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The Conception of Photons 5 Towards the Birth of the – Part II Quantum

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The Conception of Photons 5 Towards the Birth of the – Part II Quantum The conception of photons Urjit A. Yajnik keywords : Photons, light quanta, birth of the quantum, Planck spectrum, photoelectric effect, quantum indistinguishability, Bose-Einstein statistics, Glauber-Sudarshan representation, principle of linear superpo- sition. Contents 1 Prologue 3 1.1 From an embarrassment to a paradigm shift . .......... 3 2 The antecedents 4 2.1 Thequietbeforethestorm .. .. .. .. .. .. .. .. ...... 4 2.2 Thechinksinthearmour ............................ ..... 5 3 The stage is set 6 3.1 Achallengetotheorists . .. .. .. .. .. .. .. ....... 6 3.2 StatisticalMechanics. ........ 10 3.3 Anactofdesperation .............................. ..... 11 arXiv:1701.06867v2 [physics.hist-ph] 25 Jan 2017 4 The light quantum proposal 13 4.1 Aheuristicviewpoint ............................. ...... 13 4.2 Entropy as a hint to discretisation . .......... 14 4.3 Photoelectriceffect............................... ...... 15 1 5 Towards the birth of the quantum 18 5.1 SeedsofthedreadedrulesoftheQuantum? . .......... 18 5.2 Opportunismoftheorists . ....... 19 5.3 A curious case of inadequate diffusion of scientific knowledge?............. 20 5.4 Confirmation from far away, far later . .......... 21 6 Quantum Mechanics 23 6.1 Ideaswhosetimehadcome .. .. .. .. .. .. .. .. ..... 23 6.2 States and quanta : the essence of quantum physics . ............ 24 7 Conclusion and outlook 26 7.1 Finalstoryoflight ............................... ...... 26 7.2 TheenigmaticQuantum. .. .. .. .. .. .. .. .. ..... 27 2 Part I of its own only if the contemporary people ac- cept it and propagate it as interesting. There Planck, Einstein, and key events in the early are many ideas for which it is said their time history had come, and in this case several different peo- ple independently think of the same thing within Abstract : In the year 1900 Max Planck was a short period of time. Einstein’s was an excep- led by experimental observations to propose a tional case to have come up with not one but strange formula for the intensity as a function of several different profound ideas within just a few frequency for light emitted by a cavity made in a years’ time and to have articulated them within hot substance such as a metal. lPlanck provided a single year, 1905, and to have received a quick a derivation based on peculiar properties to be acceptance for them. There is some evidence obeyed by the emitters and absorbers in the cav- that Special Relativity was being contemplated ity. I attempt to point out some nuts and bolts by several others, some of them stalwarts, at the reasoning that could have provided a clue to the same time. But the conviction and clarity with physical reasoning. which Einstein expounded its fundamental na- In 1905, Einstein made the bold hypothe- ture probably got it instant fame. sis that under certain circumstances, radiation However another of Einstein’s profound ideas could be absorbed and emitted as packets of en- from the same year, contained in a paper “On ergy and also propagated without spreading out a heuristic point of view concerning the produc- like waves. Einstein was able to predict the for- tion and transformation of light” had a rather mula for the photoelectric effect based on his hy- different fate. This is the paper that introduced pothesis. While the formula was experimentally the idea of what we now call a photon. It was verified by 1913, his peers seem to have rejected the only paper to take forward the rather het- its interpretation in terms of light quanta. Ein- erodox ideas put forward by Max Planck about stein himself was aware of its inherent contradic- the behaviour of light in his early papers in the tions. The first part of this article goes over this year 1900. This too was written with the same period of struggle with the photon concept, and clarity and conviction that characterised Ein- sets the stage for the entry of S N Bose’s critical stein’s papers. Not only was this idea not ac- contribution in 1923. cepted, it was in fact considered to be an em- barrassment by his contemporaries. And even while he became reputed for his other papers, 1 Prologue which earned him a full professorship at Berlin, there was pressure on him to withdraw this par- 1.1 From an embarrassment to a ticular paper. In practical terms, the patently paradigm shift ludicrous nature of the idea delayed his admis- sion into the Prussian Academy by several years, and therefore also probably delayed his Nobel If ideas could speak they would tell us very prize. It was not until S. N. Bose from India strange tales. Firstly how the idea arose is it- provided him with a “missing link” derivation in self an interesting question. And it has any life 3 1924 that Einstein himself fully, and the rest of Newton proposed, or a wave, as per Huygens’ so- the world for the first time, became convinced phisticated constructions, finds a culmination in of the correctness of the idea. It is ironic in- this modern description. It does not endorse ei- deed that Einstein received his Nobel Prize for ther side as “true”, but shows both descriptions none of his other astounding ideas but precisely as merely two facets of a multifaceted, subtle this one which was causing so much embarrass- phenomenon! ment. However, the Prize was not given for the While the new Mechanics opened up the gates profoundness of its core concept, but merely for to new phenomena, new materials and new forces it being a correct phenomenological prediction. of nature, its originator seems to have remained And the award of the Prize, however circum- unconvinced of its additional conceptual founda- spect, happened in 1921, before the clinching tions. In this sense, this is the story of an idea proof provided by Bose. which was arduously protected by its proposer The goal of this article is to put these events in for decades under attack from the contempo- perspective, while also discussing the science in- raries, but whose subsequent implications were volved, along with the evidence it is based upon. rejected by the same originator just after the idea We begin with a discussion of what the challenge received a resounding confirmation by numerous of Black Body radiation was, followed by a possi- experiments and an enthusiastic acceptance by ble reasoning that may make plausible Planck’s the rest of the world. path to the leap into the unknown. Next I dis- cuss Einstein’s paper, his argument for the core new concept it advanced and the possible rea- sons for the conviction Einstein carried for an apparently irreconcilable stance which came to 2 The antecedents be eschewed by all his colleagues. I also try to conjecture why it fell to S. N. Bose in the dis- 2.1 The quiet before the storm tant colonial Indian university of Dhaka and with a gap of two decades, to provide the systematic The end of the nineteenth century appeared to derivation. In the later parts of the article I take mark an epoch of triumphs in the science of up the aftermath of the revolution started by this Physics. Heat, light and electricity, indepen- paper, viz., the emergence of Quantum Mechan- dent subjects under Physics in any school text- ics. We shall be concerned mainly with Ein- book, were suddenly coming closer. The science stein’s own response to the later developments, of Thermodynamics had been put on sound and in that he came to disapprove of the schema of consistent footing. Maxwell had put together the new Mechanics that his path breaking paper a comprehensive mathematical and conceptual had helped to unravel. I also briefly give the fol- framework of Electromagnetism. The several low up story of the circumstances that led to the laws due to Coulomb, Amp`ere, Faraday and oth- development of the complete definitive theory of ers painstakingly put together over a century light in the hands of Glauber and Sudarshan. were beautifully united in a common conceptual The great debate of whether light is a particle as framework. An added wonder of this accom- 4 plishment was that light for the first time could dard conditions, was putting an atomistic view be clearly understood to be an Electromagnetic of the world on a sound footing. phenomenon. Finally, radiated heat could be un- A dichotomy immediately becomes apparent, derstood and a form of light. since the continuum mechanics of solids and flu- It may be these developments that led Lord ids assumed substances to be ideal continua, Kelvin to announce that all the major discov- while all the materials were slowly being revealed eries of Physics had already been made and fu- as an agglomeration of only a fixed basic list ture explorations will only help to improve the of “atoms”. To be sure, atomistic view of the preciseness of the value of “this or that con- world had long been proposed in many schools of stant”. To be sure, Newton’s schema of Mechan- thought around the world. The reason is some- ics was the conceptual and mathematical frame- what obvious, with hindsight. Iron or copper work to which all motion should conform. Euler, from any mine in the world had the same prop- Bernoulli, Poisson and others had extended the erties. Wood or oil always burned; water in any Newtonian framework to deal with continuum water body was more or less the same substance, systems like fluids and solids. Heat had been with some differences. Thus it was easy to guess recognised as a form of energy and interconvert- that there were some primary substances, with ible with mechanical energy. Energy was also varying manifestations. Further, since each had getting a place in the scheme of Maxwell’s Elec- a characteristic property differentiating it from tromagnetism which in turn was also unifying the others, there had to be a basic unit that car- the phenomenon of light with the rest of Physics.
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