Burgess COMMENTARY

Peter Burgess

Viktor T. Toth, IT pro, part-time physicist

Answered Apr 20 · Upvoted by Daniel Merthe, Physics Ph.D. Candidate, University of Southern California and Mike Nightingale, MPhys Physics & Astrophysics, University of Exeter (2019)

Allow me to offer a somewhat technical answer to this question (a good question, by the way). Yes, this means a bit of math. Hopefully not too off-putting.

The so-called Lagrangian density functional that describes the electromagnetic field in classical physics is given by
L=−14FμνFμν−jμAμ,L=−14FμνFμν−jμAμ,
where AμAμ is the electromagnetic 4-potential, Fμν=∂μAν−∂νAμFμν=∂μAν−∂νAμ, and jμjμ is the 4-current.
In plain(er) English, AμAμ is the electromagnetic field; FμνFμν is its rate of change; and jμjμ represents the electric properties of matter.



As for the Lagrangian, its first term is kinetic energy; its second term is potential energy.

In empty space, there is no matter. Which means there are no charges or currents: jμ=0jμ=0. The second part of the Lagrangian just evaporated. Poof!

So all we are left with is the first part. Pure kinetic energy. Everything the electromagnetic field does in empty space is pure kinetic energy.

And what does the electromagnetic field do in empty space? Well, it forms plane waves that propagate at the invariant velocity cc. That is to say, electromagnetic radiation, including that narrow part of the electromagnetic spectrum that our eyes can detect.

So yes, light energy is pure kinetic energy. Potential energy, if present, is there because some matter is there and jμjμ is not zero.

In short, potential energy is responsible for creating light, absorbing light, refracting light. But when light does not do any of these things, its energy is purely kinetic.

This, by the way, has general validity going beyond light. Kinetic energy describes what things do when they are left alone; potential energy describes what happens when things interact. (A special case is when a thing interacts with itself, in which case the theory is said to be nonlinear. Light does not interact with itself, at least not in the classical theory.)

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