Does an electron have an internal structure?

[Qubix]

Ok, I know this question is very old, and it has probably been answered by now, but if the electron does not have an internal structure (like the proton for example), how does it maintain itself as an entity? Why does it not disintegrate?
I've asked this question a couple of times before ,and people answered with things like "it's a fundamental particle so it does not have an internal structure"... this is obviously not a scientific answer, for 100 years ago, we might have said the same about the atom.

 

[muppet]

Does an electron have an internal structure?
Ok, I know this question is very old, and it has probably been answered by now, but if the electron does not have an internal structure (like the proton for example), how does it maintain itself as an entity? Why does it not disintegrate?
I've asked this question a couple of times before ,and people answered with things like "it's a fundamental particle so it does not have an internal structure"... this is obviously not a scientific answer, for 100 years ago, we might have said the same about the atom.

What's not scientific about it?
Science is the investigation of the physical world by means of experiment in order to advance our understanding of nature such that we not only know why we obtain the results of the experiments already perfomed, but are able to predict the outcome of future experiments (or explain why a certain experiment is intrinsically impossible to perform, or why a certain prediction is intrinsically impossible to make, etc.) Sometimes an experiment proves a well-established theory wrong, and that's when science is perhaps most interesting. But at other times you have to accept that the scientific method is intrinsically incapable of proving something beyond absolutely all doubt, and you just have to accept that a theory which continually churns out the right answers is probably at least a very good appproximation to what's going on, an approximation that is so good you might as well call it correct for expedience's sake until something proves it wrong.
The theories that are currently the best we have predict that the electron is a structureless, fundamental particle with zero size. It doesn't disintegrate because there is nothing for it to disintegrate into, and nothing to "maintain". At some point, it is almost logically necessary for such a fundamental particle to exist, or you'd have an infinite regress- how would the particles which made up the electron maintain their structural integrity?
We know that atoms aren't fundamental for lots of reasons, but perhaps the most obvious piece of evidence that they have structure is that we can smash them into bits. You can't do this with an electron. People have tried investigating the size of the electron, which if it were non-zero would tell us that our present best theories are wrong. So far the upper bound on any potential size of the electron is (I think) about 10^-18m -or a one-hundred millionth the size of the atom.

 

[Qubix]

What's not scientific about it?

Saying something is "fundamental" is the same as saying "it was made by god". It is not a scientific definition because if you do not have a theory capable of understanding a phenomenon, it does not mean that the phenomenon itself is the problem, but most likely, your theory.
What if I asked another question: What is the electric charge? The purpose of the question is to go beyond (or around) the "it's fundamental" lame answer, and to see if modern theories (even hypotheses like string theory), can say something about it.

People have tried investigating the size of the electron, which if it were non-zero would tell us that our present best theories are wrong. So far the upper bound on any potential size of the electron is (I think) about 10^-18m -or a one-hundred millionth the size of the atom.

In the first sentence, you are implying the size of the electron is 0? Size 0 would mean the electron is a point. Can you really have a point in a (at least) 3 D space?

 

[malawi_glenn]

Yes it is a point. The thing is that our ideas of the world in our daily life contradicts what is going on in the Quantum level. Also the problem might lay in the mathematical language we use, which was developed to explain classical physics (Newton etc.)

But you know that geometric series etc converge to a finite value, even though each terms goes to zero but never becomes zero? That also contradicts how we add things in our daily life, but in the world of math it is just fine.

So if we want to be really pragmatic scientific, the answer is that our theories for electrons (The Standard Model) has a delta-function as the electrons charge distribution and that quantity can be tested experimentally - the form factor should then equal unity. And that is what is found in all experiments so far, the upper limit for the electron radius is around 10^18m. So that is the most scientific answer you can get today.

 

[DrChinese]

Saying something is "fundamental" is the same as saying "it was made by god". It is not a scientific definition because if you do not have a theory capable of understanding a phenomenon, it does not mean that the phenomenon itself is the problem, but most likely, your theory... In the first sentence, you are implying the size of the electron is 0? Size 0 would mean the electron is a point. Can you really have a point in a (at least) 3 D space?

