Causality means that for any two events A,B, there has to exist an ordering that says whether A can influence B or B can influence A, and in the normal examples with "time", the ordering is the condition
$$ t(A) < t(B). $$
If the condition above is satisfied (i.e. if A precedes B), then A may influence B.

An ordering - a transitive relation - has to exist in order to avoid logical contradictions. If the relationship were not transitive, for example, it would be possible to find triplets of events A,B,C such that A influences B, B influences C, C influences A. That would be a "closed time-like curve" and it would lead to logical inconsistencies because in general, there would be no way to choose the outcomes of the events A,B,C so that all the three implications are preserved.

Those contradictions are avoided in any causal theory because the outcome of event A (in a causal and deterministic theory, to be specific) is never calculated from conditions at event B if A is the cause of B (if A precedes B). It's the other way around. Causality makes it clear which data are "inputs" and which data are their "outputs", so because of this orientation, there can't be any contradiction.

In a geometric setup, the comparison of a coordinate associated with the events is the only way how to produce ordering as a relationship. We call this coordinate "time".

In special (and similarly general) relativity, the condition for A to be able to influence B becomes sharper - $t(A)<t(B)$ has to hold in all reference frames which means that B has to belong to the future light cone of A.

Actually, the electric and magnetic fields from one *combined* tensor called the electromagnetic field tensor. This is a rank-2 tensor and takes the form*
$$
F^{\mu\nu}=\left(\begin{array}{cccc}
0 & -E_x & -E_y & -E_z \\
E_x & 0 & -B_z & B_y \\
E_y & B_z & 0 & -B_x \\
E_z & -B_y & B_x & 0
\end{array}\right)
$$
It has the following properties:

- It is anti-symmetric (so $F^{12}=-F^{21}$)
- It is traceless
- It has 16 elements, but only 6 distinct values
- When multiplied by its dual tensor ($G^{\mu\nu}$) it gives a Lorentz invariant value of $4\mathbf{B}\cdot\mathbf{E}$
- The inner product, $F_{\mu\nu}F^{\mu\nu}=2(B^2-E^2)$, is also a Lorentz invariant

You can also derive Maxwell's equations through the tensor by applying $\partial_\mu$ to it. Gauss's law and Ampere's law come from
$$
\partial_\mu F^{\mu\nu}=4\pi J^\nu
$$
where $J^\mu=\left(\rho,\,\mathbf{j}\right)$ is the four-current. The magnetic Gauss' law and Faraday's law come from applying the Bianchi identity to get
$$
\partial_\gamma F_{\mu\nu} + \partial_\mu F_{\nu\gamma} + \partial_\nu F_{\gamma\mu}=0
$$
Or more concisely,
$$\partial_{[\mu}F_{\nu\gamma]}=0$$

_{I am an astrophysicist, so I use cgs units; in SI, all electric fields have a factor of $1/c$.}

## Best Answer

As far as the electric and magnetic fields go, neither one is the cause/effect of the other changing, since the very presence of an electric or magnetic field depends on your frame of reference. Rather there is a single quantity changing, the field strength tensor, $F_{\alpha\beta}$. A change in one doesn't

causea change in the other, simply one thing changes.Causality is a extremely gigantic subject, and people have different interpretations of what it means. I think a fairly classical description is that events can only be causally connected, if the event under consideration as the cause is in the past light cone of the event that is considered the effect, and visa versa (except with the future light cone). Then causation is determined primarily through inductive reasoning and correlation, though the arrow need not be $\iff$, rather I believe the necessary condition is correlation, that is $\text{causation}\implies\text{correlation}$. More frankly, if you flip the light switch and a light comes on and those two events are in each others light cones, and you inductively verify after numerous different experiments that those two events are correlated, then you imply causation (note it's a deductive logical fallacy, but its completely legitimate as an inductive method, vis-'a-vi by the method explained above). Though, you wouldn't do that with the light would you...

I hope this helps.