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## The forces exerted on the neutron can give energy for nothing!

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**Paradox IV (Aharonov)**The forces exerted on the neutron can give energy for nothing! d d**Paradox V**W. Shockley and R.P. James, PRL 171, 1370 (1967) A cannon with no recoil**Paradox V**W. Shockley and R.P. James, PRL 171, 1370 (1967) A cannon with no recoil An isolated system consists of a current loop (two oppositely rotating and oppositely charged disks) and a charge which are originally at rest. When the current dies out, the charge starts moving, while the disks apparently stay in place.**Resolution of Paradoxes V, IV,III**(Re)discovery of “hidden momentum” Y. Aharonov, P. Pearle, and L. Vaidman, PRA 38, 1863 (1988) A current loop in a static electric field has a nonzero linear momentum Resolution of Paradox V (recoil-free cannon) When the current stops, the hidden momentum of the current loop is transferred to the mechanical momentum of the tube. The loop recoils to the left.**Resolution of Paradoxes V, IV,III**(Re)discovery of “hidden momentum” Y. Aharonov, P. Pearle, and L. Vaidman, PRA 38, 1863 (1988) A current loop in a static electric field has a nonzero linear momentum Resolution of Paradox V (recoil-free cannon) When the current stops, the hidden momentum of the current loop is transferred to the mechanical momentum of the tube. The loop recoils to the left. There is no recoil-free cannon.**Resolution of Paradox IV**but exactly**Resolution of Paradox III**The motion of the electron inside the interferometer is the same with or without the solenoid ELECTRON ELECTRON AC dual to AB NEUTRON NEUTRON The motion of the neutron inside the interferometer is the same with or without the line of charge. LINE OF CHARGE The motion of the electron is identical to the motion of the neutron**Paradox I**At every place on the paths of the wave packets of the particle there is no observable action, but nevertheless, the relative phase is obtained. Aharonov-Bohm Effect Aharonov-Casher Effect ELECTRON NEUTRON SOLENOID LINE OF CHARGE Conclusion Paradox I is an unavoidable property of both Aharonov Bohm and Aharonov Casher effects which makes them nonlocal topological effects**How comes hidden momentum?**A current loop in a static electric field has a nonzero linear momentum Hint: paradox VI Paradox of Two Lorentz Observers**Paradox VI**Charged particle, charged plate, and two Lorentz Observers Alice’s view**Paradox VI**Charged particle, charged plate, and two Lorentz Observers Bob’s view**V**i q p i hid E Hidden momentum The current loop model: free charges moving inside a frictionless tube (This and other models: L. Vaidman, AJP 58, 978 (1990))**Bohm versus Everett**30.08.2010 21st-century directions in de Broglie-Bohm theory and beyond THE TOWLERINSTITUTE The Apuan Alps Centre for Physics VallicoSotto, Tuscany, Italy**Hope:**Today’s physics explains all what we see. Big hope: Today’s physics explains All. The quantum mechanical formalism does not provide physicists with a ‘pictorial’ representation: the ψ-function does not, as Schrödinger had hoped, represent a new kind of reality. Instead, as Born suggested, the square of the absolute value of the ψ-function expresses a probability amplitude for the outcome of a measurement. Bohr (SEP): Bohr and today’s majority of physicists gave up the hope I think, we should not. Bohm and Everett are candidates for a final theory.**Bohm:**All is and**Everett:**All is**Everett:**Allis Many-Worlds**http://qol.tau.ac.il/TWS.html**The Quantum World Splitter Choose how many worlds you want to split by pressing one of the red dice faces.**http://qol.tau.ac.il/TWS.html**left right**All**All is a closed system which can be observed**All**All is a closed system which might include an observer which can be observed**What is ψ ?**There is no sharp answer. Theoretical physicists are very flexible in adapting their tools, and no axiomization can keep up with them. But it is fair to say that there are two core ideas of quantum field theory. First: The basic dynamical degrees of freedom are operator functions of space and time- quantum fields. Second: The interaction of these fields are local in space and time. F. Wilczek(in Compendium of Quantum Physics, 2009) Bohm: At the end of the day, the only variables we observe are positions.**Bohm:**All is and evolving according to deterministic equations Everett: All is evolving according to deterministic equation**A CENTURY AGO:**All is particles evolving according to Newton’s equations Laplacian determinism**Laplacian determinism**TRIVIAL Observation Bohmian mechanics TRIVIAL Observation Everett Interpretation Observation HARD**Laplacian determinism**TRIVIAL Observation Bohmian mechanics TRIVIAL Observation Everett Interpretation Observation HARD**Laplacian determinism**TRIVIAL Observation Bohmian mechanics TRIVIAL Observation Everett Interpretation HARD Many parallel Observations**What is “a world” in the Everett Interpretation ?**many worlds Many parallel Observations world i Observation i An observer has definite experience. Everett’s Relative State World A world is the totality of (macroscopic) objects: stars, cities, people, grains of sand, etc. in a definite classically described state. is a Localized Wave Packet for a period of time The MWI in SEP**What is our world in the BohmianInterpretation ?**Observation We do not observe (experience)