The Transactional Interpretation of Quantum...

The Transactional InterpretationThe Transactional Interpretation

of Quantum Mechanicsof Quantum Mechanics

[email protected]

http://www.npl.washington.edu/ti

Presented at

Georgetown University

Washington, D.C.

October 2, 2000

John G. CramerJohn G. CramerProfessor of Physics

Department of Physics

University of Washington

Seattle, Washington, USA

Recent Research at RHIC

RHIC Au + Au

collision at

130 Gev/nucleon

measured with

the STAR

time projection

Chamber on

June 24, 2000.

Colllisions may

resemble the 1stmicrosecond of the Big Bang.

γ = 60β = 0.99986

γ = 60β = −0.99986

Outline• What is Quantum Mechanics?

• What is an Interpretation?– Example: F = m a

– “Listening” to the formalism

• Lessons from E&M

– Maxwell’s Wave Equation

– Wheeler-Feynman Electrodynamics & Advanced Waves

• The Transactional Interpretation of QM– The Logic of the Transactional Interpretation

– The Quantum Transactional Model

• Paradoxes:

1. The Quantum Bubble

2. Schrödinger’s Cat

3. Wheeler’s Delayed Choice

4. The Einstein-Podolsky-Rosen Paradox

• Application of TI to Quantum Experiments

• Conclusion

Theories andTheories and

InterpretationsInterpretations

What is Quantum Mechanics?

Quantum mechanics is a theory that is ourcurrent “standard model” for describingthe behavior of matter and energy at thesmallest scales (photons, atoms, nuclei,quarks, gluons, leptons, …).

Like all theories, it consists of amathematical formalism and aninterpretation of that formalism.

However, while the formalism has beenaccepted and used for 75 years, itsinterpretation remains a matter of controversy anddebate, and there are several rival interpretationson the market.

Example of an Interpretation:

Newton’s 2nd Law

• Formalism: F = m a


Newton’s 2nd Law


• Interpretation: “The vector force on a bodyis proportional to the product of its scalar mass, which is positive, and the 2nd time derivative of its vector position.”


Newton’s 2nd Law


• What this Interpretation does:

•It relates the formalism to physical observables

•It avoids paradoxes that arise when m<0.

•It insures that F||a.

• Interpretation: “The vector force on a bodyis proportional to the product of its scalar mass, which is positive, and the 2nd time derivative of its vector position.”

What is an Interpretation?

The interpretation of a formalism should:

• Provide links between the mathematical

symbols of the formalism and elements of

the physical world;





the physical world;

• Neutralize the paradoxes; all of them;





the physical world;


• Provide tools for visualization or for

speculation and extension.





the physical world;


• Provide tools for visualization or for

speculation and extension.

• It should not make its own testable predictions!

• It should not have its own sub-formalism!

“Listening” to the Formalism of

Quantum Mechanics

Consider a quantum matrix element:

<S> = ∫v ψ∗ S ψ dr3 = <f | S | i>

… a ψ* - ψ “sandwich”. What does this suggest?


Quantum Mechanics


<S> = ∫v ψ∗ S ψ dr3 = <f | S | i>


Hint: The complex conjugation in ψ∗ is the Wigner operator for time reversal.


Quantum Mechanics


<S> = ∫v ψ∗ S ψ dr3 = <f | S | i>


Hint: The complex conjugation in ψ∗ is the Wigner operator for time reversal. If ψ is a retarded wave, then ψ∗ is an advanced wave.


Quantum Mechanics


<S> = ∫v ψ∗ S ψ dr3 = <f | S | i>


Hint: The complex conjugation in ψ∗ is the Wigner operator for time reversal. If ψ is a retarded wave, then ψ∗ is an advanced wave.

If ψ = Α ψ = Α ψ = Α ψ = Α ei(kr-ωωωω t) then ψ∗ = Α ψ∗ = Α ψ∗ = Α ψ∗ = Α ei(-kr+ωωωω t)

(retarded) (advanced)

Lessons fromLessons from

Classical E&MClassical E&M

Maxwell’s Electromagnetic

Wave Equation

∇∇∇∇2 2 2 2 Fi = 1/= 1/= 1/= 1/c2 2 2 2 ∂∂∂∂2Fi /∂/∂/∂/∂t2

This is a 2nd order differential

equation, which has two time

solutions, retarded and advanced.


Wave Equation

∇∇∇∇2 2 2 2 Fi = 1/= 1/= 1/= 1/c2 2 2 2 ∂∂∂∂2Fi /∂/∂/∂/∂t2




Conventional Approach: Choose only the retarded solution(a “causality” boundary condition).


