Light and Vacuum

The following sections are included:

• Dedication
• Prologue
• Table of Contents

Man has always been fascinated by light. Since the rise of humanity, light is related to life and darkness to death. This concept seems to have intrinsic roots in the human mind whatever the tribe or nation, on any continent and during any historic or pre-historic period…

The concepts of light during the last 2500 years: corpuscles, ray optics, wave optics, electromagnetic wave theory and finally quantum particle theory.

The following sections are included:

• Maxwell's Equations
• Electromagnetic Wave Propagation
  • Dispersion relation
  • Physical quantities involved in the electromagnetic field
  • Propagation equations of electromagnetic waves
  • Helmholtz equation
  • Energy flux of electromagnetic waves
  • TEM waves — laplace equation
• Scalar and Vector Potentials
• Vector Potential and Electromagnetic Field Polarization
• Guided Propagation of Electromagnetic Waves
  • Rectangular waveguide of cross section a, b(a > b)
  • TE_m,n Modes
  • TE_m,n Components
    • Circular waveguide of radius r₀
  • TE_m,n Modes
  • TE_m,n Modes
    • Case of two parallel plates
    • Density of states
• Conclusion Remarks
• Bibliography

The following sections are included:

• Elements of Quantum Mechanics
  • Blackbody radiation and the ultraviolet catastrophe
  • Energy and momentum operators in quantum mechanics
  • Particle in a square potential well — correspondence with the waveguides
• Harmonic Oscillator in Quantum Mechanics
  • From the classical expressions to the quantum mechanical ones
  • Dirac representation, creation and annihilation operators a, a⁺
• Quantum Electrodynamics (QED) and the Photon Description
  • Brief description of selected experiments that have historically played an important role for the introduction of the photon concept
    • The photoelectric effect and the quantum interpretation
    • Compton scattering
    • Low intensity Young's double-slit interferences
  • Second Quantization
    • Quantization process of the electromagnetic field
  • Interaction between Electromagnetic Waves and Charged Particles, Reality of the Vector Potential
    • Interaction Hamiltonian between an electromagnetic wave and a charged particle
    • Reality of the vector potential, Ehrenberg–Siday or Aharonov–Bohm effect
  • Transition Rates and Vacuum Induced Spontaneous Emission
    • Photoelectric effect and the semi-classical interpretation
    • Spontaneous emission rate
    • Dipole approximation and the spontaneous emission
    • The photon spin
  • Lamb Shift
    • Nonrelativistic calculations: Bethe's approach
  • Conclusion Remarks
  • Bibliography

In what follows, we analyze the questions raised from the quantum theory of radiation and we point out the mathematical difficulties encountered mainly from the second quantization procedure which has been developed to provide photons description from the quantum point of view. We first make a theoretical analysis of some particular aspects of QED, including the well known singularities, and then we present some experiments which strongly support the simultaneous wave-particle nature of photons.

The following sections are included:

• Quantized Vector Potential Amplitude of a Single Photon State
  • Dimension analysis from Maxwell's equations. Vector potential amplitude proportional to the frequency
  • Wave equation for the photon vector potential
  • Photon wavelength dimensions following the experimental evidence
  • Wave-particle formalism
  • Relation between the photon vector potential and the electron charge
• Quantum Vacuum Representation
• The Quantum VacuumField Effects
  • Spontaneous emission
  • Lamb shift
  • Cosmic vacuumenergy density
• Conclusion Remarks
• Bibliography

The mathematical expressions of a valid theory should correctly describe the physical mechanisms involved in a complete ensemble of experimentally observed phenomena. When many theories, each based on different concepts, interpret only partially some measurable observables, then it becomes obvious that they cannot be epistemologically valid, entailing that they have to be improved, if possible, or abandoned. Hence, the historical evolution over twenty five centuries of the concepts on light's nature followed the sequence: corpuscles, ray optics (without having any idea on the nature of the particles composing the rays), wave optics (with no idea about the nature of the waves), electromagnetic waves theory and finally quantum particle theory. Despite all these evolutions, the general picture of the nature of light is not satisfactory and Bohr's complementarity principle was, and still remains, the artificial mask behind which is hidden the difficulty of our comprehension of the simultaneous wave-particle concept. However, the mutual exclusiveness of Bohr's complementarity principle, according to which light has both wave and particle natures but only one of those is expressed explicitly in a given physical situation, is strongly put in doubt by recent experiments…

The following section is included:

• Index