Field Notes

B receives energy from A via the wave in the rope, even though no mass is exchanged.

Dave Brown/North Coast Journal

Of Photons and Cormorants

By Barry Evans

fieldnotes@northcoastjournal.com

We were paddling on Stone Lagoon, cormorants in formation overhead, when out of the blue …

“Hey, you know about science, right?”

“A bit. I’m a science writer, not a scientist …”

“Yeah, well. E = mc2, you know? Energy and mass?”

“Um … OK.”

“And photons don’t have any mass, right?”

“Right.”

“So if they’re massless, they don’t have any energy. So how do solar panels work?”

Not the fi rst time I’ve been asked to explain how photons of light, whose rest mass is zero, can possibly do all they do: create electricity from solar panels, energize photosynthesis, start fi res when the sun’s rays are focused with a magnifying glass and so on. The fi rst thing you need to know is that Einstein’s famous equation linking energy and mass is a special case of a more general equation:

E2 = p2c2 + m2c2

E is the total energy of a particle, p is its momentum (from Latin petere, to go to, to seek), m is its mass and c is the speed of light. So its total energy is mass energy plus momentum energy. At rest, p = 0, so we get back to the familiar E = mc2. Photons, with no mass, get all their energy from their momentum — they act like they have mass — that’s how a spacecraft’s solar sail works — but no actual exchange of mass takes place. It’s all momentum. (What you learned in high school physics, momentum = mass x velocity, is an approximation for slow-moving objects, not for photons traveling at the speed of light.)

Now, a particle with neither mass nor momentum isn’t anything at all, so a photon of light must be moving. And here’s where it gets a bit tricky: It has to move at the speed of light. Why? Because at any lower speed, you could move along with it, so that, from your point of view, its speed would be zero, and we’ve just said it has to be moving. The only speed at which you couldn’t move along with it is c, the speed of light, which has the weird property that c in one reference frame is c in all reference frames. (You, an object with mass, can’t move at the speed of light because that would take infi nite energy, since your mass would increase infi nitely.) So a photon, traveling at the speed of light (by defi nition — it is light!) has no mass energy but does have momentum energy.

Here’s a picture that might explain it better. A and B are holding the ends of a length of rope. A gives the rope a sharp upward pull and a wave travels down the rope from A to B, who feels it. Even though no mass has been exchanged, energy, in the form of a wave, has been transferred from A to B. Incidentally, like light, the shorter the wavelength, the more energy is transferred.

You can think of light as either a massless particle — a photon — or as a wave, in which case, it carries energy of momentum. Which is really, really useful if you happen to be a plant, a solar panel or a twist of kindling needing energy to ignite.

Then it was back to the cormorants. Bet they don’t worry about photons. ● Barry Evans (he/him, barryevans9@ yahoo.com) knows what’s really wrong with the world: too many photons.