Light And Vacuum: The Wave-particle Nature Of The Light And The Quantum Vacuum Through The Coupling Of Electromagnetic Theory And Quantum Electrodynamics

The Wave¬タモParticle Nature of the Light and the Quantum Vacuum through the Coupling of Electromagnetic Theory and Quantum Electrodynamics

Constantin Meis

• Publisher: WSPC
• Year: 2014
• ISBN:
  9789814630917
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

Light and Vacuum presents a synthesis of selected fundamental topics of electromagnetic wave theory and quantum electrodynamics (QED) and analyzes the main theoretical difficulties encountered to ensure a coherent mathematical description of the simultaneous wave–particle nature of light, put in evidence by the experiments. The notion and the role of the quantum vacuum, strongly related to light, are extensively investigated.

Classical electrodynamics issued from Maxwell's equations revealed the necessity of introducing the notion of volume for an electromagnetic wave to stand entailing precise values of cut-off wavelengths to account for the shape and dimensions of the surrounding space. Conversely, in QED, light is considered to be composed of point particles disregarding the conceptual question on how the frequency of oscillating electric and magnetic fields may be attributed to a point particle.

To conciliate these concepts, the book provides a comprehensive overview of the author's work, including innovative contributions on the quantization of the vector potential amplitude at a single photon state, the non-local simultaneous wave–particle mathematical representation of the photon and finally the quantum vacuum. The purpose of the advanced elaborations is to raise questions, give hints and answers, and finally aspire for further theoretical and experimental studies in order to improve our knowledge and understanding on the real essence of Light and Vacuum.

Contents:

• Introduction
• Historical Survey and Experimental Evidence
• Basic Principles of the Electromagnetic Wave Theory
• From Electromagnetic Waves to Quantum Electrodynamics
• Theory, Experiments and Questions
• Analysis of the Electromagnetic Field Quantization Process and the Photon Vector Potential. The Non-Local Photon Wave-Particle Representation and the Quantum Vacuum
• Epilogue

Readership: This book is recommended for advanced postgraduate students and researchers who are interested in Quantum Mechanics and Electrodynamics.
Key Features:

• The main mathematical ambiguities of the quantum electrodynamics formalism are clearly put in evidence, such as: derivation of the Hamiltonian without respecting Heisenberg's commutation relations, lack of an interaction Hamiltonian between the vacuum state and the electrons, singularities … etc.
• The basic aspect of Quantum Electrodynamics related to the quantization of the vector potential amplitude of the electromagnetic field to a single photon state α 0 k ( ω k ) = ξω k, which derives directly from Maxwell's equations, is uniquely described in this manuscript
• A coherent mathematical coupling of the electromagnetic wave theory and quantum electrodynamics is fully provided resulting in a unique simultaneous wave particle formalism for the photon, in agreement with the experimental evidence
• The quantum vacuum issues arise naturally from the vector potential quantization procedure and corresponds to a very low energy density, compatible with recent astrophysical observations. Furthermore, it is explicitly expressed as a function of creation and annihilation operators permitting direct interactions with the electrons

Chapter 1

Introduction

 

“Light is the means nature employs to observe itself”.

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 natural entities emitting light, helping man and animals to see while eliminating the fears of darkness, like the sun, the moon and fire were venerated since the beginning and the absolute divine was associated with them. Man quickly understood that life, as it is met on the surface of this planet, would be inexistent or at least completely different without light. The forests are the main lags of the earth’s atmosphere contributing to the production and to the recycling of oxygen, a so crucial for the life element. In the absence of the sun’s light, plants, trees and forests are condemned to disappear and consequently animals would be unable to survive.

Within a biological point of view, light is the basic medium of nature conferring the possibility to organisms possessing an appropriate detection system, optical or not, to see or detect the shapes of the objects of the surrounding cosmos. By the same token, light is the means nature has chosen to watch itself by way of live beings. The exchange of energy and information between atoms, molecules and more complex systems occurs through light, permitting life to emerge in the cosmos. This notion, once understood, automatically attributes a unique character to light in the universe.

