Why doesn't Parmenides argument hold for fields - or does it?

Question

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.

and

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?

Answer 1

You can interpret the wave equation as expressing this. There is only 'possibility' everywhere, and it becomes more '[thing]like' some places than others for various values of [thing].

Or, focussing upon virtual particles, there is a field of [thing]iness and anti-[thing]iness that is uniformly balanced almost everywhere, but when they are out of balance we notice [thing]s or anti-[thing]s. Electrons are not items in space they are places where the wave-mediums of electrons and positrons are not balanced.

From such perspective, a field becoming stronger or weaker in different places is only apparent motion, like the sequenced flashing lights that point the way to a casino doorway. Nothing moves, the light just gets more intense in one place and less intense in another.

So this rescues both Parmenides intuition and the actual motion we see. But isn't it just linguistic trickery to dodge the weakness of our basic intuitions of particle, wave and field? The infinite wait for the elusive graviton notwithstanding, we know that they are all of a piece somehow, but that each intuition fails in its own way.

The field component's weakest fit for bosons is obviously quantization. Electrical field theory predicts the occasional partial electron. Electrons cannot come in just any size, like photons.

But for leptons like photons, it saddles us with all of the thinking about aether that preceded Relativity. The field should be borne by something that acts rigid to some degree. There should either be an intrinsic push-back against propagating change in the field too quickly, or there should not. But space acts otherwise for leptons: It resists being driven too fast, but does not begin to resist until right then.

Answer 2

Parmenides is just wrong. His argument doesn't work because it takes as a premise that things don't change (by badly abusing the notion of "something from nothing", and possibly also because of what counts as a distinct object). It's not, to my mind, even interestingly wrong (unlike, say, Zeno's paradox).

So, yes, fields, or the components of Descartes' hydrodynamical universe, would be subject to the same flawed reasoning. The solution is simple: don't make that mistake when reasoning!