Does sun reflecting on sea ice still transfer energy to the Earth?

Question

From reading about climate change, I read that sea ice is reflective, which means some of the sunlight isn't absorbed, so it doesn't contribute to heat.

However, any photons reflected would cause the ice to gain momentum. This momentum would then push against the rest of the Earth, and wouldn't that just end up creating heat anyway?

I don't see why reflecting should be "good" for climate change. If anything it might cause double trouble. Say the light's momentum is p, then reflecting causes a delta of p - (-p) = 2p, whereas absorbing causes p - 0 = p.

Answer 1

It would impart momentum to the thing it is reflecting off of. However, for photons $ E = pc$ where $c=3\cdot10^8$ m/s in SI units. $c$ is such a large number, so that the momentum that the photon would give to the sea once reflecting is of order $ p = \frac{E}{c}$ which is very small, since E is of order $1eV$ for visible light, which is then divided by a number of magnitude $3\cdot 10^8$. So the (kinetic) energy it would give the sea is of order $\Delta E_{sea} = \frac{p^2}{2m}=\frac{E^2}{2mc^2} $ which is $ really $ small.

Only the other hand, assuming that the sea $absorbs $ the photon it gains a lot more energy. Because then it doesn't only gain momentum (kinetic energy) but also electric energy (its electrons will absorb the photon energy.)