Following a path from the posts ‘Light’, ‘Superposition’, and ‘Superposition 2’: I doubt that classical physics has the kind of clarity whose absence is supposed to be surprising in quantum physics. For instance, if the act of weighing an object to whatever level of precision we desire were truly repeatable, the use of physical objects as standards for our units of measurement would be straightforward and feasible. However, while the kilogram used to be defined as the mass of a particular chunk of metal, it is now defined in terms of the speed of light, Planck’s constant, and the transition frequency of caesium-133. This should strike anyone who’s heard the standard narrative about quantum physics as very odd. The field of physics famous for measurement effects and probabilism is where we turn when we want reliable, precise, objective units of measurement.

One way of phrasing the difference between classical physics and quantum physics is to say that, given perfect knowledge of the initial conditions in a classical system, we can predict its future behavior perfectly; given perfect knowledge of the initial conditions in a quantum system, we can only make probabilistic predictions about its future behavior. I think that formulation has some sleight of hand in it, with the limits of knowledge moved from one side of the balance sheet to the other without our noticing. Suppose we define “perfect knowledge” as “knowledge that would be sufficient to make perfect predictions”. Now it is a tautology to say that, given perfect knowledge, we could make perfect predictions. So there’s no point asking whether that’s true in classical physics or in quantum physics. Instead, let’s ask ourselves a related question: can we have perfect knowledge? I’m pretty certain that the answer is “no” in both cases. All measurements have error. Classical physics, as encountered in the real world where we have imperfect knowledge, is probabilistic. So is quantum physics. Another related question: can we create a hypothetical scenario in which we have perfect knowledge? If we stipulate values for all of the relevant variables, can we predict the future behavior of the hypothetical system and be certain that a real system that had precisely those values would behave the same way? Here, I think that both classical and quantum physics include some very simple cases that allow for perfect knowledge, and more complicated cases that do not. In classical physics, a “one-body problem”, a single object not acted upon by any force, presumably falls into the first category, while at some n the n-body problem is analytically impossible given current computing power; barring a dramatic change in analytical methods, I assume that increasing computing power simply increases the n at which the problem becomes impossible. What if we had unlimited computing power? Maybe at this point we hit the difference between classical and quantum physics, or at least the point at which I don’t think I can make a particularly educated guess. Unlimited computing power, though, seems so counterfactual as to not leave much actual difference between a “solvable given unlimited computing power” problem and an “unsolvable even with unlimited computing power” problem. There’s some fun math out there, for instance, about the relationship between the number of possible phylogenetic trees depicting relationships between a particular number of species and the estimated number of atoms in the universe. I don’t remember it nearly well enough to insert an actual number here, but the take-home message was that once you get to one of the larger plant genera, which might have a few hundred species, an exhaustive search through all candidate phylogenetic trees is not possible within our universe. I assume even very modestly complicated prediction problems in classical physics are going to run into the same kind of problem–perhaps solvable in principle, but not solvable in our universe even if we somehow corralled the entire universe’s resources to that single task. “Solvable in principle” doesn’t seem to mean much when there is a hard external limit. The idea that certain things are inherently unknowable in quantum physics seems to derive from the same kind of limit–we can’t imagine a possible measurement that would fill the gap within the rules of our universe as we understand them. If the classical physicist gets to toss such limits aside and mark as “solvable in principle” problems that can’t be solved within our universe, surely we should grant our hypothetical quantum physicist the same powers.

To the extent there is a real difference between classical physics and quantum physics along these lines, my best guess is that the problems with measurement effects and so forth are similar in absolute magnitude across the two, but become quite large in quantum physics if viewed as a kind of ratio of measurement effect to thing we are trying to measure, but that this ratio remains quite small in classical physics.

One of the odd features of the standard quantum physics narrative is that it gives its narrator some conflicting motives. First, you set up the expectations we have of classical physics: everything is nice and orderly and predictable. Then you pull the rug out: look how bonkers all this quantum physics stuff is! Then, unless you’re going the new age route and proceed to say something vacuously mystical, you try to give the reader some tools to make sense of quantum physics. The third step would probably be a lot easier if you omitted step two, and probably if you omitted step one as well. My wandering down this path is prompted in part by having recently read Anil Ananthaswamy’s Through Two Doors at Once, and starting to wonder what it would look like if one started out by trying to explain quantum physics, rather than starting out trying to convince the reader that the topic is confusing and counter-intuitive. No criticism of Ananthaswamy is intended in this, I think he did a fine job and in this respect errs, if he errs, only in following precedent.