Atlantis studies in mathematics for engineering and science

From MM1MS1 Models to Traditional Theories

Thomas J. Buckholtz

Published Jan 1, 2016• 0 citations

Abstract

This chapter starts with models this monograph features, discusses extents to which people might correlate or integrate our models with traditional physics theories, and discusses extents people might use our models to extend or improve on traditional physics theories. People might say that results in this chapter might correlate with or provide insight about the following aspects of physics. Similarities and differences regarding concepts that pertain regarding MM1MS1 models, traditional quantum physics, and classical physics. The Dirac equation. Relationships among quadratic operators, linear operators, and conservation laws. Relationships between models correlating with conservation laws and models correlating with internal properties of elementary particles. For the hydrogen atom, energy levels, fine-structure splitting, hyperfine splitting, and the Lamb shift. Possible alternatives to some traditional-physics correlations between some aspects of quantum chromodynamics and some applications of concepts correlating with special relativity. Facets of, uses of, and limits regarding models based on general relativity. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI: 10.2991/978-94-6239-166-6_6

Related papers

The Transition Region as Predicted by Quantum Mechanics

Theo van Holten

In the present chapter the connection between quantum mechanics and classical physics is treated, as derived in established quantum theory. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Atlantis Press eBooksDec 9, 20160 citations

Classical Quantum Mechanics

Randell L Mills

Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].

Physics EssaysDec 1, 200326 citations

Some Quantum Relations

Selected traditional quantum relations are discussed. The intention is roughly to complement a text connected to quantum dynamics with mathematical approaches to some quantum concepts; of course no exhaustive presentation should be expected and parallel reading of traditional books on quantum mechanics is highly recommended. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Basel eBooksJan 1, 20090 citations

Motivation for This Work

Gerard ’t Hooft

The fundamental laws of Nature that govern the physics of atoms, elementary particles, light quanta, and everything else that is small and light, have been found to fit in one grandiose framework called Quantum Mechanics. The internal logic of this framework appears to be counter intuitive and mysterious, while extremely coherent and effective. In this general introduction the author explains why he feels the need for expressing his views on how to understand these facts, even if many known scientists have already given extensive reviews of numerous ideas and approaches. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Fundamental theories of physicsJan 1, 20168 citations

Quantum Mechanics

Susan Loepp, William K. Wootters

The early twentieth century was a revolutionary time in the history of physics. People often think of Einstein's special theory of relativity of 1905, which changed our conceptions of time and space. But among physicists, quantum mechanics is usually regarded as an even more radical change in our thinking about the physical world. Quantum mechanics, which was developed between 1900 and 1926, began as a theory of atoms and light but has now become the framework in terms of which all basic physical theories are expected to be cast. We need quantum ideas not only to understand atoms, molecules, and elementary particles, but also to understand the electronic properties of solids and even certain astronomical phenomena such as the stability of white dwarf stars. The theory was radical in part because it introduced probabilistic behavior as a fundamental aspect of the world, but even more because it seems to allow mutually exclusive situations to exist simultaneously in a “quantum superposition.” We will see later that the possibility of quantum superposition is largely responsible for a quantum computer's distinctive advantage over an ordinary computer. The present chapter is devoted to introducing the basic principles of quantum mechanics. There are essentially four components of the mathematical structure of quantum mechanics. We need to know how to represent (i) states, (ii) measurements, (iii) reversible transformations, and (iv) composite systems. We will develop the first three in stages, starting with a very simple case – linear polarization of photons – and working toward the most general case.

Cambridge University Press eBooksJul 10, 20061 citation

Atom Optics in a Nutshell

Pierre Meystre

This chapter presents a brief introduction to atom optics, assuming only a basic knowledge of elementary physics ideas such as conservation of energy and conservation of momentum, and making only limited use of elementary algebra. Starting from a historical perspective we introduce the idea of wave-particle duality, a fundamental tenet of quantum mechanics that teaches us that atoms, just like light, behave sometimes as waves, and sometimes as particles. It is this profound but counter-intuitive property that allows one to do with atoms much of what is familiar from conventional optics. However, because in contrast to photons atoms have a mass, there are also fundamental differences between the two that have important consequences. In particular this property opens up a number of applications that are ill-suited for conventional optical methods. After explaining why it is particularly advantageous to work at temperatures close to absolute zero to benefit most readily from the wave nature of atoms we discuss several of these applications, concentrating primarily on the promise of atom microscopes and atom interferometers in addressing fundamental and extraordinarily challenging questions at the frontier of current physics knowledge. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Springer eBooksJan 1, 20160 citations