Book Title: Cosmology Old and New
Author(s): G R Jain
Publisher: Bharatiya Gyanpith

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Page 128
________________ COSMOLOGY OLD AND NEW cases of abnormal condensation like the superposition of lights from different lamps in a single room. The same reason has been assigned for this crowding by other writers. For instance : "अधिकरणविरोधादानन्त्याभाव इति चेन्न, सूक्ष्मपरिणामावगाहन 96 सामर्थ्यात् ।। Or 11216 अवगाहनसामर्थ्यात् सूक्ष्मत्वपरिणामिनः । तिष्ठन्त्येकप्रदेशेऽपि बहवोऽपि हि पुद्गलाः ॥ 217 This distribution of atoms in pradesas or cells of space has a very great likening to the distribution of particles in BoseEinstein or Fermi-Dirac Statistics where probabilities of various combinations have been mathematically calculated. We can only make a passing mention of this highly complex piece of mathematics. In the standard work A Treatise on Heat' by Dr. M. N. Saha, F.R.S. and B.N. Srivastava, the calculation of probability from Bose-Einstein Statistics is given on p. 717. "The next operation is to distribute these N-particles amongst A,-cells so that each cell may contain 0,1,2,......up to N, identical particles." Then follows the expression for the probability of the various states. Also on page 718 "In the Bose-Einstein Statistics a particular cell or degree of freedom was supposed to be capable of accommodating any number of particles. Fermi conceives a third kind of statistics in which one cell should not accommodate more than one particle." How an infinite number of atoms in a subtle (Süksma) state can be accommodated in one cell has been discussed in pages 13-14 ante. 216. Tattvärtha-rājavārtika on sutra 5.10. 217. Tattvärtha-sära, 3.26.

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