First, welcome to PhysicsForums, Qubix.

Electrons have mass and charge even though they act as point particles. Same thing is true of quarks, the other major building blocks of matter. However, electrons and quarks can act as either a particle or a wave according to how they are observed.

Saying a particle is fundamental is not at all the same as saying it was made by god. The theory says that an electron is fundamental (i.e. does not degenerate to other particles like free neutrons do, for instance). It does not do so as far as anyone knows (and people have looked).

Theory also says an electron is a point particle, and it acts like a point particle. So yes, you can have a point in spacetime. (There are a lot of that are seen in physics that are counter-intuitive, no point in denying what is known to occur.) Experiment again matches theory.

What do YOU think an electron is? How does your concept differ from accepted theory? And do you have any experimental basis for your opinion?

 

[Algr]

Is it perhaps better to say "We can't see any evidence that the electron has an internal structure." ?

I take it then that we have never seen an electron decay or turn into anything else without something impacting it first.

BTW, protons and neutrons are made of quarks - are there any particles that have electrons in them? Or are electrons always solitary?

 

[malawi_glenn]

DrChinese, we should not perhaps encourage doubters to do wild speculations here?

Algr, the atom has electrons. You would then say that an atom is not a particle, but then I would not call the proton a particle. It is all about energy scales here.

And to the OP, suppose THAT the electrons was made up of smaller particles, or strings, we would then ask the question "what are those particles made of?", so we have to accept that a smallest entity exist I think.

 

[dx]

We don't know whether the electron has internal structure. If it does have internal structure, it is not accessible at the energy levels that we can currently probe.

 

[AEM]

So if an electron has no internal structure and for all intents and purposes can be regarded as a point particle, what is the origin of its mass?

 

[ZapperZ]

So if an electron has no internal structure and for all intents and purposes can be regarded as a point particle, what is the origin of its mass?

If the LHC finds the symmetry breaking in the electroweak sector, then that's your possible source of leptonic mass.

Zz.

 

[Qubix]

What do YOU think an electron is? How does your concept differ from accepted theory? And do you have any experimental basis for your opinion?

Well, besides what the accepted theory tells us, I do not know what the electron is, that was the whole purpose of my question :)

Thank you for all your answers, I hope we find out more about the electron in the future.

 

[AEM]

If the LHC finds the symmetry breaking in the electroweak sector, then that's your possible source of leptonic mass.

Zz.

Can anyone cite a reference that will elaborate on this a little?

 

[friend]

Saying something is "fundamental" is the same as saying "it was made by god". It is not a scientific definition because if you do not have a theory capable of understanding a phenomenon, it does not mean that the phenomenon itself is the problem, but most likely, your theory.

I think your question is the same as what reason do we have to believe that the electron is fundamental. You don't trust experimental results because experiment can only rule out some theories, but never prove a theory since we might not be doing the right experiment (not high enough energy, or not done the experiment enough times, etc.)

Others here can correct me if I'm wrong or expound on this idea. But IIRC, particles emerge from symmetries of spacetime, you know SU(3)XSU(2)XU(1). And it seems that the electron has all the properties of one or some of these properties which indicate that it is fundamental.

If this is true, then it is interesting to consider what particles say about spacetime itself. And I'd have to wonder how quantum gravity theories would change the description of particles.

 

[ZapperZ]

Can anyone cite a reference that will elaborate on this a little?

http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.2232v2.pdf

Zz.

 

[AEM]

Thanks. Precisely what I was looking for.

 

[humanino]

particles emerge from symmetries of spacetime, you know SU(3)XSU(2)XU(1)

This is not spacetime symmetry, this is gauge symmetry.

 

[Algr]

Algr, the atom has electrons. You would then say that an atom is not a particle, but then I would not call the proton a particle. It is all about energy scales here.

