Physics energy are no longer valid. The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics. Classical mechanics approximates nature as continuous, while quantum theory is concerned with the discrete nature of many phenomena at the atomic and subatomic level and with the complementary aspects of particles and waves in the description of such phenomena. The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory
Theoretical and experimental justification for the Schrödinger equation the clock in the observer frame. A wave-like picture of particles is thus consistent with special relativity. In fact, we now know that these relations can be succinctly written using special relativistic 4-vector notation: The relevant four-vectors are: The relations between the four-vectors are as follows: The phase of the wave is the relativistic invariant: The de Broglie hypothesis helped resolve outstanding issues in atomic physics. Classical physics was unable to explain the observed behaviour of electrons in atoms. Specifically, accelerating electrons emit electromagnetic radiation according to the Larmor formula. Electrons orbiting a nucleus should lose energy to radiation and