Reversal.10.3 The Aharonov-Bergmann-Lebowitz Formula.10.4 The Arrow of Time Revisited.10.5 Boundary stipulations at the Universe.References.11 Superselection Rules.11.1 Superselection Rule for Angular Momentum?11.2 T and Spin.11.3 The Wick-Wightman-Wigner Argument.11.4 every little thing is Relative.11.5 Superposing cost States.References.12 Quantum gradual Dance.12.1 A Watched Pot by no means Boils.12.2 The Adiabatic Approximation.12.3 Feynman Paths.12.4 Classical Analogues.References.13 fees and Fluxons.13.1 Hidden Momentum?13.2 Duality of the Aharonov-Bohm Effect.13.3 The Aharonov-Bohm impression and Berry's Phase.13.4 The Aharonov-Casher Effect.References.14 Quantum Measurements and Relativity.14.1 cave in and Relativity.14.2 Relativistic Constraints on Measurements.14.3 Nonlocal Measurements.14.4 Which Nonlocal Operators are Measurable?14.5 Measuring a Nonlocal Operator.14.6 cave in and Relativity Revisited.References.15 how one can become aware of a Quantum Wave.15.1 Dipole Paradox.15.2 How to not discover a Quantum Wave.15.3 protecting Measurements.15.4 Galilean Dialogue.15.5 protecting Measurements and Causality.15.6 in the direction of Quantum box Theory.References.16 vulnerable Values.16.1 A susceptible Measurement.16.2 A Paradox of Errors.16.3 Pre- and Postselected Ensembles.16.4 susceptible Measurements and vulnerable Values.16.5 A Quantum Shell Game.16.6 The Quantum Walk.16.7 swifter than Light.16.8 Galilean Dialogue.References.17 vulnerable Values and Entanglement.17.1 Interaction-free Paradox.17.2 a smile and not using a Cat.17.3 Alice and Bob in Wonderland.17.4 Galilean Dialogue.17.5 advanced susceptible Values.References.18 The Quantum World.18.1 vulnerable Measurements and Interference.18.2 From Amplitudes to Probabilities.18.3 The destiny of the Universe.18.4 The position of h.18.5 Causality and Nonlocality as Axioms.18.6 Causality, Nonlocality and Scaling.18.7 what's the Quantum World?References.Index
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We arrange that initially, p1 = p2 = 0; the initial momenta are horizontal. Also, before and after each pair arrives at the board, we accurately measure the momentum component of the board itself. Since the total momentum of the particles and the board remains constant during the passage, this experiment yields the total momentum p1 + p2 of the particles after they pass through the board (even if they knock against the slots as they pass through). It also yields the vertical distance x2 − x1 between the particles as they pass through the board (if they pass through the two slots).
But in another frame, Bob measures first, and we cannot distinguish subjective from objective uncertainty. Does the EPR claim have implications for experiment? We might well wonder. Pauli, writing to Born in 1954, expressed doubt: “As O. Stern said recently, one should no more rack one’s brain about the problem of whether something one cannot know anything about exists all the same, than about the ancient question of how many angels are able to sit on the point of a needle. But it seems to me that Einstein’s questions are ultimately always of this kind” [3].
By assumption, the particles do not interact, so the result of the p2 measurement cannot depend on whether we measure x1 or p1 . What is p2 ? If we measure p1 and obtain p1 = p, we also obtain p2 = −p because p1 + p2 = 0. If we measure x1 we cannot measure p1 , and quantum theory does not predict the result of the p2 measurement. But the result of the p2 measurement cannot depend on whether we measure x1 or p1 , by assumption. e. some predetermined result independent of what we measure on the other particle (and which particle we measure first).