The%20Transactional%20Interpretation%20of%20Quantum%20Mechanics

1
The Transactional Interpretationof Quantum
Mechanics
http//www.npl.washington.edu/ti

• John G. Cramer
• Professor of Physics
• Department of Physics
• University of Washington
• Seattle, Washington, USA

cramer_at_phys.washington.edu
Presented atGeorgetown University Washington,
D.C. October 2, 2000
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Recent Research at RHIC
g 60 b 0.99986
g 60 b -0.99986

• RHIC Au Au
• collision at
• 130 Gev/nucleon
• measured with
• the STAR
• time projection
• Chamber on
• June 24, 2000.
• Colllisions may
• resemble the 1st microsecond of the Big Bang.

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Outline

• What is Quantum Mechanics?
• What is an Interpretation?
• Example F m a
• Listening to the formalism
• Lessons from EM
• Maxwells Wave Equation
• Wheeler-Feynman Electrodynamics Advanced Waves
• The Transactional Interpretation of QM
• The Logic of the Transactional Interpretation
• The Quantum Transactional Model
• Paradoxes
• The Quantum Bubble
• Schrödingers Cat
• Wheelers Delayed Choice
• The Einstein-Podolsky-Rosen Paradox
• Application of TI to Quantum Experiments
• Conclusion

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Theories andInterpretations
5
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.

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Example of an Interpretation Newtons 2nd Law

• Formalism F m a

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Example of an Interpretation Newtons 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.

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Example of an Interpretation Newtons 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.

• What this Interpretation does
• It relates the formalism to physical observables
• It avoids paradoxes that arise when mlt0.
• It insures that Fa.

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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

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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

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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.

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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!

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Listening to the Formalism of Quantum Mechanics

• Consider a quantum matrix element
• ltSgt òv y S y dr3 ltf S igt
• a y - y sandwich. What does this suggest?

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Listening to the Formalism of Quantum Mechanics

• Consider a quantum matrix element
• ltSgt òv y S y dr3 ltf S igt
• a y - y sandwich. What does this suggest?

Hint The complex conjugation in y is the
Wigner operator for time reversal.
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Listening to the Formalism of Quantum Mechanics

• Consider a quantum matrix element
• ltSgt òv y S y dr3 ltf S igt
• a y - y sandwich. What does this suggest?

Hint The complex conjugation in y is the
Wigner operator for time reversal. If y is a
retarded wave, then y is an advanced wave.
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Listening to the Formalism of Quantum Mechanics

• Consider a quantum matrix element
• ltSgt òv y S y dr3 ltf S igt
• a y - y sandwich. What does this suggest?

Hint The complex conjugation in y is the
Wigner operator for time reversal. If y is a
retarded wave, then y is an advanced wave. If
y A ei(kr-wt) then y A ei(-krwt)
(retarded) (advanced)
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Lessons fromClassical EM
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Maxwells Electromagnetic Wave Equation

• Ñ2 Fi 1/c2 2Fi /t2
• This is a 2nd order differential equation, which
  has two time solutions, retarded and advanced.

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Maxwells Electromagnetic Wave Equation

• Ñ2 Fi 1/c2 2Fi /t2
• 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).
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Maxwells Electromagnetic Wave Equation

• Ñ2 Fi 1/c2 2Fi /t2
• 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).
Wheeler-Feynman Approach Use ½ retarded and ½
advanced(time symmetry).
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Lessons fromWheeler-FeynmanAbsorber Theory
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A Classical Wheeler-Feynman Electromagnetic
Transaction

• The emitter sends retarded and advanced waves.
  It offersto transfer energy.

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A Classical Wheeler-Feynman Electromagnetic
Transaction

• The emitter sends retarded and advanced waves.
  It offersto transfer energy.
• The absorber responds with an advanced wave
  thatconfirms the transaction.

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A Classical Wheeler-Feynman Electromagnetic
Transaction

• The emitter sends retarded and advanced waves.
  It offersto transfer energy.
• The absorber responds with an advanced wave
  thatconfirms the transaction.
• The loose ends cancel and disappear, and energy
  is transferred.

