Is Quantum Theory Complete?

Can quantum theory as currently formulated be all there is to the theory?

That was Einstein's greatest doubt, and many people doubt it today. Quantum theory seems to offer us probabilities for the results of well constructed experiments. But it does not offer us insight of the internal workings of those experiments. Can that really be all we can know about the quantum world?

That's what Randy and Jim discuss in this episode while talking about Aharonov and Rohrlich's Quantum Paradoxes, chapter 3: "Is Quantum Theory Complete?"

Einstein's Clock in a Box Paradox (last episode) failed to prove that quantum theory was inconsistent -- that the postulates of quantum theory have some contradictory implications. So, he turned to proving that they were incomplete: additional postulates were required to provide a full understanding of the physics of the theory (similar the necessity of Euclid's fifth postulate in geometry). So he and two others invented the Einstein-Poldosky-Rosen Paradox (this episode), which many years later would be formalized as Bell's Theorem and then shown to be consistent with measurements in the Aspect experiment.

Also discussed in this episode: quantum entanglement and the block universe.





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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 popular, and short, introduction to quantum mechanics that includes a lot of the topics in the first half of this books is Rae's Quantum Physics. If the equations in Quantum Paradoxes get you down, this might perk you up.

Two other books that were mentioned in this podcast were:

Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy: This is a collection Bell's papers that includes his formulation of the EPR in a way that there is a measurable difference between classical and quantum results.

Quantum Theory (Dover Books on Physics): David Bohm's classic text on quantum mechanics. In Chapter 14, he formulates the EPR paradox mathematically using electron spin and Stern-Gerlach devices.

How to Weigh a Quantum: Randy and Jim talk about consistency

Why do we need quantum mechanics?

Is the way that physicists formulate quantum mechanics viable?

That's what Randy and Jim answer in this episode, talking about Aharonov and Rohrlich's Quantum Paradoxes. Including:

(1) Mathematical Consistency:

A set of mathematical postulates is consistent if they don't have contradictory implications.

(2) Black Body Radiation:

A black body is a hot object, like a kiln. Being hot, the cavity of the kiln has a large thermal energy. It transfers some of that energy to the electromagnetic field -- it glows.

In 1899, Max Planck proposed that the thermal energy from the black body can only transfer to the electromagnetic field in discrete chunks, called quanta.

(3) The Compton Effect

The Compton effect is one where a photon (a massless quantum particle of light) strikes and electron, but momentum is transferred from the photon to the electron -- meaning the massless photon has momentum to transfer.

(4) Uncertainty Relationships

In quantum mechanics, there are pairs of variables called conjugate variables that cannot be both simultaneously and and precisely measured together.

This is discussed in terms of the light from a microscope.

(5) Single Slit Diffraction

Light diffracts in a single slit experiment, not just a double slit like we talked about last time.

(6) The Clock in the Box Paradox

Einstein's last attempt to prove that the mathematical formulation of quantum mechanics is inconsistent.

Thanks to Neal Tircuit for our new theme music!

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 popular, and short, introduction to quantum mechanics that includes a lot of the topics in the first half of this books is Rae's Quantum Physics. If the equations in Quantum Paradoxes get you down, this might perk you up.

The Uses of Paradox: Randy and Jim talk about Quantum Paradoxes, Chapter 1

What good do paradoxes do?

Randy and Jim discuss paradoxes, their use in physics, quantum mechanics, and the twin paradox, all as an introduction to Quantum Paradoxes by Yakir Aharonov and Daniel Rohrlich. This is the first of 18 planned podcasts on this book, one per chapter.

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.



Books (probably) mentioned in this episode (Amazon links):

Quantum Paradoxes: Quantum Theory for the Perplexed, Yakir Aharonov and Daniel Rohrlich -- The book we're discussing.

Paradoxes in Probability Theory, William Eckhardt. A fun little book that helps guide you to a better understanding of probabilistic concepts using paradoxes. What I was reading just before recording the first episode.

Paradoxes, R.M. Sainsbury -- A very interesting book on paradoxes in general. It's had many editions, so I assume it's used in classes somewhere.

Zeno's Paradoxes, Wesley C. Salmon, Ed. -- A collection of articles on the meaning of Zeno's Paradoxes.

Potential Theory, Oliver D. Kellogg -- Classic book on potential theory (discussion deleted, but you should know about it, anyway.)

Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians, Anthony Sudbury -- Absolutely awesome book on quantum mechanics; at least I thought so when I first read it twenty years ago. Very readable textbook.

Introduction to Quantum Mechanics, John S. Townsend -- The current edition of the book I used as an undergraduate. I find the approach taken here to be well grounded and intuitive.

Introduction to Quantum Mechanics, David J. Griffiths -- A more commonly used quantum mechanics textbook; we use it at Xavier (but I don't teach QM).