# The Problem with Point Particles

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• PhysicsExplorer

#### PhysicsExplorer

There is a clear problem with the continuing belief that (any) point particles exist in nature. Quantum mechanics, relativity and even classical physics all forbids this approach. Let's explore why:

1). Quantum theory forbids point particles, because points themselves do not make sense in phase space. (For more, read Von Neumann).

2) Relativity does not make sense of point particles, because the curvature tends to infinity for such systems! So that doesn't make sense physically-speaking.

3) Classical physics forbids point particles by stating that a vanishing radius permits singularities in the self energy of the particle!

Is it that, we worked with point particle systems, because they behaved like point particles? Is it enough they behave like point particles to call them as such? Well no, because we have theories that have been developed to avoid these problems, one such case is string theory, in which particles are extended objects in space (not pointlike). I vaguely recall, there is a situation in classical physics, in which the scattering of particles will always behave pointlike. I wish I could remember the source.

Either way, how does the community feel about this situation? Clearly, point like particles posits serious problems, in all scales of our theory, from quantum, to classical, to the relativistic.

jerromyjon

## Answers and Replies

In my experience, one only assumes a particle is a point particle when it is very small compared to the distances between objects, so that assuming it is a point does not introduce any material errors. That doesn't mean that anybody believes the particle is a point. It's just a convenient fiction.

jerromyjon, Demystifier and fresh_42
In my experience, one only assumes a particle is a point particle when it is very small compared to the distances between objects, so that assuming it is a point does not introduce any material errors. That doesn't mean that anybody believes the particle is a point. It's just a convenient fiction.

Oh you would be surprised, I have met many competent posters over the years who have taken the idea of point particles, more than seriously.

Quantum theory forbids point particles, because points themselves do not make sense in phase space. (For more, read Von Neumann).
I wouldn't say this. QM means something different when it says something is a point particle than what classical physics does, but as far as I know the quantum meaning is self consistent.

Oh you would be surprised, I have met many competent posters over the years who have taken the idea of point particles, more than seriously.
Hmm. "Over the years"? You have been a member for about a day. I agree with @andrewkirk. Perhaps some students misunderstand at the beginning, but that is usually quickly rectified.

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I wouldn't say this. QM means something different when it says something is a point particle than what classical physics does.

What do you mean?

A point particle makes no sense in phase space, Von Neumann was quite clear about it. In what way, does a point particle differ in quantum mechanics, I mean apart from the quantum domain pertaining to different physics? A point particle is a point particle, in both theories.

What do you mean?
I mean that in QM a "point particle" is just a system with no internal structure. It doesn't mean that it has a definite position, just that it scatters like a point.

Von Neumann was quite clear about it
Please cite the specific reference you are talking about

I mean that in QM a "point particle" is just a system with no internal structure. It doesn't mean that it has a definite position, just that it scatters like a point.

Please cite the specific reference you are talking about

Ok, well, I am not talking about definite positions. I am talking about internal structure and yes, point particles has R=0 and presents serious problems - the divergenece problems of relativity and general classical theory shouldn't be ignored - I am not a big fan of singularities, I often see them as a breakdown in a theory. As for the last thing, its a quote I have taken from Von Neumann, source evades me right now but will look. As I understand his argument, points don't make sense in phase space because they are smeared out. But as I said, I will look.

I would like to see that reference, but in the end it is a rather pointless point that you are making. We will always have some limitation to the minimum length scale that we can probe. As long as whatever we are talking about has an internal structure smaller than that length scale, then we can treat it as a point particle. It makes calculations easier.

Edit: we cross posted, I will read the reference

There is a reference above I found. It's not the one I learned this originally.

It seems to me to be like using COM in classical physics, a point can have other attributes. But who's to say how they work? String theory just says we got anything covered, with enough DOF to cover anything's possible and them some forever...

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I read the reference, it is pretty unconvincing on the point you are making. Simply having a non-local formalism is hardly a proof of anything. Often a local formalism is equivalent to a non local formalism (e.g. Differential and integral formulations of Maxwell's equations)

The reference certainly does not appear to support your claim that a particle with no internal structure is "forbidden by quantum theory".

I am sorry you don't find it convincing, nor that you can't trust my integrity when I say point particles don't make sense in phase space according to Von Neumann. What else can I do?

The reference in my opinion, absolutely supports my claim. You asked for evidence that day, and I found a separate article from the one I learned the quote from, supporting the view that points do not make sense in phase space. And phase space, is very much part of modern approaches in quantum mechanics.

I am sorry you don't find it convincing, nor that you can't trust my integrity when I say point particles don't make sense in phase space according to Von Neumann. What else can I do?
You could tell us exactly which piece of von Neumann's work you're thinking about. You're misunderstanding something he wrote, but unless you give us a reference or a quote with source, we can't figure out what it is.

I am sorry you don't find it convincing, nor that you can't trust my integrity when I say point particles don't make sense in phase space according to Von Neumann. What else can I do?
You can find a valid professional scientific reference that supports your argument. When your integrity is published in a peer reviewed journal then it can be used as a reference here.

supporting the view that points do not make sense in phase space.
That is a much weaker claim than the one I objected to. I objected to your claim that particles with no internal structure are "forbidden by quantum theory".

In any case, your overall objection to point particles seems like wasted effort to me. As long as the size of the object is much smaller than the length scale of interest, then treating things as point particles simplifies the math without changing the outcome. So what if it is not a point at smaller scales than the scale of interest?