The field lines, however, are only a crude way of describing a field, and it is very difficult to give the correct, quantitative laws directly in terms of field lines.
Also, the ideas of the field lines do not contain the deepest principle of electrodynamics, which is the superposition principle.
Even though we know how the field lines look for one set of charges and what the field lines look like for another set of charges, we don’t get any idea about what the field line patterns will look like when both sets are present together.
From the mathematical standpoint, on the other hand, superposition is easy―we simply add the two vectors.
The field lines have some advantage in giving a vivid picture, but they also have some disadvantages.
The direct interaction way of thinking has great advantages when thinking of electrical charges at rest, but has great disadvantages when dealing with charges in rapid motion.


電気力線は定量的には未完成で困難な代物であり、重ね合わせも表現できないので、厳密に議論するにはベクトルを使うべきである、と書かれていますね

ファインマンさんが困難だという電気力線による電場の厳密な定義を、ここの回答者はいとも簡単にやってのけるわけです