Quantum Cats

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.

Schrodinger's Cat

I've put together a video describing Schrodinger's cat and explaining why its important to have an interpretation of quantum mechanics.  It doesn't give any answers, just explains why the question is so important.  We overview some of the answers in the next podcast, which I will hopefully get up tomorrow (I'm putting in the breaks right now.  I need to record the intro and upload it, so it's pretty likely).

Plus, I drew the pictures.

Videos

I've got the first of the explanatory videos up. Randy and I have talked about putting up videos to help explain what is going on in the experiments for almost a year now. It can be really hard for someone to visualize what's happening in the experiments for the paradoxes just from our description. I've even found that in writing descriptions: the more precise someone describes something, the harder it is for someone else to understand it.

That's just not how we talk.

Unfortunately, the vaguer the description the more easily the listener misconstrues what is being said. And it turns out it's not an easy needle to thread: it takes many years for someone to be able to reliably read a geometrical description of a problem without getting confused.

But never fear, video is here! I can draw out what I want to talk about for you, as I have in this video.

Measurement and Compensation

Unfortunately, I deleted much of the intro. I'll fix it later.

e-mail me if this is still here after September. Thanks!

In this episode, we talk about Aharonov and Rohrlich's Quantum Paradoxes, chapter 8: "Measurement and Compensation":



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.

Early Edition Is Up!

I finally got Show 8 mostly edited and uploaded to Patreon. As per my promise there, I won't publish it here for a day or two, but I've got both of those working. Last month I tried to put up the special discussion we had on quantum interpretations and had a lot of problems for no known reason. Now that I've got that working, I'll try putting that up again in about two weeks. Show 8 is the first show that goes up early, so I wanted to inform people that I'd made the Patreon feed work the way it's supposed to. This is the last time I'll post about Patreon here unless there is some important change.

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

Modular Variables

The heavy hitting starts this month with the introduction of modular variables.

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".





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.

Phases and Gauges

How can a quantity that has no effect on a classical object change the dynamics of a quantum particle?

That's what Randy and Jim explore as we discuss two paradoxes that try to explain this. Both paradoxes are similar in nature in that they involve a double slit experiment and a measurement that should allow the experimenter to determine which slit the electron goes through and without disturbing the electron. The first of these uses a charged capacitor with movable plates situated directly behind the screen in which the slits are cut and in the gap behind the slits, and whose capacitance will differ depending upon the path the electron takes. The second has a charged, cylindrical capacitor situated within the screen that will rotate in different directions depending upon the slit the electron passes through. In both situations, the electron feels no net force from the the charged capacitor and so should not react to it.

In this episode, we talk about Aharonov and Rohrlich's Quantum Paradoxes, chapter 4: "Phases and Gauges". Additional topics we discuss are the Aharonov-Bohm effect, the vector potential.





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 of quantum mechanics are discussed in the middle chapter, an interpretation of quantum mechanics is explored with paradoxes based on weak quantum measurements.