[Paper Review] The Story of Bose, Photon Spin and Indistinguishability

Partha Ghose|arXiv (Cornell University)|Jun 14, 2023

Quantum Mechanics and ApplicationsPhysics and Astronomy3 citations

TL;DR

This paper re-examines Satyendra Nath Bose's 1924 derivation of Planck's law, revealing that his original work implicitly introduced two foundational quantum concepts: photon indistinguishability and intrinsic spin (later identified as spin-1). By deriving the phase space factor $8\pi\nu^2/c^3$ purely from quantum mechanics—without classical electrodynamics—Bose established the statistical foundation for Bose-Einstein statistics, which later led to the prediction of Bose-Einstein condensates and the classification of particles into bosons and fermions based on spin.

ABSTRACT

As we approach the centenary of the discovery of quantum statistics in 1924, it is important to revisit Bose's original derivation of Planck's law usually ignored in most standard presentations of Bose-Einstein statistics. It introduced not only the novel concept of the indistinguishability of photons but also of their intrinsic spin, a fact unknown to most physicists.

Motivation & Objective

• To re-express Bose's original 1924 derivation of Planck's law, emphasizing insights often omitted in standard textbooks.
• To highlight that Bose's derivation independently introduced the concept of photon indistinguishability, later formalized in Bose-Einstein statistics.
• To demonstrate that Bose anticipated the photon's intrinsic spin (spin-1) through the polarization factor of 2, long before it was experimentally confirmed.
• To argue that Bose’s work, though initially overlooked, laid the groundwork for quantum statistics and the modern classification of particles as bosons or fermions.
• To correct the historical record by showing that the spin-1 nature of photons was first suggested by Bose and later confirmed by the Raman-Bhagavantam experiment.

Proposed method

• Reconstructs Bose’s derivation of the phase space factor $8\pi\nu^2/c^3$ using quantum mechanical phase space cells of size $h^3$, applied to photons.
• Analyzes the derivation’s key step: dividing the total phase space volume $V \cdot 4\pi p^2 dp$ by $h^3$, yielding $4\pi\nu^2 d\nu / c^3$, which is then multiplied by 2 to account for polarization.
• Interprets the factor of 2 as evidence of an intrinsic two-state degree of freedom—later identified as photon spin—corresponding to right- and left-handed circular polarization.
• Cites Einstein’s endorsement of Bose’s method, which validated the statistical approach and led to the development of Bose-Einstein statistics.
• Uses Einstein’s response to Ehrenfest to show that Bose’s counting method uniquely satisfies Nernst’s heat theorem, confirming its physical consistency.
• Reviews the Raman-Bhagavantam experiment as the first experimental confirmation of photon spin, validating Bose’s original insight.

Experimental results

Research questions

• RQ1 How did Bose derive the phase space factor $8\pi\nu^2/c^3$ in Planck’s law without relying on classical electrodynamics?
• RQ2 What was the physical origin of the factor of 2 in Bose’s derivation, and how did it relate to photon properties?
• RQ3 Why was Bose’s concept of photon indistinguishability not recognized as foundational in early quantum statistics?
• RQ4 How did Einstein’s endorsement of Bose’s method lead to the development of Bose-Einstein statistics and the prediction of Bose-Einstein condensates?
• RQ5 What experimental evidence confirmed Bose’s prediction of photon spin, and when was it first observed?

Key findings

• Bose derived the phase space factor $8\pi\nu^2/c^3$ purely from quantum mechanics by dividing the total phase space volume by $h^3$, without invoking classical electrodynamics.
• The factor of 2 in the derivation arises from the two polarization states of the photon, which Bose interpreted as evidence of an intrinsic angular momentum of $\pm h/2\pi$—the first hint of photon spin.
• Einstein recognized Bose’s derivation as a major advance and used it to develop Bose-Einstein statistics, which correctly predicts the entropy of an ideal gas at absolute zero.
• Bose’s method uniquely satisfies Nernst’s heat theorem, as it assigns only one microstate to the ground state, ensuring entropy vanishes at absolute zero.
• The Raman-Bhagavantam experiment (1931) provided the first experimental confirmation of photon spin, validating Bose’s insight into the two-fold polarization degree of freedom.
• Bose’s original paper contained the first theoretical suggestion of photon spin, predating its formal recognition in relativistic quantum field theory by decades.