Derivations of black-body radiation formula and their implication to the formulation of modern physics

Black-body radiation, or Hohlraumstrahlung or Wärmestrahlung, is a duck that laid gold eggs in modern physics. In a sense it is the cradle for modern physics. The significance of black-body radiation lies in the fact that it is the only physical situation involving all the three universal constants, i.e., c, k and h. Being immune to experimental errors, it provides a norm for the radiators, and serves the standard for absolute temperature. The derivation of the spectral distribution formula sets an exemplar model for physics research. The correct spectral distribution formula has been derived by Planck, Debye, Ehrenfest, Pauli, Bose and Einstein based on various distinct assumptions in the early period of last century, and even derivations from the theory of relativity have been obtained in recent years, which lead to a lot of modern physics establishments such as quantum mechanics, the quantum theory of solids, stimulated emission of radiation, quantum statistics, relativistic statistics, etc. A detailed review of the study of black-body radiation problem brings us to a voyage through the legendary history of modern physics helping us get the feel of doing physics, for instance, the author was inspired to find a new simple proof for the necessity of radiation energy localization.