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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

A Quantum Metaphor

(With apologies to Americans with Disabilities)

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,

Quantum Theory andInterpretations

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

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)!

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.

Four QuantumParadoxes

Paradox 1 (non-locality)Einsteins Bubble

Situation A photon is emitted from an

isotropic source.

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.

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?

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.

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?

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?

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?

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.

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!

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

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.

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.

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!

ThreeInterpretationsof Quantum Mechanics

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.

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.

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.

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.

The TransactionalInterpretationof

QuantumMechanics

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)

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).

A Classical Wheeler-Feynman Electromagnetic

Transaction

- The emitter sends retarded and advanced waves.

It offersto transfer energy.

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.

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.

The QuantumTransactional Model

- Step 1 The emitter sendsout an offer wave Y.

The QuantumTransactional Model

- Step 1 The emitter sendsout an offer wave Y.

Step 2 The absorber responds with a

confirmation wave Y.

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).

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.

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.

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.

TestingInterpretations

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.

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.

Wheelers DelayedChoice Experiment

- Thus, one observes either
- Wave-like behavior with theinterference

patternor - Particle-like behavior in determiningwhich slit

the photon passed through.

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?)

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.

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.

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).

Afshar Experiment Results

No Grid No Loss

Grid 1 Slit 6 Loss

Grid 2 Slits lt0.1 Loss

Afshar Test Results

Copenhagen

Many Worlds

Predicts no interference.

Predicts no interference.

Transactional

Predicts interference, as does the QM formalism.

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.

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

TheEnd

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