Quantum Measurements

How can you measure the velocity?

Randy and Jim discuss how difficult it is to measure quantities like velocity in quantum mechanics. In doing so they discuss von Neumann's five-requirement theory of quantum measurement and a mathematical treatment of the measuring process that involves a quantum mechanical treatment of the measuring device and the interaction between it and the system under measurement. In this episode, we talk about Aharonov and Rohrlich's Quantum Paradoxes, chapter 7: "Quantum Measurement."



Please comment on our subreddit! It will help us respond to what you're saying if we can collect all the comments in the same place.

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.

New Things to Play With

Alright!

Sorry about the tardiness of the last post. I was in a rush to upload the previous one before Easter break, and I found out that I screwed up the upload somehow and so I couldn't get your post up while I was away. Then, after I got back to NOLA, I had a lot of other things to do for the end of the semester and so even though I got the podcast uploaded to Podomatic, I didn't get any blogging stuff done.

But today, I got two things up and running. The first is our YouTube page, which will feature supplementary videos about the things we're discussing. I'll get that in better order over the summer.

The second is our Patreon account, which has been waiting for a video to explain what the whole Patreon thing is. So now you have the option to help us out directly if you want to.

Nonlocality and Causality

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."



Please comment on our subreddit! It will help us respond to what you're saying if we can collect all the comments in the same place.

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