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How much does a shadow weigh?
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I'm aware this is a dumb question, but in a way that reassures me because I'm relieved of the task of checking to see if any of your other readers have posed it before: do shadows weigh anything at all? Of course, I know we're talking extremely small amounts-fractions of fractions of fractions of pounds. Or perhaps the reverse is true? -cHeMiCaL iMBaLaNcE, Toronto

Let's think about this: (a) this question is dumb; (b) the Teeming Millions don't ask dumb questions; ergo (c) this question must never have been asked. Surely you can identify the fatal defect in this logic. We'll let that slide, though, because your question isn't garden-variety dumb-it's dumb but interesting, a rarer and more prized breed. We'll proceed cautiously.

1. Peter Pan is said to have had a tangible shadow, albeit one so flimsy that it was "not more material than a puff of smoke." Peter Pan was, of course, fictional-although at the quantum level that may not be an important distinction-and J.M. Barrie, his creator, lacked scientific training. But we'll accept this estimate as establishing the upper bound.

2. However, it's directionally wrong. Using one frame of reference you could say our shadows actually weigh less than nothing. Four hundred years ago Johannes Kepler observed that comets always had a tail pointing away from the sun and concluded that the sun's rays exerted pressure that blasted material away from these celestial bodies. In the late 19th century the physicist James Clerk Maxwell formulated equations predicting the pressure of light, a value confirmed experimentally in 1903.

3. You see where I'm headed with this. If you're standing there catching some rays, said rays aren't impinging on the surface commonly thought of as your shadow, thus creating a shadow-shaped zone of reduced pressure. Compared to the rest of the landscape, then, your shadow (or, more precisely, the area it covers) weighs less.

4. How much less? Not a lot. The pressure we receive from sunlight is incredibly small: less than a billionth of a pound per square inch at the Earth's surface. It would take several million human shadows to account for one blocked pound of light force. The light falling on the city of Chicago has a total force of about 300 pounds.

5. However, incredibly small doesn't mean inconsequential. When Japan's Hayabusa space probe approached the asteroid Itokawa in 2005, light pressure equal to 1 percent of the probe's engine thrust had to be taken into account to enable the craft to hover near the rock rather than blow past or crash into it.

6. Equally cool is the solar sail dreamed of by science fiction writers for at least 50 years and finally realized when the Japanese IKAROS (Interplanetary Kite-craft Accelerated by Radiation of the Sun) probe launched last May. The idea is that the solar sail uses light pressure plus the solar wind (a much weaker zephyr of charged particles from the sun) to propel itself plus a payload. In June, IKAROS successfully unfurled its sail, a square of ultrathin film 46 feet on a side equipped with solar cells that power the craft's electronics. In July, the Japanese space agency reported that IKAROS was being scooted along by solar pressure of 1.12 millinewtons, or 0.0002 pounds of force-which, OK, is not so much. But it's being produced by sunlight! It's free! The scientists managed to do this from more than four million miles away! So let's have a little respect.

7. More miracles await. Last year researchers based at the Australian National University showed that light could be used to heave tiny particles and have them land at a precise spot 20 inches away. They thought they'd eventually be able to do the same at a distance of 33 feet (10 meters)-which, again, may not seem like much. However, if the tiny particle is a deadly virus, living cell, or gas molecule that can't be moved any other way . . . you get the picture.

So, cHeMiCaL, is asking whether shadows weigh anything a dumb question? Well, yeah. However, making the small but crucial leap to asking whether light weighs anything-that's the impulse of genius, experienced by Kepler, Maxwell, and now you.



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