Well that defines some terms, but doesn't answer the question at all. Is there anything smaller then an atom that has an election as a component?

 

[malawi_glenn]

Well that defines some terms, but doesn't answer the question at all. Is there anything smaller then an atom that has an election as a component?

Well it was due to a sloppy usage of the word "particle" that I raised that issue.

No, there are no other composite particles which are made up of electrons.

 

[humanino]

Is there anything smaller then an atom that has an election as a component?

The size of the atom is determined by the strength of electromagnetism. By which interaction would your thing be bound by ? Electrons do not feel the strong force.

 

[malawi_glenn]

well one can also have positronium, but if one can classify that as smaller than an atom, I don't know.

 

[gendou2]

... the upper limit for the electron radius is around 10^18m. So that is the most scientific answer you can get today.

I would love to read about this.
Could you post your source for this number?

Myself, whenever I see "electron radius" I usually read it as the Lorentz radius...

 

[malawi_glenn]

I would love to read about this.
Could you post your source for this number?

Myself, whenever I see "electron radius" I usually read it as the Lorentz radius...

first, notice the typo, 10^-18 m is a standard quoted result. It results from the deBroigle wavelenght of probes when performing scattering experiements. The higher energy you have, the smaller radius you can determine. And all experiemts so far shows constant form factor, i.e delta-function charge distribution. But what the current highest energy that the constant form factor have been verified I postpone to someone else to state. PDG should have it quoted i guess.

 

[per.sundqvist]

The main problem of having an inner structure of the electron is the spin. Suppose you divide e into two sub-electrons with charge e/2 (and maby also mass me/2). This is fine. But when you add spin, and its z-component of two fermions, things get different. Spin of one electron is 1/2, so our two sub-electrons would have 1/4 each. But the z-component of the TOTAL spin could then be_ -1/2, 0, 1/2 Thats three states! Stern-Gerlach experiment tell us that it is only two states -1/2 and +1/2 (not 0). If you continue sub-dividing the electron into finer parts, you get z-comp of total spin to be continuously ranging from -1/ to 1/2, which is wrong!

However for the proton it was shown that it has two different total spins 3/2 and 1/2 (four different z-components) 1/2+1/2+1/2=3/2, 1/2+1/2-1/2=+1/2 etc. This implies that we can model this as three fermions carrying each exactly spin 1/2 ->quarks theory was born (perhaps more than this was behind but anyway).
/Per

 

[malawi_glenn]

And as far I know, one can only have integer or half integer spin, so spin 1/4 particles?.. hmm

 

[per.sundqvist]

And as far I know, one can only have integer or half integer spin, so spin 1/4 particles?.. hmm

Hmm, yes, that's also a good reason... When you derive the Pauli contribution of the Hamiltonian from Diracs equation, you would get
H_P=-\frac{e\hbar}{4m_e}\vec{\sigma}\cdot\vec{B}

so if e'=e/2 and m'=m/2 the spin remains constant (1/2) (e/m=constant). But then if you add the spin of two e/2 electrons you would get s=0 or s=1, with sz=-1,0,1 again 3 levels, and also of wrong magnitude!

/Per

 

[bomanfishwow]

Saying something is "fundamental" is the same as saying "it was made by god". It is not a scientific definition because if you do not have a theory capable of understanding a phenomenon, it does not mean that the phenomenon itself is the problem, but most likely, your theory.

But the problem here is that there is NO phenomenology that points to lepton compositness, therefore it is fundamental. These results are always interpreted in the limits of the available energy to probe the object; that is understood by all in the field. People are going to be looking at the LHC, so you never know...

 

[Meir Achuz]

The angular momentum commutation relation [L_x,L_y]=iL_z, only allows integral or half integral eigenvalues for L_z, since (2m+1) must be an integer.

 

[JustinLevy]

The angular momentum commutation relation [L_x,L_y]=iL_z, only allows integral or half integral eigenvalues for L_z, since (2m+1) must be an integer.

