Two Types of Space in the Hydrogen Atom not Predictable with Quantum Mechanics

Einstein’s energy-momentum relationship is not applicable to the electron in a hydrogen atom. Therefore, the author has previously derived an energy-momentum relationship applicable to the electron inside the hydrogen atom where potential energy exists. However, the initially-derived relationship did not incorporate the discontinuities in energy which are characteristic of quantum mechanics. Therefore, the author derived a new quantum condition to take the place of Bohr’s quantum condition, i.e., , and that was used to incorporate discontinuity into the relationship derived by the author. When that relationship is solved, it is evident that, in addition to the existing energy levels, there are also ultra-low energy levels where the electron mass becomes negative. A previously unknown state of the hydrogen atom exists, formed from an electron with negative mass and a proton with positive mass. The electron with negative mass exists near the proton. The author predicts that this unknown matter is the true nature of dark matter, an unknown source of gravity whose true nature is currently unknown.

High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph

The Kubo–Martin–Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and Verboven, proposed an analogue to the KMS condition for infinite classical mechanical systems and highlighted its relationship with the Kirkwood–Salzburg equations and with the Gibbs equilibrium measures. In this paper, we prove that in a certain limiting regime of high temperature the classical KMS condition can be derived from the quantum condition in the simple case of the Bose–Hubbard dynamical system on a finite graph. The main ingredients of the proof are Golden–Thompson inequality, Bogoliubov inequality and semiclassical analysis.

The Relationship Enfolded in Bohr’s Quantum Condition and a Previously Unknown Formula for Kinetic Energy

Bohr’s quantum condition is an indispensable assumption for classical quantum theory. However, strictly speaking, Bohr's quantum condition does not hold when deriving the energy of an electron forming a hydrogen atom from the perspective of the theory of relativity. In this paper, it is thought that the relationship enfolded in Bohr's quantum condition, i.e.,  is suitable as a new quantum condition to replace Bohr’s quantum condition. Also, in quantum mechanics, the energy of an electron is derived based on the theory of relativity, as exemplified in the theory of Sommerfeld. However, this paper points out that the previous energy formula based on the theory of relativity is mistaken. It also proposes a previously unknown formula for the kinetic energy of an electron.

Black Holes and Information: A New Take on an Old Paradox

Interest in the black hole information paradox has recently been catalyzed by the newer “firewall” argument. The crux of the updated argument is that previous solutions which relied on observer complementarity are in violation of the quantum condition of monogamy of entanglement, with the prescribed remedy being to discard the equivalence principle in favor of an energy barrier (or firewall) at the black hole horizon. Differing points of view have been put forward, including the “ER = EPR” counterargument and the final-state solution, both of which can be viewed as potential resolutions to the apparent conflict between quantum monogamy and Einstein equivalence. After reviewing these recent developments, this paper argues that the ER = EPR and final-state solutions can—thanks to observer complementarity—be seen as the same resolution of the paradox but from two different perspectives: inside and outside the black hole.

The Quantum Condition and an Elastic Limit

Charles-Augustin de Coulomb introduced his equations over two centuries ago. These equations quantified the force and the energy of interacting electrical charges. The electrical permittivity of free space was factored into Coulomb’s equations. A century later James Clear Maxwell showed that the velocity of light emerged as a consequence this permittivity. These constructs were a crowning achievement of classical physics. In spite of these accomplishments, the philosophy of classical Newtonian physics offered no causative explanation for the quantum condition. Planck’s empirical constant was interjected, ad-hoc, into a description of atomic scale phenomena. Coulomb’s equation was re-factored into the terms of an elastic constant and a wave number. Like Coulomb’s formulation, the new formulation quantified the force and the energy produced by the interaction of electrical charges. The Compton frequency of the electron, the energy levels of the atoms, the energy of the photon, the speed of the atomic electrons, and Planck’s constant, spontaneously emerged from the reformulation. The emergence of these quantities, from a classical analysis, extended the realm of classical physics into a domain that was considered to be exclusively that of the quantum.

Quantum Approximation for Josephson's Tunneling in Thx DUO2 Nano Material for 535 Tesla at Muon Cyclotron

The convergence quantum states of free covariant equation in Einsteins space with quantum condition is studied using the ABR (Abrikosov-Balseiro-Russell) formulation in convergence approximation for Josephson tunneling is important role for determine of neutrino particle existing, especially after Cerenkovs effect for 517 tesla super magnetic at Large Hadron Collider (LHC) Cyclotron in CERN, Lyon, France based on ThxDUO2nanomaterial. This approaching will be solved the problem for determine the value of interstellar Electrical Conductivity (EC) on DUO2chain reaction, then the post condition of muon has been known exactly. In this research shown the value of EC is 4.32 μeV at 378 tesla magnetic field for 2.1 x 104ci/mm fast thermal neutron floating in 45.7 megawatts adjusted power of CERNs Cyclotron. The resulted by special Electron-Scanning-Nuclear-Absorbtion (ESNA) shown any possibilities of Josephsons tunneling must be boundary by muon particles without neutrino particle existing for 350 456 tesla magnetic field on UO2more enrichment nuclear fuel at CERN, whereas this research has purpose for provide the mathematical formulation to boundary of muons moving at nuclear research reactor to a high degree of accuracy and with Catch-Nuc, one of nuclear beam equipment has a few important value of experimental effort.