The shape and extension of the fundamental particles

Question

You could say that particles are just 0-dimensional points. But point particles are just an idealization. If particles are taken to exist physically, and anything which has physical existence has physical extension, does that not imply that fundamental particles have shape, or have I made an error in this inference?

How does contemporary philosophy of physics deal with the question of the nature of the physical extension of fundamental particles, and what answers does it provide with regards to shape?

Answer 1

This is one of the reasons why we switched to quantum field theory. Instead of referring to individuated particles and waves otherwise operating in a quasi-void, we took this quasi-void to be the potential background for what we otherwise were describing as particles and waves, such that excitations of the fields correspond to those things. No more need to wonder whether matter is reducible to zero-dimensional points or multidimensional waves. We just need functions that describe the dynamics, and these functions can submap to specific points and waves.

OTOH, in string theory, the ultimate elements of matter are nonzero-dimensional strings.

From a Kantian point of view, it is impossible to completely perceive matter as zero-dimensional. (In fact, I think that Kant's third analogy of experience, the principle of material community, is a philosophical precursor to QFT itself, but I digress.) Whatever level of perception we're on, the objects we perceive will be divisible into further parts. At most, we will reach a threshold where we can't materially divide the content of our perception, though we will still recognize that the ambient space is divisible, and so it would still be true that, if it were otherwise physically workable (say by technological development), we could perceive the material divisibility of our perceptual contents, too.

Answer 2

"Particle" is an idealization, as is "the shape of a particle". The current observational evidence is that electrons are pointlike, which technically means that in the set of interactions that involve electrons that have been observed, there are no observations that are inconsistent with the electron having an arbitrarily small geometric size. And the concept of "arbitrarily small geometric size" is a particular formal mathematical generalization/extrapolation of the more everyday concept.

Usually this is expressed as observations putting an upper limit on the size of the electron. For example this result: https://iopscience.iop.org/article/10.1088/0031-8949/1988/T22/016 claims

From the close agreement of experimental and theoretical g-values a new, 10⁴ × smaller, value for the electron radius, R_g < 10^-20 cm, may be extracted.

in its abstract. That the "size" of the electron bounded is really a statement about the results of particular models in particle physics relate to particular observations of the world. We have models for electrons (idealization) that correspond, within the mathematical framework of the quantum physics, to point like particles, and can construct alternative models that correspond, in some formal sense, to non-zero sized particles. Current observations of electrons are consistent with the former, and some flavors of the latter provided that the size is small enough.

In terms of "shape", that's stymied by the current observations that indicate that electrons are pointlike (again, technically, this is "have no spatial structure on the length scales experiments are able to probe"). Since pointlike, no shape. Electrons do have spin though. This feature of electrons can be manipulated in ways that might be considered analogous to re-orienting a shaped object, and these re-orientations can have observable effects. However, this is not viewed as "electrons having shape", in part due to the observational limits on the size of the electron, and also due to the fact that there are dis-analogies, indeed a lot of quantum wierdness, in manipulating spin.

To me, this whole issue is closely related to Quinian underdetermination in science, but I can't quite put my finger on how.

Answer 3

(Note, I am more of a physicist than a philosopher)

Particles not only have shape, they have two shapes!

The first shape is the wave function of the particle. Quantum particles are spread out all over the universe, but they usually have places where they are more present than elsewhere. The shape of these places can be said to be the shape of the particle. Note that these shapes are not in any way fixed.

For small particles, like electrons, this shape is much larger than the actual size of the particle.

Larger particles, like neutrons, have a size. If you observe them closely, their wave functions can be smaller that this size.

But what does it mean for a neutron to have a size? It means that if you let two neutrons collide at a low speed they will "bump" at this distance, behaving very much like two billiard balls. (At high speed, they smash and break)

Size gives particles a second shape. As far as we can tell, this shape is always a sphere. Two cubes would meet at different distances depending on if they meet corner to corner or side to side. We have seen no such effects. (I have no idea how accurate these measurements are)

Photons (light particles) are bosons (integer-spin particles). Bosons do not bump off each other, so there are no reason assign a size to them other than their wave function.

It is possible that neutrons and other large particles have a size because they consist of parts, quarks. These parts like to keep their distance, and that includes keeping the distance to other neutrons.

It is unknown if quarks themselves have a size in the "bump" sense. It is very hard to experiment on quarks.