# Relativistic Traffic

Relativistic Traffic

Length contraction with increasing velocity is predicted by special relativity, and helps explain the relationship between electricity and magnetism, as proposed by Einstein. Imagine two lanes of traffic moving in opposite directions at nearly the speed of light. An observer at rest in the reference frame of the road sees cars driving past that can apparently fit neatly into the available parking spaces. However, if the observer begins to move parallel to the road, the parking spaces and cars in one lane will appear to contract while cars in the other lane appear to lengthen.

It is expected that the cars either can or cannot fit into the parking spaces, yet different observers will reach different conclusions. An observer standing in the street will see a single car passing by each parking space at any given moment, while a moving observer might see two cars simultaneously passing each parking space or a single car occupying three spaces at the same time. How is this possible?

Now replace the roads with wires, the parking spaces with stationary positive charges, and the cars with negative charges flowing through the wires. Both wires appear to have roughly equal densities of positive and negative charges, and should therefore be electrically neutral; an observer would measure the Coulomb force between the wires to be zero. However, an observer moving alongside an electron (negative charge) in the lower wire will perceive a different scenario, in which the upper wire has a net negative charge and exerts a repulsive force on the lower-wire electrons. In a moving frame, the electrons in the wires therefore experience a repulsive electric force; how can this be reconciled with the lack of any electric force in the rest frame?