As we started the last week of the advent calendar, I was trying to map out the final days, and was coming up one equation short. I was running through various possibilities– the Dirac equation, Feynman’s path integrals, the Standard Model Lagrangian, when I realized that the answer was staring me right in the face:
This is, of course, the Heisenberg Uncertainty Principle, saying that the product of the uncertainties in position and momentum has to be greater than some minimum value. Strictly speaking, this should’ve come before the Schrödinger equation, if we were holding to chronological order, because Heisenberg got there first, but it’s also the equation that gave this blog its name, so I held it for last.
So, what does this mean?
What does this one mean? A lot of popular descriptions of the principle put it in terms of measurement perturbing a system, saying that any attempt to do a better measurement of the position of a particle will necessarily introduce uncertainty in the position, and so on. You can even get the basic form of the relationship right, by thinking in these terms, and using a little knowledge of optics.
This is a little problematic, though, in that it presumes that the particle has a well-defined position and velocity, even if those things aren’t known to the experimenter. While there are ways to look at quantum theory where that’s a sensible statement, the underlying mathematics point to a different way of thinking about it, which is to say that these quantities are simply not well defined to begin with. You can’t do a perfect measurement of the position of a particle not because of practical limitations on your measuring apparatus, but because it doesn’t make sense to talk about the position of a quantum particle having a definite value at all.
This, of course, brings with it a whole host of problems, and the probabilistic interpretation of the theory turned off a lot of physicists, including people like Einstein and Schrödinger who had helped launch the theory. But if you’re willing to roll with it, it’s an incredibly cool way of looking at the world. Which is why I appropriated it for the name of the blog. It’s also useful as a reminder that you can never really know everything about anything, which is important to keep in mind.
This brings us to the end of our physics advent calendar. Newton’s birthday is tomorrow, but we’ll all be too busy to blog, let alone solve equations. But whether you mark the date with a Christmas tree, a menorah, or an obsessive personal quest for alchemical secrets, take a moment on the 25th to appreciate physics, and all the cool things it does for us. And try to carry that appreciation through the rest of the year– for that’s the real meaning of Newton’s birthday…