Some comments on the original Kaluza-Klein theory (Q1113476)

In this short note the authors criticise the original assumption of 5- dimensional Kaluza-Klein theory that the geodesic equation in five dimensions gives rise to the Newton-Lorentz equation of motion for a charged body in four dimensions. Actually the Lorentz force arises in four dimensions if the particle's velocity in the fifth dimension is constant and equal to charge to mass ratio; this is a very restrictive and unattractive assumption. Moreover, a constraint on the electromagnetic field in four dimensions follows from the geodesic equation in \(d=5\) under the assumption. The constraint cannot be satisfied for a general electromagnetic field and is not gauge-invariant.