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NeuroQuantology

Acceleration beyond the speed of light, a contradiction, and a synthesis of quantum mechanics and special relativity

Published Jun 17, 2023• 1 citation
Publisher

Abstract

Both the intuitive (classical) and counter-intuitive (quantum) phenomena/effects of light have attracted layman and educated specialists alike.Optics is one of the oldest subfields of physics and is dedicated to the study of these phenomena.Geometrical optics, also known as ray optics, deals with light phenomena like diffraction, interference, polarisation, etc., for which the ray approximation is not valid, while physical optics, also known as wave optics, deals with these phenomena and more.

DOI
10.48047/nq.2022.20.10.nq551271

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Both the intuitive (classical) and counter-intuitive (quantum) phenomena/effects of light have attracted layman and educated specialists alike.Optics is one of the oldest subfields of physics and is dedicated to the study of these phenomena.Geometrical optics, also known as ray optics, deals with light phenomena like diffraction, interference, polarisation, etc., for which the ray approximation is not valid, while physical optics, also known as wave optics, deals with these phenomena and more.
What light is and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: geometrical optics, wave optics and quantum optics are increasingly sophisticated descriptions, each referring to a larger class of phenomena than its predecessor. But how exactly are these theories related? How and when wave optics reduces to geometric optics is a rather simple problem. Similarly, how quantum optics reduces to wave optics has also been considered to be a very simple business. It is not so. As we show here the classical limit of quantum optics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects.
Ever splitting the light! How often do they strive to divide that which, despite everything, would always remain single and whole. Goethe (quoted in Zajonc 1993) Introduction The use of electromagnetic wave theory and geometrical optics to describe propagation of light is satisfactory when there is no exchange of energy between radiation and matter. All observable characteristics – direction of propagation, polarization, diffraction, interference, the energy of radiation, and so forth – are accurately described by one of these so-called classical theories. However, with the exception of absorption by lossy media (eqn. 4.36) or the effects of dispersion (eqn. 4.22), classical theories fail to give reasons for many phenomena that have practical consequences in modern technology and that involve interaction between radiation and matter. Even the partially successful descriptions of dispersion or loss cannot explain the existence of the multitude of spectrally distinct absorption lines; cannot predict the wavelengths for absorption or the wavelengths for anomalous dispersion; cannot account for all the absorbed energy; and, most importantly, cannot predict or describe the effect of optical gain, which is closely related to absorption. Thus, the principles of operation of many important devices of modern optics such as lasers, photodiodes, electronic cameras, and television screens cannot be explained by classical theories. Even the emission by the sun or an incandescent lamp are beyond the scope of these theories. It is evident therefore that a new, modern theory is necessary – one that is either more complete than, or simply complements, the classical theories.
The behavior of light and its interaction with matter is certainly one of the most interesting phenomena of physics. It has puzzled thinkers and scientists in ancient Greece (Archimedes) and through the Middle Ages, at least since the times of Robert Grosseteste (1168–1235), right up to the theories of Galileo Galilei and Isaac Newton. The classical electromagnetic theory of light (see Tab. 13.1) was beautifully established in the second half of the nineteenth century with the Maxwell equations. Quantum optics is nothing other than the quantum theory of light. It finds its roots in Planck's discovery (1900) that the assumption of energy quantization for a harmonic oscillator allowed us to solve the black-body problem (see Subsec. 1.5.1). The successive early steps that led to the quantization of the electromagnetic field include Einstein's explanation of the photoelectric effect with the introduction of the quantum of light (see Subsec. 1.2.1) and the interpretation of atomic spectra (see Subsec. 1.5.4). Quantum optics is usually not covered by conventional textbooks on quantum mechanics. We include its discussion here for two main reasons: first, because it is a fundamental and advanced application of the basic framework of quantum mechanics, and, second, because in the last 30 years quantum optics has played (and is still playing) a major role in the advancement and understanding of quantum mechanics.
Wave mechanics In the classical dynamics the state of the system whose coordinates are q 1 … q s and momenta p 1 … p s is denoted by a point in 2s-dimensional space (the q-space); changes in the system are indicated by the passage of the point along some curve in this space, a ‘ray,’ it may be called. Schrödinger's new concept is that changes in the system should be represented in the q-space not by ‘rays’ but by ‘waves.’ He regards the classical mechanics as only an approximation to actual mechanical events, which he says can only be described by wave mechanics; the former in his view bears to the latter just the same relation as geometrical (or ‘ray’) optics does to physical (or ‘wave’) optics. A large scale (macroscopic) mechanical process corresponds to a wave signal in the g-space, which can be regarded as a point in comparison with the geometrical structure of its path. But for small scale (microscopic) processes, such as atomic phenomena are, the rigorous wave theory must be used. The wave equation must replace the usual dynamical equations. The latter are just as unfruitful for the purposes of atom mechanics as geometrical optics alone would be to clear up the fine points of diffraction phenomena.
It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical characterization of electromagnetic radiation is isomorphic to the treatment of the orientation of a spin-1/21/21/2 particle. In this paper, motivated by Grover's original intuition and starting from this mathematical equivalence, we present a quantitative link between the geometry of time-independent optimal-speed Hamiltonian evolutions on the Bloch sphere and the geometry of intensity-preserving propagation of light with maximal degree of coherence on the Poincar\'e sphere. Finally, identifying interference as the fundamental physical ingredient underlying both physical phenomena, we propose that our work can provide in retrospect a quantitative geometric background underlying Grover's powerful intuition.