> We now take it for granted that electric and magnetic fields are abstractions not reducible to mechanical models. To see that this is true, we need only look at the units in which the electric and magnetic fields are supposed to be measured. The conventional unit of electric field-strength is the square-root of a joule per cubic meter... This does not mean that an electric field-strength can be measured with the square-root of a calorimeter. It means that an electric field-strength is an abstract quantity, incommensurable with any quantities that we can measure directly.
A more conventional way to think of the dimensions of the electric field is [force]/[charge] (e.g. units of Newtons/Coulomb), and you can observe the electric field by observing the force it exerts on a charged particle through
f=qE
for example by observing the trajectory of an electron in a cloud chamber.
Dyson says that the square of the field is a measurable energy density, but it’s arguably harder to measure an energy density than it is to measure a force.
Dyson’s point is much more true for quantum mechanics, where the only measurable things seem to be quadratic combinations of the wave function, and I do like the analogy he points out with electromagnetism, but I think he oversimplifies a bit to make his point.