DUALITY OF TIME:
Complex-Time Geometry and Perpetual Creation of Space
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3.4.2 Pauli Exclusion Principle
In 1924, to resolve the inconsistencies between the observed molecular spectra and the predictions of Quantum Mechanics, Wolfgang Pauli (1900-1958) proposed a new quantum degree of freedom, or a quantum number with two possible values. The spectrum of atomic hydrogen had a doublet, or pair of lines differing by a small amount, where only one line was expected. Pauli formulated his exclusion principle, stating that “there cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers.” After one year, Pauli’s new degree of freedom was identified with the property of spin, whose effects were observed in the famous Stern-Gerlach experiment.
Schroedinger calculated the energy levels of hydrogen by treating its electron as a wave, represented by the wave-function, in an electric potential well created by the proton. The solutions to Schroedinger’s equation are distributions of probabilities for electron positions and locations. Orbitals have a range of different shapes in three dimensions. The energies of the different orbitals can be calculated, and they accurately match the energy levels of the Bohr model. Schroedinger found that each electron has four properties:
1.An “orbital” designation, indicating whether the particle wave is one that is closer to the nucleus with less energy or one that is farther from the nucleus with more energy. 2.The “shape” of the orbital, spherical or otherwise. 3.The “inclination” of the orbital, determining the magnetic moment of the orbital around the z-axis. 4.The “spin” of the electron.
The collective name for these properties is the quantum state of the electron, given by its wave-function, and it can be described by giving a quantum number to each of these properties. The Pauli exclusion principle demands that no two electrons within an atom may have the same values of all four quantum numbers. This gives rise to different possible arrangements of the orbitals, and how the electrons fill them, which that leads to the organization of the periodic table of chemical elements. Also, the way the atomic orbitals on different atoms combine to form molecular orbitals determines the structure and strength of chemical bonds between atoms.
... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...
... the theory is also invariant under a local change of phase, so one may shift the phase of all wave-functions so that the shift may be different at every point in space-time. This is called LOCAL SYMMETRY . However, in order for a well-defined derivative operator to exist, one must introduc ...
... new field, called the gauge field, which also transforms in order for the local change of variables not to affect the derivative. In Quantum Electrodynamics, this gauge field is the electro MAGNETIC FIELD . According to Noether’s theorem, for every such symmetry there exists an assoc ...
... oduce a new field, called the gauge field, which also transforms in order for the local change of variables not to affect the derivative. In Quantum Electrodynamics, this gauge field is the ELECTROMAGNETIC FIELD . According to Noether’s theorem, for every such symmetry there exists a ...
... known fundamental interactions in nature are described by gauge theories, including: •Quantum Chromodynamics, whose gauge group is , and the gauge bosons are eight gluons. •The ELECTROWEAK THEORY , whose gauge group is , and the gauge bosons are the photon and the massive and b ...
... whose classical theory is General Relativity, relies on the equivalence principle, which is essentially a form of gauge symmetry, and its action may also be written as a gauge theory of the Lorentz group on tangent space. Read Other Books: The Single Monad Model of the Cosmos ...
... ent to having no fluctuations at all, and they, therefore, have no physical meaning. Such fluctuations are usually called non-physical degrees of freedom or gauge artifacts. Therefore, if a CLASSICAL FIELD theory has a gauge symmetry, then its quantized version will have this symmetry as w ...
... of gauge bosons is the group dimension, i.e., the number of generators forming the basis of the corresponding Lie algebra. All the known fundamental interactions in nature are described by GAUGE THEORIES , including: •Quantum Chromodynamics, whose gauge group is , and the gauge boson ...
... itesimal gauge transformations are the gauge group generators. Thus, the number of gauge bosons is the group dimension, i.e., the number of generators forming the basis of the corresponding Lie algebra. All the known fundamental interactions in nature are described by gauge theories, inclu ...
... represent something physical. Consequently, the theory is invariant under a global change of phases, such as adding a constant to the phase of all wave-functions everywhere. This is called GLOBAL SYMMETRY . In Quantum Electrodynamics, the theory is also invariant under a local change of ph ...
... om, simply because some fluctuations of the fields can be transformed to zero by gauge transformations, so they are equivalent to having no fluctuations at all, and they, therefore, have no PHYSICAL MEANING . Such fluctuations are usually called non-physical degrees of freedom or gauge arti ...
... nsion, i.e., the number of generators forming the basis of the corresponding Lie algebra. All the known fundamental interactions in nature are described by gauge theories, including: •Quantum Chromodynamics, whose gauge group is , and the gauge bosons are eight gluons. •The ele ...
The science of Time is a noble science, that reveals the secret of Eternity. Only the Elites of Sages may ever come to know this secret. It is called the First Age, or the Age of ages, from which time is emerging.
