Correspondence and Commensurability in Modern Physics (a Study of the Compton Effect)
Keywords: Compton effect, correspondence and commensurability, non-relativistic particle, mathematics
The concepts of correspondence and commensurability are studied in the light of the Compton effect. We compare the Compton formula for the photon-electron scattering with another derivation in which the electron is considered as a non-relativistic particle. Although based on a less general theory, the second derivation leads to a formula which seems to be more general than the original Compton scattering formula. We show that this generality is only apparent. This circumstance means that the inclusion of additional terms does not necessarily imply more generality. We discuss some difficulties with the concepts of commensurable theories and correspondence, in particular those involving the passage from one theory into another through the concept of a limit of mathematics. We conclude that the problem goes beyond the mere mathematical limit.