qm interpretations

“Those who are not shocked when they first come across quantum theory cannot possibly have understood it.”

Neils Bohr

The Reality of Quantum Mechanics

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

WorldWorld

Adapted from the lecture ofAdapted from the lecture ofJohn G. CramerJohn G. Cramer

Dept. of Physics, Univ. of Washington

QuantumMechanics

Jamaico C. MagayoMSciEd Physics

A Quantum A Quantum MetaphorMetaphor

(With apologies to people with disabilities)

The Blind MenThe Blind Menand the Elephantand the Elephant

by John Godfrey Saxe (1816-by John Godfrey Saxe (1816-1887)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: “E’en 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, And prate about an Elephant, Not one of them has seen!

Quantum Quantum Theory andTheory and

InterpretationInterpretationss

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 we’ll consider three QM interpretations, and we’ll 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: Newton’s 2nd Law

• Formalism:

• What this interpretation does:

•It relates the formalism to physical observables.

•It avoids the paradoxes that would arise if m<0.

•It insures that F||a.

• 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.”

F = m a

Four QuantumFour QuantumParadoxesParadoxes

Paradox 1 (non-locality):Einstein’s Bubble

Situation: A photon is emitted from an isotropic source.


Situation: A photon is emitted from an isotropic source. Its spherical wave function expands like an inflating bubble.


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

Situation: A photon is emitted from an isotropic source. Its spherical wave function expands like an inflating bubble. It reaches a detector, and the bubble “pops” and disappears.

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.

That’s what quantum mechanics says happens to electrons and photons when they move from place to place.


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 ( collapse):Schrödinger’s Cat

1 12 2

( dead + alive ?)

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?

1 12 2

( dead + alive ?)


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):

Wheeler’s Delayed ChoiceA 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 requiring that the photon travels through both slits.

or(b) measure at plane 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.

***

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 3 (wave vs. particle):

Wheeler’s Delayed Choice

Paradox 4 (non-locality):EPR ExperimentsMalus and Furry

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



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



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.


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.

ThreeThreeInterpretationInterpretation

ssof Quantum of Quantum MechanicsMechanics

Heisenberg’s uncertainty principle:Wave-particle duality, conjugate variables, e.g., x and p, E and t;The impossibility of simultaneous conjugate measurements

Born’s statistical interpretation: The meaning of the wave function as probability: P = *;Quantum mechanics predicts only the average behavior of a system.

Bohr’s 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 with knowledge of an observer; collapse and non-locality reflect changing knowledge of observer.

Heisenberg’s positivism: “Don’t-ask/Don’t tell” about the meaning or reality behind formalism;Focus exclusively on observables and measurements.

The Copenhagen Interpretation Quantum

Mechanics

Retain Heisenberg’s uncertainty principle andBorn’s statistical interpretation from the Copenhagen Interpretation.

No Collapse.The wave function 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 Many-Worlds Interpretation Quantum

Mechanics

Heisenberg’s uncertainty principle and Born’s statistical interpretation are not postulates, because they can be derived from the Transactional Interpretation..

Offer Wave:The initial wave function is interpreted as a retarded-wave offer to form a quantum event.

Confirmation wave:The response wave function (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 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 transactions;Observers and their knowledge play no special roles.

No Paraoxes:Transactions are intrinsically nonlocal, and all paradoxes are resolved.

The Transactional Interpretation (JGC)

Summary of QM Interpretations

CopenhagenMany

Worlds

Transactional

Uses “observer knowledge” to explainwave function collapse and non-locality.Advises “don’t-ask/don’t tell” about reality.

Uses “world-splitting” to explain wave function collapse. Has problems with non-locality. Useful in quantum computing.

Uses “advanced-retarded handshake” to explainwave function collapse and non-locality. Providesa way of “visualizing” quantum events.

The TransactionalThe TransactionalInterpretationInterpretationof Quantumof QuantumMechanicsMechanics

“Listening” to the Formalism of Quantum

MechanicsConsider a quantum matrix element:

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

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

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

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

(retarded) (advanced)

Maxwell’s Electromagnetic Wave

Equation (Classical)Fic2Fit2

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

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

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

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

• The loose ends cancel and disappear, and energy is transferred.

The QuantumTransactional Model

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



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



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

Step 3: The process repeats until energy and momentum is transferred and the transaction is completed (wave function collapse).

The Transactional Interpretation and

Wave-Particle Duality• The completed transaction

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

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

• This explains wave-particleduality.

The Transactional Interpretation and the Born Probability Law

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

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

The Role of the Observer 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.

TheTheEndEnd

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