Photon sails & relativistic mass

So I was reading a couple threads today, one current and one long dead, and rather than resurrect or hijack, I’m starting a new one.

Given that photons and other massless particles have effective “mass” of m=e/c[sup]2[/sup] (since e=mc[sup]2[/sup]), and “momentum” p=e/c (since p=mv, and by substitution ec/c[sup]2[/sup]=e/c)…

My question is this:
Assuming that a photon sail is an achievable concept, would it be preferable to make it reflective, thus bouncing the photons back away from the intended direction of travel, or light-absorbent, thus fully absorbing the momentum and energy of the photons?

Maybe an absorbent back with a reflective surface facing it from the front, so that radiated heat is directed to the rear for extra thrust? Or would that be the same effect as reflection, and lose efficiency from the extra mass of the reflective layer?

This question is, in fact, addressed in treatments on solar sails. If you can, it’s best to make the sail reflective, because you get bigger momentum transfer .The photon rebounds with the reverse of its initial momentum, so you gain a factor of two over the case where it’s absorbed. Crookes thought that this was what he was hoing to demonstrate in his famous radiometer, with its anemometer-like vanes painted black on one side and white on the other, suspended in vacuum. The problem was that his vacuum wasn’t quite good enough, and the dominant force turned out to be rebounding from residual gas molecules being heated by the absorbed radiation of the dark vanes, so the radiometer spun the wrong way. I’ve heard that later tests in a properly evacuated radiometer confirmed Crookes’ theory.

IIRC you would get 2x the energy ‘push’ from a reflected photon then an absorbed photon. But once absorbed it can be re-ratiated

What you are talking about here, of course, is relativistic mass, and the concept of relativistic mass causes some very real problems. What this equation says is that a photon has mass in its direction of motion but does not have mass in any other direction.

This flys in the face of the concept of mass as a scalar quantity. Instead it forces us to consider mass as a vector quantity. This is not necessarily wrong it’s just confusing. It’s much cleaner to just think of a photon as having a momentum equal to h*f /c. Although this in effect is the same final equation it can be derived without the use of relativistic mass.

You can avoid considerations of relativistic mass ltogether. The principles of light ressure were derived well before quantum theory, first using thermodynamic arguments, then using electromagnetic arguments (I think the former is in R.W. Wood’s “Physical Optics”, while you can find a treament of the latter in George Bekefi’s book on Waves). I any case, reflection is better.