dd The forces exerted on the neutron can give energy for nothing! Paradox IV (Aharonov)

W. Shockley and R.P. James, PRL 171, 1370 (1967) A cannon with no recoil Paradox V

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. W. Shockley and R.P. James, PRL 171, 1370 (1967) A cannon with no recoil Paradox V

Resolution of Paradoxes V, IV,III (Re)discovery of “hidden momentum” A current loop in a static electric field has a nonzero linear momentum Y. Aharonov, P. Pearle, and L. Vaidman, PRA 38, 1863 (1988) 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 Paradox V (recoil-free cannon)

Resolution of Paradoxes V, IV,III (Re)discovery of “hidden momentum” A current loop in a static electric field has a nonzero linear momentum Y. Aharonov, P. Pearle, and L. Vaidman, PRA 38, 1863 (1988) There is no recoil-free cannon. 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 Paradox IV but exactly

ELECTRON The motion of the electron is identical to the motion of the neutron Resolution of Paradox III The motion of the neutron inside the interferometer is the same with or without the line of charge. ELECTRON NEUTRON LINE OF CHARGE NEUTRON AC dual to AB The motion of the electron inside the interferometer is the same with or without the solenoid

LINE OF CHARGE NEUTRON Aharonov-Bohm Effect Aharonov-Casher Effect SOLENOID ELECTRON Paradox I is an unavoidable property of both Aharonov Bohm and Aharonov Casher effects which makes them nonlocal topological effects 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. Conclusion

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

i q i V The current loop model: free charges moving inside a frictionless tube E p hid Hidden momentum (This and other models: L. Vaidman, AJP 58, 978 (1990))

Bohm versus Everett 21st-century directions in de Broglie-Bohm theory and beyond THE TOWLER INSTITUTE The Apuan Alps Centre for Physics Vallico Sotto, Tuscany, Italy

Hope: Today’s physics explains all what we see. Big hope: Today’s physics explains All. Bohm and Everett are candidates for a final theory. 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.

All is and Bohm:

All is Everett:

All is Many-Worlds Everett:

The Quantum World Splitter Choose how many worlds you want to split by pressing one of the red dice faces.

left right

right

World-splitter of Tel Aviv University

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.

Space is taken for granted

Everett:

Bohm:

All is evolving according to deterministic equations All is Everett: Bohm: and evolving according to deterministic equation

All is particles evolving according to Newton’s equations Laplacian determinism A CENTURY AGO:

Everett Interpretation Observation Laplacian determinism Observation TRIVIAL Bohmian mechanics Observation TRIVIAL HARD

Everett Interpretation Observation Laplacian determinism Observation TRIVIAL HARD Bohmian mechanics Observation TRIVIAL

Everett Interpretation Many parallel Observations Laplacian determinism Observation TRIVIAL Bohmian mechanics Observation TRIVIAL HARD

An observer has definite experience. Everett’s Relative State World What is “a world” in the Everett Interpretation ? A world is the totality of (macroscopic) objects: stars, cities, people, grains of sand, etc. in a definite classically described state. The MWI in SEP is a Localized Wave Packet for a period of time many worlds Observation i world i Many parallel Observations

What is our world in the Bohmian Interpretation ? Observation We do not observe (experience)

Bohmian trajectories

CONTEXTUALITY

EPR

MZI

IFM

Counterfactual Computation

0

Surrealistic trajectories

A tale of a single world universe The king forbade spinning on distaff or spindle, or the possession of one, upon pain of death, throughout the kingdom

A tale of a single world universe The king forbade performing quantum measurements, or the possession of quantum devices, upon pain of death, throughout the kingdom Photomultipliers Geiger counters Stern Gerlach devices Beam splitters Down conversion crystals Quantum dots Quantum tunneling Photodiods …… The Quantum World Splitter

Quantum states of all macroscopic objects are Localized Wave Packets all the time A tale of a single world universe Zero approximation: all particles remain in product LWP states Particles which do not interact strongly with “macroscopic objects” need not be in LWP states. Particles which make atoms, molecules, etc. can (and should be) entangled among themselves. Only states of the center of mass of molecules, cat’s nails etc. have to be in LWP states.

Quantum states of all macroscopic objects are Localized Wave Packets all the time A tale of a single world universe Observation TRIVIAL Almost the same as in of a cat! Bohmian trajectories

Two worlds universe This is a multiple worlds universe

Two worlds universe

One world does not disturb the other

Two worlds universe One world does not disturb the other

Two worlds universe Preferred basis: or STABILITY

Two worlds universe Preferred basis: or STABILITY

Two worlds universe Preferred basis: or STABILITY