system
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human
Do photons (ie. light) possess the property of inertia, or inertial mass?

It seems surprisingly difficult to find an authoritative (layperson-friendly) answer to this.  It's pretty obvious that a hypothetical box of photons will have a greater inertial mass than an identical-but-empty box, but can light be said to have inertia?
gpt
To talk about photons/light, it is necessary to invoke relativity. We can't use Newtonian mechanics to answer questions about things that move at the speed of light.

In relativity, photons are massless particles, where 'mass' is defined to be 'the energy that an object has at rest.' Photons are never at rest, but by carefully considering how the energy of a photon depends on its momentum, one can see that they have no mass. (The argument is roughly that E^2 = m^2 c^4 + p^2 c^(2), and photons have E=pc, so they must have m=0.)

[Sometimes, especially in older texts, one finds a different definition of mass which increases with speed. This is the 'relativistic mass' which is given by m=E/c^2 or m=m0/sqrt(1-v^(2)/c^(2)), where m0 is the 'rest mass' discussed above. Using the relativistic mass as what you mean by 'mass' makes certain equations agree with Newtonian mechanics at the cost of hiding what is really going on and making photons more confusing. The modern view is to forget about relativistic mass and always talk about rest mass.]

'Inertia' is something that is harder to quantify for a photon. If you just say that inertia is 'resistance to changes in motion' then yes, photons have inertia, because they like to keep moving in straight lines just like massive particles. If you try to define inertia quantitatively, like by inertial mass, then you say it's the resistance to motion for a given force; but F=ma doesn't hold in relativity, so it doesn't follow that photons have no 'inertia' in this sense. Note that physicists never bother saying whether or not something has 'inertia'; they'll just tell you what its mass is. That's the number that matters.

By the way, in relativity, systems of multiple particles have a mass that is, in general, not equal to the sum of the masses of the constituents. So a box full of photons does, in fact, have nonzero mass even though each photon is massless.