[thebrain13 (OP)]

how does special relativity imply magnetism from electrostatics?

[lightarrow]

how does special relativity imply magnetism from electrostatics?

http://chip-architect.com/physics/Magnetism_from_SR.pdf

Simplyfing (a lot):
In your laboratory's frame of reference you have a charged particle (for example, positively charged) moving along an uncharged conductive thread, with speed v. The number of positive charges in the thread equals the number of the negative, so the coulombian force on the particle is zero.

Now you apply a voltage to the thread so that an electric current flows; for example electrons inside the thread moves, and the positively charged ions stays still. Still for semplicity, let's imagine the particle's speed equals the electrons speed in intensity, direction and versus. Then the particle will see the electrons as still, but the positive ions moving at -v, so they are Lorentz contracted along the thread, so theyr relative distance from each other is contracted, and this means theyr linear density increases.

So the particle see more positive ions (per unit distance) than negative electrons and it will experience a coulombian repulsion from the thread.
From laboratory's frame of reference this force is called "Lorentz Force" and is attributed to a magnetic field B: F = qvΛB where Λ means vectorial product.

[Soul Surfer]

That is fascinating!  I had always thought of electricity and magnetism as direct properties of still and moving charges as in Faradays experiments long before relativity and had not relised that they were linked via relativity in that way.

It is quite obvious when you see it!  The speed of light just slots in there as part of the standard electromagnetic radiation equations which are just like the relatavistic ones.

This helps a great deal with my understanding of the gravitomagnetic effect associated with relatavistic motions around gravitating bodies.  A subject that I am trying to get a better grip on

[lightarrow]

That is fascinating!  I had always thought of electricity and magnetism as direct properties of still and moving charges as in Faradays experiments long before relativity and had not relised that they were linked via relativity in that way.
It is quite obvious when you see it!  The speed of light just slots in there as part of the standard electromagnetic radiation equations which are just like the relatavistic ones.

Yes, this is one of the (spectacular) reasons SR it's not simply "a theory", as some detractors would like to make others think.

[rosy]

Yes, a lot of what drew Einstein and others (people like Lorenz were almost there) to develop relativity was an attempt to unify electricity and magnetism.




[I've just noticed this post. It ain't mine, so I assume it belongs to Daveshorts. Oops. Failed to log off again.]

[lyner]

So the particle see more positive ions (per unit distance) than negative electrons and it will experience a coulombian repulsion from the thread.
From laboratory's frame of reference this force is called "Lorentz Force" and is attributed to a magnetic field B: F = qvΛB where Λ means vectorial product.

I can't quite picture your model here. The force from the vector product would be at right angles(?) to the other two.
Have you a reference (not too hard) that I could look up?

Also, charges move VERY slowly in metals. SR doesn't usually have much of an effect at 0.001m/s.

[lightarrow]

So the particle see more positive ions (per unit distance) than negative electrons and it will experience a coulombian repulsion from the thread.
From laboratory's frame of reference this force is called "Lorentz Force" and is attributed to a magnetic field B: F = qv?B where ? means vectorial product.

I can't quite picture your model here. The force from the vector product would be at right angles(?) to the other two.
Have you a reference (not too hard) that I could look up?

If the vector A is this way ↑ and B this way → then the vectorial product AΛB is perpendicular to this plane of the screen and goes inside the screen; if instead: A→ and B↑ then AΛB comes out of the screen.
If the electrons current (negative charges!) in the thread is this ------------> then the field B is this way ↑ between the thread and you, and this way ↓ behind the thread. The opposite versus if the current is of opposite sign (electrons going to the left, or positive charges going right).
So, if the particle is between the thread and you, its charge is positive and the velocity is this →, then you have:  v→  B↑
So the force comes out of the screen, and the particle is rejected off the thread.

Also, charges move VERY slowly in metals. SR doesn't usually have much of an effect at 0.001m/s.

But in this case it does! (Because the number of charged particles inside a conductor is very high). This is an example of the fact SR doesn't only apply on Very fast objects!

[Mr Andrew]

So how does the gravitomagnetic effect work then?  If I'm moving very quickly over a flat plane of matter then the density will increase and I will be attracted to it, right?  OH, so that's how the Podkletnov anti-grav machine works (in theory)!...but wait, spinning something very fast should generate an attraction to it, not a repulsion?!?!  So how does the Podkletnov machine work then?

