From quantum miracles to many worldsLev Vaidman

FQXi Lecture Series on Quantum Foundations 14.3.2018

Local action

Good explanation

Good explanation

Local action

Objects create fields

Fields affect other objects locally Fa

m=

gm

m= g=

Good explanation

F ma= Good explanationlocal action

2

1

2

( , ) 02

t

t

pS U r t dt

m

= − =

global picture

Is it an explanation?

Mach Zehnder Interferometer with particles

Classical physics failed to provide an explanation for

Quantum mechanics: particles are waves

Quantum physics provides a good explanation:

Local interactions and interference

Quantum mechanics: particles are waves

Aharonov-Bohm Effect: a counter example?!

Aharonov-Bohm Effect: a counter example?! The solenoid causes a relative phase without classical lag?!

Nonlocality: Electromagnetic potential acts in a global topological way?!

Do we have only global explanation ?0S =

Aharonov-Bohm Effect: a counter example?!

AB effect does have local explanation if everything, including the source of the magnetic flux is treated quantum mechanically

The AB phase is acquired by the solenoid, entangled with the electron, due to local action of electromagnetic field of the electron

Role of Potentials in the Aharonov-Bohm Effect

L. Vaidman, Phys. Rev. A R86, 040101 (2012)No!Do we have only global explanation ?0S =

The solenoid causes a relative phase without classical lag?!

Nonlocality: Electromagnetic potential acts in a global topological way?!

Quantum physics provides a good explanation:

Local interactions, interference and entanglement

The EPR argument

Bell: Quantum theory cannot be completed

Quantum theory has miracle: action at a distance

The GHZ game

2 2 2 2 2 21A B C A B CX X X Y Y Y = −

34

Classical

winP =

1A B CX X X = −

1A B CX Y Y =

1A B CY X Y =

1A B CY Y X =

Winning

conditions

X=?

Y=?or

X=?

Y=?or

X=?

Y=?or

1 or -1

1 or -1

1 or -1

+ + −

+

+

−

+ +

+ +

++

1Quantum

winP =

The GHZ Game Quantum Strategy

X=?

Y=?or

X=?

Y=?or

X=?

Y=?or

( )1

| | | | | | |2

A B C A B CGHZ = −

X1

1−

Y1

1−

x

y

( )1

2z z z z z z

A B C A B CGHZ = −

( )1

2x y y x y y x y y x y y

A B C A B C A B C A B C= + + +

( )1

2x x x x x x x x x x x x

A B C A B C A B C A B C= + + +

( )1

| | | | | | |2

A B C A B CGHZ = −

1

1

A B C

y x y

A B C

y y x

=

=

1A B CX X X = −

1A B CX Y Y =

1A B CY X Y =

1A B CY Y X =

( )

( )

1

2

1

2

z x x

z x x

= +

= −

1A B C

x x x = −

1A B C

x y y =

The GHZ Game Quantum Strategy

X=?

X=?

X=?

1x = −

1x = −

1

1

A B C

y x y

A B C

y y x

=

=

1A B C

x x x = −

1A B C

x y y =

( )1

| | | | | | |2

A B C A B CGHZ = −

Miracle: change of a spin state by remote action

Teleportation

Teleportation

Teleportation

Science Fiction: Matter cannot “jump” in space time

Science Fiction: Matter cannot “jump” in space time

Quantum mechanics: We do not have to move matter

All matter is the same. We need to move only the shape,

the quantum wave function Ψ

Teleportation

= Ψ

Teleportation

2 bits

Teleportation

BELL MEASUREMENT

1 1 +

3 3 +

( )2 3 2 3

1

2 −

Bell States

( )

( )

( )

( )

1 2 1 2

1 2 1 2

1 2 1 2

1 2 1 2

1

2

1

2

1

2

1

2

−

+

−

+

= −

= +

= −

= +

1 2

EPR− =

EPR=

EPR= z

EPR=

EPR=

x

y

spin rotation

spin rotation

2 bits

BELL MEASUREMENT

( ) ( )1 1 2 3 2 3

1

2 + −

( ) ( )

( ) ( )

( ) ( )

( ) ( )

1 2 1 2 3 3

1 2 1 2 3 3

1 2 1 2 3 3

1 2 1 2 3 3

1

2 2

1

2 2

1

2 2

1

2 2

− − +

− + −

+ + −

+ − +

=

=

z

x

y

Continuous Variables Teleportation

output

input

a

b

EPR

2 numbers

Teleportation

BELL MEASUREMENT

=Ψ of particles2810

2810

2 bits

Teleportation

BELL MEASUREMENT

cos sin ie = +

,

,

Miracle: sending 2 real numbers with just 2 bits

THE PARADOX OF

THE INTERACTION-FREE MEASUREMENT

A. Elitzur and L. Vaidman

Found. Phys. 23, 987 (1993) .

