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

Lev Vaidman

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 t TRIVIAL

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 t TRIVIAL

Everett Interpretation

Many parallelObservations

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 t 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

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 t many

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 parallelObservations

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

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

Bohm and Everett have no randomness

so the concept of probability needs explanation

Probability of what?A

B

0.9

0.1

Bohm – simple ignorance probability

Everett – an illusion of probability due to ignorance of the decedents

A

B

A

B

Bohmian Mechanics

Ignorance probability: the observer does not know the initial Bohmian position

Everett:

Probability of what?Ignorant of what?

A

B

A

B

A

A

B B

Sleeping Pill Experiment

Ignorance probability of the descendants A and B

Vaidman (1998) ISPS

0.9

0.1

Everett:

AA

B

B

What is the probability that you are in A?

0.9

What is the probability that you are in A?

0.9

0.9

0.1

Only and can give this answerAI BI

AA

B

B

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 probability that you are in A?

0.9

What is the probability that you are in A?

0.9

0.9

0.1

What is the past of a quantum particle?

The “past” and the “Delayed Choice” Double-Slit Experiment J.A. Wheeler 1978

The present choice of observation influences what we say about the “past” of the photon; it is undefined and undefinable without the observation.

The “past” of the photon is defined after the observation

Wheeler:

No phenomenon is a phenomenon until it is an observed phenomenon.

My lesson:

Wheeler delayed choice experiment

Wheeler: The photon took the upper pathIt 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 pathsOtherwise, the interference cannot be explainedBohm: 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 pathsOtherwise, the interference cannot be explainedBohm: The photon took one of the pathsThe trace shows both paths

Kwiat’s proposal

Kwiat’s proposal

Wheeler: The photon took the lower pathIt could not come the other wayBohm: The photon took the lower pathThe trace shows a different picture!

What is “a world” in the many-worlds picture? 1 2( , , ...., , )Ni r r r t world i

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

OBJECT

i is a Localized Wave Packet for a period of time

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

Observation i

t

P 1

1t

2t

P 1

The pre- and post-selected particle is described by the two-state vector

w

CC

The outcomes of weak measurements are weak values

?C

t

The two-state vector formalism expalnation

A A BB

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 | i

A A BB

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

One world | i i

i

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

The description of the past of a quantum particle should characterize the (weak) trace it leaves

i

Bohm and Everett are good candidates for a final deterministic theory of everything

i i

Bohm provides clear and immediate explanation of our observationsEverett requires a lot of work to explain our observations

My preferred Bohm requires additional postulate that we only observe (experience) the Bohmian postionsIn my preferred Everett All is , but for description of our world we need and also of some key quantum particles