Our mission during this session is to understand what is meant by "quantum contextuality", and to consider the implications for interpreting QM.

Contextuality is one of the most characteristic features of QM. Historically the concept goes back to Bohr's emphasis on the importance of specifying the complete experimental arrangement, and Heisenberg's formal discovery of the uncertainty principle in the case of non-commuting observables. Von Neumann's infamous 1932 "proof" of the impossibility of hidden-variable interpretations relied on a strong assumption that such variables must be "non-contextual", and thereby helped to define the issue.

Although the assumption of non-contextuality in Von Neumann's demonstration was later recognized to be too strong, over 30 years later Bell, Kochen and Specker tightened the argument, and successfully demonstrated that QM is contextual, and that no non-contextual hidden variable formulation is possible.

This result is often viewed as confirming Bohr's ideas of complementarity and the interdependence between measurement contexts and outcomes, although other interpretations of QM can accommodate contextuality. For example, the de Broglie-Bohm pilot wave theory is explicitly contextual (unfortunately in a way that violates special relativity).

Exercise: How does Everett's Many-Worlds interpretation account for contextuality?

The Kochen-Specker (sometimes Bell-Kochen-Specker) theorem is mathematically complex. Meetup participants can skip the details of the proof as desired, but are encouraged to familiarize themselves with the conceptual framework.

**Reading assignment**

* "The Spooky Quantum Phenomenon You’ve Never Heard Of"

[https://www.quantamagazine.org/the-spooky-quantum-phenomenon-youve-never-heard-of-20220622/](https://www.quantamagazine.org/the-spooky-quantum-phenomenon-youve-never-heard-of-20220622/)

* "Contextuality — The most quantum thing"

[https://plus.maths.org/content/contextuality-most-quantum-thing](https://plus.maths.org/content/contextuality-most-quantum-thing)

* "Quantum contextuality in theCopenhagen approach"

[https://royalsocietypublishing.org/doi/epdf/10.1098/rsta.2019.0025](https://royalsocietypublishing.org/doi/epdf/10.1098/rsta.2019.0025)

**Optional resources**
(none of these are required for our meeting!)

* A simple YouTube video "Kochen–Specker Theorem Explained" -

[https://www.youtube.com/watch?v=IqTmxg4LhSk](https://www.youtube.com/watch?v=IqTmxg4LhSk)

* Gemini summary of video:
[https://gemini.google.com/share/1984cb3416d0](https://gemini.google.com/share/1984cb3416d0)
* "K-S proofs made simple" (generated with the help of Perplexity AI)

[https://docs.google.com/document/d/10yD_8PHKUqqkb4oqQVMn39Jh3L41YAZ89TUq04gm1UQ/edit?tab=t.0#heading=h.okz4xs6mlgwq](https://docs.google.com/document/d/10yD_8PHKUqqkb4oqQVMn39Jh3L41YAZ89TUq04gm1UQ/edit?tab=t.0#heading=h.okz4xs6mlgwq)

* Wikipedia articles

[https://en.wikipedia.org/wiki/Quantum_contextuality](https://en.wikipedia.org/wiki/Quantum_contextuality)
[https://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem](https://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem)

* Stanford Encyclopedia of Philosophy

[https://plato.stanford.edu/entries/kochen-specker/](https://plato.stanford.edu/entries/kochen-specker/)

* A rigorous and more complex YouTube lecture by the late, great John Conway: "Conway Free Will Theorem Lecture 2- Kochen-Specker Theorem"

[https://www.youtube.com/watch?v=hox6ZIj7JPI&t=102s](https://www.youtube.com/watch?v=hox6ZIj7JPI&t=102s)

For those who want to delver even deeper, please see the footnotes in the "K-S proofs made simple" document!

**Meeting information:**

Our live meeting will take place on Zoom.

Text-based discussions during and between live meetings will be hosted on the Blinding Cyclops Discord server. You can also find resources related to this seminar and reading assignments there. Join link: [https://discord.gg/urPBsNTWuK](https://discord.gg/urPBsNTWuK). Channels related to this seminar can be found under the "Quantum Physics" category.

**Syllabus:**

We meet alternating Fridays at 4pm PT to discuss interpretations of quantum physics and the philosophy of Niels Bohr.

This seminar has begun with a close reading of a book critical of Niels Bohr, “What is Real?” by Adam Becker, so that we can become grounded in an opposing and critical viewpoint. It's also likely that we'll semi-regularly read source materials as a supplement.

Suggested secondary readings (which we’ll not cover directly but which may be referenced):

* “Quantum Reality,” by Nick Herbert
* “Beyond Weird,” by Philip Ball
* “Elegance and Enigma,” edited by Maximilian Schlosshauer

Rhett Savage

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Quanta and Complementarity – The Philosophy of Niels Bohr

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Quanta and Complementarity – The Philosophy of Niels Bohr

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