In chapter 2 of How to Teach Physics to Your Dog, there’s a footnote about the ubiquity of uncertainty principle analogies in the mass media:

To give you an idea of the breadth of subjects in which this shows up, in June 2008, Google turned up citations of the Heisenberg Uncertainty Principle in (among others) an article from the Vermont Free Press about traffic cameras, a Toronto Star article citing the influence of YouTube on underground artists, and a blog article about the Phoenix Suns of the NBA. Incidentally, all of these articles also use the Uncertainty Principle incorrectly–by the end of this chapter, you should hopefully understand it better than any of them.

Add the Washington University in St. Louis psychology department to the list of institutions that don’t understand quantum mechanics as well as my dog– in an otherwise interesting New York Times article about study skills Benedict Carey writes:

Dr. [Henry L.] Roediger [III] uses the analogy of the Heisenberg uncertainty principle in physics, which holds that the act of measuring a property of a particle alters that property: “Testing not only measures knowledge but changes it,” he says — and, happily, in the direction of more certainty, not less.

Once again, that’s not really what the Uncertainty Principle says. It’s a semi-classical analogy used to make the fundamental physics of uncertainty more palatable to classically trained physicists in the 1930’s. Quantum uncertainty is really about the fundamental nature of matter, and is an unavoidable consequence of the dual particle and wave nature of quantum objects. You cannot measure both the position and momentum of a particle arbitrarily well not because the act of measuring one perturbs the system, but because those quantities *do not exist*.

OK, “do not exist” is a little strong, but then, I needed something provocative to get people to click through to the full post. Werner Heisenberg probably would’ve been ok with that phrasing, though– he was a big proponent of the idea that it doesn’t make any sense to talk about what quantum objects are doing between measurements. I’m not quite that radical, though.

Provocative phrasing or no, the origin of uncertainty really does spring from the idea of particle-wave duality rather than any ideas related to the act of measurement. It comes from the fact that, fundamentally, the position of a quantum object, like an electron or a photon, is a particle-like characteristic, while its momentum is associated with the wave nature of the object. Mathematically, the momentum of a quantum object is given by Planck’s constant divided by its wavelength (or, equivalently, the wavelength associated with a quantum object is determined by Planck’s constant divided by its momentum).

You can’t have a quantum object with both an arbitrarily well-defined position and an arbitrarily well-defined momentum because that is a contradiction in terms. An arbitrarily well-defined position would be described, mathematically, by a wavefunction that looks like a spike– the probability of finding the particle at a given position in space would be zero everywhere except the one point where the particle is really located. There’s no way to assign a wavelength to a spike, though– it doesn’t oscillate in any meaningful way– so the momentum of such a particle is completely undefined.

If you want to come at this from the other direction, a particle with a perfectly well-defined momentum would look like a perfect sine wave extending through all of space. Anywhere you looked, you would find the wavefunction oscillating up and down in a perfectly regular manner. Such a perfect wave, though, has a completely undefined position– the probability of finding the particle at any given position is the same non-zero value for every point in space.

Thus, there is absolutely no way to describe something that has a well-defined position at the same time as a well-defined momentum. The best you can do is to construct a “wavepacket,” a wavefunction that oscillates in a fairly regular manner in some region of space, but is zero outside that region. This necessarily leaves both position and momentum uncertain, though– the oscillation region needs to be big enough to contain a few wavelengths, which means the position is uncertain by at least that much, and the fact that the oscillation is constrained in space leaves the wavelength slightly uncertain as well. You can arrange for both of these uncertainties to be fairly small, if you put your wavepacket together in the right way, but you can never make either of them zero.

(If you’d like more math jargon and less hand-waving, formally, the position and momentum descriptions of the wavefunction are Fourier transforms of one another. The Fourier transform of a delta function is a constant, which gives you the result for the extreme cases. The minimum uncertainty state is a Gaussian wavepacket, whose Fourier transform is another Gaussian, and if you work through the math, you find their widths are related in exactly the way you expect from the Uncertainty Principle.)

(I should also insert the obligatory disclaimer here about this being the state of affairs for conventional quantum mechanics. A proponent of Bohmian mechanics would say that the position and momentum of any individual particle are, in fact, perfectly well-defined, but they are not known to the observer. And the initial position and momentum of any individual particle are randomly distributed over a small range of values, so that repeated measurements of the properties of many individual particles will give you exactly the same probability distribution that you would find from using conventional quantum mechanics. The end result is the same, but the path to it is a little different.)

Incidentally, this particle-wave argument is also the basis for the famous “zero point energy,” the energy that any quantum system has when it’s in the lowest energy state available. The lowest energy state is the one that makes the energy as close to zero as you can get while still allowing the object to have both particle and wave nature. This energy cannot be extracted, because it’s a fundamental consequence of the dual particle and wave nature of every object in our universe. Anybody claiming to have a device that produces free energy by extracting the zero-point energy by whatever means (a famous scam involves a “state below the ground state” in hydrogen, for example) is a fraud and very likely an evil squirrel.

So, quantum uncertainty does not, in fact, have anything to do with perturbing a system by measuring it. It’s true that measuring a quantum system changes its state, but that’s a different part of the theory, and nothing to do with Heisenberg’s famous principle. Quantum uncertainty is built into the deep structure of the universe, and is an inescapable consequence of things having both particle and wave characteristics.

Of course, that doesn’t make as catchy and educated-sounding a reference for lazy writers who aren’t physicists, so I don’t expect to see the measurement-based version of this analogy disappear any time soon. But now you know more than lazy writers (and psychology professors), so you’ll understand why they’re wrong, and why it makes me mutter angrily every time I hear this line trotted out.

(If you’d like a longer version of this explanation, with graphs of probability distributions, and discussions of bunnies, have I got a book for you…)