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, …).
Like all theories, it consists of a mathematical formalism, plus an interpretation 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 (including mine), and we’ll talk about ways for choosing between them.
It avoids the paradoxes that would arise if m < 0 .
It insures that F||a .
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.”
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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.
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.
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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.
Experiment: A cat is placed in a sealed box containing a device that has a 50% chance of killing the cat.
Question 1: What is the wave function of the cat just before the box is opened?
When does the wave function collapse?
Paradox 2 ( collapse): Schrödinger’s Cat Question 2: If we observe Schrödinger, what is his wave function during the experiment? When does it collapse?
The question is, when and how does the wave function collapse.
What event collapses it?
How does the collapse spread to remote locations?
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Paradox 3 (wave vs. particle): Wheeler’s Delayed Choice
A source emits one photon. Its wave function passes through slits 1 and 2, making interference 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 that it 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): 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
An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [ P( rel ) = Cos 2 rel ]
An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [ P( rel ) = Cos 2 rel ]
The measurement gives the same result as if both filters were in the same arm.
Paradox 4 (non-locality): EPR Experiments Malus and Furry
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Paradox 4 (non-locality): EPR Experiments Malus and Furry
An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [ P( rel ) = Cos 2 rel ]
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.
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Paradox 4 (non-locality): EPR Experiments Malus 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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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
Consider a quantum matrix element:
< S > = v S dr 3 = <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 e i(kr - t ) then e i(-kr + t ) ( retarded ) ( advanced )
This is a 2 nd 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).
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A Classical Wheeler-Feynman Electromagnetic “Transaction ”
The emitter sends retarded and advanced waves. It “offers” to transfer energy.
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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.
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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.
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
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.
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The Transactional Interpretation and the Born Probability Law
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.
Translating this to quantum mechanical terms, the “echo” that the emitter receives from each potential absorber is *, leading to the Born Probability Law.
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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.
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.
Put wires with 6% opacity at the positions of the interference minima at 1 , and
Place detector at 2’ on plane 2 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?)
Copenhagen-influenced expectation: The measurement-type forces particle-like behavior, so there should be no interference, and no minima. Therefore, 6% of the particles should be intercepted.
Many-Worlds-influenced expectation: The 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.
Transactional-influenced expectation: The 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 ( << 6%).
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Afshar Experiment Results Grid + 1 Slit 6% Loss Grid + 2 Slits <0.1% Loss No Grid No Loss
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Afshar Test Results Copenhagen Many Worlds Transactional Predicts no interference. Predicts no interference. Predicts interference, as does the QM formalism.
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Afshar Test Results Transactional Thus, it appears that the Transactional Interpretation is the only interpretation of the three discussed that has survived the Afshar test. It also appears that other interpretations on the market (Decoherence, Consistent- Histories, etc.) fail the Afshar Test. However, quantum interpretational theorists are fairly slippery characters. It remains to be seen if they will find 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 “ Schroedinger’s Kittens” by John Gribbin (1995). The PowerPoint version of this talk will soon be available at: http://faculty.washington.edu/jcramer
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