In this brief note I address the question not frequently asked, namely, why did it take two decades between Einstein's first proposal of photons and derivation of the full Planck formula from first principles of Statistical Mechanics, albeit with a fundamental new approach to counting of states. Secondly, why did it fall to an independent inquirer, S. N. Bose, in far away Dacca to arrive at the correct derivation of this formula, arguably a most crucial one of the first half of the twentieth century? Reasonable hypotheses are proposed for answers to both. I also argue that the timing of Bose's communication to Einstein played a crucial role in Einstein's approval of de Broglie's thesis and hence the emergence of the definitive version of quantum mechanics in the late 1920's.
In this brief note I address the question not frequently asked, namely, why did it take two decades between Einstein's first proposal of photons and derivation of the full Planck formula from first principles of Statistical Mechanics, albeit with a fundamental new approach to counting of states. Secondly, why did it fall to an independent inquirer, S. N. Bose, in far away Dacca to arrive at the correct derivation of this formula, arguably a most crucial one of the first half of the twentieth century? Reasonable hypotheses are proposed for answers to both. I also argue that the timing of Bose's communication to Einstein played a crucial role in Einstein's approval of de Broglie's thesis and hence the emergence of the definitive version of quantum mechanics in the late 1920's.
It is widely accepted that the papers by Bose in 1924 and by Einstein in 1924-1925 definitely opened the path to
the quantum concept of ‘indistinguishability’. Since then, distinction in physics between ‘identity’ and
‘indistinguishability’ of particles has come to be required.
However, even before the rise of quantum physics, Maxwell, Boltzmann and Gibbs, among others, had to tackle
the difficulties and paradoxes that appear when counting identical particles. Later, after Sackur’s and Tetrode’s
first quantum derivation of the canonical partition function of an ideal gas, much confusion arose around its
dependence on the number of molecules in the system. Many other physicists, such as Planck, Lorentz or
Schrodinger took part in those debates. In 1921, Ehrenfest and Trkal devoted a whole paper to this subject.
Clearly, in the days before Bose’s seminal work, embroiling and misunderstanding were commonplace.
In considering the emergence of the distinction between ‘identical’ and ‘indistinguishable’ particles, we will go
through the so-called statistical route to quantum mechanics. The first developments in statistical mechanics
became immediately confused and entangled with the irruption of quantum physics. In the first quarter of the
twentieth century the mutual influence between both disciplines was profuse.
We will pay special attention to the story of the so-called ‘Gibbs Paradox.’ We will argue that what is now often
known by this name in some textbooks of statistical mechanics did not exist as such in those foundational days.
In the year 1900 Max Planck was led by experimental observations to propose a strange formula for the intensity as a function of frequency for light emitted by a cavity. It relied on peculiar properties to be obeyed by the emitters and absorbers in the cavity. I highlight the mathematically suggestive nature of the formula, accessible even to a high school student, that could have provided a clue to the physical reasoning of Planck. In 1905, Einstein made the bold photon hypothesis and was able to predict the formula for the photoelectric effect which was not fully explored then. The first part of this article concerns the period 1905 to 1923 with a possible explanation for the difficulties in acceptance of the new concept. In the second part of the article I present how S. N. Bose's 1924 paper provided a systematic derivation of Planck formula by consistently adopting the conception of photons within Boltzmann's framework. In conclusion we discuss the implications of Quantum Mechanics that eventually emerged, showing that the seeds of some of its uncanny conceptual content were already foreshadowed in Einstein's proposal.
This is an account of Einstein's work and thoughts on the quantum theory. The following topics will be discussed: The light-quantum hypothesis and its gradual evolution into the photon concept. Early history of the photoelectric effect. The theoretical and experimental reasons why the resistance to the photon was stronger and more protracted than for any other particle proposed to date. Einstein's position regarding the Bohr-Kramers-Slater suggestion, the last bastion of resistance to the photon. Einstein's analysis of fluctuations around thermal equilibrium and his proposal of a duality between particles and waves, in 1909 for electromagnetic radiation (the first time this duality was ever stated) and in January 1925 for matter (prior to quantum mechanics and for reasons independent of those given earlier by de Broglie). His demonstration that long-known specific heat anomalies are quantum effects. His role in the evolution of the third law of thermodynamics. His new derivation of Planck's law in 1917 which also marks the beginning of his concern with the failure of classical causality. His role as one of the founders of quantum statistics and his discovery of the first example of a phase transition derived by using purely statistical methods. His position as a critic of quantum mechanics. Initial doubts on the consistency of quantum mechanics (1926-1930). His view maintained from 1930 until the end of his life: quantum mechanics is logically consistent and quite successful but it is incomplete. His attitude toward success. His criterion of objective reality. Differences in the roles relativity and quantum theory played in Einstein's life. His vision regarding quantum theory in the context of a unified field theory. His last autobiographical sketch, written a few months before his death, concluding with a statement about the quantum theory, a subject to which (by his own account) he had given more thought than even to general relativity.
