We should change how we talk about change in quantum theory

Let me start with the short version:

Stop staying

If I change the axis along which I measure the spin to Z, Alice will obtain the value 1.

Start saying

If I had measured the spin along axis Z, Alice would have obtained the value 1.

And now, for the long version:

It will soon have been 18 years since I started collaborating with Jean-Pierre Dupuy on counterfactuals, in the Spring of 2004, at Stanford. It started with game theory and the definition of free choice.

Free choice in game theory

Dupuy suggested that a careful distinction between causal dependencies ("It is raining and as a consequence I am taking my umbrella with me.") and counterfactual dependencies ("If it had been raining, I would have taken my umbrella with me.") was needed to solve some of the challenges encountered by the community (backward induction paradox, etc).

The most important insight is that free choice as economists view it -- that is, that people can change their decisions unilaterally (independently of anybody else) -- can and should be challenged to a weaker form. In this weaker form of free choice, non-Nashian free choice, we still decide freely, in the sense that any decision is possible, but take into account in our reasoning that others can predict our decisions, akin to Douglas Hofstadter's superrationality: "If my decision had been different, then this other person would have known it and would have acted differently."

Dupuy proposed that a new solution concept in game theory could be designed, which gave birth to the Perfect Prediction Equilibrium for dynamic games (where players take turn like chess, go...), to the Perfectly Transparent Equilibrium for strategic games (where players think of their strategies in separate rooms), and later to a complete generalization for decisions located anywhere in spacetime.

Free choice in quantum physics

In the past few years I started working on taking it over to the field of quantum physics, where the exact same assumption of free choice is made when physicists decide what to look at: they assume that the decision of what to look at is completely independent of anything that is not in the future. Does it sound like game theory? Yes, absolutely and if you are interested in knowing more, there is this recent preprint co-authored with Michal Baczyk.

But I would like to focus on the key message I am trying to share with the physicists community. It is detailed in this letter in which I explain how it is crucial to be careful distinguishing causation, correlation and counterfactuals. Indeed, the three are often confused in pairs! In spite of the numerous viral posts on LinkedIn on correlation vs. causation (have you seen the Nobel prize winners per country vs. chocolate consumption?), they are still confused in a way people are unaware of: in particular it is based on a confusion of the two that the mainstream assumption of free choice is justified: if my decision is causally independent of anything not in the future (obviously!), then it must be statistically independent of anything not in the future as well... is it so obvious? If you conflate causation and correlations, yes. But if you do not, you immediately realize that this opens a new door, which we are suggesting: a different hypothesis of free choice called non-Nashian free choice, in which it is possible for you to make any choice you want, while it can still be that your choice is correlated with the past and predictable to some extent.

Jumping over the non-Nashian fence is challenging for any scientist who has been born and raised in Nash free choice. In my case, it took me five years until, in 2009, I had an epiphany and it suddenly dawned on me that Jean-Pierre Dupuy is a genius. Before it, working on the topic felt like manipulating algorithms with counterfactuals, and it was purely mechanical. But since this realization, it keeps feeling like our small but growing community is exploring a completely uncharted territory that keeps feeling bigger the more we walk around it it.

Changing how to think about change

If you are a physicist and have an open mind, let me challenge you with this very simple idea. Many physicists use the word "change" in order to explore the various possibilities of a decision (the choice of a measurement axis, which we can talk about as choosing a button to push to see what light comes on, to speak like Richard Feynman) and its impact: "If I change which button to push, then this happens", In fact, this is similar to how game theorists think of the Nash equilibrium. It is this use of the word "change" that prevents people from leaving the Nash way of thinking: mentally, using this word creates a mental image in which the past is fixed, my decision of which button to push is open as well as which light remotely comes on after it. So changing the decision feels like a little slider that one pushes to see how the future changes along.

But this is unsatisfactory because of the so-called "spooky action at a distance" as Einstein called it: if I "change" my decision of what button to push here, then it "changes" the light that switches on very far away, so far away that the information would not even have time to travel.

Rather than accepting the spooky action at a distance, we suggest that we can instead reconsider how we describe it, and in particular, without referring it to it as a change triggering another change.

So, what is really "change"? The most rigorous definition of change I can think of is this: the weather changes when, for example, it was Sunny, and now it is raining. I change what button to push if I actually pushed a first button, and then change my mind and push another. Something changes if it was like this, and now -- later -- it is like that, and that is different from this.

But changing a decision on what button to push (the "measurement axis") is nothing like it! Rather, it is pushing a button and hypothetically considering what other button one could instead have pushed. This is a counterfactual. What this means is that the choice is not "changed", but rather the reasoning goes with a subjunctive conditional as "If I had, instead, pushed that other button, then this other light would have come on on the other side." This is very different, because the semantics of counterfactuals are based a possible-worlds semantics suggested in the 1970s by David Lewis: in the closest world in which I push that other button, this other light comes on. And this makes the causal inconsistency go away. In fact, quantum experiments push us to more carefully make this distinction -- or at least, this is what I think they are telling us we should do.

This alternate way of thinking and revisiting the quantum world takes time to get used to, but if you are interested in learning more, you can click on the links spread all over this post in order to dive more into the non-Nashian approach.

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