"Physics is formulated in terms of timeless axiomatic mathematics. However, time is essential in all our stories, in particular in physics. For example, to think of an event is to think of something in time. A formulation of physics based of intuitionism, a constructive form of mathematics built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality and may help bridging the gap between static relativity and quantum indeterminacy.
Historically, intuitionistic mathematics was introduced by L.E.J. Brouwer with a very subjectivist view where an idealized mathematician continually produces new information by solving conjectures. Here, in contrast, I’ll introduce intuitionism as an objective mathematics that incorporates a dynamical/creative time and an open future. Standard (classical) mathematics appears as the view from the “end of time” and the usual real numbers appear as the hidden variables of classical physics. Similarly, determinism appears as indeterminism seen from the “end of time”.
Relativity is often presented as incompatible with indeterminism. Hence, at the end of this presentation I’ll argue that these incompatibility arguments are based on unjustified assumptions and present the “relativity of indeterminacy”.
References:
C. Posy, Mathematical Intuitionism, Cambridge Univ. Press, 2020.
N. Gisin, Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?, Erkenntnis (2019), https://doi.org/10.1007/s10670-019-00165-8
N. Gisin, Real Numbers are the Hidden Variables of Classical Mechanics, Quantum Studies: Mathematics and Foundations 7, 197-201 (2020).
Flavio Del Santo and N. Gisin, Physics without determinism: Alternative interpretations of classical physics, Physical Review A 100.6 (2019).
N. Gisin, Mathematical languages shape our understanding of time in physics, Nature Physics 16, 114-119 (2020).
N. Gisin Indeterminism in Physics and Intuitionistic Mathematics, arXiv:2011.02348
Flavio Del Santo and N. Gisin, The Relativity of Indeterminacy, arXiv:2101.04134"