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proton—you’d never even notice that.”
    “Yeah? Well, where’s my bone, smart guy?”
    “I don’t know. Did you look under the TV cabinet? Sometimes it gets kicked under there.”
    She trots over to the TV, and sticks her nose under the cabinet. “Oooh! Here’s my bone!” She paws at it for a minute, and eventually succeeds in knocking it out from under the cabinet. “I have a bone!” she announces proudly, and begins chewing it noisily, the uncertainty principle forgotten.
    The Heisenberg uncertainty principle is probably the second most famous result from modern physics, after Einstein’s
E = mc 2
(the most famous result from relativity). Most people wouldn’t know a wavefunction if they tripped over one, but almost everyone has heard of the uncertainty principle: it is impossible to know both the position and the momentum of an object perfectly at the same time. If you make a better measurement of the position, you necessarily lose information about its momentum, and vice versa.
    In this chapter, we’ll describe how the uncertainty principle arises from the particle-wave duality we’ve already discussed. The uncertainty principle is often presented as a statement that a measurement of a system changes the state of that system, and in this form, references to quantum uncertainty turn up in all sorts of places, from politics to pop culture to sports. * Ultimately,though, uncertainty has very little to do with the details of the measurement process. Quantum uncertainty is a fundamental limit on what
can
be known, arising from the fact that quantum objects have both particle and wave properties.
    Uncertainty is also the first place where quantum physics collides with philosophy. The idea of fundamental limits to measurement runs directly counter to the goals and foundations of classical physics. Dealing with quantum uncertainty requires a complete rethinking of the basis of physics, and leads directly to the issues of measurement and interpretation in chapters 3 and 4.
HEISENBERG’S MICROSCOPE: SEMICLASSICAL ARGUMENTS
    The traditional description of uncertainty as the act of measurement changing the state of the system is essentially based in classical physics, and was developed in the 1920s and ’30s in order to convince classically trained physicists that quantum uncertainty needed to be taken seriously. This is what physicists call a semiclassical argument—the physics used is classical, with a few modern ideas added on. It’s not the full picture, but it has the advantage of being readily comprehensible.
    The idea behind the semiclassical treatment of uncertainty is familiar to any dog. Imagine you have a bunny in the yard whose position and velocity you would like to know very well. When you attempt to make a better determination of its position (by getting closer to it), you inevitably change its velocity by making it run away. No matter how slowly you creep up on it, sooner or later, it always takes off, and you never really have a good idea of both the position and the velocity.
    An electron isn’t a sentient being like a bunny, so it can’t run off of its own accord, but a similar process takes place.

    An incoming photon bounces off a stationary electron, and is collected by a microscope lens in order to measure the electron’s position. In the collision, though, the electron acquires some momentum, leading to uncertainty in its momentum.
    To measure the position of an electron, you need to do something to make it visible, such as bouncing a photon of light off it and viewing the scattered light through a microscope. But the photon carries momentum (as we saw in chapter 1 [page 24]), and when it bounces off the electron, it changes the momentum of the electron. The electron’s momentum after the collision is uncertain, because the microscope lens collects photons over some range of angles, so you can’t tell exactly which way it went.
    You can make the momentum change smaller by increasing