How can you go from a probabilistic description of a phenomenon to a physical measurement?
Contrary to classical probability and statistical mechanics, where we have a separation between the governing physics of a situation (mechanical laws) and our knowledge of it (thermodynamics), in quantum mechanics the governing physics is in some way probabilistic in nature. This means that we cannot interpret probability in the same way that we do in macroscopic phenomena. The Schroedinger's Cat Paradox shows us that we need to have an interpretation of the transition from the probabilistic regime of theory to the material regime of reality to understand what the wave function -- the complete description of a quantum system -- means
The thing is: there is no adequate interpretation of the wave function.
In this episode, we talk about Aharonov and Rohrlich's Quantum Paradoxes, chapter 9: "Quantum Cats:"
We're reading the book 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.