Newton versus Heisenberg

Death of a microbe

The Heisenberg Uncertainty Principle has become famous well outside quantum physics, but it is often cited in garbled form. I once found it mentioned in a textbook on social science research methods, where it was defined as the fact that electron microscopes can damage samples when they observe them by electron bombardment. Physicists roll their eyes at such misunderstandings, but I think that physicists themselves often misunderstand the Uncertainty Principle, by confounding Heisenberg’s specifically quantum mechanical relation with a principle of measurement that goes back to Newton. 

What the Uncertainty Principle really means, in practical terms, is that if you construct an apparatus to control one experimental property more tightly, so that the variations in its value between different repetitions of the experiment will be smaller, then past a certain point there will always be some other thing that becomes correspondingly less well controlled, so that its run-to-run variations become wilder. The ‘certain point’ at which this trade-off sets in represents a degree of precise control so high as to be quite unattainable anyway in the macroscopic world. So although the Uncertainty Principle is profound, it is really irrelevant to fields like social science research.

Observing something means letting it act on you.

What even many physicists think the Uncertainty Principle means, however, is something that really is widely relevant: the fact that no measurement can ever be purely passive, but always affects the thing being measured. This principle is both true and important, but it is not specifically quantum mechanical.

Observation is a physical process. A meter can only register the position of an object if there is some interaction that makes the object’s position act on the meter. Newton told us, long before Heisenberg, that this means that any meter is also going to react upon the the thing it measures. Such ‘observer effects’ are apt to be important when large meters measure tiny things; the Heisenberg Principle, however, is not this, but an additional complication in microscopic measurements.

In the early days of quantum mechanics, critics of the new theory tried to argue that the Uncertainty Principle was not self-consistent, by describing hypothetical experiments that would obey the Principle in each individual process, but yet still lead to an indirect violation of the Principle as an end result. These arguments all had subtle flaws, and the most famous flaws involved reaction effects. Thus the only really solid connection between the Uncertainty Principle and measurement reaction is historical.

Newton observes Heisenberg stealing credit for his ideas.

Newtonian reaction in physical measurements is a distinct concept from Heisenberg Uncertainty, but it does at least seem that one must get the former right in order to understand the latter. So perhaps there really is some deep connection between them. Until that connection comes to light, however, anyone who wants to relate observer effects in general to a basic principle of physics should really be citing Newton, not Heisenberg.

Statistical Mechanics

Most people these days have heard of quantum mechanics, and how it somehow brings chance and probability into physics on a basic level. This is a misleading truth, because actually quantum mechanics is perfectly deterministic, and not probabilistic at all, until we come to measure anything. Then the probabilities come in, and only then. The problem is that quantum measurement is a very subtle thing that is far from fully understood. And one thing we do know is that inferring how things really are, from how things look, is uniquely tricky in quantum mechanics.

To appreciate the subtlety of quantum mechanics, it helps to know about the older and less tricky place that probability has in physics: statistical mechanics. I doubt that most non-physicists have ever heard of statistical mechanics. In many places one can even earn a Bachelor's degree in physics without ever taking a course in it. This is unfortunate, because statistical mechanics is so important, that a physicist who doesn't know about it is like a Scout who doesn't know that fire needs air. Statistical mechanics is a sort of post-processing stage that has to be performed on virtually all the rest of physics — even including quantum mechanics — in order to make sense of anything but the very simplest and most controlled experiments.

Mechanics without statistics is the physics we learn in school. A rock flies through the air, falling under gravity. Ignore air friction, and model the rock as a point with a given mass — a particle. Apply Newton's Laws to particles: that's mechanics.

'In principle,' we may be told, 'the universe is a large number of particles, governed by Newton's Laws.' In practice, of course, most of these particles are beyond our control, beyond our observation, or at least beneath our notice. We do not see the vast swarms of air molecules that surround us and fill our lungs. And even if we could mark their paths, solving Newton's equations for so many interacting particles is far beyond our computational power. Thus do we see the vast gap between the pristine principles of physics, and the practical real world.

Bah. Physics doesn't care about pristine. Sure, part of physics is about trying to reduce everything, 'in principle', to some elegant little Theory of Everything. We're writing one big long footnote to Plato, who wanted everything to boil down to the five regular polyhedra. But that whole grand unified simplicity thing is really the hood ornament of physics, not the engine. The thing that drives physics is putting principles into practice, and codifying practice into principle. So no, the fact that we can't follow every atom does not make a huge gap between physics and reality. There is a whole huge branch of physics which is all about the principles and the practice of dealing with huge numbers of particles that cannot be individually observed, predicted, or controlled.

And that is the branch of physics called statistical mechanics. It uses probability theory to get the best results we can from what we do know, in spite of what we don't. Whether or not God plays dice with the universe, physicists do, to make up for the fact that we're not God.