2003/07/28 by Field, J. H.
#Classical Physics (physics.class-ph) #FOS: Physical sciences #Physics Education (physics.ed-ph)
paper · doi:10.48550/arxiv.physics/0307133
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector electromagnetic potential plays a crucial role, of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field in terms spatial derivatives of the 4--vector potential. The time component of the relativistic generalisation of the Lorentz force law is discussed. An important physical distinction between the space-time and energy-momentum 4--vectors is also pointed out.