The principal mathematical idea behind the statistical properties of black-body radiation (photons) was introduced already by L. Boltzmann (1877/2015) and used by M. Planck (1900; 1906) to derive the frequency distribution of radiation (Planck’s law) when its discrete (quantum) structure was additionally added to the reasoning. The fundamental physical idea – the principle of indistinguishability of the quanta (photons) – had been somewhat hidden behind the formalism and evolved slowly. Here the role of P. Debye (1910), H. Kamerlingh Onnes and P. Ehrenfest (1914) is briefly elaborated and the crucial role of W. Natanson (1911a; 1911b; 1913) is emphasized. The reintroduction of this Natanson’s statistics by S. N. Bose (1924/2009) for light quanta (called photons since the late 1920s), and its subsequent generalization to material particles by A. Einstein (1924; 1925) is regarded as the most direct and transparent, but involves the concept of grand canonical ensemble of J. W. Gibbs (1902/1981), which in a way obscures the indistinguishability of the particles involved. It was ingeniously reintroduced by P. A. M. Dirac (1926) via postulating (imposing) the transposition symmetry onto the many-particle wave function. The above statements are discussed in this paper, including the recent idea of the author (Spałek 2020) of transformation (transmutation) – under specific conditions – of the indistinguishable particles into the corresponding to them distinguishable quantum particles. The last remark may serve as a form of the author’s post scriptum to the indistinguishability principle.
This invaluable book takes the reader from Planck's discovery of the quantum in 1900 to the most recent interpretations and applications of nonrelativistic quantum mechanics. The introduction of the quantum idea leads off the prehistory of quantum mechanics, featuring Planck, Einstein, Bohr, Compton, and de Broglie's immortal contributions. Their original discovery papers are featured with explanatory notes and developments in Part 1. The invention of matrix mechanics and quantum mechanics by Heisenberg, Born, Jordan, Dirac, and Schrödinger is presented next, in Part 2. Following that, in Part 3, are the Einstein–Bohr debates on the interpretation of quantum mechanics culminating in Bell's inequality and Aspect's experiment demonstrating the actuality of the long range quantum correlations to which Einstein, Podolsky, and Rosen took great exception. Resolutions of quantum paradoxes and the current state of such debates are summarized. Part 4 presents a selection of the most dramatic modern developments, both theoretical and experimental. These include Feynman path integrals, the modern interpretation based on decoherence, quantum optics experiments leading to teleportation, DeWitt's wave function of the universe, and a brief introduction to the end-of-the-millennium prospects of quantum computation. A concluding chapter presents the authors' conjectures for the next 100 years of the quantum. This book is ideally suited to anyone with a junior level background in modern physics and quantum mechanics, and a cultural interest in the original sources of the greatest ideas of the greatest founders of this subject as derived from their first discovery papers. These papers have led, in giant strides across the whole of the twentieth century, to the revolutionary experimental advances of the last decade. The book makes accessible - physically and intellectually - both the deepest roots and the highest branches of nonrelativistic quantum physics
In 1924, Satyendra Nath Bose's pioneering work laid the foundation for Bose-Einstein statistics, which describes particles with integral spins. His derivation of Planck's law for blackbody radiation bypassed classical assumptions, relying instead on the statistical mechanics of light quanta. Bose's methodology addressed limitations in existing theories, such as Einstein's dependence on classical concepts like Wien's displacement law and Bohr's correspondence principle. Further, his work underscored the incompatibility between classical electrodynamics and quantum theory, proposing innovative statistical approaches to thermodynamic equilibrium. The insights from Bose's work extend beyond theoretical physics. As was immediately noticed by Einstein, for temperatures below a critical threshold, Bose-Einstein statistics predicts the formation of a Bose-Einstein condensate (BEC), where particles condense en-masse into the ground state. This quantum phenomenon on a macroscopic scale opened avenues to explore new technologies in recent times, apart from throwing light on new phases of matter. This article revisits Bose's groundbreaking contributions, highlighting their enduring impact on quantum mechanics, statistical physics, and field theory.