In my last post, I pointed out a fundamental problem in a particular paper – although the same problem appears in lots of papers: specifically, that there is no way to test whether an object is in a quantum superposition. I feel like this is a point that many physicists and philosophers of physics overlook, so to be sure, I went ahead and posted the question on a few online physics forums, such as this one. Here’s basically the response I got:
Every state that is an eigenstate of a first observable is obviously in a superposition of eigenstates of some second observable that does not commute with the first. Therefore: of course you can test whether an object is in a quantum superposition. Also, you are an idiot.
OK, so they didn’t actually say that last part, but it was clearly implied. If you don’t speak the language of quantum mechanics, let me rephrase. Quantum mechanics tells us that there are certain features (“observables”) of a system that cannot be measured/known/observed at the same time, thus the order of measurement matters. For example, position and momentum are two such observables, so measuring the position and then the momentum will inevitably give different results from measuring the momentum and then the position – that is, the position and momentum operators do not commute. And because they don’t commute, an object in a particular position (that is, “in an eigenstate of the position operator”) does not have a particular momentum, which is to say that it is in a superposition of all possible momenta. In other words, the above response basically boils down to this: quantum mechanically, every state is a superposition.
Fine. The problem is that this response has nothing to do with the question I was asking. I ended up having to edit my question to ask whether any single test could distinguish between a “pure” quantum superposition versus a mixed state (which is a probabilistic mixture), and even then the responses weren't all that useful.
This is why I think the big fundamental problems in physics will probably not be solved by insiders. They speak a very limited language that, by its nature, limits a speaker’s ability to discover and understand the flaws in the system it describes. My original question, I thought, was relatively clear: is it actually possible, as Mari et al. suggest, to receive information by measuring (in a single test) whether an object is in a macroscopic quantum superposition? But when the knee-jerk response of several intelligent quantum physicists is to discuss the noncommutability of quantum observables and come to the irrelevant (and, frankly, condescending) point that all states are superpositions and therefore of course we can test whether an object is in superposition – well, it makes me wonder whether they actually understand, at a fundamental level, what a quantum superposition is. I feel like there’s a huge disconnect between the language and mathematics of physics, and the actual observable world that physics tries to describe.