Angular momentum can be continuously valued, so such an argument for quantization from the commutation relation alone cannot exist.

The main problem of having an inner structure of the electron is the spin. Suppose you divide e into two sub-electrons with charge e/2 (and maby also mass me/2). This is fine. But when you add spin, and its z-component of two fermions, things get different. Spin of one electron is 1/2, so our two sub-electrons would have 1/4 each. But the z-component of the TOTAL spin could then be_ -1/2, 0, 1/2 Thats three states! Stern-Gerlach experiment tell us that it is only two states -1/2 and +1/2 (not 0). If you continue sub-dividing the electron into finer parts, you get z-comp of total spin to be continuously ranging from -1/ to 1/2, which is wrong!

You are assuming in your argument two things:
- if the electon has inner structure, the components are identical
- all spin configurations will have the same energy

I don't feel either of those are justified assumptions.
I'm not very well read up on preon models, but such models do exist.

However for the proton it was shown that it has two different total spins 3/2 and 1/2 (four different z-components) 1/2+1/2+1/2=3/2, 1/2+1/2-1/2=+1/2 etc. This implies that we can model this as three fermions carrying each exactly spin 1/2 ->quarks theory was born (perhaps more than this was behind but anyway).
/Per

The spin contribution to the proton is still a very open and debated topic. How much is from the orbital, how much is from intrinsic quark contributions, etc.

Also, a spin 3/2 'proton' would be an excited state of the proton. This is usually referred to as a different baryon. (I believe it is called a \Delta^+ and it commonly decays into a neutron and a pion ... whether you want to argue if this is still a proton or not just gets into semantics, but at the very least it is an excited state of the proton, differing from the ground state which is usually referred to as the proton.)

 

[malawi_glenn]

There is a general argument in Sakurai's book, just replace L with J, the general angular momentum operator.

There is no evidence for electron spectra which should exist then.

 

[JustinLevy]

There is a general argument in Sakurai's book, just replace L with J, the general angular momentum operator.

Hmm... I don't have Sakurai's book here. Can you outline the proof for me?

Consider for instance an electron and positron. There are infinitely many quantized energy states, but after that there is a continuum of states. Once you get into the continuum it seems like J could only be quantized if both momentum and impact parameter were quantized ... which I thought were continuously valued.

There is no evidence for electron spectra which should exist then.

Yes, as bowmanfishwow mentioned "there is NO phenomenology that points to lepton compositness". But that doesn't experimentally rule out preon models.

As mentioned before, it is probably best to state it as:
- There is no evidence for compositeness down to a length scale of 10^-18 m.


String theory as a tentative "theory of everything", has the fermions as fundamental particles (ie. they are states of just one string). So not only is there no experimental reason to expect compositeness, but theoretically it is not needed either.

 

[malawi_glenn]

we are discussing bound states, then you can't argue with a continum.

The proof is about 4pages, depending on where you want to start. There should be millons of websites presenting that proof. It uses ladder operators.

 

[JustinLevy]

we are discussing bound states, then you can't argue with a continum.

It was presented as if the commutator alone allowed proof of quantization. I felt uncomfortable with this, because it seemed like there were clear counter-examples.

With several assumptions added on, maybe it becomes possible.
Is there a way to prove that bound states of finite number of particles cannot have a phase space region allowing continuously valued states?


As for arguments against preons having non "multiple of half integer" values, I've only seen the spin-statistics theorem proof.

Anyway, thanks for pointing me in the right direction. This sounds really interesting as I have never heard of this quantization argument before.
I'll definitely read up on it tonight.

 

[malawi_glenn]

eh bound states with phase-space region?

Also in continum, consider your incoming particle against a target with impact paramter which you say that you can continuous vary. But then I just say that you decompose your incoming partile plane wave into spherical harmonics.. recall quantum mechanical scattering.

 

[JustinLevy]

eh bound states with phase-space region?

