Do shadows weigh anything? And do they affect the weight of objects they are cast over?
Ron Dippold
San Diego, California, US
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Shadows weigh nothing but can have apparent negative weight.
Consider what a shadow is: it is the lack of photons (light) bouncing off an area relative to the lit areas around it. Photons have no rest mass, but they do have energy – as encapsulated in the equation E = mc2. A stream of photons delivers a force in the direction of travel when it bounces off a surface, as does a stream of water hitting an object. It is the principle behind the solar sail and has an effect on satellites in orbit.
Imagine you have a 1-square-metre, 1-kilogram piece of wood covered in silver foil (for maximum reflection), and you set that flat on an impossibly precise scale outside at high noon on the moon (so that we can ignore the effects of Earth’s atmosphere).
You tare the scale with the square on it, so it reads exactly 0 kg. Then you hold some space cardboard over it, blocking the sun. Now, the scale reads a little less than negative one millionth of a kilogram. Of course, it isn’t that the shadow actually has negative weight, rather, the sunlight’s downward pressure has apparent weight and you have blocked that.
Some caveats. This is all relative to the angle and intensity of the light and reflectivity of the surface. If the sun is at 45 degrees, then the downward force is only 71 per cent of what it is at high noon.
If the light is underneath an object, then a shadow on the bottom can even make that part appear infinitesimally heavier than the bits around it that are being pushed up by the light. So, yes, shadows are weightless (they are just a lack of light), but they can affect apparent weight.
Guy Cox
Sydney, Australia
Shadows are the absence of light. Light consists of photons, which have no rest mass but do have energy, so they can exert a force on whatever they hit.
In other words, as photons are blocked to create a shadow, it effectively has negative mass. You would need a pretty sophisticated system to measure this, though.
Hillary Shaw
Newport, Shropshire, UK
Your shadow has a tiny negative weight, but this doesn’t affect what you are passing over.
The intensity of solar radiation per square metre at the top of our atmosphere is . This will be lower at ground level due to cloud cover, more so if the sun is low.
Your shadow isn’t totally dark, either, but is lit by light scattering and reflecting from nearby air and surfaces. Let’s say light intensity inside the shadow is reduced by 50 per cent compared with the intensity outside it.
The cross-sectional area you present to the sun to cause a shadow will vary from almost zero when the sun is at its zenith to around 0.5 square metres when it is at the horizon. Assuming an average shadow area of 0.3 square metres, we have a light reduction in your shadow of some 250 watts (joules per second). Using E = mc2, the energy blocked each second is equivalent to a mass of about 2.5 × 10-15 kilograms. That means, every second, there is an energy deficit in your shadow equivalent to the .
This will move as you or the sun moves, and it is mitigated by a small energy inflow from sunlit areas nearby. However, that energy is absorbed by you, increasing your weight by the same amount, so the net effect on the surface you are on is zero.
Mark Dirnhuber
Bristol, UK
The cheap answer is that shadows have negative weight, so an object that is illuminated from above will weigh more than it would in the shade.
This is because of the phenomenon of radiation pressure. The idea is that light, or any electromagnetic radiation, possesses momentum, which is absorbed or even reflected back with the light. Given that force is the rate of change of momentum, the transfer of momentum will press the object down, increasing its apparent weight.
That light has momentum can be explained by classical physics as due to the interaction of its electric and magnetic fields with the charged particles in the object. It might be even more intuitively explained by quantum physics as the result of the volley of photons pressing down on the object.
This effect, which was first measured around the year 1900, is ordinarily extremely weak, but the pressure generated through it by sunlight must be included in the calculation of the trajectories of interplanetary space probes, and it is largely responsible for the fact that a comet’s tail always points away from the sun, even when the comet is receding from the sun.
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