Physics and the bumper sticker
In the remote preparation for my Coursera on randomness, I read Nate Silver‘s The signal and the noise. I am not sure how much of it will enter my course, since I don’t plan to enter into the topics he deals with (politics, the stock market, climate change, prevention of terrorism, baseball and poker). But the conclusion struck a cord.
The author lists seven approximations to describe the “efficient market hypothesis”, which run: 1. No investor can beat the stock market, 2. No investor can beat the stock market over the long run, and so on until approximation 7 which a is five lines long sentence. Then he adds (emphasis is mine):
“The first approximation — the unqualified statement that no investor can beat the stock market — seems to be extremely powerful. By the time we get to the last one, which is full of expressions of uncertainty, we have nothing that would fit on a bumper sticker. But it is also a more complete description of the objective world.”
Sounds familiar? Let’s give it a try:
- Bumper sticker: No extension of quantum theory can have improved predictive power
- Expression full of uncertainty: the authors work under the assumption of no-signaling (so, if you are Bohmian, don’t worry, our result does not concern you). Then they assume a lot of quantum physics, but not all of it, otherwise the claim would be tautological. Beyond the case of the maximally entangled state, which had been settled in a previous paper, they prove something that I honestly have not fully understood. Indeed, so many other colleagues have misunderstood this work, that the authors prepared a page of FAQs (extremely rare for a scientific paper) and a later, clearer version.
- Comment: the statement “Colbeck and Renner have proved that quantum theory cannot be extended” is amazingly frequent in papers, referee reports and discussions. Often, it comes in the version: “why are people still working on [whatever], since Colbeck and Renner have conclusively proved…?” It is pretty obvious however that many colleagues making that statement are not aware of the “details” of what Colbeck and Renner have proved: they have simply memorized the bumper sticker statement. I really don’t have a problem with Colbeck and Renner summarizing their work in a catchy title; what is worrisome is other experts repeat the catchy title and base decisions solely on it.
- Bumper sticker: The quantum state cannot be interpreted statistically [Yes, I know that the title of the final version is different, but this is the title that sparked the curiosity of the media]
- Expression full of uncertainty: the authors work with a formalization of the notions of “ontic” and “epistemic” that is accepted by many people, though not by Chris Fuchs and some of his friends. They add a couple of other reasonable assumptions, where by “reasonable” I mean that I would probably have used them in a first attempt to construct an epistemic model. Then they prove that such an epistemic model is inconsistent.
- Comment: too many people have commented on this paper. The latest contrary claim has been posted online today, I have not read it because I am really not following the debate, but for those who are interested, here it is.
- Bumper sticker: either our world is fully deterministic or there exist in nature events that are fully random [the use of “either-or” makes it too elaborated for a real bumper sticker, but for someone who browses these papers, the sentence is basic enough]
- Expression full of uncertainty: the authors consider a very weak source of randomness, something like a very biased coin; in fact, it can be more perverse than that, because it can have correlation over various tosses. But it cannot be completely perverse: the authors make an assumption about its structure (technically known as “Santha-Vazirani” by the names of the first two persons who proposed it). Then they prove that, if this source is used as seed for a specific quantum experiment, the outcomes of the experiment are guaranteed to be much more random. In the limiting case of an experiment lasting infinitely long time, and whose results do not deviate by any amount from the optimal result allowed by quantum physics, the source can contain almost no randomness, while the final list will be almost fully random.
- Comment: in a paper just published, we studied what happens if we remove the Santha-Vazirani assumption, so that the source can be as perverse as you wish. Not surprisingly, the conclusions become more pessimistic: now, one would need a fair amount of initial randomness in order for the quantum step to produce further randomness. Nothing wrong at all: some guys get a good result with an assumption, others test the limit of the assumption, this is the normal course of science. But read again the bumper-sticker statement: taken in itself, out of the paper where it belongs, that statement has not been “scientifically proved” — it even sounds closer to being impossible to prove, without the crucial assumption