In the old historical times, light on earth was only emitted from fire, volcanic lava or high temperature metallic objects. Ancient Greeks had such a profound respect for light that the only origin they could imagine was undoubtedly divine. In the Greek language, light is Phos (Φωs). This one-syllable word has quite a strong and deep consonance that used to be attributed only to exceptional physical entities, like Pyr (Πυρ) fire, or even the head of the Gods, Zeus (Zευs). Hence, according to the legend, Prometheus has stolen the fire from Gods in order to offer light and heat to mankind. Disregarding the fact if mankind was worthy of it, the value of the gift was invaluable. For his action, Prometheus was punished by the Gods to be attached on the Caucasian mountains where an eagle was eating his liver in the day while it was regenerated during the night. The character of this endless torture without any chance of forgiveness or clemency gives witness to the extreme importance ancient Greeks attributed to the stolen entity from the Gods, fire. One simply has to wonder what human civilization would be like without fire.

Not surprisingly, in most religions God is identified with light.

However, light has an intrinsic nature and undergoes specific physical laws governing its behavior, and studied by science. Today, we perfectly understand the behavior laws but our mathematical representation of its wave-particle nature and its relationship to the vacuum is still incomplete.

Chapter 2

Historical Survey and Experimental Evidence

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

As far as we know, the first attempts to study the nature of light from the scientific point of view are due to ancient Greeks. They believed light to be composed of corpuscles.

Thales of Miletus in the sixth century BC knew already that in a given medium, light propagates in straight lines and that the light of the sun also obeys that property. Based on that knowledge and using his famous theorem, he measured the height of the Cheops pyramid by comparing the length of its shadow to that of his stick positioned vertically.

About two centuries later, Euclid published the book “Optica” in which, based on the rectilinear propagation of light, he developed the laws of reflection by applying principles of geometry. Archimedes, developed the geometrical study of parabolas and ellipsoids and, according to the legend, he created big metallic mirrors for focusing the sunlight in order to burn the Roman battle ships during the siege of Syracuse. That was the first time in human history that light was employed as a weapon.

A couple of centuries later, in his book “Optics”, Ptolemy of Alexandria made a full synthesis of all the previous knowledge on light following the concepts of Euclid, Archimedes and Heron of Alexandria, treating refraction, reflection and colors. Refraction of the moonlight and sunlight by the earth’s atmosphere was also analyzed.

Euclid’s “Optica” and Ptolemy’s “Optics” are the first known scientific publications on light’s properties. Only a fraction of “Optics” has been saved, and this is thanks to Arab mathematicians of the 7th to 10th centuries AC.

After the dominance of Christians during the third century AC, the first Byzantine emperors ordered the definite closure and destruction of all Greek mathematical and philosophical academies that were spread from Greece to Egypt through the Middle East. Philosophers and scientists were persecuted and murdered preventing any possibility of scientific development for more than thirteen centuries. The last one of them was Hypatia of Alexandria.

Humanity had to wait until 1620 AC for Snell’s works on refraction and Fermat’s principle, according to which light rays travel along the path of least time. It was at this period that many scientists like, Grimaldi, Boyle, Hook, Descartes and others began studying light’s properties.

Half a century later, in the year of 1670, Newton had retaken the proposals of Pierre Gassendi, who had revived the ideas of ancient Greeks, and advanced the theory that light rays are composed of corpuscles that travel rectilinearly. However, he went further beyond this description by announcing that under specific physical conditions, the light corpuscles may give birth to waves in “aether”, without giving it a precise definition. Surprisingly, in the first edition of his book “Opticks”, the light corpuscles and the generated “aether” waves were replaced by particles submitted to a kind of “periodic relief”.

Parallel to Newton, in the year of 1680, Huygens developed a remarkable wave theory for light, deducing the laws of reflection and refraction while demonstrating that wave propagation may not be in contradiction with the rectilinear propagation. Huygens’ wave theory was a hard opponent to Newton’s particles concept.