Sorry, I probably wasn't explaining myself very well.
Basically: Is there a proof that in a bound system, there does not exist a range of energy (or similarly for another observables) in which there exist a continuum of states?

Also in continum, consider your incoming particle against a target with impact paramter which you say that you can continuous vary. But then I just say that you decompose your incoming partile plane wave into spherical harmonics.. recall quantum mechanical scattering.

I don't consider such decomposition convincing. That sounds similar to arguing that since an irrational number can be represented as an infinite sum of rational numbers that it too must be a rational number... which of course it is not.


Regardless, I need to read that proof in Sakurai before I can discuss it intelligently with you. I'm sure (or at least hoping) that reading it will clear up any confusion I have on this.

 

[per.sundqvist]

"You are assuming in your argument two things:
- if the electon has inner structure, the components are identical
- all spin configurations will have the same energy"

Yes you are right, It was a very simplistic way to describe the "spin-problem". I know that S=3/2 is an excited state for protons, and also if you have 3 electrons in an external parabolic potential you normally have S=1/2 as the groundstate (but S=3/2 for strong confinement).

In fact this may be an argument for the possibility that we only can see the S=1/2 state for electrons, since excited states with higher spins have so much higher energy! (if it is composite). The difference in exchange, between different spinstates has to be worked out in the vicinity of a leptonic "glue" attractive force between the electron's components (which is heavily speculative).

 

[granpa]

http://en.wikipedia.org/wiki/Delta_baryon#List

so the spin 3/2 delta baryons and their ultimate decay products disregarding neutrinos and photons are:

Δ⁺⁺ > proton + positron
Δ⁺ > proton
Δ⁰ > proton + electron
Δ^- > proton + electron + electron

the first and last having no equivalent spin 1/2 particles.

 

[malawi_glenn]

Sorry, I probably wasn't explaining myself very well.
Basically: Is there a proof that in a bound system, there does not exist a range of energy (or similarly for another observables) in which there exist a continuum of states?


I don't consider such decomposition convincing. That sounds similar to arguing that since an irrational number can be represented as an infinite sum of rational numbers that it too must be a rational number... which of course it is not.


Regardless, I need to read that proof in Sakurai before I can discuss it intelligently with you. I'm sure (or at least hoping) that reading it will clear up any confusion I have on this.

Sorry but it is simple addition of spin in "spin space" which is a direct product space. Make an ansatz that the electron is made up of 2 spin 1/4 particles. The direct product spin space you can construct will have 1/2 or 0 as magnitute of spin. You CAN't form a continum of states in this direct product spin space.

Regarding continoum states in energy, look for instance at nuclei, all states that are above E = 0 but still below the potential edge are called continoum states, but those are unstable since the wavefunction can tunnel out of that region. But that is for energy, not spin.

 

[per.sundqvist]

Sorry but it is simple addition of spin in "spin space" which is a direct product space. Make an ansatz that the electron is made up of 2 spin 1/4 particles. The direct product spin space you can construct will have 1/2 or 0 as magnitute of spin. You CAN't form a continum of states in this direct product spin space.

Yes true, but consider you divide the electron into N (even number) particles, such that each spin is s=1/2N. Then Stot=0,2/(2N),...,1/2 (magnitude) And then you let N->infinity. In this limit the spinstates are like a continuum. For odd number M you would get 1/2M as the groundstate, but as M-> infinity this goes to zero. The ultimate z-projections would be (+/-) 1/2 for the continuum electron, but all values in between are allowed. But this is not right.

Its like a QW with large L, where the energies are quantized, but it looks like a continuum if L->infinity (you could use semi-classical theory with DOS etc. to describe it, if dE<<kB*T).

