Induced current and redefinition of electric and magnetic fields from non-compact Kaluza-Klein theory: An experimental signature of the fifth dimension

The field equations for gravitation and electromagnetism with sources in four dimensions can be interpreted as arising from the vacuum Einstein equations in five dimensions. Gauge invariance of the electromagnetic potentials leads to a “generalized” electromagnetic field tensor. We use the action principle to derive the equations of motion for free electromagnetic fields in flat spacetime, and isolate an effective electromagnetic current with a source that is purely higher-dimensional in origin. This current provides, at least in principle, a means of detecting extra dimensions experimentally.