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Exploiting quantum entanglement with photons : : feature

Melanie G. McLaren, Andrew Forbes

Published Mar 1, 2015• 0 citations
OpenAlex

Abstract

The theory of quantum mechanics was first introduced over 100 years ago when Max Planck, often referred to as the 'Father of quantum theory', planted the seed of quantum mechanics in a number of scientific minds. The origin of the science of quantum mechanics lies in Planck's theory of black body radiation - called Planck's Law.

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The theory of quantum mechanics was first introduced over 100 years ago when Max Planck, often referred to as the 'Father of quantum theory', planted the seed of quantum mechanics in a number of scientific minds. The origin of the science of quantum mechanics lies in Planck's theory of black body radiation - called Planck's Law.
Most textbooks say that quantum mechanics came into being when Max Planck, in a desperate attempt to construct a theory that explained experimental data, explored the radical idea of energy being radiated or absorbed by all bodies in discrete packets (or quanta). The energy content of a quantum of radiation is proportional to the frequency of the radiation emitted or absorbed, as in , and the proportionality constant bears the name of Planck. Planck himself was rather uncomfortable with the idea of energy packets, and spent a considerable amount of time in later years trying to “restore” the classical picture of continuous energy exchange between bodies and surroundings. However, in 1905 Einstein was able to use the idea of the quantum to explain the mechanism of the photoelectric effect, which cannot be explained in any other way! This established the reality of the quantum and so, it may be said that Einstein, rather than Planck, is the father of quantum mechanics. Within a few years, Neils Bohr constructed his model of the hydrogen atom in which the electron can only occupy certain special orbits around the nucleus, and any jump between these orbits is accompanied by energy being absorbed or emitted in the form of quanta. The nearly exact agreement of Bohr’s predictions based on the model and observed hydrogen atomic spectra was among the first impressive accomplishments of quantum mechanics.
This chapter presents the basic physical ideas that underpin the quantum theory. Historians place the beginnings of the quantum theory at 1900. That year Max Planck published his famous formula for the distribution of energy as a function of frequency in black-body radiation. Curiously, although radiation theory gave birth to quantum mechanics, the interaction of matter and electromagnetic radiation is a rather advanced topic in quantum mechanics and it took almost fifty years for an acceptable formulation to be achieved. One reason for this is that photons are quanta of the electromagnetic field, and the quantum theory of fields requires a relativistic treatment to be entirely successful. The corpuscular nature of light was only half of the input that gave birth to quantum mechanics. The other half concerns matter. Given that the discreteness of photons manifests itself during the emission and absorption process, it is not surprising to find that quantum oddities afflict the behaviour of material particles too.
This chapter begins by understanding the classical view of an electromagnetic wave and proceed step-by-step in exploring the historical development of quantum mechanics. The frequency of the electromagnetic wave is the same as the frequency of mechanical oscillation of the charge, and the intensity of the electromagnetic wave is the square of the amplitude of the mechanical oscillation of the charge. The origin of quantum mechanics is linked to the discovery of then new laws of radiation by Max Planck in 1900. The explanation of the empirical facts of radiation by Planck using an extraordinarily powerful yet simple model lead to the discovery of the "quantum" nature of radiation. The work to develop a mathematical theory of quantum mechanics continued for a very long time. Two mathematical approaches for the formalism of quantum mechanics emerged. One was developed in 1925 by Werner Heisenberg, called matrix mechanics, and the other was developed by Erwin Schrodinger in 1926 called wave mechanics.
In this chapter, we present the basic principles of the quantum mechanics of particle systems from a modern mathematical perspective. The proper study of quantum mechanics brings together several interesting mathematical ideas, ranging from group representations to the spectral theory of unbounded self-adjoint operators in Hilbert spaces and the theory of C * algebras. The facts from analysis of operators in Hilbert spaces and C * algebras needed in this chapter are presented in detail in the appendices at the end of the book. More on the mathematical foundations of quantum mechanics can be found in the books by L. Fadeev and O. Yakubovskii [FY], G. Mackey [M], and F. Strocchi [Str] listed in the bibliography. The birth of quantum theory The origins of quantum theory can be traced back to M. Planck's study, published in 1900, of so-called black-body radiation. It is well known that matter glows when heated, going from red-hot to white-hot as the temperature rises. The color (or frequency of radiation) of the radiating body is independent of its surface, and for a black body it is found to be a function of temperature alone. The behavior of the radiation energy as a function of temperature seemed quite different at high temperatures and low temperatures. In a desperate attempt to fit these different behaviors into a single law, Planck introduced the hypothesis that energy was not continuous, but came in discrete packets or quanta . At the beginning of the twentieth century, a number of experiments pointed to a breakdown of the laws of classical mechanics at very small (subatomic) scales.
Quantum theory originated from the constant introduced by Max Planck in his radiation law in 1900. Later Niels Bohr used the idea of matter waves for the explanation of atomic spectra. Heisenberg gave an algebraic treatment, called matrix mechanics, while Erwin Schrödinger formulated his wave mechanics. He published the first of four papers containing the celebrated equation in the Annalen der Physik in 1927, and showed that the atomic spectra resulted from solving his wave equation for the vibrational states. Schrödinger moved from Zürich to Berlin as Planck’s successor. In the year 1933 he shared the Nobel Prize for Physics with Dirac. With Hitler’s coming to power, however, Schrödinger was outraged and decided to leave Germany to take up a fellowship in Oxford. In 1934 he was offered a permanent position at Princeton University, but he did not accept it. He took a position at the Institute for Advanced Studies in Dublin in 1938, where he stayed till his retirement in 1955.
Newtonian mechanics is the foundation of Classical Physics. Newton’s mechanics, Thermodynamics, Wave theory of Optics and Maxwell’s electromagnetic theory belong to regime of Classical Physics and can be used to explain a wide range of phenomena in the Universe at macroscopic scale. These theories fail spectacularly when applied to phenomenain the atomic and nuclear regime, for example, proton-atom scattering or the flow of electrons in a semiconductor. Quantum mechanics is the most successful scientific theory that has ever been created and it has completely changed our view of the world. The failure of Classical Physics was highlighted by black body radiation and photoelectric effect. Max Planck and Albert Einstein provided explanations of both phenomena based on quantum hypothesis and are thus considered founders of Quantum Physics. The origin of quantum mechanics goes back to the mid-1920s.It was formulated first as matrix mechanics by Werner Heisenberg, Max Born and Pascual Jordan; then as wave mechanics by Louis de Broglie and Erwin Schrödinger; and later on asquantum statistics of subatomic particles by Fermi-Dirac and Bose-Einstein. Combining relativistic mechanics with quantum mechanics, Dirac formulated his relativistic quantum mechanics during 1930s. Uncertainty Principle is thecornerstone of Quantum Physics. The role of randomness in microscopic physical processes shatters the myth that the universe is deterministic. Quantum world is unpredictable in the classical sense and demolishes the idea of an objective universe. The Copenhagen interpretation remains the quantum mechanical formalism that is currently most widely accepted amongst physicists.Quantum theories support cosmic spirit pervading the cosmos and inter – relationship of individuals in the world society. Quantum philosophy is holistic and is going to revolutionize our world-view.