As for the quarks in the protons, it is the strong confinement energy that makes up the "total mass" of mp=1.7e-27. The rest-mass of the d and u quarks md and mu is about only 2% of mp. The size is 1e-15m roughly. Now consider an electron of size 1e-18m, would then not the restmass of the sub-particles of the electron be ridiculously small, i.e., mq<<<<me? The ratio e/m, which determines the Pauli spin would then not be easy to control... I don't even understand it for the quarks with qd=-1/3e and md=0.02mp -> S>>1/2 (S_electron). Have to check this from the Dirac equation, could be a relativistic factor here? ...

 

[per.sundqvist]

To the original question, I now think I must answer no! I have checked the Dirac equation a little and I made a simplified model which shows the absurdity of getting the small electron mass as a result of such extreme confinement, radius a<10^-18m.

Assuming one of the sub-particle having rest mass m0 and bound in a box-potential with V=0 for r<=a and infinity else one can derive the following from the Dirac equation:

-\frac{\hbar^2}{2m_0}\nabla^2\Psi=\lambda\Psi

\lambda=\frac{\hbar^2}{2m_0}\left(\frac{\pi}{a}\right)^2

E\equiv M_ec^2=m_0c^2\sqrt{1+\frac{2\lambda}{m_0c^2}}

Assuming simple addition of energies of N sub-electrons one can solve for m0 in terms of the total (known) electron mass Me, to get:

m_0=\sqrt{\left(\frac{M_e}{N}\right)^2-\left(\frac{\pi\hbar}{ac}\right)^2}

The last part in the sqrt could become large if radius a is small. Using the radius of a proton a=1e-15 one gets this term (which is a mass) to be=1.1e-27kg, which is close to the mass of the proton (surprisingly good for such a crude model!). The problem with the electron is that the value of a must be a<1e-18 (or even mush less, due to experimental observation). Even with a small number of N (number of sub particles) the sqrt becomes imaginary if

a_{el}\leq \frac{\pi\hbar}{M_e c}=1.2\cdot10^{-12}m

This value is much bigger than 1e-18 so the rest mass of the constituents of the electron must be imaginary! This seems to me to be physically absurd, why I conclude that this little "proof" (very rough) strongly indicates that the electron cannot be built up of sub-particle and that it therefore has no internal structure. Does it make sense?

 

[enotstrebor]

"You are assuming in your argument two things:
- if the electon has inner structure, the components are identical
- all spin configurations will have the same energy"

You are assuming much more.
-Your assuming the structure is a particle structure rather than some other structure (e.g. string like/type).
-Your assuming that the experimental point like radius (<10^18 m) is the size rather than the resultant effective size (e.g. gyroscopic objects react about the center point dispite the extent)

The mathematics (dirac spinor) and experiment actually suggest that there are two spin structures (the electron is mistakenly picture as having only a spin up and spin down state, but in actuallity the mathematics indicates four spin orientations). These two spin structures are spining at 90 degrees to each other (physically 90 degree orthagonal vs spinor mathematical 180 degree orthagonal).

Note that with two 90 degree spin sturctures (magnetic quadrupole) things like the stern-gerlach experiment now makes physical sense. The first magnetic field only orients one of the two orthagonal magnetic spins (up or down, 50/50 probability) with a while the second spin plane in unoriented. A second stern gerlach magnet field at 90 degrees to the first thus also result in a 50/50 probability of spin up or down because it is orientated to this second unoriented spin plane.

This thought experiment is not proof of structure, but...?

 

[ZapperZ]

You are assuming much more.
-Your assuming the structure is a particle structure rather than some other structure (e.g. string like/type).
-Your assuming that the experimental point like radius (<10^18 m) is the size rather than the resultant effective size (e.g. gyroscopic objects react about the center point dispite the extent)

The mathematics (dirac spinor) and experiment actually suggest that there are two spin structures (the electron is mistakenly picture as having only a spin up and spin down state, but in actuallity the mathematics indicates four spin orientations). These two spin structures are spining at 90 degrees to each other (physically 90 degree orthagonal vs spinor mathematical 180 degree orthagonal).

