Beta Particle Radius...

[Orion1]

...

[Yustas]

Originally posted by Orion1


What is the exact equasion that predicts the semi-classical Beta Particle Radius?

Does anyone here have a 'standard model' based upon the semi-classical Beta Particle Radius?

Please post your graphic models if you have some....



In classical E&M the classical radius of electron (beta-particle) is found by equating the electrostatic potential energy of the point-like electron to mc^2, i.e. rest energy of an electron. Since the energy obtained as an integral over energy density diverges on the lower limit, the integral is cut-off at some minimal r_e, which is defined as a classical radius of electron.

Since this quantity is rather artificial, no one is basing any theories on this. In fact, in the Standard Model of elementary particles the electron is pointlike. No experiment has revealed any structure of an electron, so the concept of non-pointlike electron is not really needed at the moment.

[Loren Booda]

Isn't the "semi-classical Beta Particle Radius" the same as the Compton wavelength of the electron?

[Yustas]

Originally posted by Orion1

The Beta Particle is a 'pointlike' particle, however, it is not an infinitesimal. There is a law of physics which states that anything with mass must occupy space. Therefore, in order to occupy space, it must posess 'volume', and therefore have a radius and density.

M = pV p = \frac{M}{V}

The Semi-Classical Beta Particle Radius is predicted around:
r_e =~10^-18 m


Stating that the particle is pointlike means that the particle is pointlike, i.e. has no volume. There is no such law that anything with mass must occupy volume -- such logic might get you in trouble with special relativity which is used in quantum field theory to describe particles (fields). In modern theories (like the Standard Model) all fermions acquire mass via Higgs mechanism -- kinda like electron acquires an "effective mass" moving through a cristal.

I think what you are looking for is an explanation of electron scattering experiments that looked for internal structure of an electron. The way those experiments are interpereted is very similar to the interpretation of electro-nucleon scattering experiments. In other words, one is probing the so-called charge formfactor of an electron, which is related to a "charge radius" of a particle (in fact, its just a Fourier transform). In the Standard Model this formfactor is just a delta-function, reflecting the fact that electron is pointlike and has no internal structure. However, in some models which describe physics beyond the Standard Model (there are models that propose compositness of quarks and leptons, for example preon model) elctron is not pointlike but a boundstate of several other subparticles. In those models charge formfactor is not a delta-function (just like nucleon formfactor in quark model), but some other function. It can be computed, but the result depends on the model and is certainly not semi-classical.

If this is what you are looking for, check any introductory book on high energy physics (like Perkins) and read the chapter about phenomenological descriptions of fomfactors of a nucleon. The same expressions would work for an electron.

[Loren Booda]

Orion1,

Is the "classical beta particle radius" the same as the electronic black hole radius?[a)]

[Yustas]

I'm sorry, I thought you really wanted to learn about this...

[selfAdjoint]

Orion, you are the one who is not going to impress anyone who knows anything about real physics. Saying physics has to go your way because "it's unreasonable" that a massive object have zero volume is just ignorant.

Try this view: there are no particles, just force fields and waves. Some of the wavy things can acquire the attributes of mass (inertia and gravitation) by interacting with other wavy things. There is no "matter" at the quantum level. Matter is an illusion of our scales of measurement.

That's not the whole story but it's good to think about things that way for a while to get yourself out of the "Matter Myth".

[Norman]

I may regret getting involved in this one, but here goes:

quote:
three fundametal laws of physics:
M=pV,...

First of all these are the same equation, not three different equations, so they are not three different laws.
Second of all, p=M/V is for average density, which is often times not a very good approximation.
Third, why is this fundamental? It is merely a definition of a quantity that is usefull, average density. It is in fact not fundamental, because we can always replace it with mass and volume, which, in my eyes, are the much more fundamental notions.


quote:
I am only a finite mortal attempting to comprehend the infinite, immortal Universe. If anyone's finite journey can exceed the infinite, I will be sure not to underestimate them.

I don't have a single clue of what this is supposed to mean (maybe a catch all in the 'small' possibility that you may be wrong), but it scares me that you would end a post in which you make definite statements and talk about reality and fact, then say this. It really doesn't lend you much credibility appealing to the fact that you are merely a mortal, since we all are.