The Transactional InterpretationThe Transactional Interpretationof Quantum Mechanicsof Quantum Mechanics

cramer@phys.washington.edu

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

Presented atGeorgetown University

Washington, D.C.

October 2, 2000

John G. CramerJohn G. CramerProfessor of Physics

Department of PhysicsUniversity of WashingtonSeattle, Washington, USA

Recent Research at RHIC

RHIC Au + Aucollision at130 Gev/nucleonmeasured withthe STARtime projectionChamber onJune 24, 2000.Colllisions mayresemble the 1st microsecond of the Big Bang.

= 60= 0.99986

= 60= 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 Bubble2. Schrödinger’s Cat3. Wheeler’s Delayed Choice4. The Einstein-Podolsky-Rosen Paradox

• Application of TI to Quantum Experiments• Conclusion

Theories andTheories andInterpretationsInterpretations

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

Example of an Interpretation: Newton’s 2nd Law

• Formalism: F = m 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.”

Example of an Interpretation: Newton’s 2nd Law

• Formalism: F = m a

• 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;

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;

• Neutralize the paradoxes; all of them;

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;

• Neutralize the paradoxes; all of them;• Provide tools for visualization or for

speculation and extension.

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;

• Neutralize the paradoxes; all of them;• 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> = vSdr3 = <f | S | i>

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

“Listening” to the Formalism of Quantum Mechanics

Consider a quantum matrix element:

<S> = vSdr3 = <f | S | i>

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

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

“Listening” to the Formalism of Quantum Mechanics

Consider a quantum matrix element:

<S> = vSdr3 = <f | S | i>

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

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

“Listening” to the Formalism of Quantum Mechanics

Consider a quantum matrix element:

<S> = vSdr3 = <f | S | i>

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

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

If ei(kr-t) then ei(-kr+t)

(retarded) (advanced)

Lessons fromLessons fromClassical E&MClassical E&M

Maxwell’s Electromagnetic Wave Equation

Fic2Fit2

This is a 2nd order differential equation, which has two time solutions, retarded and advanced.

Maxwell’s Electromagnetic Wave Equation

Fic2Fit2

This is a 2nd order differential equation, which has two time solutions, retarded and advanced.

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

Maxwell’s Electromagnetic Wave Equation

Fic2Fit2

This is a 2nd order differential equation, which has two time solutions, retarded and advanced.

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

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

Lessons fromLessons fromWheeler-FeynmanWheeler-FeynmanAbsorber TheoryAbsorber Theory

A Classical Wheeler-Feynman Electromagnetic “Transaction”

• The emitter sends retarded and advanced waves. It “offers”to transfer energy.

A Classical Wheeler-Feynman Electromagnetic “Transaction”

• The emitter sends retarded and advanced waves. It “offers”to transfer energy.

• The absorber responds with an advanced wave that“confirms” the transaction.

A Classical Wheeler-Feynman Electromagnetic “Transaction”

• The emitter sends retarded and advanced waves. It “offers”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 TransactionalInterpretation ofInterpretation of

Quantum MechanicsQuantum Mechanics

The Logic of theTransactional Interpretation

1. Interpret Maxwell’s waveequation as a relativisticquantum wave equation(for mrest = 0).

The Logic of theTransactional Interpretation

1. Interpret Maxwell’s waveequation as a relativisticquantum wave equation(for mrest = 0).

2. Interpret the relativisticKlein-Gordon and Diracequations (for mrest > 0)

The Logic of theTransactional Interpretation

1. Interpret Maxwell’s waveequation as a relativisticquantum wave equation(for mrest = 0).

2. Interpret the relativisticKlein-Gordon and Diracequations (for mrest > 0)

3. Interpret the Schrödinger equation as a non-relativistic reduction of the K-G and Diracequations (for mrest > 0).

The QuantumTransactional Model

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

The QuantumTransactional Model

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

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

The QuantumTransactional Model

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

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

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 transactionprojects out only that partof the offer wave that had been reinforced by theconfirmation wave.

• Therefore, the transactionis, in effect, a projectionoperator.

• This explains wave-particleduality.

The Transactional Interpretation and the Born Probability Law

Starting from E&M and the Wheeler-Feynman approach, the E-field“echo” that the emitter receivesfrom the absorber is the productof the retarded-wave E-field atthe absorber and the advanced-wave E-field at the emitter.

The Transactional Interpretation and the Born Probability Law

Starting from E&M and the Wheeler-Feynman approach, the E-field“echo” that the emitter receivesfrom the absorber is the productof the retarded-wave E-field atthe absorber and the advanced-wave E-field at the emitter.

Translating this to quantummechanical terms, the “echo”that the emitter receives fromeach potential absorber is *,leading to the Born Probability Law.

*

The Role of the Observer inthe 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.

The Role of the Observer inthe 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.

The Role of the Observer inthe 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.

• Thus, the observer-centric aspects of the Copenhagen interpretation are avoided.