Note that with two 90 degree spin sturctures (magnetic quadrupole) things like the stern-gerlach experiment now makes physical sense. The first magnetic field only orients one of the two orthagonal magnetic spins (up or down, 50/50 probability) with a while the second spin plane in unoriented. A second stern gerlach magnet field at 90 degrees to the first thus also result in a 50/50 probability of spin up or down because it is orientated to this second unoriented spin plane.

This thought experiment is not proof of structure, but...?

Can you please provide citations where these have been published? And how would you reconcile this with all our observations of spin-triple and spin-singlet pairings, not to mention, results from every single electron paramagnetic resonance experiments?

Zz.

 

[malawi_glenn]

And what is the string composed of? How big is the string?

 

[JustinLevy]

Sorry but it is simple addition of spin in "spin space" which is a direct product space. Make an ansatz that the electron is made up of 2 spin 1/4 particles. The direct product spin space you can construct will have 1/2 or 0 as magnitute of spin. You CAN't form a continum of states in this direct product spin space.

I don't really agree with this logic since angular momentum need not be spin. In most multi-particle states, S_z is not even a good quantum number. What we want is J_z of this bound state.

I read the argument you mentioned in Sakurai that gives angular momentum quantization just from the commutator relations. It leaves much lacking for my tastes, as it essentially only shows that "measurement J_z" < Sqrt[ "measurement J^2" ] and that there is an operator which takes you from a state with Jz = n hbar to a state with Jz = (n+1) hbar (unless that would violate the previous inequality). That is very interesting (and I've seen similar algebra worked out), but I don't consider it a proof that given the commutator relations J^2 is quantized nor do I consider it a proof that there does not exist an operator which can increase Jz by a value less than integral hbar.

But this is getting off topic. I understand that angular momentum is quantized in many cases (just from the experience of working out problems), and I believe this is indeed the case under fairly general circumstances. If there is a proof showing this for all circumstances, I'd like to see it. Please answer in a new thread though. I don't want to pull this thread any further offtopic.

 

[JustinLevy]

The mathematics (dirac spinor) and experiment actually suggest that there are two spin structures (the electron is mistakenly picture as having only a spin up and spin down state, but in actuallity the mathematics indicates four spin orientations). These two spin structures are spining at 90 degrees to each other (physically 90 degree orthagonal vs spinor mathematical 180 degree orthagonal).

What!?
Are you thinking of right handed vs. left handed electrons?
If so, it does not mean that the electron has "two spin structures are spining at 90 degrees to each other".

Regardless, this sounds more like a personal theory of yours instead of something that can be traced to Dirac, for this is highly unconventional. I agree with ZapperZ, please cite a source that lead you to believe this.

To the original question, I now think I must answer no! I have checked the Dirac equation a little and I made a simplified model which shows the absurdity of getting the small electron mass as a result of such extreme confinement, radius a<10^-18m.

...

This seems to me to be physically absurd, why I conclude that this little "proof" (very rough) strongly indicates that the electron cannot be built up of sub-particle and that it therefore has no internal structure. Does it make sense?

I would have to disagree here. This argument does not allow you to rule out preon models (otherwise, indeed, all preon models would have been ruled out long ago).

The problem is that you assumed the particles are non-interacting in your calculation. If the effective potential is very negative within the bound state, the total energy and kinetic energy due to "confinement" can still work out fine.

The ratio e/m, which determines the Pauli spin would then not be easy to control... I don't even understand it for the quarks with qd=-1/3e and md=0.02mp -> S>>1/2 (S_electron). Have to check this from the Dirac equation, could be a relativistic factor here? ...

You've mentioned something similar before as well. Where are you getting this idea that spin is determined by e/m? If it were, since spin comes in quantized units, and charge comes in quantized units, so too would m. This is obviously not the case.

 

[granpa]

the angular momentum due to spin is S=√s(s+1) or S=s√(1+1/s)
s=1/2 or 3/2 or 5/2...once you know the angular momentum of the particle then you multiply by ge/2m to get the magnetic moment. g is the fudge factor. its 2 for electrons and 5.9 for protons.

orbital angular momentum L=√l(l+1) or L=l√(1+1/l)
l=0 or 1 or 2...

