We all know the example where we say that a massless box containing photons has inertia, because the photons exert pressure of the inner walls of the box.
But my question is about a single photon traveling freely. Can it have inertia?
An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed, when no forces act upon them.
There is another definition of inertia, that is, we need to exert force on an object when we try to remove it from the geodesic it is following.
a photon of energy E confined in massless, perfectly reflecting box has a rest mass because has inertia i.e. it takes force to accelerate the box against the light pressure of the wave reflecting from inside the box: the impulse needed to reach speed v≪c is Ev/c2 so the system could be said to have rest mass and certainly inertial mass E/c2. Photons of energy E always add effective gravitational mass E/c2 to the T00 term in the stress energy tensor "source". So they have gravitational mass E/c2 and indeed there are electrovac solutions of the EFEs where intense light acts on itself through gravity. So inertial mass = gravitational mass
This answer specifically states that a photon, having stress-energy, contributes to the stress-energy tensor, thus has gravitational mass, and this fact together with the fact that photons do have their own gravitational effects means that inertial mass=gravitational mass for the photon.
Though, many on this site identify inertia with solely massive objects.
Now just like when removing a massive object from its way on a geodesic, we need to use force on it "push it" away from the geodesic, we can do the same with a photon using a mirror.
Now if we have a photon, traveling on a geodesic, and use a mirror to remove it from the geodesic, we use force (constituted by the mirror) to remove the photon from the original geodesic, and the photon will exert pressure on the mirror (opposite force).
Now the photon's pressure (momentum transfer) on the mirror might be miniscule, but it does depend on its frequency, because for photons, energy and frequency and momentum are proportional. This could be interpreted as photons having inertia, proportional to their energy, just like for massive objects, inertia is proportional to their mass (which comes down again to stress-energy).
So ultimately, stress-energy content determines inertia, and that goes for both massive and massless particles.
- Do photons have inertia?