Photons of light are massless so how can they transfer momentum?

Question

We know that photons are massless but if you heard about solar sails then these photons of light transfer momentum to the sails,how is it possible that anything which haven't it's own momentum can transfer momentum?

Answer 1

As a complementary answer to @Árpád Szendrei, let me address your point

how is it possible that anything which has no momentum itself can transfer momentum ?

The relativistic definition of momentum is $$ \mathbf{p} = \frac{m\mathbf{v}}{\sqrt{1-v^2/c^2}}, $$ so that when $v=c$ and $m=0$ the formula becomes indeterminate.
Hence, you don't actually know that photons have no momentum.

Indeed, as pointed out in the previous answer, you can use another formula for momentum: $$ E^2 = (pc)^2 + (mc^2)^2,$$ from which you get the known $h\nu = E = p/c$.

The transfer of momentum between photons and other objects is known as radiation pressure, which interestingly can be understood both in the particle picture and in the wave picture:

• particle picture: ball bounces off wall, incident momentum $p_i$ and final momentum $p_f$ so wall must have provided force $\propto -\Delta p$ which means that by Newton III the wall experiences a force/pressure $\propto \Delta p$.

• wave picture. Photons are quanta of EM radiation. That is they are oscillating electric $\mathbf{E}$ and magnetic $\mathbf{B}$ fields, oscillating (for free waves) along the polarisation $\mathbf{e}$ direction (electric) and along $\mathbf{k}\times \mathbf{e}$ (magnetic), where $\mathbf{k}$ is the direction of travel of the wave (wavevector).
  When incident on a material, the electric field oscillation induces a current $\mathbf{j}$ along $\mathbf{e}$, which then experiences a force in the magnetic field $\propto \mathbf{j}\times \mathbf{B} \propto \mathbf{k}$, i.e. a force/pressure into the material.

Answer 2

Photons are elementary particles of light, as per the Standard Model, they are massless, but they do have momentum.

Actually, photon's energy and momentum are related to their frequency.

Its energy and momentum are related by E=p*c (where p is the magnitude of the momentum vector).

$E^{2}=p^{2} c^{2} + m^{2} c^{4}$

Since the photon is massless, this will reduce to E=pc.

The energy and momentum of the photon only depend on its frequency or inversely on its wavelength. $E=h\nu=\frac{hc}{\lambda}$

Solar sails work because of something called radiation pressure.

Radiation pressure is the pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength which is absorbed, reflected, or otherwise emitted (e.g. black-body radiation) by matter on any scale (from macroscopic objects to dust particles to gas molecules).[1][2][3]

https://en.wikipedia.org/wiki/Radiation_pressure

Answer 3

Photons transport energy and energy transport is equivalent to momentum. The basis of this statement is the Noether energy-momentum tensor. See Physical meaning of the space-space components $T^{ij}$ of the stress-energy tensor $T^{\mu\nu}$ for a discussion of this fundamental quantity.