Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable (we call it Planck variable) whose distribution is just the Bose distribution yielding the Planck law of black-body radiation. The fractional part is the dark part (we call is dark variable) with a continuous distribution, which is, of course, not observed in the experiments. It is proved that the Bose distribution is infinitely divisible, and the irreducible decomposition of it is given. The Planck variable can be decomposed into an infinite sum of independent binary random variables representing the binary photons (more accurately photo-molecules or photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons follow the Fermi statistics. Consequently, the black-body radiation can be viewed as a mixture of statistically and thermodynamically independent fermion gases consisting of binary photons. The binary photons give a natural tool for the dyadic expansion of arbitrary (but not coherent) ordinary photon excitations. It is shown that the binary photons have wave-particle fluctuations of fermions. These fluctuations combine to give the wave-particle fluctuations of the original bosonic photons expressed by the Einstein fluctuation formula.Comment: 29 page

Einstein's fluctuation formula. A historical overview

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum) a comparative study is presented on the first line of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of the classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical poissonian photo-multiplets or to the binary photo-multiplets of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.Comment: 34 page

Between history and values: A study on the nature of interpretation in international law

My thesis discusses the place of evaluative judgements in the interpretation of general international law. It concentrates on two questions. First, whether it is possible to interpret international legal practices without making an evaluative judgement about the point or value that provides the best justification of these practices. Second, whether the use of evaluative judgements in international legal interpretation threatens to undermine the objectivity of international law, the neutrality of international lawyers or the consensual and voluntary basis of the international legal system. I answer both questions in the negative. As regards the first, I argue that international legal practice has an interpretive structure, which combines appeals to the history of international practice with appeals to the principles and values that these practices are best understood as promoting. This interpretive structure is apparent not only in the claims of international lawyers about particular rules of international law (here I use the rule of estoppel as an example) but also in the most basic intuitions of international theorists about the theory and sources of general international law. I then argue that some popular concerns to the effect that the exercise of evaluation in the interpretation of international law will undermine the coherence or the usefulness of the discipline are generally unwarranted. The fact that international legal practice has an interpretive structure does not entail that propositions of international law are only subjectively true, that the interpreter enjoys license to manipulate their meaning for self-serving purposes, or that international law will collapse under the weight of irresolvable disagreements, divisions and conflicts about its proper interpretation

Sur l'ionisation spontanée des gaz en vase clos

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