Undecidability and Theories of Everything with Claus Kiefer

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Recorded: 2023/08/07 Released: 2024/01/28

Jim talks with Claus Kiefer about his recent essay on the relationship between the Gödel's incompleteness theoerems and the possibility of developing a theory of everything. Incompleteness was originally developed to show that every axiomatic system that is sufficiently robust admits well-formed statements that have a liar's paradox-like structure - if you assume the statement is true, you can prove it's false, and vice-versa. This statement is then said to be undecidable. Undecidability also famously comes up in the halting problem of computer science and the continuum hypothesis. Professor Kiefer speculates here that theories of everything are similarly undecidable.
------------------------------------------- Notes:

1. The article that we discussed in this program:

• Kiefer, Claus, "Gödel's undecidability theorems and the search for a theory of everything" (2023) [arXiv]

2. Other papers referred to in this podcast:

• Cubitt, T.,D. Perez-Garcia and H.M. Wolf, "Undecidability of the Spectral Gap." Nature 528 207 (2015) [arXiv]
• Goedel,, K., "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Monatshefte für Mathematik und Physik 38 173 (1931) [Free]
• The Undecidable [Amazon], M. Davis, ed. Reprints Goedel's paper and other work from the 1930's. Dover book.

3. Related Episodes of Physics Frontiers:

• Physics Frontiers 69: The Flavor Puzzle with Joe Davighi
• Physics Frontiers 62: Deformed Special Relativity
• Physics Frontiers 45: Loop Quantum Gravity
• Physics Frontiers 35: The String THeory Landscape.

4. Books mentioned:

• Quantum Gravity, 3rd. Ed., Claus Kiefer. Claus' book on quantum gravity.
• The Physical Basis of the Direction of Time, H. Dieter Zeh. Excellent book going over how the arrow of time might be directed via different aspects of physics. Video Review
• The Undecidable [Amazon], M. Davis, ed. Reprints Goedel's paper and other work from the 1930's. Dover book.
• The Character of Physical Law, Richard Feynman
• Road to Reality, Roger Penrose
• Non Standard Analysis, Abraham Robinson or Applied Non-Standard Analysis, Martin Davis. Two books on non-standard analysis. Despite The Undecidable and Applied Non-Standard Analysis being about 6" from each other on my bookshelves for at least a decade, I didn't make the connection that the editor of the first was also the author of the second until this moment.
• Goedel, Escher, Bach, D. Hofstadter.

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