c

Vd

d EdF

d

V

V

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

0

a0

F

dt

pdF

but

hiddenpVmp

dt

pdF hidden

exactly 0

a

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

0F

0F

AC dual to AB

0

a 0

a

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 VIParadox of Two Lorentz Observers

Paradox VICharged particle, charged plate, and two Lorentz Observers

Alice’s view

Paradox VICharged particle, charged plate, and two Lorentz Observers

Bob’s view

iq

iV

0

ii

iVq

00

i

iiVm 0

i

iiVm

c

Epp hiddentot

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))

0

2

2

0

1

i itot i i

i i i

m Vp mV

Vc

Bohm versus Everett

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

30.08.2010

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 hopeI think, we should not.

All is iR

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.

http://qol.tau.ac.il/TWS.html

left right

http://qol.tau.ac.il/TWS.html

right

http://qol.tau.ac.il/TWS.html

A B

World-splitter of Tel Aviv University

A B

World-splitter of Tel Aviv University

A B

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)

( ( ), ( ))a aA r r ( )r

Bohm: At the end of the day, the only variables we observe are positions.

Space is taken for granted

( )r

Everett:

( )r

Bohm:

All isevolving according to deterministic equations

All is

1 2( , ,...., , )Nr r r t

Everett:

Bohm: 1 2( ), ( ),...., ( )Nr t r t r t

and

1 2( , ,...., , )Nr r r t

evolving according to deterministic equation

All is particlesevolving according to Newton’s equations

Laplacian determinism

A CENTURY AGO:

1 2( ), ( ),...., ( )Nr t r t r t

Everett Interpretation

Observation

Laplacian determinism

Observation 1 2( ), ( ),...., ( )Nr t r t r t

1 2( , ,...., , )Nr r r t

TRIVIAL

Bohmian mechanics

Observation 1 2( ), ( ),...., ( )Nr t r t r tTRIVIAL

HARD

Everett Interpretation

Observation

Laplacian determinism

Observation 1 2( ), ( ),...., ( )Nr t r t r t

1 2( , ,...., , )Nr r r t

TRIVIAL

HARD

Bohmian mechanics

Observation 1 2( ), ( ),...., ( )Nr t r t r tTRIVIAL

Everett Interpretation

Many parallel

Observations

Laplacian determinism

Observation 1 2( ), ( ),...., ( )Nr t r t r t

1 2( , ,...., , )Nr r r t

TRIVIAL

Bohmian mechanics

Observation 1 2( ), ( ),...., ( )Nr t r t r tTRIVIAL

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

OBSERVER RESTi i i

1 2 ...OBJECT OBJECT OBJECTK RESTi i i i i

OBJECT

i is a Localized Wave Packet for a period of time

1 2( , ,...., , )Nr r r tmany

worlds

1 2( , , ...., , )

Ni r r r t Observation i world i

1 21 2 ( , , ...., , )( , ,...., , )NN i i r r r tr r r t

Many parallel

Observations

What is our world in the Bohmian Interpretation ?

Observation 1 2( ), ( ),...., ( )Nr t r t r t

We do not observe (experience) 1 2( , ,...., , )Nr r r t

Bohmian trajectories

CONTEXTUALITY

EPR

V

V

V V

V V

VV

VV

VV

V

V

V

V

V V

V

V

/ 3V

V

1 0.5

1 0.5 3

V V V

V/ 3V

V

VVV

VV

V

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

PhotomultipliersGeiger countersStern Gerlach devicesBeam splittersDown conversion crystalsQuantum dotsQuantum tunnelingPhotodiods……The Quantum World Splitter

1 2 ...OBJECT OBJECT OBJECTKUNIVERSE WORLD REST

Quantum states of all macroscopic objects are Localized Wave Packets all the time

A tale of a single world universe

1 21 2 1 2( , ,...., , ) ( ) ( )... ( )NWORLD

N Nr r r t r r r Zero approximation: all particles remain in product LWP states

Particles which do not interact strongly with “macroscopic objects” need not be in LWP states.

1 21 2( ) ( )... ( )KWORLD REST

Kr r r

( )nnr

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.

21 1 2 1

1 21 1 2 2( ) ( ) ( ) ( )... ( ) ( )M

M

WORLD CM CM CM RESTCM rel i j CM rel i j CM rel Mi Mjr r r r r r r r r

Quantum states of all macroscopic objects are Localized Wave Packets all the time

A tale of a single world universe

1 21 2 1 2( , ,...., , ) ( ) ( )... ( )NUNIVERSE

N Nr r r t r r r

21 1 2 1

1 21 1 2 2( ) ( ) ( ) ( )... ( ) ( )M

M

WORLD CM CM CM RESTCM rel i j CM rel i j CM rel Mi Mjr r r r r r r r r

Observation 1 21 2( ) ( )... ( )N

Nr r r TRIVIAL

Almost the same as in

( )r

( )r of a cat!

Bohmian trajectories

Two worlds universe

This is a multiple worlds universe

Two worlds universe

A

B

A

B

Two worlds universe One world does not disturb the other

A

B

Two worlds universe One world does not disturb the other

Two worlds universe

A

B

Preferred basis:

| | | |MD A MDB ENVA R R R | | | |MD A MDB ENVA V R R | | | |MD A MDB ENVA V R A

| , |A B | | | |, | , |

2 2

A B A B

or

STABILITY

Two worlds universe

A

B

Preferred basis:

| | | |MD A MDB ENVA R R R | | | |MD A MDB ENVA V R R | | | |MD A MDB ENVA V R A

| | | |MD A MDB ENVB R R R

| | | |MD A MDB ENVB R V R | | | |MD A MDB ENVB R V B

| , |A B | | | |, | , |

2 2

A B A B

or

STABILITY

Two worlds universe

A

B

Preferred basis:

| | | |MD A MDB ENVA R R R | | | |MD A MDB ENVA V R R | | | |MD A MDB ENVA V R A

| | | |MD A MDB ENVB R R R

| | | |MD A MDB ENVB R V R | | | |MD A MDB ENVB R V B

| , |A B | | | |, | , |

2 2

A B A B

or

| | | |MD A MDB ENVR R R | | | | | |

|2

MD A MDB MD A MDBENV

A V R B R VR

| | | | | | | |

2MD A MDB ENV MD A MDB ENVA V R A B R V B

| | | | | | | | | | | || |

2 2MD A MDB ENV MD A MDB ENV MD A MDB ENV MD A MDB ENVV R A R V B V R A R V B

STABILITY