[lyner]

Also, charges move VERY slowly in metals. SR doesn't usually have much of an effect at 0.001m/s.

It's just an example of multiplying a very small quantity  by a big number to give  quite a big number.
It's counter-intuitive because we, as you say, usually associate SR with high speed. The Lorenz formula  works at all speeds, though.

The force from the vector product would be at right angles(?) to the other two.

The force between two parallel wires is  such as to pull them together (or push apart).  The SR treatment of the situation just predicts a bit more  more repulsion / attraction because of the apparent imbalance in the number of 'perceived' electric charges.
If you only had positive charges - say  1coulomb's worth on two objects, one metre apart, the force would be immense.  In reality, we only deal with surplus  / unbalanced charges  so electrostatic forces are usually small - as are the forces between conductors, too.

This, alternative approach does away with the need for vector products - the forces are reduced to Coulomb forces.  The results don't disagree with the classical results - it's just a different way of getting to them.

[lightarrow]

So how does the gravitomagnetic effect work then?  If I'm moving very quickly over a flat plane of matter then the density will increase and I will be attracted to it, right?  OH, so that's how the Podkletnov anti-grav machine works (in theory)!...but wait, spinning something very fast should generate an attraction to it, not a repulsion?!?!  So how does the Podkletnov machine work then?

General Relativity is still mostly out of my understanding.

[lightarrow]

Also, charges move VERY slowly in metals. SR doesn't usually have much of an effect at 0.001m/s.

It's just an example of multiplying a very small quantity  by a big number to give  quite a big number.
It's counter-intuitive because we, as you say, usually associate SR with high speed. The Lorenz formula  works at all speeds, though.

The force from the vector product would be at right angles(?) to the other two.

The force between two parallel wires is  such as to pull them together (or push apart).  The SR treatment of the situation just predicts a bit more  more repulsion / attraction because of the apparent imbalance in the number of 'perceived' electric charges.
If you only had positive charges - say  1coulomb's worth on two objects, one metre apart, the force would be immense.  In reality, we only deal with surplus  / unbalanced charges  so electrostatic forces are usually small - as are the forces between conductors, too.

This, alternative approach does away with the need for vector products - the forces are reduced to Coulomb forces.  The results don't disagree with the classical results - it's just a different way of getting to them.

Fascinating, isnt'it?

[dkv]

Here is my highly controversial theory:
(note that a speed vector consisting only of electrons without external force can be disturbed easily and entropy says such a system wont last long)
The Natural Magnetism can not always be explained using the above principle(Earth also has magnetism and there are thories which explain but shift in Magentism remains unexplained.!!).
I will take a ordinary example :
Inside a naturally occuring Magnet there is nothing which can be considered be relativity driven Electro -Magnetism. The spins of electorns are directional but we can only think of electron as probability wave. Which means there is chance of electron completing a spin in a specified time...
(You can ask me why?)
so they can easily go out of synchroization ... (as this is the case with most other materials)
Electrons are waves .. and not particle (unless the wave function collapse takes place)
When in flow the electrons appear to cricling an infinite circle.

The naturally occuring Magnet do not carry such currents otherwise there would have been no need to
create batteries.. Without EMF the electons can not move in a Vector.

However under the probability scheme one can consider the probabilistic distribution as spin oriented.
Resulting in Short lived Magnetism.
If two synchronous electrons randomly come togther (Pauli's exclusion principle)
they form a pair AND Behave as indepedent particle.(with wave properties)  In other words the two electrons find common oreintation...(there is no meaning attached to individual electron here)

This explains electron bonding as well as proton bonding.(Similar things come together)
The electron proton interactions do not take place unless there is an external force...

When another such pair(E-Pair) find common orientation they behave as another physical object.

Leading to sychronization of all the atoms inside the Magnet ...THEREFORE the magnet has directional property ... AND IT IS THE LARGET PARTICLE...
IT HAS UNIT PROPERTY. If you break Magent you still get Magent.

BUT how this happend ? What lead to creation of these
large atomic particles(rememeber we can not talk of magnet as consisting of individual atoms any more.)
The impact on one atom is felt on all the atoms of Magnet.

In my opinion there was very small chance of such an event ...And it required a highly favourable conditions to synchronize.
Until the time of solidification these pairs maintained there orientation ...
IT IS A CASE OF NATURALLY OCCURING QUANTUM SUPERCONDUCTOR.