first compute the derivatives of the retarded time. Taking the derivatives of both sides of its defining equation (remembering that ): Differentiating with respect to t, Similarly, taking the gradient with respect to and using the multivariable chain rule gives It follows that These can be used in calculating the derivatives of the vector potential and the resulting expressions are These show that the Lorenz gauge is satisfied, namely that . Similarly one calculates: By noting that for any vectors , , : The expression for the electric field mentioned above becomes which is easily seen to be equal to Similarly gives the expression of the magnetic field mentioned above: The source terms , , and are to be evaluated at the retarded time. Implications The study of classical electrodynamics was instrumental in Albert Einstein's development of the theory of relativity. Analysis of the motion and propagation of electromagnetic waves led to the special relativity description of space and time. The Liénard–Wiechert formulation is an important launchpad into a deeper analysis of relativistic moving particles. The Liénard–Wiechert description is accurate for a large, independently moving particle (i.e. the treatment is "classical" and the acceleration of the charge is due to a force independent of the electromagnetic field). The Liénard–Wiechert formulation always provides two sets of solutions: Advanced fields are absorbed by the charges and retarded fields are emitted. Schwarzschild and Fokker considered the advanced field of a system of moving charges, and the retarded field of a system of charges having the same geometry and opposite charges. Linearity of Maxwell's equations in vacuum allows one to add both systems, so that the charges disappear: This trick allows Maxwell's equations to become linear in matter. Multiplying electric parameters of both problems by arbitrary real constants produces a coherent interaction of light with matter which generalizes Einstein's theory which is now considered as founding theory of lasers: it is not necessary to study a large set of identical molecules to get coherent amplification in the mode obtained by arbitrary multiplications of advanced and retarded fields. To compute energy, it is necessary to use the absolute fields which includes the zero point field; otherwise, an error appears, for instance in photon counting. It is important to take into account the zero point field discovered by Planck. It replaces Einstein's "A" coefficient and explains that the classical electron is stable on Rydberg's classical orbits.