Even as I read the question before downloading the Podcast I grinned smugly thinking, “I know where he’ll go with this …”
And Cecil, you did not disappoint!
Perhaps the most significant demonstration we have of the pressure that light (an all encompassing term for a multitude of forms of radiation from the Sun in this context) can exert is the Sun itself. It is well established that one of the ways a star can “die” is when it runs out of nuclear fuel at the end of its main sequence it “puffs off” its outer layers and contracts down to form a white dwarf. This depends on the mass of the star falling within a certain range (measured in solar masses). The white dwarf will continue to glow from residual heat and will gradually become less luminous as the heat radiates away in the form of light.
But it is graitational collapse that shrinks the dying star down to a white dwarf. So, what keeps the star “puffed up” prior to this collapse? Radiation pressure! Indeed the “pressure” exerted by radiation is so great that it gives the star a much greater size than it would otherwise have by balancing the outer layers of the star against its own gravity. It should come as no surprise then that we can measure the effects of this in tangible ways and utilise the effects in so called “solar sails”.
The question was, “Do shadows weigh anything?”
If I recall my high school physics correctly, “weight” is a measure of the force that acts on our mass due to the gravitational attraction between our bodies and the earth.
“Weight” therefore is measured in Newtons, and not pounds or kilograms. Fortunately for us, the gravitational attraction is relatively constant near sea-level and so we have been allowed to become accustomed to assuming that our “weight” will remain closely aligned to our “mass”. It is in fact our mass that we are more interested in when we jump on the scales - I can’t remember the last time was told that my target weight was 569 Newtons! But we do often hear about our body mass index…
Back to the question, “Do shadows weigh anything?”. Whilst I would be foolish to argue that light does not exert a pressure, a shadow does not have mass and therefore cannot have weight. It would not matter if the shadow were being cast on a black hole (with gravity so strong that matter has infinite “weight”), a shadow is a lack of light. The “pressure” (not “weight”) being exerted by light falling around the shadow does not influence this.
On another note, I remember considering e=mC^2 and reading that if were able to accelerate an object to near the speed of light, relativity shows that that object would tend towards having infinite mass …