Transition from Classical, “Maxwell-Boltzmann” to Quantum, “Bose-Einstein” Partition Statistics by Stochastic Splitting of Degenerate Light

Abstract

The concept of “quantum statistics for distinguishable particles” has been introduced by a remarkable theoretical work a few years ago (1). There it is shown that the classical, Maxwell-Boltzmann (MB) partition law for an ensemble (or a stream) of n particles to be distributed in M “boxes” (or scattered over M channels) can be transformed formally into the Bose-Einstein (BE) law (or into the Fermi-Dirac (FD) law) by allowing the scattering probability over each channel, Wi, to be a stochastic variable instead of a “stationary” cross-section. Since in this process no use is made of “indistinguishability”, i.e., of the fundamental property which is generally attributed to all “quantum” particles, the authors of (1) argue that then the statistics cannot be a criterion for that property. On the other hand, according to the authors of (1), this does not contradict the fundamental prescription according to which “classical” particles obey MB Statistics while “real” particles obey BE or FD quantum-Statistics (2,3). Since the world is actually made of real particles, the interesting transformation theorem given by (1) has been generally considered as a mathematical curiosity with no real physical content. In the present paper we give the first experimental demonstration that the statistical behavior of real particles, i.e., the optical photons, is indeed described either by the classical-Statistics or by the appropriate quantum-Statistics depending on the statistical character of W₁.