skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Einstein's Photon Concept Quantified by the Bohr Model of the Photon

Abstract

The photon is modeled as a monochromatic solution of Maxwell's equations confined as a soliton wave by the principle of causality of special relativity. The soliton travels rectilinearly at the speed of light. The solution can represent any of the known polarization (spin) states of the photon. For circularly polarized states the soliton's envelope is a circular ellipsoid whose length is the observed wavelength ({lambda}), and whose diameter is {lambda}/{pi}; this envelope contains the electromagnetic energy of the wave (hv = hc/{lambda}). The predicted size and shape is confirmed by experimental measurements: of the sub-picosecond time delay of the photo-electric effect, of the attenuation of undiffracted transmission through slits narrower than the soliton's diameter of {lambda}/{pi}, and by the threshold intensity required for the onset of multiphoton absorption in focussed laser beams. Inside the envelope the wave's amplitude increases linearly with the radial distance from the axis of propagation, being zero on the axis. Outside the envelope the wave is evanescent with an amplitude that decreases inversely with the radial distance from the axis. The evanescent wave is responsible for the observed double-slit interference phenomenon.

Authors:
 [1];  [2];  [3]
  1. York University, Toronto, Ontario, M3J 1P3 (Canada)
  2. Physics Department, York University (Canada)
  3. Optech Inc., 100 Wildcat Rd, Toronto (Canada)
Publication Date:
OSTI Identifier:
20787707
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 810; Journal Issue: 1; Conference: Vaxjo conference on quantum theory: Reconsideration of foundations - 3, Vaxjo (Sweden), 6-11 Jun 2005; Other Information: DOI: 10.1063/1.2158738; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ABSORPTION; AMPLITUDES; ATTENUATION; CAUSALITY; INTERFERENCE; LASER RADIATION; LIGHT TRANSMISSION; MATHEMATICAL SOLUTIONS; MAXWELL EQUATIONS; MONOCHROMATIC RADIATION; MULTI-PHOTON PROCESSES; PHOTON BEAMS; PHOTONS; POLARIZATION; RELATIVITY THEORY; SOLITONS; SPIN; TIME DELAY; WAVELENGTHS

Citation Formats

Hunter, Geoffrey, Alexandrescu, Camil, and Kowalski, Marian. Einstein's Photon Concept Quantified by the Bohr Model of the Photon. United States: N. p., 2006. Web. doi:10.1063/1.2158738.
Hunter, Geoffrey, Alexandrescu, Camil, & Kowalski, Marian. Einstein's Photon Concept Quantified by the Bohr Model of the Photon. United States. doi:10.1063/1.2158738.
Hunter, Geoffrey, Alexandrescu, Camil, and Kowalski, Marian. Wed . "Einstein's Photon Concept Quantified by the Bohr Model of the Photon". United States. doi:10.1063/1.2158738.
@article{osti_20787707,
title = {Einstein's Photon Concept Quantified by the Bohr Model of the Photon},
author = {Hunter, Geoffrey and Alexandrescu, Camil and Kowalski, Marian},
abstractNote = {The photon is modeled as a monochromatic solution of Maxwell's equations confined as a soliton wave by the principle of causality of special relativity. The soliton travels rectilinearly at the speed of light. The solution can represent any of the known polarization (spin) states of the photon. For circularly polarized states the soliton's envelope is a circular ellipsoid whose length is the observed wavelength ({lambda}), and whose diameter is {lambda}/{pi}; this envelope contains the electromagnetic energy of the wave (hv = hc/{lambda}). The predicted size and shape is confirmed by experimental measurements: of the sub-picosecond time delay of the photo-electric effect, of the attenuation of undiffracted transmission through slits narrower than the soliton's diameter of {lambda}/{pi}, and by the threshold intensity required for the onset of multiphoton absorption in focussed laser beams. Inside the envelope the wave's amplitude increases linearly with the radial distance from the axis of propagation, being zero on the axis. Outside the envelope the wave is evanescent with an amplitude that decreases inversely with the radial distance from the axis. The evanescent wave is responsible for the observed double-slit interference phenomenon.},
doi = {10.1063/1.2158738},
journal = {AIP Conference Proceedings},
number = 1,
volume = 810,
place = {United States},
year = {Wed Jan 04 00:00:00 EST 2006},
month = {Wed Jan 04 00:00:00 EST 2006}
}
  • The interacting boson model was invented in two independent modes: The Schwinger mode using six bosons (s and five d bosons) and the Holstein-Primakoff mode using five quadrupole quasibosons. We show that the mathematical equivalence of the two modes can be used to define a number conserving quadrupole boson (the b boson). Two equivalent bases, the usual s-d basis and a new s-b basis are exhibited. By an exercise of (possibly objectionable) physical licence, the result can be interpreted as a proof of equivalence of interacting boson model I with the Bohr-Mottelson model. In the s-b basis, the Hamiltonian andmore » other operators depend only on the b boson. In this form, all the topics usually associated with Bohr-Mottleson model can be discussed: Potential energy surface, shape parameters, vibrations vs rotations, etc. The precise relationship of our method to that employed in previous work is exposed. The latter is shown to correspond to the use of the Dyson generators of SU(6).« less
  • The comparison between BMM and IBM is comprehensively discussed in the spirit of transformation theory by using the generator coordinate method (GCM). Some differences existing between these two essentially equivalent models are pointed out on the phenomenological level, and the possibility of distinguishing between them is briefly discussed.
  • Developments and applications are presented of an algebraic version of Bohr's collective model. Illustrative examples show that fully converged calculations can be performed quickly and easily for a large range of Hamiltonians. As a result, the Bohr model becomes an effective tool in the analysis of experimental data. The examples are chosen both to confirm the reliability of the algebraic collective model and to show the diversity of results that can be obtained by its use. The focus of the paper is to facilitate identification of the limitations of the Bohr model with a view to developing more realistic, computationallymore » tractable models.« less
  • Cited by 1