How do relativity and magnetism affect each other?

[Michio Cuckoo]

i apologise if the following statements may sound a little unscientific, or appear to beat about the bush.

Now if two positive charges are traveling together side by side with a certain velocity wrt to me, i will witness a magnetic attraction between them. But if i am traveling together with these charges; i.e. they are stationary wrt to me, i will not witness any magnetic force.

So whether you witness any magnetic force or not depends on your reference frame.

Light itself is an electromagnetic wave. But according to special relativity, the speed of light is independent of your reference frame.

So the existence of a magnetic force between 2 charges is dependent on your reference frame, but the speed of an electromagnetic wave is completely independent? Although both seem to be manifestations of the electric force.


This gets even more confusing when you realize the only way to explain the magnetic force between both positive charges is to use special relativity and lorentz contraction.

So its kinda like using the invariance of one electromagnetic property to demonstrate the variance of another electromagnetic property.

 

[vanhees71]

Classical (as well as quantum) electrodynamics is a Poincare-invariant theory and thus there can never be a contradiction with electrodynamics and relativity. Of course, you have to take the right perspective.

Here it's important to note that the distinction between electric and magnetic field is indeed observer dependent. The right covariant object is the antisymmetric Faraday tensor, describing the electromagnetic field as one entity.

 

[tom.stoer]

It is correct that the interpretation of effects is frame-dependent, but the effect isn't. If you start with charges at rest + you as an observer at rest what you will observe is an electric field i.e. an electric force (no magnetic field i.e. no magnetic force). For a moving observer (w.r.t. the charges) the electromagnetic field has to be transformed i.e. you will find a magnetic field as well; therefore you can interpret the effect as a mixture of electric force plus Lorentz force.

However the effect itself isn't frame dependent, i.e. the spacetime points defining the trajectories depending on the proper times of the charges are invariant objects (they become frame dependent only if you introduce frames i.e. coordinates).

 

[Muphrid]

The distinction between electric and magnetic fields is artificial, which is why a true treatment of EM theory in special relativity can avoid splitting the EM field (as expressed through the Faraday bivector) into electric and magnetic parts.

There is one electromagnetic field (in vacuum, at least), and it acts on currents, whether those currents be time-directed (stationary charges) or space-directed (what we would conventionally call a current).

 

[Nugatory]

Now if two positive charges are traveling together side by side with a certain velocity wrt to me, i will witness a magnetic attraction between them. But if i am traveling together with these charges; i.e. they are stationary wrt to me, i will not witness any magnetic force.

Yes. And the more you think about it, the odder this is. This oddity can be described in completely classical terms (you just did, in the quoted text), so predates SR. In fact, Einstein uses it in the introduction of his 1905 paper ("On the electrodynamics of moving bodies") as an example of the problem that he was solving.

Light itself is an electromagnetic wave. But according to special relativity, the speed of light is independent of your reference frame.

So the existence of a magnetic force between 2 charges is dependent on your reference frame, but the speed of an electromagnetic wave is completely independent? Although both seem to be manifestations of the electric force

Almost right... Replace the bolded words above with "electromagnetic field" and you'd have it. Mathematically, it's as vanhees71 says: the Faraday tensor describing the electromagnetic field is a single frame-invariant object that describes the electrical and magnetic fields that an observer at a given point with a given velocity will experience.