Read How to Teach Physics to Your Dog for Free Online Page B

the wavelength of the light (decreasing the momentum that the photon has available to give to the electron), but when you increase the wavelength, you decrease the resolution of your microscope, and lose information about the position. * If youwant to know the position well, you need to use light with a short wavelength, which has a lot of momentum, and changes the electron’s momentum by a large amount. You can’t determine the position precisely without losing information about the momentum, and vice versa.
    The real meaning of the uncertainty principle is deeper than that, though. In the microscope thought experiment illustrated above, the electron has a definite position and a definite velocity before you start trying to measure it, and still has a definite position and velocity after the measurement. You don’t know what the position and velocity are, but they have definite values. In quantum theory, however, these quantities are not defined. Uncertainty is not a statement about the limits of measurement, it’s a statement about the limits of reality. Asking for the precise position and momentum of a particle doesn’t even make sense, because those quantities do not exist.
    This fundamental uncertainty is a consequence of the dual nature of quantum particles. As we saw in the previous chapter, experiments have shown that light and matter have both particle-like and wavelike properties. If we’re going to describe quantum particles mathematically—and physics is all about mathematical description of reality—we need to find some way of talking about these objects that allows them to have both particle and wave properties at the same time. We’ll find that the only way is to have both the position and the momentum of the quantum particles be uncertain.
BUILDING A QUANTUM PARTICLE: PROBABILITY WAVES
    The usual way of describing particles mathematically, dating from the late 1920s, is through quantum wavefunctions. The wavefunction for a particular object is a mathematical functionthat has some value at every point in the universe, and that value squared gives the probability of finding a particle at a given position at a given time. So the question we need to ask is, What sort of wavefunction gives a probability distribution that has both particle and wave properties?
    Constructing a probability distribution for a classical particle is easy, and the result looks something like this:

    The probability of finding the object—say, that pesky bunny in the backyard—is zero everywhere except right at the well-defined position of the object. As you look across the yard, you see nothing, nothing, nothing, BUNNY!, nothing, nothing, nothing.
    This wavefunction doesn’t meet our requirements, though: it has a well-defined position, but it’s just a single spike, and a spike does not have a wavelength. Remember, the wavelength corresponds to the momentum of the bunny, which is one of the quantities we’re trying to describe, so it needs to have some value.

    Well, then, how do we draw a probability distribution with an obvious wavelength? That’s also easy to do, and it looks like this:

    Here, the probability of finding the bunny at a given position oscillates: bunny, Bunny, BUNNY, Bunny, bunny, Bunny, BUNNY, Bunny, bunny, and so on.
    This wavefunction doesn’t meet our requirements, either. The wavelength is easy to define—just measure the distance between two points where the probability is largest—so we have a well-defined momentum, but we can’t identify a specific position for the bunny. The bunny is spread out over the entire yard, with a good probability of finding it at lots of different places. There are places where the probability of seeing a bunny is low, but they don’t account for much space.
    What we need is a “wave packet,” a wavefunction that combines particle and wave properties in a single probability distribution, like this:

    This wavefunction is what we’re after: nothing, nothing,