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<ul><li>“ Those who are not shocked when they first come across quantum theory cannot possibly have understood it.” </li></ul><ul><li>Neils Bohr </li></ul>The Reality of Quantum Mechanics
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The Blind Men and the Quantum: Adding Vision to the Quantum World <ul><li>Adapted from the lecture of </li></ul><ul><li>John G. Cramer </li></ul><ul><li>Dept. of Physics, Univ. of Washington </li></ul>Quantum Mechanics Jamaico C. Magayo MSciEd Physics
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A Quantum Metaphor (With apologies to people with disabilities)
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The Blind Men and the Elephant by John Godfrey Saxe (1816-1887) <ul><li>It was six men of Indostan, To learning much inclined, Who went to see the Elephant, </li></ul><ul><li>(Though all of them were blind), That each by observation, Might satisfy his mind. . </li></ul><ul><li>The First approached the Elephant, And happening to fall, Against his broad and sturdy side, At once began to bawl: </li></ul><ul><li>“ God bless me! but the Elephant, Is very like a wall ! ” </li></ul><ul><li>The Second, feeling of the tusk, Cried, “Ho! what have we here, So very round and smooth and sharp? To me ’tis mighty clear, </li></ul><ul><li>This wonder of an Elephant, Is very like a spear ! ” </li></ul><ul><li>The Third approached the animal, And happening to take, The squirming trunk within his hands, Thus boldly up and spake: </li></ul><ul><li>“ I see,” quoth he, “the Elephant, Is very like a snake !” </li></ul><ul><li>The Fourth reached out an eager hand, And felt about the knee. “What most this wondrous beast is like, Is mighty plain,” quoth he; </li></ul><ul><li>“ ‘ Tis clear enough the Elephant, Is very like a tree ! ” </li></ul><ul><li>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, </li></ul><ul><li>This marvel of an Elephant, Is very like a fan ! ” </li></ul><ul><li>The Sixth no sooner had begun, About the beast to grope, Than, seizing on the swinging tail, That fell within his scope, </li></ul><ul><li>I see,” quoth he, “the Elephant, Is very like a rope ! ” </li></ul><ul><li>And so these men of Indostan, Disputed loud and long, Each in his own opinion, Exceeding stiff and strong, </li></ul><ul><li>Though each was partly in the right, And all were in the wrong! </li></ul><ul><li>Moral: So oft in theologic wars, The disputants, I ween, Rail on in utter ignorance, Of what each other mean, </li></ul><ul><li>And prate about an Elephant, Not one of them has seen! </li></ul>
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What is Quantum Mechanics? <ul><li>Quantum mechanics is a theory. It is our current “standard model” for describing the behavior of matter and energy at the smallest scales (photons, atoms, nuclei, quarks, gluons, leptons, …). </li></ul><ul><li>Like all theories, it consists of a mathematical formalism, plus an interpretation of that formalism. </li></ul><ul><li>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. </li></ul><ul><li>Today we’ll consider three QM interpretations, and we’ll talk about ways for choosing between them. </li></ul>Quantum Mechanics
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The Role of an Interpretation <ul><li>The interpretation of a formalism should: </li></ul><ul><li>Provide links between the mathematical symbols of the formalism and elements of the physical world; </li></ul><ul><li>Neutralize the paradoxes; all of them; </li></ul><ul><li>Provide tools for visualization or for speculation and extension. </li></ul><ul><li>It should not have its own sub-formalism! </li></ul><ul><li>It should not make its own testable predictions, </li></ul><ul><li>(but it may be falsifiable, if it is found to be inconsistent with the formalism and experiment)! </li></ul>
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Interpretation Example : Newton’s 2 nd Law <ul><li>Formalism: </li></ul><ul><li>What this interpretation does: </li></ul><ul><ul><ul><li>It relates the formalism to physical observables. </li></ul></ul></ul><ul><ul><ul><li>It avoids the paradoxes that would arise if m < 0 . </li></ul></ul></ul><ul><ul><ul><li>It insures that F||a . </li></ul></ul></ul><ul><li>Interpretation: “The vector force on a body is proportional to the product of its scalar mass, which is positive, and the 2 nd time derivative of its vector position.” </li></ul>
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Paradox 1 (non-locality): Einstein’s Bubble Situation: A photon is emitted from an isotropic source.
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Paradox 1 (non-locality): Einstein’s Bubble Situation: A photon is emitted from an isotropic source. Its spherical wave function expands like an inflating bubble.
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Paradox 1 (non-locality): Einstein’s Bubble <ul><li>Question (Albert Einstein): </li></ul><ul><li>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? </li></ul>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.
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Paradox 1 (non-locality): Einstein’s 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. That’s what quantum mechanics says happens to electrons and photons when they move from place to place.
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<ul><li>Experiment: A cat is placed in a sealed box containing a device that has a 50% chance of killing the cat. </li></ul><ul><li>Question 1: What is the wave function of the cat just before the box is opened? </li></ul><ul><li>When does the wave function collapse? </li></ul>Paradox 2 ( collapse): Schrödinger’s Cat
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<ul><li>Experiment: A cat is placed in a sealed box containing a device that has a 50% chance of killing the cat. </li></ul><ul><li>Question 1: What is the wave function of the cat just before the box is opened? </li></ul><ul><li>When does the wave function collapse? </li></ul>Paradox 2 ( collapse): Schrödinger’s Cat Question 2: If we observe Schrödinger, what is his wave function during the experiment? When does it collapse?