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The TransactionalInterpretation ofQuantum
Mechanics
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The Logic of theTransactional Interpretation

1. Interpret Maxwells waveequation as a
   relativisticquantum wave equation(for mrest
   0).

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The Logic of theTransactional Interpretation

1. Interpret Maxwells waveequation as a
   relativisticquantum wave equation(for mrest
   0).
2. Interpret the relativisticKlein-Gordon and
   Diracequations (for mrest gt 0)

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The Logic of theTransactional Interpretation

1. Interpret Maxwells waveequation as a
   relativisticquantum wave equation(for mrest
   0).
2. Interpret the relativisticKlein-Gordon and
   Diracequations (for mrest gt 0)
3. Interpret the Schrödinger equation as a
   non-relativistic reduction of the K-G and
   Diracequations (for mrest gt 0).

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The QuantumTransactional Model

• Step 1 The emitter sendsout an offer wave Y.

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The QuantumTransactional Model

• Step 1 The emitter sendsout an offer wave Y.

Step 2 The absorber responds with a
confirmation wave Y.
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The QuantumTransactional Model

• Step 1 The emitter sendsout an offer wave Y.

Step 2 The absorber responds with a
confirmation wave Y.
Step 3 The process repeats until energy and
momentum is transferred and the transaction is
completed (wave function collapse).
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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.

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The Transactional Interpretation and the Born
Probability Law

• Starting from EM and the Wheeler-Feynman
  approach, the E-fieldecho 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.

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The Transactional Interpretation and the Born
Probability Law

• Starting from EM and the Wheeler-Feynman
  approach, the E-fieldecho 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
  echothat the emitter receives fromeach
  potential absorber is yy,leading to the Born
  Probability Law.

y
yy
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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.

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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.

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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.

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QuantumParadoxes
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Paradox 1The Quantum Bubble
Situation A photon is emitted from an
isotropic source.
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Paradox 1The Quantum Bubble
Situation A photon is emitted from an
isotropic source.

• Question (Albert Einstein)
• If a photon is detected at Detector A, how does
  the photons wave function at the location of
  Detectors B C know that it should vanish?

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Paradox 1The Quantum Bubble
Situation A photon is emitted from an
isotropic source.

• Question (Albert Einstein)
• If a photon is detected at Detector A, how does
  the photons wave function at the location of
  Detectors B C know that it should vanish?

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Paradox 1 Application of the Transactional
Interpretationto the Quantum Bubble

• A transaction developsbetween 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 Einsteins question.
• This is an extension of Pilot-Wave idea of
  deBroglie.

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Paradox 2Schrödingers Cat

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

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Paradox 2Schrödingers 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? (Y ½ dead ½
  alive?)

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Paradox 2Schrödingers 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? (Y ½ dead ½
  alive?)

Question 2 If we observe Schrödinger, what is
his wavefunction during the experiment? When
does it collapse?
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Paradox 2 Application of the Transactional
Interpretationto Schrödingers 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.

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Paradox 3Wheelers Delayed Choice

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

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Paradox 3Wheelers 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

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Paradox 3Wheelers 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.

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Paradox 3Wheelers 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.

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Paradox 3 Application of the Transactional
Interpretation

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

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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.

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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.

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Paradox 4 EPR ExperimentsMalus and Furry

• An EPR Experiment measures the correlated
  polarizations of a pairof entangled photons,
  obeyingMalus Law P(qrel) Cos2qrel

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Paradox 4 EPR ExperimentsMalus and Furry

• An EPR Experiment measures the correlated
  polarizations of a pairof entangled photons,
  obeyingMalus Law P(qrel) Cos2qrel
• The measurement gives the same resultas if both
  filters were in the same arm.

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Paradox 4 EPR ExperimentsMalus and Furry

• An EPR Experiment measures the correlated
  polarizations of a pairof entangled photons,
  obeyingMalus Law P(qrel) Cos2qrel
• 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.

