The Blind Men and the Quantum: Adding Vision to the Quantum World

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The Blind Men and the Quantum Adding Vision to
the Quantum World
QuantumMechanics

• John G. Cramer
• Dept. of Physics, Univ. of Washington
• Seattle, Washington, 98195

1st Hal Clement Memorial LectureBoskone 41,
Boston, MA, February 15, 2004
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A Quantum Metaphor
(With apologies to Americans with Disabilities)
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The Blind Menand the Elephantby John Godfrey
Saxe (1816-1887)

• It was six men of Indostan, To learning much
  inclined, Who went to see the Elephant,
• (Though all of them were blind), That each by
  observation, Might satisfy his mind. .
• The First approached the Elephant, And happening
  to fall, Against his broad and sturdy side, At
  once began to bawl
• God bless me! but the Elephant, Is very like a
  wall!
• The Second, feeling of the tusk, Cried, Ho! what
  have we here, So very round and smooth and
  sharp? To me tis mighty clear,
• This wonder of an Elephant, Is very like a
  spear!
• The Third approached the animal, And happening to
  take, The squirming trunk within his hands, Thus
  boldly up and spake
• I see, quoth he, the Elephant, Is very like
  a snake!
• The Fourth reached out an eager hand, And felt
  about the knee. What most this wondrous beast is
  like, Is mighty plain, quoth he
• Tis clear enough the Elephant, Is very like a
  tree!
• The Fifth, who chanced to touch the ear, Said
  Een the blindest man, Can tell what this
  resembles most Deny the fact who can,
• This marvel of an Elephant, Is very like a fan!
  
• The Sixth no sooner had begun, About the beast to
  grope, Than, seizing on the swinging tail, That
  fell within his scope,
• I see, quoth he, the Elephant, Is very like a
  rope!
• And so these men of Indostan, Disputed loud and
  long, Each in his own opinion, Exceeding stiff
  and strong,
• Though each was partly in the right, And all
  were in the wrong!
• Moral So oft in theologic wars, The disputants,
  I ween, Rail on in utter ignorance, Of what each
  other mean,

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Quantum Theory andInterpretations
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What is Quantum Mechanics?

• Quantum mechanics is a theory. It 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, plus aninterpretation of that
  formalism.
• However, quantum mechanics differs from other
  physical theories because, while its formalism of
  has been accepted and used for 80 years, its
  interpretation remains a matter of controversy
  and debate. Like the opinions of the 6 blind men,
  there are many rival QM interpretations on the
  market.
• Today well consider three QM interpretations
  (including mine), and well talk about ways for
  choosing between them.

QuantumMechanics
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The Role of 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 have its own sub-formalism!
• It should not make its own testable
  predictions,
• (but it may be falsifiable, if it is found to
  be inconsistent with the formalism
  and experiment)!

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Interpretation Example Newtons 2nd Law

• Formalism

• Interpretation The vector forceon a body is
  proportional to theproduct 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 the paradoxes that would arise if mlt0.
• It insures that Fa.

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Four QuantumParadoxes
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Paradox 1 (non-locality)Einsteins Bubble
Situation A photon is emitted from an
isotropic source.
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Paradox 1 (non-locality)Einsteins Bubble
Situation A photon is emitted from an
isotropic source. Its spherical wave function
Y expands like an inflating bubble.
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Paradox 1 (non-locality)Einsteins Bubble
Situation A photon is emitted from an
isotropic source. Its spherical wave function
Y expands like an inflating bubble. It
reaches a detector, and the Y bubble pops
and disappears.

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

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Paradox 1 (non-locality)Einsteins Bubble
It is as if one throws a beer bottle into Boston
Harbor. It disappears, and its quantum ripples
spread all over the Atlantic. Then in Copenhagen,
the beer bottle suddenly jumps onto the dock, and
the ripples disappear everywhere else. Thats
what quantum mechanics says happens to electrons
and photons when they move from place to place.
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Paradox 2 (Y collapse)Schrödingers Cat

• Experiment A cat is placed in a sealed
  boxcontaining a device that has a 50 chance of
  killing the cat.
• Question 1 What is thewave function of the
  catjust before the box isopened?
• When does the wave function collapse?

