Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above.
At time $t_1$ we simultaneously charge both the plates. This could be done by previously sending a light signal to a charging apparatus at each plate from a source located at the mid-point between them.
According to standard electromagnetic theory a retarded electric influence travels at the speed of light from $A$ to $B$ and vice-versa.
At time $t_2$ the electric influence from $A$ produces a force at $B$ and vice-versa.
There are two points that I would like to raise about this description:
- There are no reaction forces. It is as if a pair of boxers each punched the other on the nose simultaneously but neither felt a reaction back on their boxing glove.
- Once the electric influences have left the charged plates at time $t_1$, and before they have produced forces on the opposite plates at time $t_2$, they must exist "somewhere". That somewhere is the electromagnetic field.
Now consider the picture described in Fig $2$ below which includes both retarded and advanced interactions.
Again at time $t_1$ we simultaneously charge both the plates.
Now as well as a retarded electric influence that travels at the speed of light from $A$ to $B$ we also have an advanced electric influence which travels backwards in time from $B$ to $A$. Thus the force at plate $B$ at time $t_2$ is balanced by an equal and opposite force on plate $A$ at time $t_1$ (and vice-versa).
Now as soon as we charge the plates up we measure electric forces on them.
At first glance it seems that we have "action at a distance" but in fact we only have "reaction at a distance". In terms of spacetime, each plate at time $t_1$ is linked with the opposite plate at time $t_2$ in a manner that is consistent with the principle of locality provided we include advanced interactions.
As there is no delay between charging the plates and measuring forces then there is no time interval during which the influences could be said to be in transit in the form of an electromagnetic field.
Thus in this picture we have:
- Reaction forces
- No electromagnetic field
Could one perform such an experiment to see if charged plates immediately repel each other?