Monolyth by Eric J. Heller. "This is as close as quantum mechanics can come to chaos. Classical chaos amounts to trajectories heading in every possible direction randomly; corresponding to this is the random addition of wave sets traveling in all directions. The particle executing the trajectory has a definite energy which corresponds to the waves all having the same wavelength. The result is the type of wave shown here, with characteristics not discovered until about 1986."

According to the standard model of fundamental particles and interactions, the "ultimate constituents" are the quarks (which make up, among other things, the protons and the neutrons) and the leptons (which include the electron). Is this the last word? According to the Elementary-Particle Physics Panel of the National Research Council, "[t]he question is still open experimentally, but theory and experiment are pointing more than ever before to the possibility that we have discovered the 'ultimate constituents'."

"Ultimate constituents" are objects without structure — they lack parts, and so they lack internal relations. Usually they are said to be "pointlike," which justifiably denotes the absence of structure, but which is often taken literally, as if an electron actually had the form of a geometrical point.

What does the theory have to say on this issue? Precisely nothing. Nothing in the theoretical formalism of quantum mechanics refers to the shape of a structureless particle.

And experiments? While they can furnish evidence that a particle possesses structure, they cannot furnish evidence that a particle lacks structure. (Absence of evidence is not the same as evidence of absence.) But if experiments cannot furnish evidence that a particle lacks structure, they cannot possibly furnish evidence that a particle has a pointlike shape.

The notion that a structureless object has a pointlike form is therefore unwarranted on both theoretical and experimental grounds. In addition, it explains nothing. In particular, it does not explain why a composite object — be it a nucleon, a molecule, or a galaxy — has the shape that it does, for all empirically accessible forms are fully accounted for by the relative positions of their constituents — the spatial relations between them.

All one could possibly gain from the notion that a structureless particle has a form, is the illusion that quarks and such can be visualized "as they are" (if we allow that a point can be visualized). What purpose does that serve, considering that the smallest things consisting of quarks and electrons — namely, atoms — can not be visualized "as they are"?

Recall: while we may think of those cloudlike images (here or here) as depicting possible shapes of atomic hydrogen, they do not depict these shapes as they are, without recourse to counterfactuals. Their interpretation involves probability assignments to possible outcomes of unperformed measurements.

The smallest structure that can be visualized as it is consists of the mean relative positions of a molecule's constituent nuclei — the sticks in the balls-and-sticks models found in chemistry labs. Turn the page for some popular examples.