Einstein, Equipartition, Fluctuations, and Quanta

After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Einstein relied heavily on arguments from statistical mechanics in the most revolutionary of his famous 1905 papers, the one introducing the light‐quantum hypothesis. He showed that the equipartition theorem inescapably leads to the classical Rayleigh‐Jeans law for black‐body radiation and the ultraviolet catastrophe (as Ehrenfest later called it). Einstein and Ehrenfest were the first to point this out but the physics community only accepted it after the venerable H.A. Lorentz, came to the same conclusion in 1908. The central argument for light quanta in Einstein’s 1905 paper involves a comparison between fluctuations in black‐body radiation in the Wien regime and fluctuations in an ideal gas. From this comparison Einstein inferred that black‐body radiation in the Wien regime behaves as a collection of discrete, independent, and localized particles. We show that the same argument works for non‐localized quantized wave modes. Although nobody noticed this flaw in Einstein’s reasoning at the time, his fluctuation argument, and several others like it, failed to convince anybody of the reality of light quanta. Even Millikan’s verification of Einstein formula for the photoelectric effect only led to the acceptance of the formula, not of the theory behind it. Einstein’s quantization of matter was better received, especially his simple model of a solid consisting of quantized oscillators. This model could explain why the specific heats of solids fall off sharply as the temperature is lowered instead of remaining constant as it should according to the well‐known Dulong‐Petit law, which is a direct consequence of the equipartition theorem. The confirmation of Einstein’s theory of specific heats by Nernst and his associates was an important milestone in the development of quantum theory and a central topic at the first Solvay conference of 1911, which brought the fledgling theory to the attention of a larger segment of the physics community. Returning to the quantum theory after spending a few years on the development of general relativity, Einstein combined his light‐quantum hypothesis with elements of Bohr’s model of the atom in a new quantum radiation theory.

Sensitization of TiO2 by the symmetric cationic polymethine dye for the photocatalytic reduction of methylene blue

Using the spectral, electrochemical and energy transformation characteristics of the cationic polymethine dye (D) 2-[(1E)-1,3-butadienyl-]-1-(phenylmethyl)-benindolium borfluoride, it has been found that the dye can be applied as a highly efficient sensitizer of TiO2. An intensity of the initially narrow light adsorption band becomes wider and embraces practically entire visible and near IR zones as a result of application of the dye to the surface of TiO2. Due to this effect, a wider array of light quanta can potentially be involved in the photocatalytic transformations. Some new heterostructures (HS) of the type D/TiO2 have been developed and their photocatalytic activities were determined in the test reaction of reduction of methylene blue by formaldehyde for different dye contents and under various modes of irradiation. The schemes of the energy transformation initiated by the light with different wavelengths are proposed and discussed.

Light as a wave

This chapter introduces the basic concepts, such as light as a wave, a brief overview of Maxwell’s equations, the harmonic wave solution, spatial frequency, phasors, intensity, complex representation, the scalar approximation, and light quanta.

“Uma teoria experimental dos quanta de luz” de Louis de Broglie: uma tradução comentada

Este artigo apresenta e discute uma das comunicações escritas em língua inglesa, enviada a Philosophical Magazine pelo físico francês Louis de Broglie, em 1924, intitulada “A tentative theory of light quanta”. No referido trabalho, de Broglie traz uma síntese das ideias tratadas em outros três artigos publicados em francês e propõe a elaboração de uma teoria dualística para a luz, enquanto explicação para muitos fenômenos que não podiam ser corretamente explicados pelas teorias ondulatória e corpuscular, se isoladas. Além de discutir resultados já conhecidos pela comunidade científica de sua época, os trabalhos de de Broglie apresentam ideias totalmente originais, embora já contivessem conceitos que são cruciais para a explicação de muitos fenômenos conhecidos atualmente (a exemplo do laser). Acreditamos que este material possa servir de suporte para a discussão dos principais aspectos dos trabalhos iniciais de de Broglie, haja vista que algumas de suas ideias são ainda adotadas, atualmente, e constituem parte dos conteúdos de física moderna e contemporânea.

The Obligation to Choose

Chapter 1 explores Woolf’s writings up to the end of 1925 in relation to scientific ideas on wave-particle duality, providing the ‘retrospect of Woolf’s earlier novels’ which Michael Whitworth has suggested shows that she was working ‘in anticipation of the physicists’. The chapter as a whole challenges this idea of anticipation, showing that Woolf was actually working in parallel with physicists, philosophers, and artists in the early twentieth century, all of whom were starting to question dualistic models and instead beginning to develop complementary ones. A retrospect on wave-particle duality is also provided, making reference to Max Planck’s work on quanta and Albert Einstein’s development of light quanta. This chapter pays close attention to Woolf’s writing of light and her use of conjunctions, suggesting that Woolf was increasingly looking to write ‘both/and’ rather than ‘either/or’. Among other texts, it considers Night and Day, Mrs Dalloway, and ‘Sketch of the Past’.