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.

I imagine that the quantum physicist’s response to my last post would be to suggest that the probabilistic nature of a quantum physics is “hard”, or ontological, or objective, while the probabilistic nature of a cat is “soft”, or epistemic, or subjective. Quantum physics really is probabilistic, while cats only seem probabilistic because our knowledge is limited. Suppose we assume that this is correct. I still think it worth noticing that our knowledge is in fact probabilistic in both cases, and that the prediction problem with regard to cats is not likely to be simpler, should we ever be in a position to seriously attempt it, than the prediction problem with regard radioactive decay. We might look at the gulf between the two rather differently than our hypothetical physicist. The radioactive decay of an atom is extremely simple event, while the future state of a cat is an extremely complicated event. The attention we have devoted to the former is sufficiently large in relation to the difficulty of the problem that we might reasonably expect to have arrived at a complete understanding if it is possible for us to do so. The attention we have devoted to the latter is sufficiently minute in relation to the difficulty of the problem that we can be certain our understanding is incomplete and will remain so for the foreseeable future. It is easier to imagine that a complete understanding of a cat’s future state is theoretically possible because we are so far from it that the possible realm of understanding is quite unconstrained, while we are close enough to a complete understanding of a radioactive atom that we can see some boundaries to our possible realm of understanding. This leads us to an odd inversion. The more difficult a problem is, and the further we are from solving it, the more willing we are to believe that solving it is theoretically possible.

There’s also an odd inversion in the narrative we tell about quantum physics. The traditional narrative is something like: macroscopic objects follow definite rules that make sense. We can know the location and velocity of a ball precisely, and we can predict how its location and velocity will change based on any force exerted on it. Quantum physics is a bizarre world in which none of this really seems to apply. The rules don’t make sense and violate our understanding of reality, We can’t know locations and velocities precisely, things often seem to be in multiple places at once or to affect each other even when there is no identifiable force connecting them, future states are probabilistic rather than deterministic. However, all the ways in which quantum physics differs from classical physics are also ways in which our experience of the world also differs from classical physics. The world we interact with may well follow very definite, coherent, deterministic rules, but phenomena in the actual world–and especially the social world, which occupies a great deal of our attention and interest–are so complicated that our experience of it is so full of uncertainty, confusion, and context-dependence that the world of quantum physics is really quite orderly and well-behaved in comparison. We might as well have a narrative about how bizarre classical physics is. The simplest situations we know of share some of the same uncertainties and ambiguities as the most complex situations we know of, while there is this funny realm in between where certainty and precision make an appearance.

It is tempting but hazardous for non-physicists to offer opinions on quantum mechanics. Having succumbed to that temptation in the post ‘Light’ a few days ago, I figure I may as well continue.

Schrödinger’s Cat is a thought experiment that, at least as popularly understood, brings the conceptual problem of a superposition of states at the quantum level into the familiar macroscopic world of classical physics by linking the fate of a cat to a quantum mechanical process. Suppose a radioactive atom is in a superposition of states, having in some sense both decayed and not decayed, until it is observed. Or, perhaps, until its having decayed or not has any potential to affect phenomena beyond itself. Suppose we make a device that will kill a cat if the atom has decayed, or not if it has not. Then we make a box that is perfectly impenetrable to observation. We can know nothing of what goes on inside the box until it is opened. We put the cat and the quantum device into the box, shut the lid, and the cat is in the same superposition of states as the radioactive atom. Although originally intended as a reductio ad absurdum of the Copenhagen Interpretation, it is now generally viewed more as an illustration of the counterintuitive nature of quantum mechanics.

Suppose we simplify the situation. Omit the radioactive atom, omit the device that will kill the cat or not based on the state of the atom. We just make a box, let’s call it Box 1, that prevents us from telling if there is a live or dead cat inside of it. Because I like cats, let’s also put in a feeding, watering, and waste disposal system that is, all else equal, sufficient to keep the cat in good health. We put the cat in the box and close the lid. There is some duration-dependent probability that the cat will die. Over a few hours or days, the probability is very low. If the experiment is extended across decades the probability will reach 1 at some point. Suppose we have an understanding of the cat sufficient to estimate the probability that the cat is alive at any given point in time.

OK, now let’s make Box 2 and put the quantum device in. Just to make the situation a little more straightforward, we’ll calibrate it so that at any given point in time the probability that the the device will be triggered and cause the cat’s death is equal to the probability of the cat having died of natural (well, non-quantum, at least; calling anything in this experiment ‘natural’ seems a bit strained) causes. We find some identical cats, stick one in Box 1 and the other in Box 2. Although they are identical, presumably we put the cat of which we are more fond in Box 1. We close the boxes, wait a month, then we open them. The probability that the cat has died in Box 2 is twice the probability that the cat has died in Box 1.

There’s always some probability of finding a dead cat when you open one of these boxes. Adding the quantum device only changes the probability, it doesn’t introduce a probability when there was none before.

While Box 1 is closed, to imagine that the cat is alive, or even to say that it must be alive or dead right at that moment, is to imagine an observer who can see into the box. We are describing what such an observer would see. This violates the rules of the thought experiment; we are no longer imagining an observationally impenetrable box, but one whose contents can be watched. So long as we are following the rules, there is no internally consistent representation of the situation that includes concurrent knowledge about what’s going on inside the closed box and outside of it. You can’t imagine a box no one can see into and imagine the cat in it. But it’s very difficult not to imagine the cat… it’s hard to get our minds to follow the rules of the thought experiment.

The implied observer has to be forced into the light. But, once seen, through whose eyes?