Simulating Angular Momentum and Torque in Particle Interactions

[darkdave]

I am simulating protons and electrons in a simulator that runs 1 femto seconds per second up to 1 second per second. So it can accurately show the passage of charge particles through space with data being updated on their displacement, velocity and acceleration.

However I am now adding in rotational data. This means that I need to simulate angular momentum and torque.

How do I do this?

For the electron do I have to calculate the torque at the classical electron radius at each pole due to magnetic interaction with other charged particle poles?

 

[mfb]

In a classical simulation, particles cannot rotate. If you want "rotating" particles, you need quantum mechanics - and if spin is relevant, I would expect that everything else should use quantum mechanics as well.

 

[darkdave]

I am aware of the quantum complication but at the same time i can still create a bhor model intepretation since i know the angular momentum of the particle and its mass and classical radius. I just need to know how to simulate the particles changing orientation due to torque caused by external magnetic fields. Wether i choose to show particles spinning or not is irrelevant to what I am asking since all i should be concerned about is the angular momentum of the particle.

 

[mfb]

The Bohr model works reasonably well for hydrogen-like atoms without spin, and nothing else, as far as I know.

I just need to know how to simulate the particles changing orientation due to torque caused by external magnetic fields.

For homogeneous fields, spin is irrelevant, and you just have the usual formula $F=q\vec{v}\times \vec{B}$.

 

[darkdave]

What is the vector B representing in that formula?

 

[darkdave]

ok i looked up that formula Force = charge velocity cross product magnetic field. The vector representing Magnetic field does it point to the center of the particle that acts like a magnet? For example is B pointing to the center of an electron if we are modeling 2 electrons that are interacting not just electrically but magnetically as well due to each of them having a magnetic field due to their intrinsic angular momentum

 

[darkdave]

Also what if the velocity of the particle is ZERO? Isnt the current orientation more relevant here?

 

[darkdave]

so think about it this way, we have 2 electrons each with a north and south magnetic pole and i want to simulate each electron turning its North Poles toward the other electron's South Pole. And each like poles repelling each other. So basically i need to know torque.

 

[mfb]

The vector representing Magnetic field does it point to the center of the particle that acts like a magnet?

No. A proper classical treatment would involve retarded potentials.
Don't forget the electric part, it will be retarded as well.

Also what if the velocity of the particle is ZERO?

Then the force due to the magnetic field is zero.

Isnt the current orientation more relevant here?

Electric current implies a non-zero velocity, I don't understand the question.

so think about it this way, we have 2 electrons each with a north and south magnetic pole

Electrons do not have poles. And they cannot rotate in a classical way.

 

[darkdave]

What about this article? Sounds to me electrons have a magnetic field of their own.

http://en.wikipedia.org/wiki/Electron_magnetic_dipole_moment

Also are you saying that an electron HAS NO ORIENTATION?

No. A proper classical treatment would involve retarded potentials.
Don't forget the electric part, it will be retarded as well.

Then the force due to the magnetic field is zero.

Electric current implies a non-zero velocity, I don't understand the question.

Electrons do not have poles. And they cannot rotate in a classical way.

 

[mfb]

What about this article? Sounds to me electrons have a magnetic field of their own.

http://en.wikipedia.org/wiki/Electron_magnetic_dipole_moment

This is their spin, and it is not a classical property of the electron.

Also are you saying that an electron HAS NO ORIENTATION?

Not in the way that could always say "it points in this direction" in a meaningful way.
Electrons are point-like. What is the orientation of a point?

 

[darkdave]

This is their spin, and it is not a classical property of the electron.

Not in the way that could always say "it points in this direction" in a meaningful way.
Electrons are point-like. What is the orientation of a point?

That link proves that Electrons have a MAGNETIC DIPOLE like MAGNETS. Meaning they have a NORTH AND SOUTH MAGNETIC POLE due to their "spin".

What I want to do is simulate electrons behaviour much like how real magnets behave when they are in close proximity. Their poles should point toward or away from other particle's dipoles.

 

[darkdave]

That link proves that Electrons have a MAGNETIC DIPOLE like MAGNETS. Meaning they have a NORTH AND SOUTH MAGNETIC POLE due to their "spin".

What I want to do is simulate electrons behaviour much like how real magnets behave when they are in close proximity. Their poles should point toward or away from other particle's dipoles.

Wiki says

The electron is a charged particle of charge (−e), where e is the elementary charge. Its angular momentum comes from two types of rotation: spin and orbital motion. From classical electrodynamics, a rotating electrically charged body creates a magnetic dipole with magnetic poles of equal magnitude but opposite polarity. This analogy holds as an electron indeed behaves like a tiny bar magnet. One consequence is that an external magnetic field exerts a torque on the electron magnetic moment depending on its orientation with respect to the field.

