Does relativity affect velocity dependent events?

[Wittyname6]

I've heard that a changing magnetic field creates an electric field and vice versa. So if shoot an electron in a straight line, it would create a magnetic field in a circle around it.

Let's say the electron is moving quickly down a road. But there is another particle moving exactly the same speed as the electron beside it. Relative to this particle, the electron is not moving at all, but relative to an observer on the road, it is moving very quickly. Would this not mean that from the particles perspective, there is no field being created, and the observer on the sidewalk experiences some sort of field?

 

[WannabeNewton]

Yes. But the better way to think about it is that there is just an electromagnetic field. How we decompose this electromagnetic field into an electric part and a magnetic part depends on the frame of reference.

The usual notion of time-varying electric fields "inducing" rotational magnetic fields and time-varying magnetic fields "inducing" rotational electric fields often leads to conceptual issues (or even conceptual breakthroughs) for people first learning electrodynamics simply because the "induction" language works in an approximate framework. See for example this recent thread: https://www.physicsforums.com/showthread.php?t=759414

 

[Dale]

Would this not mean that from the particles perspective, there is no field being created, and the observer on the sidewalk experiences some sort of field?

You have reasoned exactly correctly. As WBN mentioned, the "cleanest" way of looking at Maxwell's equations is not in terms of separate vector electric and magnetic fields, but rather in terms of a single tensor electromagnetic field.

 

[Nugatory]

Let's say the electron is moving quickly down a road. But there is another particle moving exactly the same speed as the electron beside it. Relative to this particle, the electron is not moving at all, but relative to an observer on the road, it is moving very quickly. Would this not mean that from the particles perspective, there is no field being created, and the observer on the sidewalk experiences some sort of field?

From the particle's perspective, there is no magnetic field. There is still an electrical field; there has to be because the particle is sitting right next to a stationary charged electron, and that charge has to create an electrical field.

The sidewalk observer experiences both a magnetic and an electric field, both varying with time as the electron moves closer, passes, starts to move away, and eventually recedes to infinity.

As others have already pointed out, this whole problem is easier to solve if you think in terms of a single electromagnetic field instead of separate electrical and magnetic fields.