# [Physics] Is the electromagnetic mass real

classical-electrodynamicselectromagnetismelectronsparticle-physics

In his Lectures on Physics vol II Ch.28-2 Feynman calculates the field momentum of a moving charged sphere with charge $q$, radius $a$ and velocity $\mathbf{v}$. He finds that the total momentum in the electromagnetic field around the charged sphere is given by:

$$\mathbf{p} = \frac{2}{3} \frac{q^2}{4\pi \epsilon_0} \frac{\mathbf{v}}{ac^2}.$$

He calls the coefficient between the field momentum, $\mathbf{p}$, and the velocity, $\mathbf{v}$, the electromagnetic mass:

$$m_\textrm{elec}=\frac{2}{3} \frac{q^2}{4\pi \epsilon_0 a c^2}.$$

He claims that this electromagnetic mass $m_\textrm{elec}$ has to be added to the standard "mechanical mass" of the sphere to give the total observed mass of the object.

Would this view be accepted by most physicists today?

Have any experiments been performed that show the effect of the additional electromagnetic mass on the dynamics of a macroscopic charged object?

I guess the problem is that such an effect would only be large enough to be observable for charged particles like electrons. In that case it would be difficult to distinguish mechanical mass, presumably due to the Higgs field, from electromagnetic mass. Maybe one could perform a high energy/short length scale experiment on an electron that excluded the effect of the electromagnetic mass?

This view would not be accepted by physicists today.

Charged particles have mechanical mass, momentum, and energy (rest and kinetic) and the fields have energy and momentum. Total energy is conserved. Total momentum is conserved.

Are there cases where it can be sensible to imagine field momentum as an additional mechanical momentum? Sure, consider the paper "Electrostatic potential energy leading to an inertial mass change for a system of two point charges" by Timothy Boyer in the American Journal of Physics 46(4) 383-385 (1978); http://dx.doi.org/10.1119/1.11328

It's a short paper but the point is that if you ignore the forces that the charges exert on each other then they can together and collectively act like a particle of different mass. In reality there is more than one particle, each with their own mass, their own mechanical energy, and their own mechanical momentum. And there are fields, both external and from each charge. And the fields collectively have field energy and field momentum. And when you exert forces on the charges each particle feels a force and changes its energy and momentum accordingly and they also exchange energy and momentum with the fields through which the charged particles within the system also affect each other.

So it's not that you must add field momentum to bare mechanical momentum to get some kind of total mechanical momentum. The correct physics is that you need total momentum which includes all the mechanical momentum (i.e. $\gamma m \vec v$ for each particle of mass $m$) and all the field momentum. And the only deviation allowed is that if you want to ignore some effects you can try to get away with doing it wrong by trying to compensate by adjusting some other things.

But be warned. Sometimes people fudge things in a frame dependant manner. For instance with your charged sphere you have to include the binding energy keeping the charge on the sphere before you get something that is relativistically covariant. If you include everything then it works out fine. But if you've included everything you just have the regular mechanical momentum of each charge and the total field momentum from the total field. Or more likely, you measure changes in momentum.

Also, it can be important to have momentum located in the correct place for relativistic reasons.