Twistor theory and quantum mechanics

Roger Penrose

Maciej Dunajski, Roger Penrose

We discuss the equivalence principle in quantum mechanics in the context of Newton–Cartan geometry, and non-relativistic twistor theory.

Daniel Heredia González

Since the late 1960s, Roger Penrose has had the ambition to develop a new theory that rethinks the foundations of quantum mechanics. His twistor theory aims to carry out this difficult task. Although today the theory is still in development, it is no less true that it is finding more and more followers and its results are beginning to seem not as far-fetched as initially believed. The goal is still far away, but his impetus for wanting to change things is still valid.

Joginder Singh Galsin

Eleanor March, James Alexander Mabyn Read

Abstract Recently, Dunajski and Gundry (Commun. Math. Phys., 342 (3), 2016) have developed a version of twistor theory for the non-relativistic domain. Unlike relativistic twistor theory, their approach is able to reproduce the entire space of models of Newton–Cartan theory. We critically assess the significance of non-relativistic twistors, in particular with respect to proposals by Dunajski and Penrose (Ann. Phys., 451 , 2023) that using non-relativistic twistors to describe gravitationally induced collapse could play a part in solving the quantum measurement problem.