 

[mfb]

A magnetic dipole is not something with a north- and a south-pole. The dipole has an orientation, but that can be a superposition of multiple possible orientations, and the strength of the dipole, measured in an arbitrary direction, is always a fixed number (for electrons) and just the sign is variable. There is no way to model this classically.

What I want to do is simulate electrons behaviour much like how real magnets behave when they are in close proximity.

I understand that you want to do that. But electrons do not behave like macroscopic magnets.

 

[darkdave]

so what do you suggest is the best way to simulate electrons in as much classical way as possible?

I mean I know they don't have "spin": in the classic sense, but I can still make them spin based on known facts for example: the classical radius of the electron, the known mass and the known angular momentum. This way they behave in a way that is not true to reality but its still based on real data so intuitively it has some hidden truth.

What could I do for magnetic fields of the electron to do something similar to what i just proposed?

 

[mfb]

so what do you suggest is the best way to simulate electrons in as much classical way as possible?

That depends on the setup you want to evaluate.

I mean I know they don't have "spin": in the classic sense, but I can still make them spin based on known facts for example: the classical radius of the electron, the known mass and the known angular momentum. This way they behave in a way that is not true to reality but its still based on real data so intuitively it has some hidden truth.

Well, you don't have the g-factor there, for example.

What could I do for magnetic fields of the electron to do something similar to what i just proposed?

Depends on the setup.

 

[darkdave]

can you propose a setup?

So far I know I want to show the electron spinning based on the available data of known intrinsic angular momentum, mass and classical electron radius. Can you use that as a setup? And fill in any blanks for me at your discretion.

I basically want to show the particle changing orientation in real time in reaction to a neighboring particle's magnetic influence.

If it cannot be continuus then make compromises. I can make the particle perform discrete changes in orientation if need be. BUT I NEED A MODEL ANYKIND OF MODEL ASAP! :)

 

[mfb]

can you propose a setup?

I thought you want to calculate something. How can I guess what that is?

I basically want to show the particle changing orientation in real time in reaction to a neighboring particle's magnetic influence.

Are those particles slow (relative to the speed of light)? It might be possible to neglect any magnetic effects, as they have a relative influence of the order of v/c.

I doubt that the results will be good, but maybe you can add dipole-dipole interactions with the electron magnetic moment in a classical way. But if it does not influence anything, where is the point?

 

[darkdave]

There may be thousands of particles in the simulation, each with a magnetic dipole. Inwhich case the effects i assume would be multiplied?

 

[mfb]

Or they could average out.

Again, it is impossible to be specific if you are so vague about the situation you want to simulate.

 

[darkdave]

Or they could average out.

Again, it is impossible to be specific if you are so vague about the situation you want to simulate.

My point is either possibility exists in the simulator depending on how the particles are initialized. Using a first pson shooter as an analogy imagine if u were to say to me pistols do so little damage its not worth simulating in the game. Then ill say to u well if u do head shots with them up close to the enemy they will , then u come back and say, but the player may be wearing a helmet so its impossible to be specific if youre going to be vague, then ill say but he may not and there may be more friendly players on my team firing pistols at him simultaneusly...My point is the situations can vary, I am not being vague, I am saying that my simulation can simulate many initial posibilities that may or may not make magnetic dipoles signficant, so i want to simulate them to,cater for those scenarios where they are.

Imagine a game where there are thousands of levels u can choose to load. Sme of those levels are pistols only levels, some are not. So some levels make pistols significant and some dont. S i still need to design pistols in the game for the sake of some of those levels that make them significant.

The only thing i need specifically from u is which formulas to use to simulate elctrons as tiny magnets so that their orientations will change according to their interactions. Wether they are significant or not is not relevant here because the simulaotr will have many levels some of which will make them significant.

 

[mfb]

In every simulation, you have to make some approximations, and those approximations depend on the system you want to simulate. You won't find a simulation which can handle both proton-proton collisions in the LHC and vehicle collisions on a street in any reasonable way, as they require completely different analysis methods.

Do you want to simulate electrons in some material (which material? where? how?), electrons in a plasma (at which energy?), macroscopic charged objects, or whatever?

 

[darkdave]

I want to simulate protons and electrons as individual particles as close to the bhor model as possible. So to answer your question: perhaps as a plasma. Temperature is something that I will also simulate eventually but I will worry about that later, first I want to put in the equations for magnetic fields interactions between the particles. At the moment it already has gravitational as well as electrostatic simulation accurately, I know because the elctron orbits the proton in a stable orbit when simulating a hydrogen atom with the correct distance between the electron and proton and the correct relative velocity of the electron. And yes while gravity is weak in the femto scale it does cause movements in the particles. I know because i disabled the electrostatic functions and there were tiny movements due to gravity when i accelerated time beyone 1 fempto second per real second the interactions due to gravity increased to more significant levels.

