Let 2 electrons A and B be moving parallel with constant velocity $c/10$ in (near) vacuum without a strong gravity field (where $c$ is speed-of-light).
A and B create an electromagnetic field that is proportional to their speed. But then observer A measures ( approx ) the speed of both A and B , and likewise observer B measures ( approx ) the speed of both A and B.
A and B influence each other because of the electromagnetic field differently then if they stood still.
Assuming I made no mistake there , does this not violate relativity since :
- The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
- The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.
Where did I go wrong? Do the electrons move each other due to the field and does that make me loose the notion of uniform motion relative to one another so that the law does not apply? Or was i wrong about the dependency with speed upon magnetism and electricity ( and right hand rule ) if one uses a time-dilation correction?
In my question I picked $c/10$ to avoid very strong relativistic effects (as with $c/2$) so that classical electromagnetism is still quite good.
I'm confused here.
How to explain this apparent paradox?