Download The Transactional Interpretation of Quantum Mechanics http://www

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
[email protected]
Presented at
Georgetown University
Washington, D.C.
October 2, 2000
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.
Outline
•
•
What is Quantum Mechanics?
What is an Interpretation?
–
–
•
Lessons from E&M
–
–
•
The Logic of the Transactional Interpretation
The Quantum Transactional Model
Paradoxes:
1.
2.
3.
4.
•
•
Maxwell’s Wave Equation
Wheeler-Feynman Electrodynamics & Advanced Waves
The Transactional Interpretation of QM
–
–
•
Example: F = m a
“Listening” to the formalism
The Quantum Bubble
Schrödinger’s Cat
Wheeler’s Delayed Choice
The Einstein-Podolsky-Rosen Paradox
Application of TI to Quantum Experiments
Conclusion
Theories and
Interpretations
What is Quantum Mechanics?
Quantum mechanics is a theory that is our
current “standard model” for describing
the behavior of matter and energy at the
smallest scales (photons, atoms, nuclei,
quarks, gluons, leptons, …).
Like all theories, it consists of a
mathematical formalism and an
interpretation of that formalism.
However, while the formalism has been
accepted and used for 75 years, its
interpretation remains a matter of controversy and
debate, and there are several rival interpretations
on 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 body
is 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
• Interpretation: “The vector force on a body
is 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 m<0.
•It insures that F||a.
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> = v y* S y dr3 = <f | S | i>
… a y* - y “sandwich”. What does this suggest?
“Listening” to the Formalism of
Quantum Mechanics
Consider a quantum matrix element:
<S> = v y* S y dr3 = <f | S | i>
… a y* - y “sandwich”. What does this suggest?
Hint: The complex conjugation in y* is the
Wigner operator for time reversal.
“Listening” to the Formalism of
Quantum Mechanics
Consider a quantum matrix element:
<S> = v y* S y dr3 = <f | S | i>
… 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.
“Listening” to the Formalism of
Quantum Mechanics
Consider a quantum matrix element:
<S> = v y* S y dr3 = <f | S | i>
… 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(-kr+wt)
(retarded)
(advanced)
Lessons from
Classical E&M
Maxwell’s Electromagnetic
Wave Equation
2 Fi = 1/c2 2Fi /t2
This is a 2nd order differential
equation, which has two time
solutions, retarded and advanced.
Maxwell’s Electromagnetic
Wave Equation
2 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).
Maxwell’s Electromagnetic
Wave Equation
2 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).
Lessons from
Wheeler-Feynman
Absorber 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 Transactional
Interpretation of
Quantum
Mechanics
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
Transactional Interpretation
1. Interpret Maxwell’s wave
equation as a relativistic
quantum wave equation
(for mrest = 0).
2. Interpret the relativistic
Klein-Gordon and Dirac
equations (for mrest > 0)
The Logic of the
Transactional Interpretation
1. Interpret Maxwell’s wave
equation as a relativistic
quantum wave equation
(for mrest = 0).
2. Interpret the relativistic
Klein-Gordon and Dirac
equations (for mrest > 0)
3. Interpret the Schrödinger equation as a nonrelativistic reduction of the K-G and Dirac
equations (for mrest > 0).
The Quantum
Transactional Model
Step 1: The emitter sends
out an “offer wave” Y.
The Quantum
Transactional Model
Step 1: The emitter sends
out an “offer wave” Y.
Step 2: The absorber responds
with a “confirmation wave”
Y*.
The Quantum
Transactional Model
Step 1: The emitter sends
out 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).
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.
The Transactional Interpretation
and the Born Probability Law
Starting from E&M and the WheelerFeynman 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 advancedwave E-field at the emitter.
The Transactional Interpretation
and the Born Probability Law
Starting from E&M and the WheelerFeynman 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 advancedwave E-field at the emitter.
Translating this to quantum
yy*
mechanical terms, the “echo”
that the emitter receives from
each potential absorber is yy*,
leading to the Born Probability Law.
y
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.
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.
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.
• Thus, the observer-centric aspects of the
Copenhagen interpretation are avoided.
Quantum
Paradoxes
Paradox 1:
The Quantum Bubble
Situation: A photon is emitted
from an isotropic source.
