[elashri]

> we often think as though it were dirt, or a billiard ball, or something

The problem lies that it is hard to imagine something that does have zero dimensions. You can get the example of ant walking into 2D and it is unaware of third dimension to explain we are have something similar for space-time 4D (although not the same picture exactly as time is different from spatial dimensions). But we don't have an idea how to approximate a mental picture of what a zero dimension could be. So you have something that does not occupy a volume in space (Talking strictly about elementary particles here) in the classical sense.

This does not mean they are abstract concept. According to QFT -Quantum field theory- you would think (by training) of particles are excitations or quanta of their respective fields. Fields are there always (vacuum is just filled with fields) and particle appears when they are excited (more complex processes occurs). So you would think of each particle as a manifestation of a quantum field that permeates the universe. What is interesting (and probably confusing to most people) is that these fields are not zero-dimensional, instead, they exist everywhere in space and time. But the quanta (particles themselves) are considered point-like with no spatial extension.

In practice physicists will think about particles properties (i.e charge, mass, interactions, spin) ..etc instead of what this particle actually is from that point of view. This is often for practical reasons. You are a working physicist and you learned from your training that you shut up and calculate (or implement if you are doing experimental particle physics as you spend most of your time coding) by this stage.

[hughesjj]

I just think of a zero dimensial object as a ghost.

Topological defect. The unpictured thing the contour lines are swirling around. It's influence is only felt by seeing the effects on higher dimensional space, but you can never see the ghost itself.

[mock-possum]

So more like a poltergeist really

Or a magnet

[Traubenfuchs]

So we have the three spatial dimensions, + time as 4. dimensions and at any of those 4-part coordinates there are additional properties like mass/spin/etc., some of much always come together or at least strongely correlate, and those values not being zero means there is a particle there and every value corresponds to a certain „field“ and it not being zero means the field is excited?

[xanderlewis]

> The problem lies that it is hard to imagine something that does have zero dimensions.

Do you really think so? It’s not hard to picture the real number line, with the point zero (or any other single point) distinguished. Sure — if you draw it in the standard schematic way you have to give it some area, but it still seems quite intuitive that it’s ‘zero-dimensional’. Especially if you play around with converging sequences and open sets and stuff; you quickly develop intuition for what it means to be a point rather than something higher dimensional.

[mock-possum]

I do - specifically, it’s hard to imagine a group of things which collectively constitute mass, but individually constitute no mass.

How can something come from nothing?

[xanderlewis]

I thought you were just speaking geometrically.

What particles are you talking about exactly? I was under the impression that most particles that constitute things with mass do themselves have mass.