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arXiv:2504.03689 · Quantum Sensing and Nano Electronics and Photonics

Quantization of the electromagnetic field, entropy of an ideal monoatomic gas, and the birth of the Bose-Einstein statistics

Masud Mansuripur

Published Mar 21, 2025• 0 citations
arXivHTMLPDF

Abstract

In 1924, Einstein received a short manuscript in the mail from the Indian physicist S.N. Bose. He quickly translated Bose’s manuscript to German and submitted it to Zeitschrift für Physik. Within a few weeks, Einstein presented his own findings (using a generalization of Bose’s counting method) to a session of the Prussian Academy of Sciences. Whereas Bose had suggested a new counting method for the quanta of the electromagnetic field—one that yielded Planck’s blackbody radiation formula—Einstein applied Bose’s method to an ideal monoatomic gas. Shortly afterward, Einstein presented to the Academy a follow-up paper in which he described the Bose-Einstein condensation for the first time. The present paper describes some of the fascinating issues that Einstein struggled with as he attempted to unify the quantum-statistical properties of matter with those of the electromagnetic field.

DOI
10.1117/12.3052584

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In 1924, Einstein received a short manuscript in the mail from the Indian physicist S.N. Bose. He quickly translated Bose’s manuscript to German and submitted it to Zeitschrift für Physik. Within a few weeks, Einstein presented his own findings (using a generalization of Bose’s counting method) to a session of the Prussian Academy of Sciences. Whereas Bose had suggested a new counting method for the quanta of the electromagnetic field—one that yielded Planck’s blackbody radiation formula—Einstein applied Bose’s method to an ideal monoatomic gas. Shortly afterward, Einstein presented to the Academy a follow-up paper in which he described the Bose-Einstein condensation for the first time. The present paper describes some of the fascinating issues that Einstein struggled with as he attempted to unify the quantum-statistical properties of matter with those of the electromagnetic field.
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In 1924 the Indian physicist Satyendra Nath Bose sent a paper to Einstein in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein arranged for Bose's paper to be translated into German and published. He also extended Bose's calculations to particles with mass and showed that, at sufficiently low temperatures, they would all condense into the same quantum ground state. And for the next 70 years physicists struggled to make a Bose-Einstein condensate – which is sometimes called the fifth state of matter – in the laboratory.
Abstract Planck’s original introduction of the quantum idea was based on a statistical mechanical treatment of black body radiation. S. Bose, a physicist working in India, found a new way of deriving Planck’s law. Einstein applied Bose’s method to a gas of massive particles. This led to the prediction of a new physical effect (Bose-Einstein condensation). With the introduction of the exclusion principle by Pauli, Fermi, and Dirac independently introduced a new kind of statistics. Considerations by Einstein and Schrödinger introduced a preliminary form of second quantization.
In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for “bosons” – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.
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.
Satyendra Nath (S.N.) Bose is one of the great Indian scientists. His remarkable work on the black body radiation or derivation of Planck’s law led to quantum statistics, in particular, the statistics of photon. Albert Einstein applied Bose’s idea to a gas made of atoms and predicted a new state of matter now called Bose-Einstein condensate. It took 70 years to observe the predicted condensation phenomenon in the laboratory. With a brief introduction to the formative period of Professor Bose, this research survey begins with the founding works on quantum statistics and, subsequently, provides a brief account of the series of events terminating in the experimental realization of Bose-Einstein condensation. We also provide two simple examples to visualize the role of synthetic spin-orbit coupling in a quasi-one-dimensional condensate with attractive atom-atom interaction.