Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1932 · 201 citations · 0 references
Natural SciencesPhysicsPhysics EducationQuantum MechanicsTheoretical PhysicsElementary ParticlesModern PhysicsPhilosophy Of PhysicsQuantum PhysicsRelativistic PhysicsRelativistic Quantum MechanicsQuantum Physics CurriculumRelativistic Dynamics Of ParticlesRelativistic Wave Equations
Quantum theory’s progress has hinged on Bohr’s Correspondence Principle, which links classical and quantum descriptions, yet classical electrodynamics shows that particle interactions are mediated by finite‑speed waves rather than instantaneous energy terms. The goal is to incorporate relativistic electrodynamics into quantum theory by developing a relativistic quantum mechanics that replaces the Correspondence Principle. Heisenberg’s 1925 formalism translated classical equations into quantum mechanics, quantitatively establishing the Correspondence Principle and enabling a Hamiltonian‑based quantum theory for interacting particles.
The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approximation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.