# Properties of Invariant Set Theory

**Authors:** J. R. Hance, S. Hossenfelder, T. N. Palmer  
**arXiv:** [2108.08144](https://arxiv.org/abs/2108.08144)  
**Date:** 2021-08-18  
**Summary page:** https://www.summarizepaper.com/en/paper/2108.08144v2/

## Key points

- J.R. Hance, S. Hossenfelder, and T.N. Palmer respond to a critique by Sen on Invariant Set Theory (IST)
- Sen claimed that IST is unlikely to solve the puzzle posed by Bell correlations and is neither local nor $\psi$-epistemic
- The authors point out inaccuracies in Sen's arguments, notably that the hidden-variable model of quantum physics he uses to critique IST bears no relation to IST itself
- IST is a deterministic theory based on classical mechanics and topology which proposes a new interpretation of quantum mechanics without violating locality or realism
- According to IST, particles are not point-like objects but rather continuous fields defined over an invariant set in spacetime
- The authors argue that while IST does not rely on wave functions as fundamental entities, it can still reproduce all the predictions of standard quantum mechanics through its own mathematical formalism

## Summary

In their paper titled "Properties of Invariant Set Theory," J. R. Hance, S. Hossenfelder, and T. N. Palmer respond to a recent critique by Sen on the superdeterministic model of quantum physics known as Invariant Set Theory (IST). Sen had concluded that superdeterminism is unlikely to solve the puzzle posed by Bell correlations and claimed that IST is neither local nor $\psi$-epistemic. However, the authors point out multiple inaccuracies in Sen's arguments, notably that the hidden-variable model of quantum physics he uses to critique IST bears no relation to IST itself. In this paper, Hance et al. aim to clarify the properties of IST as clearly as possible in light of these inaccuracies. They explain that IST is a deterministic theory based on classical mechanics and topology which proposes a new interpretation of quantum mechanics without violating locality or realism. According to IST, particles are not point-like objects but rather continuous fields defined over an invariant set in spacetime. The authors also address Sen's claim that IST is not $\psi$-epistemic; meaning it does not assign physical reality to wave functions in quantum mechanics. They argue that while IST does not rely on wave functions as fundamental entities, it can still reproduce all the predictions of standard quantum mechanics through its own mathematical formalism. Overall, Hance et al. 's response provides a detailed and nuanced defense of IST against Sen's critique and sheds light on some key features of this alternative approach to understanding quantum phenomena.