I was wondering. You put a box full of mirrors over a scale. Then you point a source of light to the first mirror - there was no light at all entering the box before. Now the light bounces on an on and on on those mirrors. Therefore, the box is full of… photons, right?
So… will the scale (imagine that the scale is amazingly precise) show any change on the weight of the illuminated box?
Yes, but not very much. In other words, they’d be fairly light.
Thanks, I’ll be here all week.
OK, as the above may indicate, I’m not the best guy to answer this, but as I understand it, photons are considered to have no rest mass, as this would apparently screw up some other aspects of physics. Presumably, any measured value on your scale would come from some other interaction of the photons with the measuring surface, rather than the mass of the particles themselves. I’ll now get out of the way for someone who really knows what they are talking about.
Nope. Light moves astonishingly fast, and no material is perfectly reflective. So within fractions of a millisecond the photons will be absorbed and the box will be dark.
Yes, the weight will change. Mass is related to energy. The more energy an object has, the more massive it becomes. Once the box absorbs the energy of the photons it will become more massive, by an amount that can only be measured by your amazingly precise scale.
Note that this isn’t caused by the photons themselves having mass, but rather because they have energy which the rapidly impart to the box. It’s the act of adding energy to an object that already has mass that causes the mass to increase.
I am aware that I could not trap light inside the box - that would be indeed an amazing source of energy! But… how much does light weight? Would the “impact” of light on the mirrors be somehow measurable?
Yes, in theory; it’s called “radiation pressure”.
“Weight” is a tricky thing here–light does not have mass, but it does have momentum, and it is affected by gravity. Since “weight” basically means the force that an object exerts in response to gravity, it’s fair to say that photons have weight.
Light’s momentum is proportional to its frequency. What happens to your mirror box is a little strange: as a given photon bounces around, it decreases in frequency as it rises and increases in frequency as it falls (it’s a little hard to say why, but the short answer is “General Relativity”). This is called redshifting and blueshifting respectively. What this means is that a given photon will hit the bottom of the box a tiny bit harder than it hits the top, and so the box will experience a downward force overall (just as if it were full of atoms bouncing around).
Is “solar wind” this, or something different? The wiki article you cite seems to speak of radiation pressure and solar wind as two different things, in this sentence:
“Solar wind” is a stream of particles from the sun. “light pressure” or “radiation pressure” is due to momentum transfer from photons. They’re very different effects, due to different particles (calling a photon a particle), and both affect solar sails.
An individual photon is massless. A system of multiple photons, traveling in different directions, does have mass. Your hypothetical box falls into this second category. Mass is not strictly additive, like it’s usually thought of.
Help me out. I get that light has momentum but no rest mass. What is m=p/c?
Also, would the above frequency shift occur if the box isn’t in a gravitational field?
photons move at the speed of light. If they had a “rest mass” it would take an infinite amount of energy to accelerate them to the speed of light. They can carry momentum, however, which seems counterintuitive. But the concept of light pressure was derived in the 19th century on the basis of thermodynamic arguments, and then on electromagnetic ones*. It was already well established by the time quantum mechanics came around, and we started thinking of light quantized into photonic bullets, each carrying momentum proportional to the frequency.
As for the idea of a collection of light having mass, think of the equivalence of mass and energy – the concentration of electromagnetic energy in a small space results in the samew sort of distortion of spacetime as a mass does. Look up the geon, first proposed by theoretical physicist John Wheeler in 1955, and defined (on this Wikipedisa page) as “an electromagnetic or gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy”
See also Kugelblitz: