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