# Symmetry and shape of elementary particles

1. Aug 9, 2007

### pangsiukwong

Hi!

Although nobody can see the shape of elementary particles, we always assume that their shapes are symmetrical, for example, sphere. Why? Is the symmetry a law? Otherwise, are there any other reasons?

Patrick

2. Aug 9, 2007

### ZapperZ

Staff Emeritus
We do? Where? Can you point to me the sources that you have that actually assumed this?

Zz.

3. Aug 9, 2007

### CompuChip

Most of the time, we do assume that for example electrons are hard spheres which describe circular orbits around the nucleus (or at least elliptical), etc.
Of course, we know that quantum mechanically, the electron does not have a shape at all and we should be working with wave functions and probability densities. But, when you want to calculate - for example - the average distance of an electron to the nucleus, or talk about any other "long time-scale" or averaged behavior, we usually neglect this and make the "classical" approximation to reduce calculational trouble.
That this image is not always correct was proven historically by numerous effects, which are classically not (sufficiently) explicable and where we do need QM.

4. Aug 9, 2007

### Meir Achuz

The QM calculations for atomic properties are simpler (and correct) than the classical (incorrect). The electron is considered a point particle in the QM calculations. The shape of atoms is determined by the electronic wave function, and is not generally spherical. The wave functions of baryons and nuclei are also not generally spherical.

5. Aug 9, 2007

### marlon

Shouldn't you be talking about orbitals in stead of the "shape of atoms". I would think this lingo can be quite confusing since most people relate shape to spatial structure, which atoms do not have but orbitals do.

To the OP, here is a nice link on the intro of group theory (ie symmetry) in physics : https://www.physicsforums.com/showpost.php?p=510750&postcount=42

marlon

Last edited: Aug 9, 2007
6. Aug 9, 2007

### pangsiukwong

The magnetic moment of an electron is g x (e / 2 x m) x S.
The term (e / 2 x m) x S is the classical expression of the magnetic moment which can be deduced by the model of (for example) a spinning charged sphere/disc/ring...etc (symmetric shape). Dirac's formula predicts the magnetic moment to be e / m x S, and thus g is equal to 2.
Although many physicists and chemists always say the spin angular momentum of an electron has no classical analog, However, the model and the mathematical expression appear that there is a relation between the "quantum" and "classic".

7. Aug 9, 2007

### marlon

Err, what is your point and what does this have to do with your original question ?

marlon

8. Aug 9, 2007

### malawi_glenn

There is no classical analogy regarding spin (intristinc angular momentum) in that sense that the particle rotates about its axis, as a planet for example. An elementary particle has no spatial shape, and the reason for why their intristinc angular momentum is/was observed is beacause of its magnetic moment among others.

9. Aug 9, 2007

### arivero

It seems he refers to old pre-Dirac calculations/models of electron spin, for instance in the textbook of Brillouin. Of course a calculation with a rotation of, say, a cubic shape, was possible too, but if you want to rotate, it is a good idea to calculate with rotationally symmetric shapes.

10. Aug 10, 2007

### pangsiukwong

I do not understand why some scientistists think that elementary particles are a point without a spatial shape. Is it due to the wave nature of these particles?

Born interpreted the wave function as a probability of finding the particle (e.g. electron). However, it is just an interpretation. Is there any DIRECT and SUBSTANTIAL experimental findings, which prove this interpretation true? Furthermore, this interpretation does not contain any information about the shape. Right?

If particles are wavepockets, wavepockets have a shape (occupy a certain space). Right?

Assuming everything has a shape, a symmetric shape (sphere, ring, disc) will resulted in the lowest energy. For example, a water drop is a sphere. In addition, the molecules arrange their atoms at positions in order to form the highest symmetry. Therefore, in my opinion, if elementary particles such as electrons has a shape, this shape exhibits a high symmetry.

Patrick

11. Aug 10, 2007

### malawi_glenn

Consider electron scattering on a Nucleus (protons and neutrons); that gives you the charge distribution. Have higher energy of the incoming electron, you will se charge distribution of individual NUECLONS (quark-model of Hadrons). But no experiment has ever shown other charge distribution than point like of an electron. Keywords: Coluomb scattering, charge distribution, Form factor; if you want more information on this.

12. Aug 10, 2007

### ZapperZ

Staff Emeritus
But then you run into another problem. See how a "wave packet" is constructed. It is a Fourier sum of a number of waves with different frequencies. Yet, for a photon for example, when you measure it, it has only ONE frequency (or energy). Same with an electron. What happened to all the waves that made up this wave packet?

Besides, what is the nature of these waves that somehow made up the particle? Since you are arguing that these waves are spatially real, then it must be a physical wave (not the solution to the Schrodinger Equation). So how do we detect it?

Zz.

13. Aug 10, 2007

### jostpuur

We say that electrons are point like because the wave function $\Psi:\mathbb{R}^3\to\mathbb{C}$ assigns complex numbers to points of space, which can be identified with the location eigenstates of a point like particle.

If you wanted to have a wave function for some other kind of object than a point particle, then the wave function would have to be of a different kind. For example, if a particle is a ring that can be classically characterized by a vector $(x,n)\in\mathbb{R}^3 \times\mathbb{R}^3$, where $x$ is the location of the center of a ring, and $n$ is an axis vector describing the orientation of the ring, then the wave function would be $\Psi:\mathbb{R}^3\times\mathbb{R}^3\to\mathbb{C}$.

It is true that wave packets can have shape, but that is not in contradiction by what is meant with the point likeness of the particle.

14. Aug 10, 2007

### pangsiukwong

Hi! jostpuur,

I know some physicists make use the model of a vibration of a point charge with subsequent a EM wave generation in order to explain the wave nature of the electron. Does it support the your statment "It is true that wave packets can have shape, but that is not in contradiction by what is meant with the point likeness of the particle"?

Is there any experimental evidence supporting the point-like elementary particle?

Patrick

15. Aug 10, 2007

### malawi_glenn

See my post #11

16. Aug 10, 2007

### pangsiukwong

Hi! ZapperZ,

The concept of wavepackets also confuses me. I do not know why ONE frequency of electrons is measured if electrons are wavepackets.

I guess the difference in frequency between waves, which superimpose together to form wavepackets, is very small. Therefore, one freqency is detected.

Does anybody know the answer?

Patrick

17. Aug 10, 2007

### jostpuur

Even though it is true, that you cannot explain spin angular momentum as rotating ball with volume, you cannot explain it with rotating point without volume either! Spin angular momentum doesn't seem to be a reason for particles to be point like, since also larger objects could have spin density.

It seems rather reasonable to assume, that point like particles are only an approximation of some more complicated objects, but if I have understood correctly, we cannot detect any shape of fundamental particles yet experimentally, and that is the real reason to stay with the point like particles for awhile.

18. Aug 10, 2007

### malawi_glenn

I am aware of this, and I have never stated that spin angular momentum in QM has anything to do with rotating balls. I talked about Form factors of electrons etc..

19. Aug 10, 2007

### jostpuur

I mixed your two earlier posts, was looking at the post #8, and thought that the explanation of the spin there was your response to pangsiukwong's #14 post...

20. Aug 10, 2007

### malawi_glenn

Thats ok mate =)

And yes, I think the experimental evidence for the point like structure of the electron (and the other) are very firm. But who knows? Maybe in the future with higher energies, we will se spatial shape of the elctrons charge distribution. And there is no evidence (as I know of) that supports "parton model" of the electron [analogy with the nucleon and its quarks].

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