Free will, undecidability, and the problem of time in quantum gravity

TL;DR

This paper proposes a relational notion of time in quantum gravity, leading to fundamental undecidability in quantum measurement outcomes, which may have implications for understanding free will.

Contribution

It introduces a consistent relational time in quantum gravity that results in undecidability between collapse and evolution, offering a novel perspective on quantum measurement.

Findings

Experimental results match ordinary quantum mechanics

Undecidability arises between collapse and evolution

Implications for free will and fundamental physics

Abstract

In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a "clock". We have recently introduced a consistent way of defining time relationally in general relativity. When quantum mechanics is formulated in terms of this new notion of time the resolution of the measurement problem can be implemented via decoherence without the usual pitfalls. The resulting theory has the same experimental results of ordinary quantum mechanics, but every time an event is produced or a measurement happens two alternatives are possible: a) the state collapses; b) the system evolves without changing the state. One therefore has two possible behaviors of the quantum mechanical system and physical observations cannot decide between them, not just as a matter of experimental limitations but as an issue of principle. This first-ever example of fundamental undecidability in physics suggests that nature may behave sometimes as described by one alternative and sometimes as described by another. This in particular may give new vistas on the issue of free will.