eli5 – if photons have no mass, how can they be used to push hypothetical “solar sails”?
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I’ve copied a comment I made a while back because I think it’s a good explanation but bear in mind there are some errors.
**tl;dr:**
My understanding is that we know that photons have Energy, Velocity, and Frequency. We know that Energy can be represented as a product of Velocity and Something1 or Frequency and Something2. Energy’s units include mass, but Velocity’s and Frequency’s don’t, so the units of Something1 and Something2 must include mass. Well, Something1 is called Momentum in other contexts, so to be consistent it must be Momentum here, but expressed differently. Through experiments, we see that it’s just an unavoidable thing in the Universe which helps us to tie things together.
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Well, through experiments, we have determined that there are other properties of a wave or of the universe that come into play. All light with frequency F1 has energy E1, all light with frequency F2 has energy E2, etc., in such a nice way that we can say that there is Something2 is some constant value in the universe that can represent the energy of a photon when multiplied by its frequency. Let’s call this constant Planck’s constant (h-bar). So, E = Frequency * h-bar, and h-bar has units of kgm2s-1.
Through other experiments (not involving light), we see that Energy is Velocity * Momentum, and photons have Energy and Velocity, so they must have Momentum (since physics is supposed to work the same everywhere, more or less). So, their Momentum necessarily has units of Mass, but how? Well, through other experiments (involving light) we see that the Momentum of light can be represented as a product between other things.
Momentum has units of kgms-1 (Mass * Velocity), which can be seen as a product of things with units kgm2s-1 and m-1. Why these in particular? Well, we know that there’s a property of a photon that has units m, so this can fit in nicely. The property in question is the wavelength of light. If we can divide something by the wavelength of a photon, we’ll get something else which, when multiplied with Something, will return Momentum.
Light is a Wave and thus is a Vector because it has Magnitude and Direction. This Magnitude can be represented as 2*pi/wavelength, because Math. This Magnitude has units of m-1, so perhaps this can be multiplied by Something to return Momentum. This mean that Something needs to have units of kgm2s-1 since the Magnitude has m-1. Well, we already know of Something with those units: h-bar. And, through experiments, we see that it’s Momentum is simply h-bar * Magnitude.
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