QuantumQuantumParadoxesParadoxes

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: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 Transactional Interpretation

to the Quantum Bubble• A transaction develops

between the source anddetector 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 Cat

Experiment: A cat isplaced in a sealed boxcontaining a devicethat has a 50% probabilityof killing the cat.

Paradox 2:Schrödinger’s Cat

Experiment: A cat isplaced in a sealed boxcontaining a devicethat has a 50% probabilityof killing the cat.

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

Paradox 2:Schrödinger’s Cat

Experiment: A cat isplaced in a sealed boxcontaining a devicethat has a 50% probabilityof killing the cat.

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

Question 2: If we observe Schrödinger, what is his wavefunction during the experiment? When does it collapse?

Paradox 2: Application of the Transactional Interpretation

to Schrödinger’s Cat • A transaction either

develops 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:Wheeler’s Delayed Choice

A source emits one photon. Its wave function passes through two slits, producing interference.

The observer can choose to either:(a) measure the interference pattern (wavelength) at E

Paradox 3:Wheeler’s Delayed Choice

A source emits one photon. Its wave function passes through two slits, producing interference.

The observer can choose to either:(a) measure the interference pattern (wavelength) at E or(b) measure the slit position with telescopes T1 and T2.

Paradox 3:Wheeler’s Delayed Choice

A source emits one photon. Its wave function passes through two slits, producing interference.

The observer can choose to either:(a) measure the interference 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.

Paradox 3: Application of the Transactional Interpretation

• If plate E is up, atransaction forms betweenE and the source S andinvolves waves passingthrough both slits.

Paradox 3: Application of the Transactional Interpretation

• If plate E is up, atransaction forms betweenE and the source S andinvolves waves passingthrough both slits.

• If the plate E is down, atransaction forms betweentelescope T1 or T2 and thesource S, and involves wavespassing through only one slit.

Paradox 3: Application of the Transactional Interpretation

• If plate E is up, atransaction forms betweenE and the source S.

• If the plate E is down, atransaction forms betweenone of the telescopes(T1, T2) and the source S.

• In either case, when thedecision was made isirrelevant.

Paradox 4: EPR ExperimentsMalus and Furry

An EPR Experiment measures the correlated polarizations of a pairof entangled photons, obeyingMalus’ Law [P(rel) = Cos2rel]

Paradox 4: EPR ExperimentsMalus and Furry

An EPR Experiment measures the correlated polarizations of a pairof entangled photons, obeyingMalus’ Law [P(rel) = Cos2rel]

The measurement gives the same resultas if both filters were in the same arm.

Paradox 4: EPR ExperimentsMalus and Furry

An EPR Experiment measures the correlated polarizations of a pairof entangled photons, obeyingMalus’ Law [P(rel) = Cos2rel]

The measurement gives the same resultas if both filters were in the same arm.

Furry proposed to place both photons inthe same random polarization state.This gives a different and weaker correlation.

Paradox 4: Application of the 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 aconsistent double advanced-retarded handshake betweenthe emitter and the twodetectors.

The “lines of communication”are not spacelike butnegative and positivetimelike. While spacelikecommunication hasrelativity problems, timelike communication does not.

Paradox 4: Application of the Transactional Interpretation to EPR

Faster Than Light?Faster Than Light?

Is FTL CommunicationPossible with EPR Nonlocality?

Question: Can the choice of measurementsat D1 telegraph information as themeasurement outcome at D2?

Question: Can the choice of measurementsat D1 telegraph information as themeasurement outcome at D2?

Answer: No! Operators for measurementsD1 and D2 commute. [D1, D2]=0. Choiceof measurements at D1 has no observableconsequences at D2. (Eberhard’s Theorem)

Is FTL CommunicationPossible with EPR Nonlocality?

Question: Can the choice of measurementsat D1 telegraph information as themeasurement outcome at D2?

Answer: No! Operators for measurementsD1 and D2 commute. [D1, D2]=0. Choiceof measurements at D1 has no observableconsequences at D2. (Eberhard’s Theorem)

Levels of EPR Communication:

1. Enforce conservation laws (Yes)

Is FTL CommunicationPossible with EPR Nonlocality?

Question: Can the choice of measurementsat D1 telegraph information as themeasurement outcome at D2?

Answer: No! Operators for measurementsD1 and D2 commute. [D1, D2]=0. Choiceof measurements at D1 has no observableconsequences at D2. (Eberhard’s Theorem)

Levels of EPR Communication:

1. Enforce conservation laws (Yes)

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

Is FTL CommunicationPossible with EPR Nonlocality?

Conclusions (Part 1)

• The Transactional Interpretation isvisible in the quantum formalism

• It involves fewer independentassumptions 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 Interaction-FreeAn Interaction-Free

MeasurementMeasurement

Elitzur-VaidmannInteraction-Free Measurements

Suppose you are given a set of photon-activatedbombs, which will explode when a singlephoton touches their optically sensitive triggers.

