# Can we combine electric and magnetic fields?

It is known that electric fields and magnetic fields are really the same thing viewed from different frames of reference (following from Special Relativity), similar to space and time. Now space and time do exist together to create the so called fabric of space time, so do electric fields and magnetic fields take part in something similar? Furthermore, is it possible to merge different types of physical phenomena, such as time and magnetism?

You have some confusion, let me try to clarify...

In Relativity, electrodynamics and magnetodynamics can be conceived as the manifestation of the same kind of "interaction" (this is a more modern term, but think of it as the way through two particles comunicate): electromagnetism. The four-dimensional formalism, proper of Relativity, allows us to perceive this in such a clear way, through the electromagnetic tensor $F_{\mu\nu}$. Indeed, since it is a tensor, by changing reference frame/coordinates with a boost (Lorentz transformation) it changes it this way: $$F'_{\mu\nu}=(\Lambda^{-1})_\mu^\alpha(\Lambda^{-1})_\nu^\beta F_{\alpha\beta},$$ where $\Lambda$ is a matrix implementing a boost and repeated indices are summed.

Even without taking into account Maxwell equations, you see that a change of coordinates/frame mixes the components of our tensor. So electric and magnetic fenomena become a part of a whole: electromagnetism.

Exactly the same happens to the position 4-vector, indeed $$x'^\mu=\Lambda^\mu_\alpha x^\alpha$$ and this is why one may say that Lorentz transformations mix space and time components, making them part of a unique element: space-time.

So don't get confused about the words "they become a whole", basically what they mean is that they are no more two independent fenomena but they become intrinsic bounded together, depending on which coordinates you use or in which frame you are.

I went quite fast, but I hope to have been clear enough...

• I do see the difference now. Please excuse me, I am not so familiar with the Lorentz transformation, but is it possible to apply the Lorentz transformation to mix different interactions such as electromagnetism and space-time? – Supernova Jan 6 '18 at 2:46
• Space-time in SR is not an interaction... Your question is a bit meaningless. But somehow I can answer yes. If you take the energy momentum tensor and you change coirdinates your energy and your momentum components change as well. Since they have a meaning of energy/momentum through a direction, you are mixing EM and space-time. But this is REALLY borderline and also not pretty meaningful. So I would say to ignore this point of view :) – Bellem Jan 6 '18 at 9:07