Help me with a calculation

[Kygron]

I read something about spin in electrons and I wanted to try an idea I have. Unfortunatly I don't know many of the formulas I need, so I'm asking for help.

 

Here's the problem. I want to account for spin by having the electron actually spinning. I figure the fastest it can go is if it were orbiting a black hole. I want a small BH so I'm assuming its mass is the mass of the electron in question. I'll also assume the electron is moving with velocity = c, unless there's a more appropriet velocity someone knows of. For ease of calculation let's use a static BH, non-spinning, non-charged (I'd love to use a BH spinning and charged, but I doubt the formulas will even be legible for me).

 

The electron will orbit at the photon sphere, 3/2 the horizen radius. I don't know how to calculate this circumference. I haven't looked up how to calculate angular momentum in this system, nor how to relate it to spin. Lastly I'd want info about the EM field strength, but that shouldn't be difficult once we have the other info.

 

Anyone know how to help?

[Martin]

The electron will orbit at the photon sphere' date=' 3/2 the horizen radius. I don't know how to calculate this circumference. I haven't looked up how to calculate angular momentum in this system, nor how to relate it to spin. ...[/quote']

 

for general education about BH here is Andy hamilton website

http://casa.colorado.edu/~ajsh/schw.shtml

 

he has a lot of interesting information which you may have seen

like if R is the schw. radius then\

3R is the radius of the smallest stable circular orbit

he gives orbit speeds

he explains about unstable circular orbits, closer in.

 

it is easy to calculate the schw. radius for BH with mass M

 

you just say GM/c^2

 

that is newton gravitational const G, times the mass, divided by the square of the speed of light.

 

the way it works out is that a solar mass Bh would have schw. radius of about 3 kilometers

 

I am sleepy now but if you want help calculating a Schwarzschild radius for some mass M then ask tomorrow and if I am around I will help

[quick silver]

i read your post, and i too am on a quest to find a few mathamatical formulas. try looking at the hisenburg uncertanty principle. it tells you that you can only know one or the other. either speed or direction. you can know what you are looking for, lets say direction, with a 90% acuracy and speed with a 10% acuracy. you may be able to find it under a quantum physic site. that would be important in your case.

 

schrodinger is another person you may want to look up. but, as for formulas, i don't have any with me. nuclear and quantum physics may give you the information that you need.

 

signed,

B. Bourget

 

PS. you don't happen to have a formula for electromagnitism and light? if you do, look up quick silver and post a reply to my thread. thank you.

[mezarashi]

Your Schwarzschild ambition is impressive, I thought I'd just light to drop in my two cents, though I might be wrong, doesn't an "electron spin" refer to its quantum state. The best analogy is to visualize electrons as round balls, and the spin is the revolving around itself.

[swansont]

Your Schwarzschild ambition is impressive, I thought I'd just light to drop in my two cents, though I might be wrong, doesn't an "electron spin" refer to its quantum state. The best analogy is to visualize electrons as round balls, and the spin is the revolving around itself.

 

Spin is intrisic angular momentum. The problem with modeling it as an actual spin, as in a rotating ball, is that the electron is a point particle and you get into a lot of trouble trying to assign it a size, charge distribution and rotation speed. Classical physics fails to address the issue. It is a purely QM effect.

[Kygron]

hisenburg uncertanty principle

 

I purposely ignored it. The thing I read that led to this showed a conceptual planetary model of a hydrogen atom and calculated the electron's angular momentum. They clearly stated that the QM model was more complex, but for the basic math the planetary model was sufficient. I was hoping to do the same general thing.

 

I've temporarily abandoned this quest, because in one of the references I looked up I found that the electron had been modeled as a spinning, charged black hole as soon as that BH model was available. This was somewhere in the '60's - '80's, I forget exactly, but it was enought to discourage me since I hadn't heard of it it prob'ly never went anywhere. I'll have to look up that model again when I'm feeling up to it.