Wave Equation

∇∇∇∇2 2 2 2 Fi = 1/= 1/= 1/= 1/c2 2 2 2 ∂∂∂∂2Fi /∂/∂/∂/∂t2




Wheeler-Feynman Approach: Use ½ retarded and ½ advanced(time symmetry).

Conventional Approach: Choose only the retarded solution(a “causality” boundary condition).

Lessons fromLessons from

WheelerWheeler--FeynmanFeynman

Absorber TheoryAbsorber Theory

A Classical Wheeler-Feynman

Electromagnetic “Transaction”

• The emitter sends retarded and

advanced waves. It “offers”

to transfer energy.





to transfer energy.

• The absorber responds with an

advanced wave that

“confirms” the transaction.





to transfer energy.

• The absorber responds with an

advanced wave that

“confirms” the transaction.

• The loose ends cancel and

disappear, and energy is

transferred.

The TransactionalThe Transactional

Interpretation ofInterpretation of

Quantum Quantum

MechanicsMechanics

The Logic of the

Transactional Interpretation

1. Interpret Maxwell’s wave

equation as a relativistic

quantum wave equation

(for mrest = 0).

The Logic of the





(for mrest = 0).

2. Interpret the relativistic

Klein-Gordon and Dirac

equations (for mrest > 0)

The Logic of the





(for mrest = 0).

2. Interpret the relativistic

Klein-Gordon and Dirac

equations (for mrest > 0)

3. Interpret the Schrödinger equation as a non-

relativistic reduction of the K-G and Dirac

equations (for mrest > 0).

The Quantum

Transactional Model

Step 1: The emitter sendsout an “offer wave” Ψ.

The Quantum

Transactional Model


Step 2: The absorber responds with a “confirmation wave” Ψ*.

The Quantum

Transactional Model


Step 2: The absorber responds with a “confirmation wave” Ψ*.

Step 3: The process repeats until energy and momentum is transferred and the transaction is completed (wave function collapse).

The Transactional Interpretation

and Wave-Particle Duality

• The completed transaction

projects out only that part

of the offer wave that had

been reinforced by the

confirmation wave.

• Therefore, the transaction

is, in effect, a projection

operator.

• This explains wave-particle

duality.


and the Born Probability Law

Starting from E&M and the Wheeler-

Feynman approach, the E-field

“echo” that the emitter receives

from the absorber is the product

of the retarded-wave E-field at

the absorber and the advanced-

wave E-field at the emitter.


and the Born Probability Law

Starting from E&M and the Wheeler-

Feynman approach, the E-field

“echo” that the emitter receives

from the absorber is the product

of the retarded-wave E-field at

the absorber and the advanced-

wave E-field at the emitter.

Translating this to quantum

mechanical terms, the “echo”

that the emitter receives from

each potential absorber is ψψ*,leading to the Born Probability Law.

ψψ*

ψ

The Role of the Observer in

the Transactional Interpretation

• In the Copenhagen interpretation,

observers have a special role as the

collapsers of wave functions. This leads

to problems, e.g., in quantum cosmology

where no observers are present.








• In the transactional interpretation,

transactions involving an observer are the

same as any other transactions.








• In the transactional interpretation,

transactions involving an observer are the

same as any other transactions.

• Thus, the observer-centric aspects of the

Copenhagen interpretation are avoided.

QuantumQuantum

ParadoxesParadoxes

Paradox 1:

The Quantum Bubble

Situation:A photon is emitted

from an isotropic source.

Paradox 1:

The Quantum Bubble

Question (Albert Einstein):

If a photon is detected at

Detector A, how does the

photon’s wave function at the

location of Detectors B & C

know that it should vanish?

Situation:A photon is emitted

from an isotropic source.

Paradox 1: Application of the


to the Quantum Bubble• A transaction develops

between the source and

detector A, transferring the energy there and

blocking any similar transfer to the other potential

detectors, due to the 1-photon boundary condition.

• The transactional handshakes acts nonlocally to

answer Einstein’s question.

• This is an extension of Pilot-Wave idea of

deBroglie.

Paradox 2:

Schrödinger’s CatExperiment: A cat isplaced in a sealed boxcontaining a devicethat has a 50% probabilityof killing the cat.

Paradox 2:


Question 1: When does thewave function collapse?What is the wave functionof the cat just before thebox is opened? (Ψ = ½ dead + ½ alive?)

Paradox 2:


Question 1: When does thewave function collapse?What is the wave functionof the cat just before thebox is opened? (Ψ = ½ dead + ½ alive?)

Question 2: If we observe Schrödinger, what is his wave

function during the experiment? When does it collapse?



to Schrödinger’s Cat • A transaction eitherdevelops between thesource and the detector,or else it does not. Ifit does, the transactionforms nonlocally, notat some particular time.

• Therefore, asking whenthe wave functioncollapsed was asking the wrong question.

