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?

  • a) in order for a point to exist, at least one dimension is required b) a different thing is to consider that a point has no extension, which just implies position, not existence. c) The term "particle" implies composition ("part"). ERGO: Expanding the empirical notion of space to particles is a rational flaw (you are applying the rules of macroscopic experience to entities that exist moreover in an ideal context).
    – RodolfoAP
    Commented Nov 18, 2021 at 14:41
  • 2
    Fundamental "particles" are not particles at all, point or otherwise, they are quantum-particles and that is an idiom. They are described by complex valued amplitudes spread out over the entire universe, and are as much waves as they are particles. Since they are not bodies in space, speaking of shape makes no sense. And even if we visualize the amplitude's graph, its configuration depends on external forces.
    – Conifold
    Commented Nov 18, 2021 at 14:47
  • Edited to add links, clarify terminology regarding methodology of resasoning, and explicitly introduce questions of physical extension implicitly conveyed by the original version.
    – J D
    Commented Nov 18, 2021 at 16:16

3 Answers 3


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.

  • So I'm going task what I ask Dave. Wavefunctions inherently have extension in space by design, right? That under QM, they have a shape of sorts?
    – J D
    Commented Nov 18, 2021 at 16:21
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    The wave function traces a wave in space, yes. In way oversimplified terms, graphing the relevant f(x) = y yields a wavy graph. (At least, this is how I understand it. I have yet to learn calculus, among other things, so I can't be too confident even in this statement.) Commented Nov 18, 2021 at 16:23
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    Thanks for a response! :D
    – J D
    Commented Nov 18, 2021 at 16:26

"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, Rg < 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.

  • This stuff isn't my cup of team, but doesn't a wavefunction inherently have extension in equations?
    – J D
    Commented Nov 18, 2021 at 16:19
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    Yes, that's why "pointlike" when applied to particles is a particular formal extension of the normal language sense of the term. Being "non-point like" shows up as particular characteristics in particular interactions, all of which are, as far as we can tell, going on in the context of quantum theory.
    – Dave
    Commented Nov 18, 2021 at 16:40
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    @JD you are also reifying the QM wavefunction. It's not certain that the wavefunction is physical; or more accurately it is not clear that the structures implied by a wavefunction do in fact correspond to /physical/ characteristics of the world beyond allowing one to calculate the probabilities of different observations.
    – Dave
    Commented Nov 18, 2021 at 17:34
  • Well said, sir. It's almost as if the nature of the Copenhagen Interpretation is intimately tied into the nature the debate between scientific realists and instrumentalists. Of course, if claims that wavefunctions are mental artiface with no basis in physical reality, and the fundamental things of the universe arent directly perceptible, it leaves one with empirically acceptable entities that aren't physical in the phenomenological sense which takes us out of intuition into something more abstract.
    – J D
    Commented Nov 18, 2021 at 18:54

(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.

  • Why do you say that bosons do not have size. Does it not make sense to assign a finite size to mesons?
    – Sandejo
    Commented Nov 23, 2021 at 5:39

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