Paradox 1:
The 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
photon’s wave function at the
location of Detectors B & C
know that it should vanish?
Paradox 1:
The 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
photon’s wave function at the
location of Detectors B & C
know that it should vanish?
Paradox 1: Application of the
Transactional Interpretation
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 Cat
Experiment: A cat is
placed in a sealed box
containing a device
that has a 50% probability
of killing the cat.
Paradox 2:
Schrödinger’s Cat
Experiment: A cat is
placed in a sealed box
containing a device
that has a 50% probability
of killing the cat.
Question 1: When does the
wave function collapse?
What is the wave function
of the cat just before the
box is opened? (Y = ½ dead + ½ alive?)
Paradox 2:
Schrödinger’s Cat
Experiment: A cat is
placed in a sealed box
containing a device
that has a 50% probability
of killing the cat.
Question 1: When does the
wave function collapse?
What is the wave function
of the cat just before the
box is opened? (Y = ½ dead + ½ alive?)
Question 2: If we observe Schrödinger, what is his wave
function during the experiment? When does it collapse?
Paradox 2: Application of the
Transactional Interpretation
to Schrödinger’s Cat
• A transaction either
develops between the
source and the detector,
or else it does not. If
it does, the transaction
forms nonlocally, not
at some particular time.
• Therefore, asking when
the wave function
collapsed 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, a
transaction forms between
E and the source S and
involves waves passing
through both slits.
Paradox 3: Application of the
Transactional Interpretation
• If plate E is up, a
transaction forms between
E and the source S and
involves waves passing
through both slits.
• If the plate E is down, a
transaction forms between
telescope T1 or T2 and the
source S, and involves waves
passing through only one slit.
Paradox 3: Application of the
Transactional Interpretation
• If plate E is up, a
transaction forms between
E and the source S.
• If the plate E is down, a
transaction forms between
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(qrel) = Cos2qrel]
Paradox 4: EPR Experiments
Malus and Furry
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law [P(qrel) = Cos2qrel]
The measurement gives the same result
as if both filters were in the same arm.
Paradox 4: EPR Experiments
Malus and Furry
An EPR Experiment measures the
correlated polarizations of a pair
of entangled photons, obeying
Malus’ Law [P(qrel) = Cos2qrel]
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.
Paradox 4: Application of the
Transactional Interpretation to EPR
An EPR experiment requires a
consistent double advancedretarded handshake between
the emitter and the two
detectors.
Paradox 4: Application of the
Transactional Interpretation to EPR
An EPR experiment requires a
consistent double advancedretarded 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.
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?
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)
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)
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)
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, waveparticle duality, and nonlocality.
• ERP communication FTL is not possible!
Application:
An Interaction-Free
Measurement
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
Interaction-Free Measurements
Suppose you are given a set of photon-activated
bombs, which will explode when a single
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
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.
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-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 trigger.
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!
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.
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 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.
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
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
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.
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.
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 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.
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 the
bomb in A. If it is a dud,
the photon will always
go to D1. If it is a live
bomb, ½ of the time the
bomb will explode, ¼ of
the time it will go to D1 and ¼ of the time to D2.
How to Sort the Bombs
Send in a photon with the
bomb in A. If it is a dud,
the photon will always
go to D1. If it is a live
bomb, ½ of the time the
bomb will explode, ¼ of
the 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
Thus, we have used quantum
mechanics to gain a kind of
knowledge (i.e., which
or
unexploded 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.
Quantum Knowledge
Thus, we have used quantum
mechanics to gain a kind of
knowledge (i.e., which
or
unexploded 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?
Quantum Knowledge
Thus, we have used quantum
mechanics to gain a kind of
knowledge (i.e., which
or
unexploded 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.
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 y to D1 will interfere constructively, while the
offer y 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 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.
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).
Application:
The Quantum
Xeno 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
Interaction-Free Measurements
If the object is present,
the emerging photon
at DH will be detected
with a probability
PD = Cos2N(p/2N).
The photon will interact
with the object with a
probability 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.
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 p/2N.
The photon emerges with V polarization.
Offer Waves
with 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.
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-freemeasurements.
• 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 counterintuitive quantum optics results.
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
[email protected]
Presented at the
Breakthrough Physics Lecture Series
Marshall Space Flight Center
Marshall, Alabama
August 17, 2000