BOMB: explodes when any particle “touches” it

interacts only through explosion

HOW TO FIND BOMB WITHOUT EXPLODING IT?

QUANTUM MECHANICS SOLVES THIS [ PARADOX

Interaction-free measurement

Interaction-free measurement

Interaction-free measurement

Interaction-free measurement

Interaction-free measurement

We know the bomb is there

Nothing touched the bomb: PARADOX!

I. The fundamental ontology: All is evolving according to the relativistic generalization of the Schrodinger equation

II. The connection between ontology and experience:There are multiple worlds similar to the one we experience.

The experience of an observer in a world is completely specified by the textbook (collapsing) wave function .WORLD

Quantum states of all macroscopic objects are Localized Wave Packets

Alternatively, is defined by .WORLD

The probability of self-location of an observer in a particular world is proportional to its measure of existence

2 2|WORLD i WORLD i i = =

i WORLD i

i

=

MWI

BORN-VAIDMAN RULE:

plato.stanford.edu/entries/qm-manyworlds/

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

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

A

B

Test of the MWI

A

B

Test of the MWI

The GHZ Game Quantum Strategy

X=?

X=?

X=?

1x = −

1x = −

1

1

A B C

y x y

A B C

y y x

=

=

1A B C

x x x = −

1A B C

x y y =

( )1

| | | | | | |2

A B C A B CGHZ = −

Miracle: change of a spin state by remote action

The GHZ Game Quantum Strategy

X=?

X=?

X=?

1x = +

1x = −

1

1

A B C

y x y

A B C

y y x

=

=

1A B C

x x x = −

1A B C

x y y =

( )1

| | | | | | |2

A B C A B CGHZ = −

Miracle: change of a spin state by remote action

The GHZ Game: the universe picture

X=?

X=?

X=?

1x =

1x =

1

1

A B C

y x y

A B C

y y x

=

=

1A B C

x x x = −

1A B C

x y y =

( )1

| | | | | | |2

A B C A B CGHZ = −

Miracle: change of a spin state by remote action

=No miracle: no change of the remote spin

The GHZ Game: the universe picture

X=?

X=?

X=?

1

1

A B C

y x y

A B C

y y x

=

=

1A B C

x x x = −

1A B C

x y y =

( )1

| | | | | | |2

A B C A B CGHZ = −

Miracle: change of a spin state by remote action

=No miracle: no change of the remote spin

BEFORE

The GHZ Game: the universe picture

X=?

X=?

X=?

1x =

1x =

1

1

A B C

y x y

A B C

y y x

=

=

1A B C

x x x = −

1A B C

x y y =

( )1

| | | | | | |2

A B C A B CGHZ = −

Miracle: change of a spin state by remote action

=No miracle: no change of the remote spin

AFTER

2 bits

BELL MEASUREMENT

( ) ( )1 1 2 3 2 3

1

2 + −

( ) ( )

( ) ( )

( ) ( )

( ) ( )

1 2 1 2 3 3

1 2 1 2 3 3

1 2 1 2 3 3

1 2 1 2 3 3

1

2 2

1

2 2

1

2 2

1

2 2

− − +

− + −

+ + −

+ − +

=

=

z

x

y

Teleportation

2 bits

BELL MEASUREMENT

( ) ( )1 1 2 3 2 3

1

2 + −

( ) ( )

( ) ( )

( ) ( )

( ) ( )

1 2 1 2 3 3

1 2 1 2 3 3

1 2 1 2 3 3

1 2 1 2 3 3

1

2 2

1

2 2

1

2 2

1

2 2

− − +

− + −

+ + −

+ − +

=

=

z

x

y

=

Interaction-free measurement

We know the bomb is there

Nothing touched the bomb: PARADOX!

Interaction-free measurement

The many worlds picture

Nothing touched the bomb in our world!

The photon touched the bomb in another world

Our intuition comes from physics which

describes all worlds together: NO PARADOX!

Bell theorem (GHZ(: The nature is apparently random and

it has some kind of action at a distance

Teleportation transfers huge amount of (unreadable)

information using a few bits

The MWI removes randomness and action at a distance

from physics explaining why we have an illusion of

randomness and Bell nonlocality

Conclusions

IFM provides information about presence of an object in

a particular location without any particle being there