As kinetic energy is the "energy of motion", it cannot exist without matter. However, the energy in an E/M wave can. I understand that E/M waves have been described in structure as electrical and magnetic waves in a sinusoidal configuration. This means that kinetic energy cannot be made of EM waves or it would be mass-independent.
So my question is, what is kinetic energy made of?
Energy is an extraordinarily elusive concept, so much so that experienced physicists will use the term only with care and in well defined circumstances.
For example it might seems obvious that if I fire a pistol then the bullet has kinetic energy. But Einstein's theory of special relativity tells us that all inertial frames are equally valid, and in the bullet's frame the bullet is stationary and it's me and the pistol that are moving. So in this frame where did the kinetic energy of the bullet go and where did my and the pistol's kinetic energy come from?
If you say the bullet has a kinetic energy of $\frac{1}{2} m v^2$ what this really means is that to make the bullet move at a velocity $v$ I had to supply an energy of $\frac{1}{2} m v^2$. If I have lost an energy of $\frac{1}{2} m v^2$ then conservation of energy means the bullet has gained an energy of $\frac{1}{2} m v^2$, and this is what I measure as it's kinetic energy.
This is the way to think of kinetic energy. If some observer, like you or me, measures a kinetic energy $E$ this means we would have to put an energy $E$ into making the object move. And this carries straight over into measuring the energy carried by light. If I create a photon then this costs me energy, and that energy goes into the photon. If/when the photon hits something the energy is then transferred to whatever it hits. So the photon carries energy just like a bullet does, even though the photon has zero mass.
Now you may say this all sounds a bit contrived, because what I've just described is the total energy of the photon and not its kinetic energy, and in fact you'd be absolutely correct. This is because kinetic energy is a low energy approximation and the concept doesn't really exist in relativity. In relativity we only talk about the total energy of an object, and the total energy is given by the equation:
$$ E^2 = p^2 c^2 + m^2 c^4 $$
where $m$ is the object's mass and $p$ is its momentum. The first term, $p^2c^2$ is sort of the kinetic energy and the second term, $m^2c^4$, is sort of the rest energy, though thi separation isn't clear for fast moving particles. Anyhow, for a photon the mass, $m$, is zero so the expression simplifies to:
$$ E^2 = p^2 c^2 $$
And this could be regarded as the kinetic energy because it's the same term that is considered the kinetic energy for a massive object.
