For a zeroth slogan about quantum mechanics, I’ve chosen

What’s hard to understand is classical mechanics, not quantum mechanics.

The slogan is labeled by zero because it’s preliminary to what I’ve been writing about here. It explains why I don’t intend to cover part of the standard story about quantum mechanics: it’s too hard, too poorly understood, and I’m not expert enough to do it justice.

While there’s a simple, beautiful and very deep mathematical structure for fundamental quantum mechanics, things get much more complicated when you try and use it to extract predictions for experiments involving macroscopic components. This is the subject of “measurement theory”, which gives probabilistic predictions about observables, with the basic statement the “Born rule”. This says that what one can observe are eigenvalues of certain operators, with probability of observation proportional to the norm-squared of the eigenvector. How this behavior of a macroscopic experimental apparatus described in classical terms emerges from the fundamental QM formalism is what is hard to understand, not the fundamental formalism itself. This is what the slogan is trying to point to.

When I first started studying quantum mechanics, I spent a lot of time reading about the “philosophy” of QM and about interpretational issues (e.g., what happens to Schrodinger’s famous cat?). After many years of this I finally lost interest, because these discussions never seemed to go anywhere, getting lost in a haze of complex attempts to relate the QM formalism to natural language and our intuitions about everyday physics. To this day, this is an active field, but one that to a large extent has been left by the way-side as a whole new area of physics has emerged that grapples with the real issues in a more concrete way.

The problem though is that I’m just knowledgeable enough about this area of physics to know that I’ve far too little expertise to do it justice. Instead of attempting this, let me just provide a random list of things to read that give some idea of what I’m trying to refer to.

Other suggestions of where to learn more from those better informed than me are welcome.

I don’t think the point of view I take about this is at all unusual, maybe it’s even the mainstream view in physics. The state of a system is given by a vector in Hilbert space, evolving according to the Schrodinger equation. This remains true when you consider the system you are observing together with the experimental apparatus. But a typical macroscopic experimental apparatus is an absurdly complicated quantum system, making the analysis of what happens and how classical behavior emerges a very difficult problem. As our technology improves and we have better and better ways to create larger coherent quantum systems, thinking about such systems I suspect will lead to better insight into the old “interpretational” issues.

From what I can see of this though, the question of the fundamental mathematical formalism of QM decouples from these hard issues. I know others see things quite differently, but I personally just don’t see evidence that the problem of better understanding the fundamental formalism (how do you quantize the metric degrees of freedom? how do these unify with the degrees of freedom of the SM?) has anything to do with the difficult issues described above. So, for now I’m trying to understand the simple problem, and leave the hard one to others.



Update: There’s a relevant conference going on this week.



Update: I’ve been pointed to another article that addresses in detail the issues referred to here, the recent Physics Reports Understanding quantum measurement from the solution of dynamical models, by Allahverdyan, Balian and Nieuwenhuizen.