Collapse models collapse in my esteem
In preparing my teaching for the coming semester, I was lead to consider the possibility of introducing the students to collapse models. From afar, I was keen to adopt a moderate stance like “yeah, this is not standard stuff, but it’s intriguing, and it’s worth knowing”. (un)Fortunately, while in my research I fall every now and then into the sin described in my previous post, when it comes to teaching I am really incapable of regurgitating material from a book or a review article. So I spent some time thinking how I would present collapse models to an audience, who will have already studied Bell’s theorem in its device-independent approach (lecture notes available here). And I came to the conclusion that — I probably won’t present them.
Let us take one step back. The desire for collapse is triggered by the quantum description of setups like the double slit experiment. Each electron produces a very sharp dot on the screen, as one would expect from a particle. However, after detecting many electrons, the overall distribution of dots is an interference pattern, like the one expected for a wave. These are the facts. The rest depends on how you narrate the story. In the most frequently encountered narrative, the electron is delocalized like a wave before hitting the screen, then it “collapses” to a given location upon hitting the screen. A collapse model is a model that aims at describing how this transition happens.
Some very smart people, rigorously trained in quantum thinking since the cradle, realize immediately that such a narrative is fishy, denounce it as such and ask us to move on. Less smart and/or less rigorously trained people, like me, need more evidence to be convinced. What happened to me in preparing my teaching is that I suddenly collected for myself such evidence. And now I am trying to share it with you.
So, let’s take my starting point and that of my future students: we know Bell inequalities. We know in particular that any classical mechanism aimed at reproducing quantum correlations must be non-local. “Wow, cute: non-locality!” Well, not so cute. For one, the hypothetical mechanism must be infinitely rigid in space-time, or in other words, it must propagate information at infinite speed (yes, infinite, not “just” faster-than-light). For two, the predictions of quantum physics are more restrained than those of the most general non-local theory (even under the so-called “no-observable-signaling” assumption): so, if you toy around with a non-local mechanism, you must further constrain it ad hoc in order to recover the observations. In other words, not only a non-local mechanism does not bring additional predictive power: it must be so fabricated as to match the observations, which we continue predicting using quantum theory. Really, not so cute.
Back to collapse now. A collapse model worth of its name would certainly be applicable beyond the example localization in double slit experiment. Specifically, take a Bell experiment: two photons are prepared in an entangled state, so the polarization of each one is undetermined. Upon measurement, one is found with horizontal polarization (H), the other with right circular polarization (R). This is also a case of “collapse”, where something got determined that was previously undetermined. So the collapse model should describe it too.
Now it’s time to be more precise: what is your aim exactly, in constructing a collapse model? Here come two options:
- You want a deterministic process: something that explains that in this run of the experiment, given whatever variable in the measurement apparatus, the first photon would necessarily collapse into H; and the second photon would necessarily collapse into R. This would certainly be a very pleasant complement to quantum physics for a classical mind. But Bell’s theorem is clear: the “whatever variable” that triggers such a collapse must be unpleasantly non-local as defined above. Are you ready to buy it? Then I have infinitely many collapse models ready for you. But think twice: are you really making physics more understandable by choosing this path?
- You want a stochastic description: here, I am a bit at a loss at what this wish is. If by “stochastic” one means “classically stochastic”, we are back to the previous case. In fact, Bell’s theorem does not apply only to deterministic models, but also to classically stochastic ones (i.e. all those where the stochastic element can be attributed to ignorance; mathematically, those that can be described as convex combinations of deterministic models). If by “stochastic” one means “any form of mathematical model with some stochastic element” — well, then quantum mechanics is there, and there does not seem to be the need to complement it with a collapse model.
In a nutshell, it seems to me that collapse models were maybe a legitimate quest at a time when “localization” was presented as the fundamental non-classical feature of quantum physics (the very smart fellows mentioned above will tell you that there has never been such a time for them, but again, this post is for normal people like me). Now we have Bell’s theorem and the corresponding experiments. You don’t need to make of Bell’s theorem your new foundational cornerstone, if you don’t want to; just take it as one of the many discoveries made in the 20th century thanks to quantum physics. Under the light of this discovery, the fog of collapse models, which could be entertained for some time, seems to be dissipating leaving little trace.
P.S. This ends up being a “negative” post: I criticize collapse models without proposing my own positive solution. At least, I know that there is one path that is not worth exploring. I am leaving now for three weeks of holidays and maybe I’ll find time to explore some other path (though, most probably, I won’t think of physics altogether).