Q:- Atoms were originally conceived as indivisible, massy particles - so why do we keep finding more and more substructure in them and why do they have volume?




Yes, it is true that Democritus’s original conception of atoms arose from thinking about dividing up a finite piece of material into smaller and smaller pieces. In order for this process of division not to be endless, it was thought that it must reach a limit or ‘point of pure mass’, just short of where it would disappear into nothingness, where no further division would be possible. This ultimate solid ‘particle’ or ‘point-mass’ was called an ‘atom’, and for millennia, up until the advent of quantum mechanics and the wave theory of matter, was considered to be the elemental ‘building block’ from which all material form is assembled. It was closely related conceptually to the abstract geometry of Euclid, in which matter consists of zero-dimensional points, one-dimensional lines, two-dimensional planes and three-dimensional solids. Even curved lines or surfaces were considered to be mathematically reducible to this geometry and this supposition was at the root of Newton and Liebniz’s invention of calculus, in which such lines or surfaces are reduced to ‘infinitesimal points’, larger than zero but less than the smallest fractional number that can be defined. And it featured also in the so-called ‘non-Euclidean geometries of convex and concave surfaces.

Notice that space (conceived as ‘nothingness’) and matter are regarded here as mutually exclusive. This leads to paradox, because we are faced with the proposition of material particles that have mass but no size. This is not a realistic proposition, and yet it is core to mathematical physics theory.

In practice, all atomic and subatomic structures, down to and including ‘quark strings’ MUST have size, because they must include space. In fact they must be 100 % full of space – a condition that can only realistically be understood through accepting that they are combinations of space and energy as mutually inclusive, motionless and motion-full presences. As such, the more minutely we examine them, the more minute substructure we will find in them until all that we’ll have left is the space in their core. But this is a condition that abstract mathematical theory refuses to admit, and abstract physics expends more and more energy attempting to get to the bottom of.