Previously in series: The Quantum Arena

At this point I would like to introduce another key idea in quantum mechanics. Unfortunately, this idea was introduced so well in chapter 2 of QED: The Strange Theory of Light and Matter by Richard Feynman, that my mind goes blank when trying to imagine how to introduce it any other way. As a compromise with just stealing his entire book, I stole one diagram—a diagram of how a mirror really works.

In elementary school, you learn that the angle of incidence equals the angle of reflection. But actually, saith Feynman, each part of the mirror reflects at all angles.

So why is it that, way up at the human level, the mirror seems to reflect with the angle of incidence equal to the angle of reflection?

Because in quantum mechanics, amplitude that flows to identical configurations (particles of the same species in the same places) is added together, regardless of how the amplitude got there.

To find the amplitude for a photon to go from S to P, you've got to add up the amplitudes for all the different ways the photon could get there—by bouncing off the mirror at A, bouncing off the mirror at B...

The rule of the Feynman "path integral" is that each of the paths from S to P contributes an amplitude of constant magnitude but varying phase, and the phase varies with the total time along the path. It's as if the photon is a tiny spinning clock—the hand of the clock stays the same length, but it turns around at a constant rate for each unit of time.

Feynman graphs the time for the photon to go from S to P via A, B, C, ... Observe: the total time changes less between "the path via F" and "the path via G", then the total time changes between "the path via A" and "the path via B". So the phase of the complex amplitude changes less, too.

And when you add up all the ways the photon can go from S to P, you find that most of the amplitude comes from the middle part of the mirror—the contributions from other parts of the mirror tend to mostly cancel each other out, as shown at the bottom of Feynman's figure.

There is no answer to the question "Which part of the mirror did the photon really come from?" Amplitude is flowing from all of these configurations. But if we were to ignore all the parts of the mirror except the middle, we would calculate essentially the same amoun...

jason martin

jason martin