In The Feynman Lectures on Physics Vol. II Ch. 1: Electromagnetism, the following is stated:
There have been various inventions to help the mind visualize the behavior of fields. The most correct is also the most abstract: we simply consider the fields as mathematical functions of position and time. We can also attempt to get a mental picture of the field by drawing vectors at many points in space, each of which gives the field strength and direction at that point. Such a representation is shown in Fig. 1–1. We can go further, however, and draw lines which are everywhere tangent to the vectors—which, so to speak, follow the arrows and keep track of the direction of the field. When we do this we lose track of the lengths of the vectors, but we can keep track of the strength of the field by drawing the lines far apart when the field is weak and close together when it is strong. We adopt the convention that the number of lines per unit area at right angles to the lines is proportional to the field strength. This is, of course, only an approximation, and it will require, in general, that new lines sometimes start up in order to keep the number up to the strength of the field. The field of Fig. 1–1 is represented by field lines in Fig. 1–2.
That contradicts what I have read elsewhere. The model I originally learned is very adamant that electric field lines only originate or terminate at charges.
I guess if we are to broaden the scope of application of field lines to other situations, there may be situations, for example the flow of a wet fluid, where field lines might appear "out of nowhere".
So, I ask, in the mathematical sense, will electric field lines ever begin or terminate at points other than charges?