Transcript Slide 1

Bohm versus Everett
Lev Vaidman
30.08.2010
21st-century directions in de Broglie-Bohm theory and beyond
THE TOWLER INSTITUTE The Apuan Alps Centre for Physics
Vallico Sotto, Tuscany, Italy
Hope:
Big hope:
Today’s physics explains all what we see.
Today’s physics explains All.
Bohr (SEP): 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 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 R i
and

Everett:
All is 
Everett:
All is
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
http://qol.tau.ac.il/TWS.html
right
World-splitter of Tel Aviv University
A
B
World-splitter of Tel Aviv University
A
B
World-splitter of Tel Aviv University
A
B
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.
 ( A  ( r ),  ( r ))
a
a
 (r )
Space is taken for granted
Everett:
 (r )
Bohm:
 (r )


Bohm:
All is
 r1 ( t ), r2 ( t ), ...., rN ( t ) 
and  ( r1 , r2 ,...., rN , t )
evolving according to deterministic equations
Everett:
All is
 ( r1 , r2 ,...., rN , t )
evolving according to deterministic equation
A CENTURY AGO:
All is particles
evolving according to Newton’s equations
 r1 ( t ), r2 ( t ), ...., rN ( t ) 
Laplacian determinism
Laplacian determinism
TRIVIAL
Observation

 r1 ( t ), r2 ( t ), ...., rN ( t ) 
Bohmian mechanics
TRIVIAL
Observation

 r1 ( t ), r2 ( t ), ...., rN ( t ) 
Everett Interpretation

HARD
Observation
 ( r1 , r2 ,...., rN , t )
Laplacian determinism
TRIVIAL
Observation

 r1 ( t ), r2 ( t ), ...., rN ( t ) 
Bohmian mechanics
TRIVIAL
Observation

 r1 ( t ), r2 ( t ), ...., rN ( t ) 
Everett Interpretation

HARD
Observation
 ( r1 , r2 ,...., rN , t )
Laplacian determinism
TRIVIAL
Observation

 r1 ( t ), r2 ( t ), ...., rN ( t ) 
Bohmian mechanics
TRIVIAL
Observation

 r1 ( t ), r2 ( t ), ...., rN ( t ) 
Everett Interpretation
Many parallel
Observations

HARD
 ( r1 , r2 ,...., rN , t )
What is “a world” in the Everett Interpretation ?
Many parallel
Observations

 ( r1 , r2 , ...., rN , t ) 
Observation i


many
worlds

 i ( r1 , r2 , ...., rN , t )

world i
An observer has definite experience.
 i ( r1 , r2 , ...., rN , t )
i i
O BSERVER
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.
The MWI in SEP
i
 ( r1 , r2 ,...., rN , t )
i i
O BJECT1
i
O BJECT
i
O BJECT2
i
REST
... i
O BJECT K
i
is a Localized Wave Packet
for a period of time
REST
What is our world in the Bohmian Interpretation ?
Observation

 r1 ( t ), r2 ( t ), ...., rN ( t ) 
We do not observe (experience)  ( r1 , r2 ,...., rN , t )
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
The Quantum World Splitter
Photomultipliers
Geiger counters
Stern Gerlach devices
Beam splitters
Down conversion crystals
Quantum dots
Quantum tunneling
Photodiods
……
A tale of a single world universe

U N IVERSE

W O RLD

O BJECT1

O BJECT2
...
O BJECT K

REST
Quantum states of all macroscopic objects are
Localized Wave Packets all the time
Zero approximation: all particles remain in product LWP states ( rn )
W O RLD

( r1 , r2 , ...., rN , t )   1 ( r1 )  2 ( r2 )... N ( rN )
Particles which do not interact strongly with “macroscopic objects”
need not be in LWP states.
n

W O RLD
  1 ( r1 )  2 ( r2 )... K ( rK ) 
REST
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.