Paradox 3:

Wheeler’s Delayed Choice

A source emits one photon. Its

wave function passes through

two slits, producing interference.

Paradox 3:





The observer can choose to either:

(a) measure the interference

pattern (wavelength) at E

Paradox 3:







pattern (wavelength) at E or

(b) measure the slit position with

telescopes T1 and T2.

Paradox 3:







pattern (wavelength) at E or

(b) measure the slit position with

telescopes T1 and T2.

He decides which to do after the

photon has passed the slits.



• If plate E is up, a

transaction forms between

E and the source S and

involves waves passing

through both slits.





E and the source S and

involves waves passing

through both slits.

• If the plate E is down, a


telescope T1 or T2 and the

source S, and involves waves

passing through only one slit.





E and the source S.

• If the plate E is down, a


one of the telescopes

(T1, T2) and the source S.

• In either case, when the

decision was made is

irrelevant.

Paradox 4: EPR Experiments

Malus and Furry

An EPR Experiment measures the

correlated polarizations of a pair

of entangled photons, obeying

Malus’ Law [P(θθθθrel) = Cos2θθθθrel]


Malus and Furry





The measurement gives the same result

as if both filters were in the same arm.


Malus and Furry





The measurement gives the same result

as if both filters were in the same arm.

Furry proposed to place both photons in

the same random polarization state.

This gives a different and weaker

correlation.


Transactional Interpretation to EPR

An EPR experiment requires a

consistent double advanced-

retarded handshake between

the emitter and the two

detectors.

An EPR experiment requires a

consistent double advanced-

retarded handshake between

the emitter and the two

detectors.

The “lines of communication”

are not spacelike but

negative and positive

timelike. While spacelike

communication has

relativity problems, timelike communication does not.


Transactional Interpretation to EPR

Faster Than Light?Faster Than Light?

Is FTL Communication

Possible with EPR Nonlocality?

Question: Can the choice of measurements

at D1 telegraph information as the

measurement outcome at D2?




Answer: No! Operators for measurements

D1 and D2 commute. [D1, D2]=0. Choice

of measurements at D1 has no observable

consequences at D2. (Eberhard’s Theorem)










Levels of EPR Communication:

1. Enforce conservation laws (Yes)










Levels of EPR Communication:

1. Enforce conservation laws (Yes)

2. Talk observer-to-observer (No!) [Unless nonlinear QM?!)



Conclusions (Part 1)

• The Transactional Interpretation is

visible in the quantum formalism

• It involves fewer independent

assumptions than its alternatives.

• It solves the quantum paradoxes;

all of them.

• It explains wave-function collapse, wave-

particle duality, and nonlocality.

• ERP communication FTL is not possible!

ApplicationApplication::

An InteractionAn Interaction--FreeFree

MeasurementMeasurement

Elitzur-Vaidmann

Interaction-Free Measurements

Suppose you are given a set of photon-activated

bombs, which will explode when a single

photon touches their optically sensitive triggers.

Elitzur-Vaidmann




photon touches their optically sensitive trigger.

However, some fraction of the bombs are “duds” which

will freely pass an incident photon without exploding.

Elitzur-Vaidmann







Your assignment is to sort the bombs into “live” and “dud”

categories. How can you do this without exploding all

the live bombs?

Elitzur-Vaidmann




photon touches their optically sensitive trigger.





the live bombs?

Classically, the task is impossible. All live bombs explode!

Elitzur-Vaidmann









the live bombs?

Classically, the task is impossible. All live bombs explode!

However, using quantum mechanics, you can do it!

The Mach-Zender Interferometer

A Mach-Zender intereferometer

splits a light beam at S1 into

two paths, A and B, having

equal lengths, and recombines

the beams at S2. All the light

goes to detector D1 because the beams interfere

destructively at detector D2.









D1: L|S1r|Ar|S2t|D1 and L|S1t|Br|S2r|D1 => in phase









D1: L|S1r|Ar|S2t|D1 and L|S1t|Br|S2r|D1 => in phase

D2: L|S1r|Ar|S2r|D2 and L|S1t|Br|S2t|D2 => out of phase

A M-Z Inteferometer with

an Opaque Object in Beam A

If an opaque object is placed in

beam A, the light on path B

goes equally to detectors D1

and D2.






and D2.

This is because there is now no interference, and splitter S2divides the incident light equally between the two

detector paths.






and D2.

This is because there is now no interference, and splitter S2divides the incident light equally between the two

detector paths.

Therefore, detection of a photon at D2 (or an explosion)

signals that a bomb has been placed in path A.

How to Sort the Bombs

Send in a photon with thebomb in A. If it is a dud,the photon will alwaysgo to D1. If it is a livebomb, ½ of the time thebomb will explode, ¼ ofthe time it will go to D1 and ¼ of the time to D2.

