The SEP points out
For Descartes argued in his 1644 Principles of Philosophy (see Book II) that the essence of matter was extension (i.e., size and shape) because any other attribute of bodies could be imagined away without imagining away matter itself. But he also held that extension constitutes the nature of space, hence he concluded that space and matter were one and the same thing.
An immediate consequence of the identification is the impossibility of the vacuum; if every region of space is a region of matter, then there can be no space without matter. Thus Descartes' universe is ‘hydrodynamical’ — completely full of mobile matter of different sized pieces in motion, rather like a bucket full of water and lumps of ice of different sizes, which has been stirred around. Since fundamentally the pieces of matter are nothing but extension, the universe is in fact nothing but a system of geometric bodies in motion without any gaps.
A field being without gaps; should be subject to Parmenides argument: thus it should not move and be rigid; this on the face of it, seems quite surpising. But consider that a point of field, iin the usual sense, is contiguous with others - its neighbourhood; when the field has altered and we examine the same point; we see that it has the same neighbourhood - ie the principle of continuity.
This is of course very different from an electron concieved as a particle which when moved now occupies a different place or neighbourhood.
So, in this sense of motion, a field does as Parmenides point out, shows no motion - it is rigid; however this doesn't mean that it can't exhibit change which is a related notion - but how?