Notion of a zero dimensional point particle?

[Nickyv2423]

When we say a fundamental particle is 0 dimensional, is that literal or figurative?
Is it physically possible that a particle has it's properties (like charge, mass) spread out in a finite volume, but can be "shrunk" to increasingly small volumes when we measure it?

 

[Simon Bridge]

When we say a fundamental particle is 0 dimensional, is that literal or figurative?

It is a mathematical model. Strictly speaking it means that the classical extent of the particle in space has no clear meaning in QM.
The "size" of a particle depends on the interaction and is given by a quantity called the cross-section.
The location of the particle in space is given by a probability distribution which tells you the chance of detecting the particle within a particular volume within a particular time period.

Is it physically possible that a particle has it's properties (like charge, mass) spread out in a finite volume, but can be "shrunk" to increasingly small volumes when we measure it?

The statistics of the particle may, in principle, be arbitrarily tightly located - yes.
For example: if the position is described by a Gaussian distribution, then the standard deviation of that distribution may be arbitrarily small.

 

[mikeyork]

My way of looking at it is that the particle has no intrinsic spatial properties. Spatial properties like location (and even size), for instance, are meaningful only in another entity's context (such as an observer).

 

[Simon Bridge]

My way of looking at it is that the particle has no intrinsic spatial properties. Spatial properties like location (and even size), for instance, are meaningful only in another entity's context (such as an observer).

... or in the context of an interaction, or a confining potential, either of which could qualify as an observer.

 

[DaveC426913]

There is absolutely no way in which the particle can exist in a zero dimensional plane

Well, that's true but not for the reason you think.

Your "zero dimensional plane" is an oxymoron - a plane consists of two dimensions.
But that's not what the OP is talking about.

as it needs an actual base of existence in a dimension,

Can a two-dimensional plane inhabit three-dimensional space? Sure. The plane that divides my pretty neighbour's property from mine.
Can a one-dimensional line inhabit three-dimensional space? Sure. The line of sight between my land-scope and my neighbour's kitchen window. Anything that intersects that line intersects my sight line.
Can a zero-dimensional point inhabit a three-dimensional plane? Sure. The focus of the eyepiece that I'm using to ensure my neighbour is safe from creeps.