‎"EHRENFEST, PAUL. - THE ULTRAVIOLET CATASTROPHE.‎
‎Welche Züge der Lichtquantenhypothese spielen in der Theorie der Wärmestrahlung eine wesentlich Rolle ? (Which Features of the Quantum Hypothesis Play an Essential Role in the Theory of Heat Radiation).‎

‎Leipzig, Johann Ambrosius Barth, 1911. Later full cloth. Stamps on title-page. In ""Annalen der Physik"", Vierte Folge, Band 36. - VIII,1088 pp. and 4 plates. (Entire volume offered). Ehrenfest's paper: pp. 91-118.‎

Reference : 53367

‎First edition of the paper in which the term ""Ultraviolet Catastrophe"" appeared for the first time. ""Ehrenfest was one of the first to try to understand the significance of the strange new concept of energy quanta that Max Planck had introduced into physics in 1900 in his theory of blackbody radiation. In a series of papers culminating in his major study of 1911 (the paper offered), ""Which Features of the Quantum Hypothesis Play an Essential Role in the Theory of Heat Radiation?,"" Ehrenfest picked out the essentials of the early quantum theory and showed how they fit together. He proved rigorously that the energy of electromagnetic vibrations cannot take on all values - cannot vary continuously - if the total energy of the blackbody radiation in an enclosure is to be finite: Planck’s assumption that energy is a discrete variable was, therefore, logically necessary and not just sufficient. Ehrenfest also showed, by an analysis of Wien’s displacement law, that the ratio of energy to frequency was the only variable that could be quantized for a harmonic oscillator, if one wanted to maintain the statistical interpretation of entropy.""(DSB).‎