Albert Einstein did not use Maxwell's equations to predict the existence of electromagnetic waves or light. Instead, Einstein's contributions to physics were focused on developing the theory of relativity and his explanation of the photoelectric effect, which earned him the Nobel Prize in Physics in 1921.
Maxwell's equations, formulated by the Scottish physicist James Clerk Maxwell in the 1860s, describe the behavior of electric and magnetic fields and their interactions. These equations successfully unified the understanding of electricity and magnetism, demonstrating that electric and magnetic fields are intertwined and can propagate through space as electromagnetic waves.
However, it was Heinrich Hertz, a German physicist, who experimentally confirmed the existence of electromagnetic waves predicted by Maxwell's equations in the late 19th century. Hertz's experiments demonstrated that electromagnetic waves could be generated and detected, verifying the fundamental nature of these waves.
Einstein's contributions to physics were more focused on understanding the nature of light itself. In his 1905 paper on the photoelectric effect, he proposed that light consists of discrete packets of energy called photons. This concept was a departure from the classical wave theory of light and marked a significant step toward the development of quantum theory.
Einstein's work on the photoelectric effect, combined with the earlier discoveries and understanding of Maxwell's equations and electromagnetic waves, laid the groundwork for the field of quantum electrodynamics, which describes the interactions between light and matter at the quantum level.