Sunday, January 28, 2024

Undecidability and Theories of Everything with Claus Kiefer

← Previous ( Measurement Problem ) ( Maxwellian Ratchets ) Next →

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:
4. Books mentioned:
5. Please visit and comment on our subreddit, YouTube Channel, or Twitter account. These are also places to look for announcements of new episodes and the like. And if you could help us keep this going by contributing to our Patreon, we'd be grateful.
← Previous ( Measurement Problem ) ( Maxwellian Ratchets ) Next →