Wednesday, July 25, 2018

Quantum Paradoxes by Aharonov and Rohrlich

You might think I like Quantum Paradoxes [Amazon] by Yakir Aharonov and Daniel Rohrlich. I mean, I started a podcast about it. I might even finish it someday.*

This book explores the meaning of quantum mechanics through paradoxical thought experiments. It uses a few standard ones, like Schrodinger's cat, and a lot of interesting variations of the double slit experiment and electron diffraction. The first eight chapters motivate mainly how quantum mechanics works using paradoxes. The last ten chapters motivate Aharonov and Rohrlich's interpretations.

I am very enamored of the format.

Each chapter follows a formula. After a short preamble, a paradox is presented in detail. The paradoxes are presented as thought experiments, first. This means that a detailed, if not physically possible, experiment is described, and then its physics discussed. The physics leads to two possible interpretations, such as: there is no physical difference in the dynamics of an electron on either side of a charged capacitor, but quantum mechanics predicts a phase shift in the wave function of the electron. How can that be?

Next, aspects of the physics are discussed in mathematical detail. In this case, what is the relationship between the gauge and the phase of the wave function. This leads to a choice, clarification, or reconciliation. The most interesting part of this for me has been the use of modular variables to clear up some points that have to do with the use of gauges, although the general set-up of the interference experiments Aharonov and Rohrlich are discussing requires a bit of careful reading. Sometimes, a section or two follows with implications and real, physical experiments.

The second half of the book deals with the interpretation of quantum mechanics in the context of weak measurements. I really don't have a great idea about how to explain a weak measurement, but the two important facets are: (1) they allow you to measure the wave function without (completely) destroying it and (2) they are only approximations to the wave function. Aharonov and Rohrlich mainly deal with their own interpretation, and (a) the Copenhagen interpretation (a favorite among users of quantum mechanics) and (b) the many-worlds hypothesis (a favorite among string theorists). Mainly, I think, because these are their main competitors.

Their own interpretation has to do with temporal boundary conditions, which is very appealing to me because it's compatible with the block universe idea of relativity, at least conceptually. It's very important to remember that every fundamental physical theory must be compatible with every other fundamental physical theory -- if two theories that should apply to a situation don't, you have a paradox. So, any interpretation of quantum mechanics must be compatible with relativity. This hasn't been a problem with the theory -- quantum electrodynamics is exactly the integration of quantum mechanics and special relativity. It has been a major problem with interpretations, and the authors detail some of those problems in the book.

I don't want to go into more detail, but if you want to get more detail, then over the next thirty-four-odd weeks, I discuss each chapter with a friend of mine in a podcast. Contact me for the address if you're not already subscribed.

So, I just love this book. It's a great way to not only explore quantum mechanics, but to explore what it means to be an interpretation of quantum mechanics in a rigorous and technical, but not exceedingly technical (to a physicist). If you have the mathematical background to play with differential equations, or even the intellectual fortitude to not be scared of them, I highly recommend this book. If you don't have that knowledge, then check out the podcast. It'll probably be more than enough for you.

* Update (5/24/2020): To be clear here: I've read through the book three times, once to get ideas for teaching well before I'd started any podcast, once when Randy agreed to do the Quantum Paradoxes podcast, and finally, once when we started the podcst over. I think we've given up hope on finishing the Quantum Paradoxes podcast.