J=L+S

 

[JustinLevy]

Can the fact that g agrees with QED calculations which assume no internal structure for the electron, be used to reduce the length scale for any possible "internal structure" even further?

True, it is not direct probing, but maybe it still provides good contraints?
(What is the main motivation behind preon models anyway... it seems like they would have to be highly contrived. What are they striving for which would make such methods "worth it"?)

 

[malawi_glenn]

JustinLevy: of course you are not thinking it as a proof, you are not a master physicists as Sakurai ;-)

Preon models of the electron, tell me which classy institute of physics are dealing with such?

If the electron has substructure, it can not have substructure of the kind "point particles" described by todays physics. It must be something else, like strings.

 

[Orbb]

Out of line of your discussion, but concerning the topic:

Imaging spin as the internal angular momentum of a particle, isn't the spin of the electron an indication for its finite size? I know that in experiments as well as in current theory, the electron appears as a point particle without any spatial extent. However, the upper bound is some 10^-18m, so before reching the Planck scale, there are many orders of magnitude yet to be uncoverd (if ever possible). If one regards spin as an emergent phenomenon like angular momentom (from circular motion), an internal structure having some orientation in space would be a necessity to give rise to spin, which of course has such orientation.

 

[JustinLevy]

Out of line of your discussion, but concerning the topic:

Imaging spin as the internal angular momentum of a particle, isn't the spin of the electron an indication for its finite size?

No, it doesn't give any indication of that. If you start with the generators of rotation, there is a term which corresponds to spin and to (essentially) r x p. It is not necessary for spin to be described by a orbital angular momentum on a smaller scale.

JustinLevy: of course you are not thinking it as a proof, you are not a master physicists as Sakurai ;-)

Oh come on now, how does that help me learn anything?

If you are saying his algebra shows more than essentially
1] "measurement J_z" < Sqrt[ "measurement J^2" ]
2] there is an operator which takes you from a state with Jz = n hbar to a state with Jz = (n+1) hbar (unless that would violate the previous inequality)

and that this somehow allows one to prove
3] J^2 is quantized
and
4] there does not exist an operator which can increase Jz by a value less than integral hbar

then please do help me learn the missing pieces.
As I said before, I understand that angular momentum is quantized in many cases (just from the experience of working out problems), and I believe this is indeed the case under fairly general circumstances. However I am not sure if I can take this as a requirement in general. If there is a proof showing this for all circumstances, I'd like to see it.

Preon models of the electron, tell me which classy institute of physics are dealing with such?

A quick search in INSPEC shows that preon models do get published in decent journals. I don't really follow any preon modelling since there currently isn't any phenomenology from experiment to guide it (so it just seems like shots in the dark to me). Most physicists probably don't spend time on preon models for the same reason.

Oh, I guess I have read one recent attempt. One of Lee Smolin's post-docs tried to build up the standard model particles in spin-network theories of quantum gravity by using geometric braiding for "preons".

Anyway, I'm not trying to advocate any preon models. My point is merely that you cannot declare them ruled out. You can only use experiment to show there is no substructure down to 10^-18 m. I would have thought this would be easily agreed upon, but yet people keep using over simplified statements which seem to claim otherwise, such as even your last statement:
"If the electron has substructure, it can not have substructure of the kind "point particles" described by todays physics. It must be something else, like strings."

I don't think current experimental data allows you to make such a sweeping general "disproof" of anything non string-theory. Can we at least agree on that?


EDIT: Huh? Why was granpa banned?

 

[malawi_glenn]

But spin is not derived by assuming any internal structure. Point particles and spin works totally fine mathematically - math is language of physics - not intuitive reasoning. Maybe it is our concept of size which we have from our daily (classical mechanics) life which is unaccurate to describe elementary particles?