W O R LD
  C1 M ( r1
CM
1
)  rel
( r1 i  r1 j )  C M ( r2
2
CM
2
)  rel
( r2 i  r2 j )... C M ( rM
M
CM
1
)  rel
( rM i  rM j ) 
R E ST
A tale of a single world universe
Quantum states of all macroscopic objects are
Localized Wave Packets all the time


W O R LD
U N IVERSE
  C1 M ( r1

CM
( r1 , r2 , ...., rN , t )   1 ( r1 )  2 ( r2 )... N ( rN )
1
)  rel
( r1 i  r1 j )  C M ( r2
2
 (r )
2
)  rel
( r2 i  r2 j )... C M ( rM
CM
M
1
)  rel
( rM i  rM j ) 
R E ST
 ( r ) of a cat!
TRIVIAL
Observation
CM

 ( r1 )  ( r2 )... ( rN )
1
N
2
Almost the same as in




Bohmian trajectories













Two worlds universe
This is a multiple worlds universe
Two worlds universe
A
B
Bohm and Everett have no randomness
so the concept of probability needs explanation
Probability of what?
0.9
B 0.1
Bohm – simple ignorance probability
Everett – an illusion of probability due to ignorance of the decedents
Bohmian Mechanics
A
A
B
B
Ignorance probability: the observer does not know the initial Bohmian
position
Everett:
A
A
B
B
Probability of what?
Ignorant of what?
Everett:
Sleeping Pill Experiment
Vaidman (1998) ISPS
A
0.9
A
0.1
B
B
Ignorance probability of the descendants A and B
0.9
0.9
A
0.1
A
0.9
B
B
Only
IA
and
What is the probability
that you are in A?
I B can give this answer
What is the probability
that you are in A?
0.9
0.9
A
0.1
What is the probability
that you are in A?
A
B
0.9
B
What is the probability
that you are in A?
Since all the descendants yield the same answer we can relate it to me
before the experiment. I put my bet for the descendants. They have probability.
Thus, my bet is for a probabilistic event.
What is the past of
a quantum particle?
Wheeler:
The present choice of observation influences what we say about the
“past” of the photon; it is undefined and undefinable without the
observation.
No phenomenon is a phenomenon until it is an observed phenomenon.
The “past” and the “Delayed Choice” Double-Slit Experiment
J.A. Wheeler 1978
My lesson:
The “past” of the photon is defined after the observation
Wheeler delayed choice experiment
Wheeler: The photon took the upper path
It could not come the other way
Wheeler delayed choice experiment



Bohm: The photon took the lower path
Wheeler delayed choice experiment
Wheeler: The photon took both paths
Otherwise, the interference cannot be explained
Bohm: The photon took one of the paths
The past of a quantum particle can be
learned by measuring the trace it left
Wheeler delayed choice experiment
Bohm: The photon took the lower path
But the trace shows the upper path
Wheeler delayed choice experiment
Wheeler: The photon took both paths
Otherwise, the interference cannot be explained
Bohm: The photon took one of the paths
The trace shows both paths
Kwiat’s proposal
Kwiat’s proposal
Wheeler: The photon took the lower path
It could not come the other way
Bohm: The photon took the lower path
The trace shows a different picture!
What is “a world” in the many-worlds picture?
Observation i
A


world i
 i ( r1 , r2 , ...., rN , t )
B
i i
O BJECT1
i
O BJECT
i
O BJECT2
... i
O BJECT K
i
REST
is a Localized Wave Packet
for a period of time
A world consist of:
•"classical" macroscopic objects rapidly measured by the environment,
• quantum objects measured only occasionally (at world splitting events),
• weakly coupled quantum objects
The two-state vector formalism expalnation
The pre- and post-selected particle is described
by the two-state vector

t
P  1
t2

t
t1

C  ?
Cw 

 C 
 
P  1
The outcomes of weak measurements are weak values
One world
A

| i
B
A
B
A world consist of:
•"classical" macroscopic objects rapidly measured by the environment,
• quantum objects measured only occasionally (at world splitting events),
• weakly coupled quantum objects
One world
A

i
| i
B
B
A
i
A world consist of:
•"classical" macroscopic objects rapidly measured by the environment,
• quantum objects measured only occasionally (at world splitting events)
which are described by the two-state vectors,
• weakly coupled quantum objects
The two-state vector formalism explanation
The two-state vector formalism explanation
The two-state vector formalism explanation
The two-state vector formalism explanation
The two-state vector formalism explanation
Summary
Bohm and Everett are good candidates for a final
deterministic theory of everything
Bohm provides clear and immediate explanation of our
observations
Everett requires a lot of work to explain our observations
My preferred Bohm requires additional postulate that we
only observe (experience) the Bohmian postions
In my preferred Everett All is  , but for description of
our world i we need  and also  i of some key
quantum particles
i
The description of the past of a quantum particle
should characterize the (weak) trace it leaves