Elitzur-VaidmannInteraction-Free Measurements

Suppose you are given a set of photon-activatedbombs, which will explode when a singlephoton touches their optically sensitive trigger.

However, some fraction of the bombs are “duds” whichwill freely pass an incident photon without exploding.

Elitzur-VaidmannInteraction-Free Measurements

Suppose you are given a set of photon-activatedbombs, which will explode when a singlephoton touches their optically sensitive triggers.

However, some fraction of the bombs are “duds” which will freely pass an incident photon without exploding.

Your assignment is to sort the bombs into “live” and “dud” categories. How can you do this without exploding all the live bombs?

Elitzur-VaidmannInteraction-Free Measurements

Suppose you are given a set of photon-activatedbombs, which will explode when a singlephoton touches their optically sensitive trigger.

However, some fraction of the bombs are “duds” whichwill freely pass an incident photon without exploding.

Your assignment is to sort the bombs into “live” and “dud” categories. How can you do this without exploding allthe live bombs?

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

Elitzur-VaidmannInteraction-Free Measurements

Suppose you are given a set of photon-activatedbombs, which will explode when a singlephoton touches their optically sensitive triggers.

However, some fraction of the bombs are “duds” which will freely pass an incident photon without exploding.

Your assignment is to sort the bombs into “live” and “dud” categories. How can you do this without exploding all 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 intereferometersplits a light beam at S1 intotwo paths, A and B, havingequal lengths, and recombinesthe beams at S2. All the lightgoes to detector D1 because the beams interfere destructively at detector D2.

The Mach-Zender Interferometer

A Mach-Zender intereferometersplits a light beam at S1 intotwo paths, A and B, havingequal lengths, and recombinesthe beams at S2. All the lightgoes 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

The Mach-Zender Interferometer

A Mach-Zender intereferometersplits a light beam at S1 intotwo paths, A and B, havingequal lengths, and recombinesthe beams at S2. All the lightgoes 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

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

A M-Z Inteferometer withan Opaque Object in Beam A

If an opaque object is placed inbeam A, the light on path Bgoes equally to detectors D1

and D2.

A M-Z Inteferometer withan Opaque Object in Beam A

If an opaque object is placed inbeam A, the light on path Bgoes equally to detectors D1

and D2.

This is because there is now no interference, and splitter S2 divides the incident light equally between the two detector paths.

A M-Z Inteferometer withan Opaque Object in Beam A

If an opaque object is placed inbeam A, the light on path Bgoes equally to detectors D1

and D2.

This is because there is now no interference, and splitter S2 divides 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 quantummechanics to gain a kind ofknowledge (i.e., whichunexploded bombs are live)that is not accessible to us classically.

or

Quantum Knowledge

Thus, we have used quantummechanics to gain a kind ofknowledge (i.e., whichunexploded bombs are live)that is not accessible to us classically.

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

Thus, we have used quantummechanics to gain a kind ofknowledge (i.e., whichunexploded bombs are live)that is not accessible to us classically.

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.

Q: How can we understand this curious quantum behavior?

or

Quantum Knowledge

Thus, we have used quantummechanics to gain a kind ofknowledge (i.e., whichunexploded bombs are live)that is not accessible to us classically.

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.

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.

Transactions for No Object

There are two allowed paths between the light source L and the detector D1. If the paths have equal lengths, the offer waves to D1 will interfere constructively, while the offer waves to D2 interfere destructively and cancel.

Transactions for No Object

There are two allowed paths between the light source L and the detector D1. If the paths have equal lengths, the offer waves to D1 will interfere constructively, while the offer waves to D2 interfere destructively and cancel. The confirmation waves * 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.

Transactions with Bomb Present (2)

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.

Transactions with Bomb Present (3)

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 QuantumXeno EffectXeno Effect

Quantum Xeno Effect Improvementof Interaction-Free Measurements

Kwait, et al, have devisedan improved scheme forinteraction-freemeasurements that canhave efficienciesapproaching 100%.

Their trick is to use thequantum Xeno effect to probe the bomb with weak waves many times. The incident photon runs around anoptical racetrack N times, until it is deflected out.

Efficiency of the Xeno Interaction-Free Measurements

If the object is present,the emerging photonat DH will be detectedwith a probabilityPD = Cos2N(/2N).

The photon will interactwith the object with aprobability PR = 1 - PD = 1 - Cos2N(/2N).

When N is large, PD 1 (/2)2/N and PR (/2)2/N.

Therefore, the interaction probability decreases as 1/N.

Offer Waveswith 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 /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 Waveswith an Object in the V Beam

Confirmation Waveswith 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 theH 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 theobject being “measured” lends supportto 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 Interpretation of Quantum

MechanicsMechanics

cramer@phys.washington.edu

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

Presented at theBreakthrough Physics Lecture Series

Marshall Space Flight Center

Marshall, Alabama

August 17, 2000

John G. CramerJohn G. CramerProfessor of Physics

Department of PhysicsUniversity of WashingtonSeattle, Washington, USA