In the beginning of the 19th century, Young’s experiments demonstrated that interference can be obtained by different waves, while Fresnel applied the wave theory to explain the diffraction patterns observed experimentally. Furthermore, Young explained some polarization observations by making the hypothesis that light oscillations are perpendicular to the propagation axis. Nevertheless, not even a scientist could seriously consider the interference theory and Young’s studies were berated by the journalists. Nearly twenty years later, the diffraction theories of Young and Fresnel, though not identical, were the only ones capable of predicting all the observed diffraction patterns and that was really the crucial turnover point in the 19th century following which the scientific community started to generally accept the wave nature of light.

The wave theory was dominant until the beginning of 20th century. It is worth noting that until that time, nearly for more than 2500 years, the main question for scientists was focused on the particle or the wave nature of light, but nobody had advanced any specific questions on the real nature of light, i.e., a corpuscle made of what? or a wave of what?

In 1865, James Clerk Maxwell published his remarkable work on the electromagnetic waves issued from … Maxwell’s equations describing the relations between the electric and magnetic fields, and has shown that the electromagnetic waves propagate in vacuum at the same speed observed by astronomers for light. For the first time the speed of light was related directly to the vacuum electric permittivity and magnetic permeability showing the natural relationship between light and vacuum. Just a few years later, Hertz discovered the long wavelength electromagnetic radiation demonstrating that it propagates at the speed of light confirming Maxwell’s theory.

It is quite amazing in the history of science that Maxwell’s and Hertz’s works, carried out within roughly ten years, were absolutely revolutionary and decisive in our understanding about the nature of light, which remained stationary for over 25 centuries.

At the same period, from 1880 to 1900, the works of Stefan, Wien and Rayleigh have shown for the first time the direct relationship between the thermal radiation energy and the temperature of the emitting body, assimilated to a black body. However, the emitted radiation energy density of the black body as a function of the temperature calculated by Rayleigh, failed to describe the experimental results obtained at short wavelengths. Scientists had given the name of “UV catastrophe” to this situation which revealed the necessity of a new theoretical approach.

In the very beginning of the 20th century, Max Planck assumed that the bodies are composed of “resonators”, a kind of oscillators that have the particularity of emitting the electromagnetic energy in packets of hν, thus proportional to the wave frequency ν times h, that was later called Planck’s constant. This hypothesis permitted Planck to establish the correct energy density expression for the radiation emitting from a black body with respect to temperature, which is in excellent agreement with the experiment.

In 1902, Lenard pointed out that the photoelectric effect, discovered by Hertz fifteen years earlier, occurs beyond a threshold frequency of light and the kinetic energy of the emitted electrons does not depend on the incident light intensity.

The experiments carried out by Michelson and Morley demonstrated that the speed of light in vacuum is a universal physical constant. This fundamental discovery was the starting point for the development of the theory of special relativity, based on Lorentz’s set of equations followed by Poincare’s theoretical studies. Einstein grouped all these works in an elaborated theory published in 1905. During the same year, based on the works of Planck and Lenard, Einstein published also an article stating that the electromagnetic radiation is composed of quanta of energy hν and advanced a simple particle interpretation of the photoelectric effect. In a second article in 1917, Einstein re-established Planck’s radiation density formula and expressed that the light quanta have a momentum hν/c, where c is the velocity of light in vacuum. He advanced that “the energy of a light ray when spreading from a point consists of a finite number of energy quanta localized in points in space, which move without dividing and are only absorbed and emitted as a whole”. That was a decisive step toward the particle theory of light, but Bohr, who was strongly opposed to the photon concept, announced in his Nobel lecture, “the light quanta hypothesis is not compatible with the interference phenomena and consequently it cannot throw light in the nature of radiation”. The concept of light composed of quanta was still not generally accepted.

Compton published his works on X-ray scattering by electrons in 1923 showing that the experimental results can only be interpreted based on the light quanta model. On the other side, Wentzel in 1926 and Beck in 1927 demonstrated that “the photoelectric effect may be quite well interpreted using Maxwell’s wave theory for radiation and quantum theory for the atomic energy levels without ever having to introduce the light quanta” in their calculations....