How can we tell the difference between light and moving charge?

Question

In the classical sense, light is an oscillation of the electric and magnetic fields.

A moving charge also brings about a magnetic field.

How can we detect whether or not we are observing light, or charges moving at the speed of light in the same direction separated at a uniform distance?

I understand a single static charge translating through the medium doesn't produce a sinusoidal wave in the way that we model classical light waves, but how exactly do we detect the difference between the two cases listed above in an experiment?

To rephrase in a poetic/unclear way: how do we know that the charge of the electron is the quanta of charge? What if charge can take much smaller magnitude than e? Can very small charges translating through the medium be mistaken for light?

Answer 1

How can we detect whether or not we are observing light, or charges moving at the speed of light in the same direction separated at a uniform distance?

We measure the E field and check if its divergence is zero. If the divergence is zero then there is no charge.

Can very small charges translating through the medium be mistaken for light?

There is always some value below the sensitivity of any experiment to detect. So there will always be some value of “very small” that could be mistaken for zero. This is not specific to charge, but is a general fact of experimental science.

That said, there is no evidence that the photon has any charge, and good theoretical reasons to believe that it does not.

Answer 2

Shoot the unknown particle in a uniform magnetic field: light will continue straight but the charged particle will enter a circular orbit with radius inversely proportional to the actual charge of the particle and proportional to its mass. This method can also me used to measure the actual charge (if the mass is known).

Answer 3

In a sense, it is the same thing. A moving charge creates changing electric and magnetic fields. This is light. In general, light originates from moving charges.

Light, being electric and magnetic fields, exerts a force on charged particles. Or moving charged particles create electric and magnetic fields, which exert a force on other charged particles.

Sometimes the charges are nearby and from their motion it is possible to calculate the fields and then the forces. Sometimes the moving charges are in a distant star, and all you measure are the fields.

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Light is not caused by movement of arbitrarily small charges.

The standard model describes all the particles we know of, and has room for some others we suspect may exist. All these particles have charges of $0$, $1/3$, or $1$. There are some suspected particles outside the standard model, such as the particles that may make up dark matter and dark energy. But these particles, if they exist, are uncharged. We have never seen smaller charges.

The standard model includes light. Light can be described in two ways: as changing electric and magnetic fields, or as particles named photons. The difference is scale. It is like air pressure. On a large scale, air pressure is a smooth force that pushes on everything air touches. On a small scale, it is caused by individual air molecules bouncing off everything air touches. On a small scale you see individual jolts. On a large scale, you see the total of many jolts.

Furthermore, all known charged particles have mass. Particles with mass travel more slowly than light. Photons are massless and do travel at the speed of light.

Perhaps you are thinking that weak charges are needed to explain low energy light? Not so. Light can be caused by arbitrarily small or slow movements of the charged particles in the standard model. Light can have arbitrarily low energy, whether described by waves or particles. See How can a red light photon be different from a blue light photon?