What's the best way to describe a physical system?
Jim and Randy discuss Aharonov and Rohrlich's proposal to use two axioms based upon the behavior of quantum mechanical particles that they discussed in the previous episodes:
(1) Interactions between quantum mechanical particles are nonlocal.
(2) Interactions between quantum mechanical particles are causal.
This is in contrast to the more mathematical Dirac-von Neumann axioms:
(1) The observables of a quantum system are defined to be the self-adjoint operators that operate of state defined in a Hilbert space.
(2) A state of the system is a set of probability amplitudes for results of orthogonal* experiments that define the Hilbert space.
(3) The expectation value of an observable of a system is the average of the values of each observable weighted by the square of the probability amplitudes of the system's state.
Aharanov and Rohrlich give us five distinct paradoxes that illustrate how to use nonlocality and causality to make predictions about the behavior of a system and the necessity for another modular variable: the modular energy.
In this episode, we talk about Aharonov and Rohrlich's Quantum Paradoxes, chapter 6: "Nonlocality and Causality."
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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.
* A state that is orthogonal is
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