QBism.org

As the person tasked with setting up this QBism website, I’m going to inaugurate it with a shameless plug of my own paper that just came out on the arXiv: A quintet of quandaries: five no-go theorems for Relational Quantum Mechanics.

As the title suggests, the paper is a critique of the relational interpretation of quantum mechanics first proposed by Carlo Rovelli in 1996. Someone reading my paper might get the impression that I dislike RQM, and would therefore be surprised to learn that before I became a QBist I was an adherent of RQM. It is a quirk of human nature that we often reserve our harshest criticisms for those ideas that we have come closest to believing in.

I remember seeing a talk by Rovelli about RQM in Vienna when I was a postdoc there. At that time I was enthralled by the idea that quantum mechanics might be a natural extension of intuitions taken from relativity theory. I hoped that RQM might provide a solution to the “Wigner’s friend paradox” by providing a mathematical transformation between Wigner and his friend that could reconcile their different quantum state assignments, by analogy to the way that a Lorentz transformation reconciles the points of view of differently moving observers in relativity theory.

After his lecture, I asked Rovelli whether he thought such a mathematical mapping could be defined. He said that he did not think the analogy with relativity should be taken that far! I was shocked. If the analogy couldn’t be taken that far, I thought, then what good was it? For a while, I struggled to define a mapping between observers that would do the trick. I even uploaded an ill-fated paper to the arXiv, which claimed to find the mapping for the special case of two-level systems. However, it turned out to contain a fatal error, which was found by a referee (to whom I am eternally grateful). After correcting the paper and reducing its claims, I was too disheartened to resubmit it to any journal.

That failure was the beginning of my disillusionment with RQM. In the second no-go theorem of my critique, I argue that under some plausible assumptions about the form such a mapping would take, no non-trivial mapping analogous to a Lorentz transform can exist between Wigner and his friend in RQM.

The history of the critique unfolded in a somewhat circuitous way. It was originally conceived of as a critique of RQM from a QBist point of view. On that pretext, in September of 2020, I had some very interesting correspondence with Rovelli and Andrea di Biagio about the similarities and differences between RQM and QBism. We ended up agreeing that the two interpretations were more different on certain points than we had previously appreciated. In subsequent months, as I tried to write the paper, it became more and more clear to me that my criticisms of RQM exposed weaknesses internal to RQM that could be appreciated even by non-QBists. That’s why I decided to split the paper into two: the first would be a straightforward critique comprising my strongest arguments against RQM, while the second would be a more amicable and non-judgemental comparison between QBism and RQM (that one is still in the works, but I hope to upload it to the arXiv in the coming weeks).

Some people have told me my critique comes across as harsh. I definitely used a rhetorical style that is quite merciless in some ways: wherever I identified weak spots in RQM, I deliberately belaboured the point and did not soften the blow by offering alternative readings or possible escape routes. I did this because I noticed that many previous analyses of RQM by other authors tended to adopt a more ambiguous tone, presenting their critiques alongside praise for what they thought were strong points of RQM, and generally claiming to endorse the spirit (if not the letter) of the interpretation. Unfortunately, this made it easier for defenders of RQM to simply ignore the previously noted critiques or to gloss over them as minor wrinkles to be smoothed out. I wanted to drive home that some of these critiques cannot be easily smoothed over, and to present the arguments provocatively in order to stimulate a creative debate. That’s also why I chose the format of a set of “no-go theorems” — instead of simply shutting down possible defenses of RQM, I force proponents of RQM to choose from a menu of unpalatable responses, which makes for a much more interesting discussion.

As Rovelli himself has said, “every interpretation has a cost”. My goal was to write the paper that I would have liked to have read when I was considering RQM as a viable interpretation: a paper that lays out its weak points in plain view for examination. At least those who choose to forge ahead with RQM will know what challenges they face!