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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.

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Paradox 4 Application of the Transactional
Interpretation to EPR

• An EPR experiment requires aconsistent double
  advanced-retarded handshake betweenthe emitter
  and the twodetectors.
• The lines of communicationare not spacelike
  butnegative and positivetimelike. While
  spacelikecommunication hasrelativity problems,
  timelike communication does not.

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Faster Than Light?
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Is FTL CommunicationPossible with EPR
Nonlocality?

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

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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, D20. Choiceof measurements at
  D1 has no observableconsequences at D2.
  (Eberhards Theorem)

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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, D20. Choiceof measurements at
  D1 has no observableconsequences at D2.
  (Eberhards Theorem)
• Levels of EPR Communication
• Enforce conservation laws (Yes)

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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, D20. Choiceof measurements at
  D1 has no observableconsequences at D2.
  (Eberhards Theorem)
• Levels of EPR Communication
• Enforce conservation laws (Yes)
• Talk observer-to-observer (No!) Unless
  nonlinear QM?!)

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Conclusions (Part 1)

• The Transactional Interpretation isvisible in
  the quantum formalism
• It involves fewer independentassumptions than
  its alternatives.
• It solves the quantum paradoxesall of them.
• It explains wave-function collapse, wave-particle
  duality, and nonlocality.
• ERP communication FTL is not possible!

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ApplicationAn Interaction-FreeMeasurement
66
Elitzur-VaidmannInteraction-Free Measurements

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

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Elitzur-VaidmannInteraction-Free Measurements

• Suppose you are given a set of photon-activatedbo
  mbs, 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.

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Elitzur-VaidmannInteraction-Free Measurements

• Suppose you are given a set of photon-activatedbo
  mbs, 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?

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Elitzur-VaidmannInteraction-Free Measurements

• Suppose you are given a set of photon-activatedbo
  mbs, 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!

70
Elitzur-VaidmannInteraction-Free Measurements

• Suppose you are given a set of photon-activatedbo
  mbs, 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!

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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.

72
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 LS1rArS2tD1 and LS1tBrS2rD1 gt in
phase
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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 LS1rArS2tD1 and LS1tBrS2rD1 gt in
phase D2 LS1rArS2rD2 and LS1tBrS2tD2
gt out of phase
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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 D1and
  D2.

75
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 D1and
  D2.
• This is because there is now no interference, and
  splitter S2 divides the incident light equally
  between the two detector paths.

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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 D1and
  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.

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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.

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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.

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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
80
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
81
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
82
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
83
Transactions for No Object

• There are two allowed paths between the light
  source L and the detector D1.

84
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 y to D1 will
  interfere constructively, while the offer y waves
  to D2 interfere destructively and cancel.

85
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 y to D1 will
  interfere constructively, while the offer y waves
  to D2 interfere destructively and cancel. The
  confirmation waves y traveling back to L along
  both paths back to L will confirm the transaction.

86
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.

87
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.

88
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).

89
ApplicationThe QuantumXeno Effect
90
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.

91
Efficiency of the Xeno Interaction-Free
Measurements

• If the object is present,the emerging photonat
  DH will be detectedwith a probabilityPD
  Cos2N(p/2N).
• The photon will interactwith the object with
  aprobability PR 1 - PD 1 - Cos2N(p/2N).When
  N is large, PD 1 - (p/2)2/N and PR (p/2)2/N.
  Therefore, the interaction probability decreases
  as 1/N.

92
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 p/2N. The photon emerges with
  V polarization.

93
Offer Waveswith an Object in the V Beam

• 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.

94
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.

95
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.

96
Applications of the Transactional Interpretation
of Quantum Mechanics
http//www.npl.washington.edu/ti

• John G. Cramer
• Professor of Physics
• Department of Physics
• University of Washington
• Seattle, Washington, USA

cramer_at_phys.washington.edu
Presented at theBreakthrough Physics Lecture
SeriesMarshall Space Flight Center Marshall,
Alabama August 17, 2000