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Paradox 2 ( collapse): Schrödinger’s Cat <ul><li>The question is, when and how does the wave function collapse. </li></ul><ul><li>What event collapses it? </li></ul><ul><li>How does the collapse spread to remote locations? </li></ul>
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Paradox 3 (wave vs. particle): Wheeler’s Delayed Choice <ul><li>A source emits one photon. Its wave function passes through slits 1 and 2, making interference beyond the slits. </li></ul><ul><li>The observer can choose to either: (a) measure the interference pattern at plane requiring that the photon travels through both slits . </li></ul><ul><li>or (b) measure at plane which slit image it appears in indicating that it has passed only through slit 2 . </li></ul>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): Wheeler’s Delayed Choice Thus, the photon does not decide if it is a particle or a wave until after it passes the slits, even though a particle must 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 Experiments Malus and Furry <ul><li>An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [ P( rel ) = Cos 2 rel ] </li></ul>
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<ul><li>An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [ P( rel ) = Cos 2 rel ] </li></ul><ul><li>The measurement gives the same result as if both filters were in the same arm. </li></ul>Paradox 4 (non-locality): EPR Experiments Malus and Furry
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Paradox 4 (non-locality): EPR Experiments Malus and Furry <ul><li>An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [ P( rel ) = Cos 2 rel ] </li></ul><ul><li>The measurement gives the same result as if both filters were in the same arm. </li></ul><ul><li>Furry proposed to place both photons in the same random polarization state. This gives a different and weaker correlation. </li></ul>
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Paradox 4 (non-locality): EPR Experiments Malus and Furry <ul><li>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. </li></ul><ul><li>This EPR “influence across space time” works even if the measurements are light years apart. </li></ul>
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The Copenhagen Interpretation 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. Quantum Mechanics
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The Many-Worlds Interpretation Retain Heisenberg’s uncertainty principle and Born’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. Quantum Mechanics
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The Transactional Interpretation (JGC) 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.
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Summary of QM Interpretations Copenhagen Many Worlds Transactional Uses “observer knowledge” to explain wave 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 explain wave function collapse and non-locality. Provides a way of “visualizing” quantum events.
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The Transactional Interpretation of Quantum Mechanics
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“ Listening” to the Formalism of Quantum Mechanics <ul><li>Consider a quantum matrix element: </li></ul><ul><li>< S > = v S dr 3 = <f | S | i> </li></ul><ul><li>… a * - “sandwich”. What does this suggest? </li></ul>Hint: The complex conjugation in is the Wigner operator for time reversal. If is a retarded wave, then is an advanced wave. If e i(kr - t ) then e i(-kr + t ) ( retarded ) ( advanced )
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Maxwell’s Electromagnetic Wave Equation (Classical) <ul><li> F i c 2 F i t 2 </li></ul><ul><li>This is a 2 nd order differential equation, which has two time solutions, retarded and advanced . </li></ul>Wheeler-Feynman Approach : Use ½ retarded and ½ advanced (time symmetry). Conventional Approach : Choose only the retarded solution (a “causality” boundary condition).
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A Classical Wheeler-Feynman Electromagnetic “Transaction ” <ul><li>The emitter sends retarded and advanced waves. It “offers” to transfer energy. </li></ul>
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A Classical Wheeler-Feynman Electromagnetic “Transaction ” <ul><li>The emitter sends retarded and advanced waves. It “offers” to transfer energy. </li></ul><ul><li>The absorber responds with an advanced wave that “confirms” the transaction. </li></ul>
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A Classical Wheeler-Feynman Electromagnetic “Transaction ” <ul><li>The emitter sends retarded and advanced waves. It “offers” to transfer energy. </li></ul><ul><li>The absorber responds with an advanced wave that “confirms” the transaction. </li></ul><ul><li>The loose ends cancel and disappear, and energy is transferred. </li></ul>
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The Quantum Transactional Model <ul><li>Step 1: The emitter sends out an “offer wave” . </li></ul>
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The Quantum Transactional Model <ul><li>Step 1: The emitter sends out an “offer wave” . </li></ul>Step 2: The absorber responds with a “confirmation wave” *.
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The Quantum Transactional Model <ul><li>Step 1: The emitter sends out an “offer wave” . </li></ul>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).
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The Transactional Interpretation and Wave-Particle Duality <ul><li>The completed transaction projects out only that part of the offer wave that had been reinforced by the confirmation wave. </li></ul><ul><li>Therefore, the transaction is, in effect, a projection operator. </li></ul><ul><li>This explains wave-particle duality. </li></ul>
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The Transactional Interpretation and the Born Probability Law <ul><li>Starting from E&M and the Wheeler-Feynman 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 advanced- wave E-field at the emitter. </li></ul><ul><li>Translating this to quantum mechanical terms, the “echo” that the emitter receives from each potential absorber is *, leading to the Born Probability Law. </li></ul>
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The Role of the Observer in the Transactional Interpretation <ul><li>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. </li></ul><ul><li>In the transactional interpretation, transactions involving an observer are the same as any other transactions. </li></ul><ul><li>Thus, the observer-centric aspects of the Copenhagen interpretation are avoided. </li></ul>
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