How to Sort the Bombs

Send in a photon with thebomb in A. If it is a dud,the photon will alwaysgo to D1. If it is a livebomb, ½ of the time thebomb will explode, ¼ ofthe time it will go to D1 and ¼ of the time to D2.

Therefore, on each D1 signal, send in another photon.On a D2 signal, stop, you have a live bomb!After 10 or so D1 signals, stop, you have a dud bomb! By this process, you will find unexploded 1/3 of the live bombs and will explode 2/3 of the live bombs.

Quantum Knowledge

Thus, we have used quantum

mechanics to gain a kind of

knowledge (i.e., which

unexploded bombs are live)

that is not accessible to us classically.

or

Quantum Knowledge






Further, we have detected the presence of an object (the live

bomb), without a single photon having interacted with

that object. Only the possibility of an interaction was

required for the measurement.

or

Quantum Knowledge










Q: How can we understand this curious quantum behavior?

or

Quantum Knowledge










Q: How can we understand this curious quantum behavior?

A: Apply the transactional interpretation.

or

Transactions for No Object

There are two allowed paths between the light source L and

the detector D1.



the detector D1. If the paths have equal lengths, the offer

waves ψ to D1 will interfere constructively, while the

offer ψ waves to D2 interfere destructively and cancel.



the detector D1. If the paths have equal lengths, the offer

waves ψ to D1 will interfere constructively, while the

offer ψ waves to D2 interfere destructively and cancel.

The confirmation waves ψ* traveling back to L along both paths back to L will confirm the transaction.

Transactions with Bomb Present (1)

An offer wave from L on path A will reach the

bomb. An offer wave on path B reaching S2 will

split equally, reaching each detector with ½

amplitude.


The bomb will return a confirmation wave on path

A. Detectors D1 and D2 will each return

confirmation waves, both to L and to the back

side of the bomb. The amplitudes of the

confirmation waves at L will be ½ from the bomb

and ¼ from each of the detectors, and a

transaction will form based on those amplitudes.


Therefore, when the bomb does not explode, it is

nevertheless “probed” by virtual offer and

confirmation waves from both sides.

The bomb must be capable of interaction with these

waves, even though no interaction takes place

(because no transaction forms).

ApplicationApplication::

The QuantumThe Quantum

Xeno EffectXeno Effect

Quantum Xeno Effect Improvement

of Interaction-Free Measurements

Kwait, et al, have devised

an improved scheme for

interaction-free

measurements that can

have efficiencies

approaching 100%.

Their trick is to use the

quantum Xeno effect to probe the bomb with weak

waves many times. The incident photon runs around an

optical racetrack N times, until it is deflected out.

Efficiency of the Xeno


If the object is present,

the emerging photon

at DH will be detected

with a probability

PD = Cos2N(ππππ/2N).

The photon will interact

with the object with a

probability PR = 1 - PD = 1 - Cos2N(ππππ/2N).

When N is large, PD ≈≈≈≈ 1 −−−− (ππππ/2)2/N and PR ≈≈≈≈ (ππππ/2)2/N. Therefore, the interaction probability decreases as 1/N.

Offer Waves

with No Object in the V Beam

This shows an unfolding of the Xeno apparatus when no object is present in the V beam. In this case the photon wave is split into horizontal (H) and vertical (V) components, and then recombined. The successive R filters each rotate the plane of polarization by π/2N. The photon emerges with V polarization.

This shows an unfolding of the Xeno apparatus when an

object is present in the V beam. In this case the photon

wave is repratedly reset to horizontal (H) polarization.

The photon emerges with H polarization.

Offer Waves

with an Object in the V Beam

Confirmation Waves

with an Object in the V Beam

This shows the confirmation waves for an unfolding of the

Xeno apparatus when an object is present in the V beam.

In this case the photon wave is reset to horizontal (H)

polarization. The wave returns to the source L with the

H polarization of the initial offer wave.

Conclusions (Part 2)

• The Transactional Interpretation can

account for the non-classical information

provided by interaction-free-

measurements.

• The roles of the virtual offer and

confirmation waves in probing the

object being “measured” lends support

to the transactional view of the process.

• The examples shows the power of the

interpretation in dealing with counter-

intuitive quantum optics results.

Applications of the Transactional Applications of the Transactional

Interpretation of Quantum MechanicsInterpretation of Quantum Mechanics

[email protected]

http://www.npl.washington.edu/ti

Presented at the

Breakthrough Physics Lecture Series

Marshall Space Flight Center

Marshall, Alabama

August 17, 2000

John G. CramerJohn G. CramerProfessor of Physics

Department of Physics

University of Washington

Seattle, Washington, USA

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