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Paradox 2 (Y collapse)Schrödingers Cat

• Experiment A cat is placed in a sealed
  boxcontaining a device that has a 50 chance of
  killing the cat.
• Question 1 What is thewave function of the
  catjust before the box isopened?
• When does the wave function collapse?

Question 2 If we observe Schrödinger, what is
his wavefunction during the experiment? When
does it collapse?
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Paradox 2 (Y collapse)Schrödingers Cat

• The question is, when andhow does the wave
  functioncollapse.
• What event collapses it?
• How does the collapsespread to remote locations?

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Paradox 3 (wave vs. particle)Wheelers Delayed
Choice

• A source emits one photon.Its wave function
  passesthrough slits 1 and 2, makinginterference
  beyond the slits.
• The observer can choose to either(a) measure
  the interference pattern at plane s1, requiring
  that the photon travels through both slits.
• or(b) measure at plane s2 which slit image it
  appears in, indicating thatit has passed only
  through slit 2.

The observer waits until after the photon has
passed the slits to decide which measurement to
do.
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Paradox 3 (wave vs. particle)Wheelers Delayed
Choice
Thus, the photon does notdecide if it is a
particle or awave until after it passesthe
slits, even though a particlemust pass through
only one slit and a wave must pass through both
slits. Apparently the measurement choice
determines whether the photon is a particle or a
wave retroactively!
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Paradox 4 (non-locality)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 (non-locality)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 (non-locality)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 (non-locality)EPR ExperimentsMalus
and Furry

• Apparently, the measurement on the right side of
  the apparatus causes (in some sense of the word
  cause) the photon on the left side to be in the
  same quantum mechanical state, and this does not
  happen until well after they have left the
  source.
• This EPR influence across space time works even
  if the measurements are light years apart.
• Could that be used for FTL signaling? Sorry, SF
  fans, the answer is No!

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ThreeInterpretationsof Quantum Mechanics
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The Copenhagen Interpretation
QuantumMechanics
Heisenbergs uncertainty principleWave-particle
duality, conjugate variables, e.g., x and p, E
and tThe impossibility of simultaneous
conjugate measurements Borns statistical
interpretation The meaning of the wave
function y as probability P y y Quantum
mechanics predicts only the average behavior of a
system. Bohrs complementarity The wholeness
of the system and the measurement apparatus
Complementary nature of wave-particle duality a
particle OR a wave The uncertainty principle is
property of nature, not of measurement. Heisenberg
s "knowledge" interpretation Identification
of y with knowledge of an observer y collapse
and non-locality reflect changing knowledge of
observer. Heisenbergs positivism
Dont-ask/Dont tell about the meaning or
reality behind formalism Focus exclusively on
observables and measurements.
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The Many-Worlds Interpretation
QuantumMechanics
Retain Heisenbergs uncertainty principle
andBorns statistical interpretation from the
Copenhagen Interpretation. No Collapse. The
wave function y never collapses it splits into
new wave functions that reflect the different
possible outcomes of measurements. The split off
wave functions reside in physically
distinguishable worlds. No Observer Our
preception of wave function collapse is because
our consciousness has followed a particular
pattern of wave function splits. Interference
between Worlds Observation of quantum
interference occurs because wave functions in
several worlds have not been separated because
they lead to the same physical outcomes.
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The Transactional Interpretation (JGC)
Heisenbergs uncertainty principle and Borns
statistical interpretation are not postulates,
because they can be derived from the
Transactional Interpretation.. Offer Wave The
initial wave function y is interpreted as a
retarded-wave offer to form a quantum
event. Confirmation wave The response wave
function y (present in the QM formalism) is
interpreted as an advanced-wave confirmation to
proceed with the quantum event. Transaction the
Quantum Handshake A forward/back-in-time y y
standing wave forms, transferring energy,
momentum, and other conserved quantities, and the
event becomes real. No Observers Transactions
involving observers are no different from other
transactionsObservers and their knowledge play
no special roles. No ParaoxesTransactions are
intrinsically nonlocal, and all paradoxes are
resolved.
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Summary of QM Interpretations
Copenhagen
Many Worlds
Uses observer knowledge to explainwave
function collapse and non-locality.Advises
dont-ask/dont tell about reality.
Uses world-splitting to explain wave function
collapse. Has problems with non-locality.
Useful in quantum computing.
Transactional
Uses advanced-retarded handshake to
explainwave function collapse and non-locality.
Providesa way of visualizing quantum events.
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The TransactionalInterpretationof
QuantumMechanics
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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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Maxwells Electromagnetic Wave Equation
(Classical)

