photon:me::tennis ball:earth

I was thinking back over an analogy I had used in a talk years ago, and I wanted to update it with some better references, and the math to show I’m not insane. I was trying to describe how weak a single photon is, I used an off-the-cuff analogy of a bb pellet hitting a tank. It turns out that the ratio between the momentum of a flying bb and the momentum of a moving tank is several orders of magnitude away from the ratio of a photon’s momentum to the momentum of any worldly object.

It took me a couple tries but I found an analogy that is more accurate:

I weigh 185 lbs. Jogging a 6 minute-mile, I have a momentum of 375 m kg / s

A photon at 780 nm has a momentum of 8 × 10^-28 m kg / s

Photon/Me = 2.25 × 10^-30

A tennis ball (56.69 grams) dropped from 1 m, has a momentum of 0.25 m kg / s

The earth (5.9736 x 10^24 kg), in orbit at 29.783 km/s, has a momentum of 1.8 × 10^29 m kg / s

Tennis Ball/Earth = 1.4 × 10^-30

So the amount of kick I get from reflecting a photon while I’m running, is approximately analogous to the kick that a tennis ball gives the earth if dropped from 1 m.

Of course I’ve ignored the fact that the tennis ball mass has it’s own gravity that will attract the earth toward it as well. But the bottom line is that photons are tiny… and it takes a lot of them to push anything.

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