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Apple Academic Press eBooks

Phenomenological Quantification of Matter

Mihai V. Putz

Published Mar 30, 2016• 0 citations
Publisher

Abstract

Abstract ..................................................................................................... 2 1.1 Introduction ...................................................................................... 2 1.2 Quantification of Waves ................................................................... 3 1.2.1 Black-body Radiation .......................................................... 3 1.2.2 Planck’s Approach ............................................................... 7 1.2.3 Einstein’s Approach ............................................................11 1.3 Quantification of Substance ........................................................... 13 1.3.1 The de Broglie Formula ..................................................... 13 1.3.2 The Wave Packet ................................................................ 15 1.3.3 Born Normalization ........................................................... 17 1.3.4 Formal Heisenberg Indeterminacy ..................................... 20 1.3.5 Bohr Hydrogenic Quantification ....................................... 21 1.3.6 Bohr’s Correspondence Principle ...................................... 24 1.4 Consequences of Matter Quantification ......................................... 27 1.4.1 Moseley Law and Spectral Atomic Periodicity ................. 27 1.4.2 Systems with Identical Particles ........................................ 30 1.4.3 Maxwell-Boltzmann Statistics: The Partition Function ..... 32 1.4.4 Fermi-Dirac Statistics ........................................................ 36 1.4.5 Bose-Einstein Statistics ...................................................... 40 1.4.6 Fundamental Forces and Elementary Particles: The Theory of Everything (TOE) ...................................... 43 1.4.7 Stefan-Boltzmann Law of Radiation ................................. 49 1.4.8 The Wien Law: The Universe’s Temperature and Anisotropy ................................................................... 54 1.5 Conclusion ..................................................................................... 60 Keywords ................................................................................................ 62 References ............................................................................................... 62 Author’s Main References ............................................................. 62 Specific References ........................................................................ 62 Further Readings ............................................................................ 63 ABSTRACT Following the “Greek dream” of Nature unification, between the sea waves and earth dust, the Matter is regarded as having two main orders or manifestations, i.e., the undulatory and corpuscular sides. Remarkably, such philosophical view is strongly sustained by the quantum theory of matter, by its prescription through waves and substance quantifications, with experimental counterpart, however, maintaining the intrinsic mystery of reciprocal connection at the microscopic level. This chapter reviews the most fundamental Planck (– Einstein) and de Broglie (– Einstein) quantifications of matter while founding the basis for the second and first quantification of fields and particles, respectively. This way the two opposite visions of Newton and Huygens as advancing on the end of XVII century the corpuscular and undulatory natures of matter seems now be unified either at micro-and macro-scales of Universe.

DOI
10.1201/b21340-7

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Abstract ..................................................................................................... 2 1.1 Introduction ...................................................................................... 2 1.2 Quantification of Waves ................................................................... 3 1.2.1 Black-body Radiation .......................................................... 3 1.2.2 Planck’s Approach ............................................................... 7 1.2.3 Einstein’s Approach ............................................................11 1.3 Quantification of Substance ........................................................... 13 1.3.1 The de Broglie Formula ..................................................... 13 1.3.2 The Wave Packet ................................................................ 15 1.3.3 Born Normalization ........................................................... 17 1.3.4 Formal Heisenberg Indeterminacy ..................................... 20 1.3.5 Bohr Hydrogenic Quantification ....................................... 21 1.3.6 Bohr’s Correspondence Principle ...................................... 24 1.4 Consequences of Matter Quantification ......................................... 27 1.4.1 Moseley Law and Spectral Atomic Periodicity ................. 27 1.4.2 Systems with Identical Particles ........................................ 30 1.4.3 Maxwell-Boltzmann Statistics: The Partition Function ..... 32 1.4.4 Fermi-Dirac Statistics ........................................................ 36 1.4.5 Bose-Einstein Statistics ...................................................... 40 1.4.6 Fundamental Forces and Elementary Particles: The Theory of Everything (TOE) ...................................... 43 1.4.7 Stefan-Boltzmann Law of Radiation ................................. 49 1.4.8 The Wien Law: The Universe’s Temperature and Anisotropy ................................................................... 54 1.5 Conclusion ..................................................................................... 60 Keywords ................................................................................................ 62 References ............................................................................................... 62 Author’s Main References ............................................................. 62 Specific References ........................................................................ 62 Further Readings ............................................................................ 63 ABSTRACT Following the “Greek dream” of Nature unification, between the sea waves and earth dust, the Matter is regarded as having two main orders or manifestations, i.e., the undulatory and corpuscular sides. Remarkably, such philosophical view is strongly sustained by the quantum theory of matter, by its prescription through waves and substance quantifications, with experimental counterpart, however, maintaining the intrinsic mystery of reciprocal connection at the microscopic level. This chapter reviews the most fundamental Planck (– Einstein) and de Broglie (– Einstein) quantifications of matter while founding the basis for the second and first quantification of fields and particles, respectively. This way the two opposite visions of Newton and Huygens as advancing on the end of XVII century the corpuscular and undulatory natures of matter seems now be unified either at micro-and macro-scales of Universe.
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Einstein's papers on quantum theory over the period 1905-1925 are reviewed. These papers played a fundamental role in the development of quantum concepts. This review traces the relationship between these papers, on the one hand, and Wien's and Planck's theoretical work on thermal radiation and Einstein's own work on statistical thermodynamics, on the other. Einstein's 1905 development of the concept of light quanta from Wien's radiation law, the application of this concept to elementary interactions of radiation with matter, Einstein's 1906–1907 analysis of the Planck radiation law, and Einstein's development of the foundations of a quantum theory of specific heat are all discussed. Particular attention is paid to Einstein's 1909 development of the concept of a particle-wave duality for radiation from a study of the energy and momentum fluctuations in a radiation field. Einstein's 1916 papers on the quantum theory of radiation are analyzed, and it is emphasized that Einstein was the first to suggest a probabilistic interpretation of the particle-wave duality, in addition to introducing coefficients to characterize the probabilities for optical transitions and offering his well-known derivation of the Planck radiation law. There is a special discussion of Einstein's expression, in his 1925 paper on the quantum theory of monatomic ideal gases, of high regard for de Broglie's concept of a particle-wave duality for material particles.
Abstract This chapter covers De Broglie’s extension to matter of wave–particle duality, which Einstein had introduced for radiation. It fills in the background in the tradition of extremal principles in classical physics that De Broglie drew on to formulate his theory. It then covers Bose’s introduction of a new statistics for light quanta and Einstein’s application of those statistics to matter in his quantum theory of the ideal gas. Providing support for De Broglie’s ideas, Einstein derived a formula for energy fluctuations in such a gas that has the exact same form as the formula for energy fluctuations in black-body radiations: it is the sum of two terms, one suggesting waves, the other one suggesting particles.