• 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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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 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
andWave-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.
• Translating this to quantummechanical terms, the
  echothat the emitter receives fromeach
  potential absorber is YY,leading to the Born
  Probability Law.

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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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TestingInterpretations
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Can Interpretationsof QM be Tested?

• The simple answer is No!. It is the formalism
  of quantum mechanics that makes the testable
  predictions.
• As long as an interpretation is consistent with
  the formalism, it will make the same predictions
  as any other interpretation, and no experimental
  tests are possible.
• However, there is a new experiment (Afshar),
  which suggests that the Copenhagen and
  Many-Worlds Interpretations may be inconsistent
  with the quantum mechanical formalism.
• If this is true, then these interpretations can
  be falsified.
• The Transactional Interpretation is consistent
  with the Afshar results and does not have this
  problem.

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Wheelers DelayedChoice Experiment

• One can choose to either
• Measure at s1 the interference pattern, giving
  thewavelength and momentum of the photon, or
• Measure at s2 which slit the particle passed
  through, giving its position.

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Wheelers DelayedChoice Experiment

• Thus, one observes either
• Wave-like behavior with theinterference
  patternor
• Particle-like behavior in determiningwhich slit
  the photon passed through.

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The Afshar Experiment

• Put wires with 6 opacity at the positions of the
  interference minima at s1, and
• Place detector at 2 on plane s2 and observe the
  particles passing through slit 2.
• Question What fraction of the light is blocked
  by the grid and not transmitted? (i.e., is the
  interference pattern still there when one
  measures particle behavior?)

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The Afshar Experiment

• Copenhagen-influenced expectationThe
  measurement-type forces particle-like behavior,
  so there should be no interference, and no
  minima. Therefore, 6 of the particles should be
  intercepted.

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The Afshar Experiment

• Many-Worlds-influenced expectationThe universe
  splits, and we are in a universe in which the
  photon goes to 2. Therefore, there should be no
  interference, and no minima. Consequently, 6 of
  the particles should be intercepted.

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The Afshar Experiment

• Transactional-influenced expectationThe initial
  offer waves pass through both slits on their way
  to possible absorbers. At the wires, the offer
  waves cancel in first order, so that no
  transactions can form and no photons can be
  intercepted by the wires. Therefore, the
  absorption by the wires should be very small
  (ltlt6).

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Afshar Experiment Results
No Grid No Loss
Grid 1 Slit 6 Loss
Grid 2 Slits lt0.1 Loss
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Afshar Test Results
Copenhagen
Many Worlds
Predicts no interference.
Predicts no interference.
Transactional
Predicts interference, as does the QM formalism.
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Afshar Test Results
Transactional
Thus, it appears that the Transactional
Interpretationis the only interpretation of the
three discussed that hassurvived the Afshar
test. It also appears that otherinterpretations
on the market (Decoherence, Consistent-Histories,
etc.) fail the Afshar Test. However, quantum
interpretational theorists are fairlyslippery
characters. It remains to be seen if they
willfind some way to save their pet
interpretations.
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References
Transactional
The Transactional Interpretation of Quantum
Mechanics http//www.npl.washington.edu/TI Schro
edingers Kittens by John Gribbin (1995). The
PowerPoint version of this talk will soon be
available athttp//faculty.washington.edu/jcrame
r
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TheEnd