The document discusses interpretations of quantum mechanics including the Copenhagen interpretation, many-worlds interpretation, and transactional interpretation. It summarizes four quantum paradoxes around wave-particle duality, quantum measurement, and non-locality. It then provides more details on the transactional interpretation, explaining how it uses advanced and retarded waves to describe quantum events and resolve the paradoxes without needing observers or wavefunction collapse. Finally, it discusses how interpretations cannot be experimentally tested but notes one potential exception with a new experiment.

2. A Quantum Metaphor (With apologies to Americans with Disabilities)

4. Quantum Theory and Interpretations

8. Four Quantum Paradoxes

9. Paradox 1 (non-locality): Einstein’s Bubble Situation: A photon is emitted from an isotropic source.

10. 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.

12. 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.

17. 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 !

22. Three Interpretations of Quantum Mechanics

23. 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

24. 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

25. 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.

26. 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.

27. The Transactional Interpretation of Quantum Mechanics

39. Testing Interpretations

47. Afshar Experiment Results Grid + 1 Slit 6% Loss Grid + 2 Slits <0.1% Loss No Grid No Loss

48. Afshar Test Results Copenhagen Many Worlds Transactional Predicts no interference. Predicts no interference. Predicts interference, as does the QM formalism.

49. 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.

50. 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

51. The End