# Point particles

1. Jun 17, 2011

### Physics-Learner

hi,

there seems to be some conflicting information when i do research on the net. point particles consist of electrons, quarks, and some others.

but many articles say they dont take up space. that i dont buy. i can buy that we havent or even cant uncover what sort of shape they really have.

but to me, a point is just a mathematical construct.

what is the accepted mainstream physics belief in this regard ?

2. Jun 17, 2011

### Staff: Mentor

At the subatomic level there is nothing that is more correct than mathematical constructs. We can measure the influence of the particles forces, such as the electromagnetic force coming from an electron, but where do you draw the "boundary" for the particle? In fact, there is no such thing. An electron is not a tiny sphere. It is a wave packet. It has uncertainty in position and momentum at all times. Yet at the same time, this wave packet occupies a volume of space. Does this volume of space constitute the boundaries of the electron? I can't say.

3. Jun 17, 2011

### Bill_K

The particles we regard as elementary - electrons, quarks, etc - are, as far as we can tell, point objects. That is to say, at the shortest distances we have been able to probe they have no discernible structure. Shortest distance corresponds to highest energy, and the energy reached by the large Hadron Collider of 7 TeV corresponds to a distance of about 10-18 cm.

You can either accept that they are really points, or you can hope that at a higher energy some structure will emerge. Maybe they are bound states of other, even more fundamental, point particles. If not, then you will then have to wonder how to describe an extended object mathematically, because quantum field theory only describes point objects. For a particle with finite size you'll have trouble maintaining consistency with relativity, because if an electron has structure, light will take a finite amount of time to get from one side of it to the other. When it interacts with a photon say, there will be a time lag before the other side can become aware. What happens in the meantime? You'll need to invent a quantum theory that is nonlocal. And then after that you'll still need to describe whatever material the electron is made of.

This could turn out to be the case as we probe shorter and shorter distances, but no one is holding his breath. So far, treating elementary particles as point particles is quite satisfactory.

4. Jun 17, 2011

### bapowell

Agree with all the above, but would like to add the following. While current particle theory considers particles to be point-like and experiments have not shown otherwise, in certain circumstances one can sensibly talk about the 'dimensions' of a particle. For example, the minimum uncertainty wavefunction has a wavelength
$$\lambda = \frac{h}{mc}$$.
This is known as the particle's Compton wavelength. If you try to localize the particle within a smaller region, then the momentum $p > mc$ and pair production will result. So the Compton wavelength can be considered the smallest effective region within which a single particle state can be localized.

An interesting recent study came out claiming that electrons were almost perfect little spheres:http://www.wired.com/wiredscience/2011/05/electrons-are-near-perfect-spheres/" [Broken]. I take some issue with this story because it's been embellished a bit for the popular science media -- from what I can tell, the group did not (could not) conclude the shape of the electron based on their experimental setup and findings. They found instead that the electron possessed spherical symmetry to a high degree of precision. This is an excellent result, but does not imply that electrons are indeed spherical -- in fact, a point-like mass is also spherically symmetric.

And don't forget about our friend string theory, which proposes that fundamental particles are 1 dimensional strings rather than 0-dimensional points.

Last edited by a moderator: May 5, 2017
5. Jun 17, 2011

### Bill_K

Yes, but it's not the size of the particle. Note that due to the 1/m, neutrinos, which are believed to be point particles, have the largest Compton wavelength of all. With a mass estimated as a fraction of an eV, the Compton wavelength of the electron neutrino is about 1000 times as big as an atom. Axions, if they exist, are hypothesized to have a mass in the μeV range, implying a Compton wavelength the size of a pingpong ball.

6. Jun 17, 2011

### bcrowell

Staff Emeritus
Bill_K has given an excellent answer. A few more random points to add to what he said:

String theory is what you get when you try to make a quantum-mechanical theory in which the fundamental particles *aren't* pointlike.

Bill_K gives an argument that finite size is inconsistent with relativity, but zero size is also inconsistent with (classical) relativity. Pointlike objects in relativity are black holes. Classically, a spinning, charged black hole has constraints on its angular momentum and its charge in relation to its mass. Otherwise, there is no event horizon, and we have a naked singularity rather than a black hole. An electron violates both of these limits, but we don't observe that electrons have the properties predicted for these naked singularities. For example, naked singularities have closed timelike curves in the spacetime surrounding them, which would violate causality, but there is no evidence that electrons cause causality violation. When you add in quantum mechanics, you get a different story, but we still end up unable to create a complete and self-consistent picture -- hence part of the motivation for string theory.

Historically, we've kept probing higher and higher energies, which revealed more and more structure inside of the previously known structures. By default, one would imagine that this could continue forever, and there would be no way, even in principle, to prove that we had finally found the deepest level of structure. However, there are fundamental reasons for believing that the process has to bottom out at the Planck scale.

-Ben

7. Jun 17, 2011

### bapowell

Yes, thanks for pointing this out. These cases would fall outside my caveat of "under certain circumstances..." The answer to the OP's question was given by you guys -- particles are represented as 0-dimensional points in the Standard Model, and experiments have not shown otherwise. Just trying to add a little color to the discussion by pointing out that in some cases, the Compton wavelength can be understood as the effective 'size' of the particle. What I have in mind is the scale on which gravitational effects become relevant in a quantum system: if the Compton wavelength of a particle becomes smaller than its Schwarzschild radius, then it will collapse into a black hole. The usefulness of the Compton wavelength as representing the size of the particle in this case derives from analogy with macroscopic objects.

8. Jun 17, 2011

### Physics-Learner

thanks for the posts.

9. Jun 30, 2011

### bugatti79

http://www.sciencedaily.com/releases/2011/06/110629132544.htm

based on this thread that particles have no discernible structure found yet how did they isolate this electron and examine it?
I thought no-one has ever seen an electron becasue of the uncertainty principle etc....

Are they examining the electron indirectly by measuring its energy it emits or something?

I am not clear on this...thanks

10. Jun 30, 2011

### ZapperZ

Staff Emeritus
What does detecting an electron has anything to do with its lack of structure? After all, an electron has one very EASILY detected feature - it's charge!

I will also direct you to a recent experiment that tries to detect if an electron has an electric dipole under an external E-field. A detection of such a dipole is an indication that an electron could have a "volume" or an internal structure. And guess what? No such dipole was detected!

https://www.physicsforums.com/showpost.php?p=3323535&postcount=135

Zz.

11. Jul 1, 2011

### bugatti79

Thank you ZapperZ :-)