You need to read the paragraph prior to the quote. He is talking about which one of field and mechanical stress is more "fundamental" or less "direct". If one measure the force exerted by electric field using a unit charge, one measures the field by measuring the mechanical stress first.

Of course, the context matters. Often if one compares potential and field, field would be the one directly measured. It is just semantics really.

I have read the prior paragraph. It does not clarify how measurement of energy is more direct than measuring the field.

You can make the electric field disappear by choosing the right gauge. Same goes for the magnetic field (can't make both disappear together though). The vector potential, in that sense, can be regarded as a more fundamental description of the electromagnetic field. It can't be observed directly though, but electric and magnetic field strengths are manifestations of the vector potential, they are not fundamental in that sense. Not sure if it's that what he's getting at, though.

>You can make the electric field disappear by choosing the right gauge. Same goes for the magnetic field (can't make both disappear together though).

What? No you can't. The fields are invariant under gauge transformations.

You're right, sorry I was thinking of a Lorentz transformation that would make either the magnetic or electric field disappear under certain conditions.

"transform into each other" would be more appropriate. The gauge choice you mentioned is not totally wrong. The gauge freedom can be used to set the electric field to zero, but only once at a single point.

Sorry, but gauge transformations do not (by construction) affect the physical fields at all. You cannot set E to 0, even at a point, with a gauge transformation.

> You can make the electric field disappear by choosing the right gauge.

That, had it been true, would have made the gauge observable.