Tuesday, January 12, 2016

Wavefunction collapse vs. unitary evolution, superdeterminism vs. free-will

Today appeared Quanta's special issue dedicated to Feynman. It is a very cool new open access journal on Quantum Mechanics.


I am happy because it contains my article, On the Wavefunction Collapse, edited by two excellent quantum theorists, Eliahu Cohen and Matt Leifer. In the paper, I discuss the possibility that the unitary evolution, governed by Schrödinger's equation, allows for the apparent wavefunction collapse. I first wrote about this idea some years ago, and its implications on free-will triggered some interesting developments. There are several great difficulties with this, mostly due to the fact that quantum measurement introduce strong constraints on the solutions of Schrödinger's equation. But I hope my arguments that these constraints are not incompatible with unitary evolution are more convincing now. The article had three completely different versions. The first one was based on integral curves in the configuration space, those called by some Bohmian trajectories. I consider the idea of interpreting these integral curves as point-particles interesting, but in order to survive, Bohmians had to transfer more and more of the physical properties initially attributed to point-particles moving along these trajectories to the pilot wave, and I think that eventually only the pilot wave matters. So in fact the wavefunction does all the job. The second version of my paper was based on Feynman's path integrals, but I realized that my original approach, to use Schrödinger's equation, is better suited.

Note that unitary evolution is deterministic. Moreover, trying to assign reality to the wavefunction leads to non-locality, as Bell's Theorem shows, and to contextualism, as the Bell-Kochen-Specker Theorem shows. And last year I published a simple proof that maintaining unitary evolution implies very fine-tuned initial conditions of the observed system and the measurement apparatus. This amounts to what is called superdeterminism. But since nobody can see the complete initial data of the wavefunction, it is also possible to consider that the initial conditions are initially not fixed, and they are more and more constrained with each measurement. While superdeterminism forces us to admit that the property we will choose to measure one day was determined from the Big-Bang, leaving the initial conditions free, and fixing them with each measurement, allows us to choose freely what to measure. And this doesn't break causality, because you can't change the observed past, only the "yet undecided" past. The required consistency between the initial conditions can also be seen, when thinking in terms of the four-dimensional block world picture from Relativity, as a global consistency principle, where "global" refers to the entire spacetime. So we have a timeless picture, based on the block world, but which does not contradict free-will, and a temporal picture, based on the delayed choice of initial conditions. These two pictures provide alternative interpretations of superdeterminism which are compatible with free-will (whatever "free-will" means).

But if there is such a thing as free-will, the free agent should at least partially be somehow above the world and outside of time, to be able to choose among the possible deterministic solutions describing the world itself. Because if it would be completely part of the solution, it could not have free-will. It is easy from here to speculate about an immortal soul and even the possibility that it is part of a supreme being, and I don't want to do this, especially since I consider myself free-will-agnostics. However, this implicit connection may be the reason why so many people are firmly either for, or against free-will.

Completely independent on this, yesterday, Sabine Hossenfelder wrote on her blog a post called Free will is dead, let’s bury it, in which she made some strong affirmations against free-will and people who believe in it. That free-will is bad science. I think that we know too little about this to call it science, but this can be said also about many things which we know exist and we would want to understand better. Then she said that people who believe in free-will have existential worries and hidden agendas. I agree that when we speak about believing in something, even in a physical law, we arrive at that belief in part because of our past experiences. Otherwise, how can we explain that people can change their opinion even about physical laws? So indeed, subjectivity is involved, but this happens all the time, not only with respect to believing in free-will. Then she said "I am afraid the politically correct believe in free will hinders progress on the foundations of physics". I think that if physicists reject their peers' papers or throw away their own results for not being consistent with free will, this is rather the exception, and they do this for many other reasons, including sex, race, or simply because they have different views. At the end, she wrote "buying into the collapse of the wave-function seems a small price to pay compared to the collapse of civilization". This is a nice pun, but quantum theorists who believe in collapse do so because they can't make sense of the outcomes of measurements without collapse, not because they want to support free-will. Many of them don't even believe in free-will, while others don't believe in collapse, but still don't reject free-will. But the reason they don't accept easily alternatives to QM (in particular hidden-variable superdeterministic theories and my unitary collapse approach) is simply that standard QM works much better, and not because they want to save their illusion of free will.