Randy and Jim wrap their heads around a diffraction paradox invented by Aharonov to help us understand why it is that Einstein's paradoxes, which were about the behavior of small, quantum particles, were solved by Bohr using the uncertainty principle

*on the apparatus*instead of the particle itself. He uses a diffraction grating instead of a double slit experiment because an effectively infinite number of repeating openings in a regular array is easier to analyze than a small number of openings. In doing this, Aharovov formulates what he calls the "complete uncertainty principle" which produces a relatively straightforward physical reason for the uncertainty principle -- although it requires some very specialized mathematics. Keep your eyes on the physics because the math will get you if you don't watch out

. In this episode, we talk about Aharonov and Rohrlich's Quantum Paradoxes, chapter 5: "Modular Variables".

We're reading Quantum Paradoxes by Yakir Aharonov and Daniel Rohrlich. This is a technical book that is making an argument for a specific interpretation of quantum theory. The first half of the book uses paradoxes to explore the meaning of quantum theory and describe its mathematics, then after interpretations are discussed in the middle chapter, an interpretation of quantum mechanics is explored with paradoxes based on weak quantum measurements.