Similarly I want to simulate magnetic interactions because they may be significant at diferent time accelerations than the default settings of 1 fempto second per second.

I am not worried about collissions at the moment I will deal with that later. At the moment collisions do nothing, the particles just bounce off each other like billard balls and conserve momentum. Yes I am using the relativistic version of momentum.

 

[mfb]

If you see effects from gravity at a timescale where you can simulate electrostatic interactions of elementary particles, something is wrong. The electrostatic forces between those particles is about a factor of 10⁴⁰ stronger than gravity. And I don't think you want to calculate 10^15 steps (to get 1 second with femtosecond steps) - and even if you did, rounding errors would completely dominate over gravitational effects.

I know because the elctron orbits the proton in a stable orbit

Without quantum mechanics, this indicates another problem: You are missing synchrotron radiation. You cannot get stable orbits with a proper classical treatment. And you influence modify Bohr orbits (added "manually") without quantum mechanics.

I am not worried about collissions at the moment I will deal with that later.

There are no collisions of point-like particles anyway.

 

[darkdave]

My simulation can accelerate time ^ 40 and beyond

'I told you i was doing a close to bhor model as possible. So I don't need synchrotron radiation at the moment, I'll worry about that when I want to do a more complex model closer to the quantum type. And believe me I DO HAVE stable electron proton orbits in my simulation... NO PROBLEM! I see the blue dot whirling around a red one and they don't fly apart unless i accelerate time to the point where there is data degredation of the simulation due to discrete steps being simlated being too long.

And yes there are no collissions thanks for pointing that out. So it's not something i need to worry about right away.

 

[darkdave]

Read carefully what i said please... I said if i disabled electro static interactions... then only i see tiny effects and only if i accelerated time can the effects be more significant.

And no i don't calculate 10^15 steps per second, i never said i do, i do however simulate about 30 steps per real second and in each of those real seconds only 1 fempto second will pass in the simulation, but this can be accelerated well beyond 1 fempto seconds hence causing the simulation to be less accurate for simulating stronger forces in smaller scales.

If you see effects from gravity at a timescale where you can simulate electrostatic interactions of elementary particles, something is wrong. The electrostatic forces between those particles is about a factor of 10⁴⁰ stronger than gravity. And I don't think you want to calculate 10^15 steps (to get 1 second with femtosecond steps) - and even if you did, rounding errors would completely dominate over gravitational effects.Without quantum mechanics, this indicates another problem: You are missing synchrotron radiation. You cannot get stable orbits with a proper classical treatment. And you influence modify Bohr orbits (added "manually") without quantum mechanics.There are no collisions of point-like particles anyway.

 

[mfb]

My simulation can accelerate time ^ 40 and beyond

But not with a reasonable model of electromagnetic interactions. Therefore, you can neglect gravity as soon as you model individual, charged particles. That's what I said, and nothing else.

'I told you i was doing a close to bhor model as possible. So I don't need synchrotron radiation at the moment, I'll worry about that when I want to do a more complex model closer to the quantum type.

Well, you cannot just pick some effects and ignore others like you want. The result will not resemble physics.

And believe me I DO HAVE stable electron proton orbits in my simulation... NO PROBLEM!.

It is a problem, as it gives wrong interactions between charged particles.

I see the blue dot whirling around a red one

... which leads to wrong positions for the particles as well.

 

[darkdave]

Yes I can, if you want to see the effects of one force alone and ignore the rest as a thought experiment.

As for the wrong positions... it's a simulation. A simulation of the Bhor model. It does not have to simulate real life just a model of it.

But not with a reasonable model of electromagnetic interactions. Therefore, you can neglect gravity as soon as you model individual, charged particles. That's what I said, and nothing else.Well, you cannot just pick some effects and ignore others like you want. The result will not resemble physics.It is a problem, as it gives wrong interactions between charged particles.... which leads to wrong positions for the particles as well.

 

[mfb]

Yes I can, if you want to see the effects of one force alone and ignore the rest as a thought experiment.

Sure, but the splitting of the electromagnetic interaction in separate "forces" is completely arbitrary.

As for the wrong positions... it's a simulation. A simulation of the Bhor model. It does not have to simulate real life just a model of it.

Just simulate what you want to simulate. If it does not have to be connected to real life, feel free to add anything you like ;).

 

[darkdave]

Gravitational forces are NOT electromagnetic.

And it's not arbitrary if you want to see the significance of one type of force vs another at various types of time increments.

Sure, but the splitting of the electromagnetic interaction in separate "forces" is completely arbitrary.

Just simulate what you want to simulate. If it does not have to be connected to real life, feel free to add anything you like ;).