scholarly journals Constraints on the String T-Duality Propagator from the Hydrogen Atom

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1478 ◽  
Author(s):  
Michael F. Wondrak ◽  
Marcus Bleicher
Keyword(s):  
Hydrogen Atom ◽  
String Theory ◽  
State Energy ◽  
Generalized Uncertainty Principle ◽  
Structure Constant ◽  
Zero Point ◽  
Fine Structure Constant ◽  
Full Agreement ◽  
Logarithmic Term ◽  
First Time

We investigated the implications of string theory in the high-precision regime of quantum mechanics. In particular, we examined a quantum field theoretical propagator which was derived from string theory when compactified at the T-duality self-dual radius and which is closely related to the path integral duality. Our focus was on the hydrogen ground state energy and the 1 S 1 / 2 − 2 S 1 / 2 transition frequency, as they are the most precisely explored properties of the hydrogen atom. The T-duality propagator alters the photon field dynamics leading to a modified Coulomb potential. Thus, our study is complementary to investigations where the electron evolution is modified, as in studies of a minimal length in the context of the generalized uncertainty principle. The first manifestation of the T-duality propagator arises at fourth order in the fine-structure constant, including a logarithmic term. For the first time, constraints on the underlying parameter, the zero-point length, are presented. They reach down to 3.9 × 10 − 19 m and are in full agreement with previous studies on black holes.

scholarly journals Fine Structure Constant, Domain Walls, and Generalized Uncertainty Principle in the Universe

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Luigi Tedesco
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Domain Wall ◽  
Uncertainty Principle ◽  
Ground State ◽  
Domain Walls ◽  
Generalized Uncertainty Principle ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
The Universe

We study the corrections to the fine structure constant from the generalized uncertainty principle in the spacetime of a domain wall. We also calculate the corrections to the standard formula to the energy of the electron in the hydrogen atom to the ground state, in the case of spacetime of a domain wall and generalized uncertainty principle. The results generalize the cases known in literature.

scholarly journals Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Sébastien Léger ◽  
Javier Puertas-Martínez ◽  
Karthik Bharadwaj ◽  
Rémy Dassonneville ◽  
Jovian Delaforce ◽  
...  
Keyword(s):  
Casimir Effect ◽  
Structure Constant ◽  
Zero Point ◽  
Fine Structure Constant ◽  
Many Body ◽  
Bloch Oscillations ◽  
Superconducting Circuits ◽  
High Impedance ◽  
Non Linear ◽  
Large Phase

AbstractElectromagnetic fields possess zero point fluctuations which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain, these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by zero point fluctuations in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modeling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about thirty environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.

scholarly journals Elucidating the Nature of the Fine Structure Constant and Indicating the Existence of an Unknown Angular Momentum

2017 ◽  
Vol 9 (4) ◽  
pp. 17
Author(s):  
Koshun Suto
Keyword(s):  
Angular Momentum ◽  
Fine Structure ◽  
Hydrogen Atom ◽  
Structure Constant ◽  
Physical Constant ◽  
Natural World ◽  
Fine Structure Constant ◽  
Relativistic Energy ◽  
Planck Constant ◽  
Virtual Particle

In this paper, the author searches for a formula different from the existing formula in order to elucidate the nature of the fine structure constant a. The relativistic energy of the electron in a hydrogen atom is expressed as E_re,n and the momentum corresponding to that energy is taken to be P_re,n. Also, P_p,n is assumed to be the momentum of a photon emitted when an electron that has been stationary in free space transitions to the inside of a hydrogen atom. When n=1, the ratio of P_re,1 and P_p,1 matches with a. That is, P_p,1/Pre,1=a Also, the formula for the energy of a photon is E=hv. However, this formula has no constant of proportionality. If one wishes to claim that the energy of a photon varies in proportion to the photon's frequency, then a formula containing a constant of proportionality is necessary. Thus, this paper predicts that, in the natural world, there is a minimum unit of angular momentum h_vp smaller than the Planck constant. (The vp in h_vp stands for “virtual particle.”)If this physical constant is introduced, then the formula for the energy of the photon can be written as E=h_vp v/a. If h_vp exists, a formula can also be obtained which helps to elucidate the nature of the fine structure constant.

scholarly journals Electric Charge and Its Field as Deformed Space

2019 ◽  
Vol 11 (4) ◽  
pp. 29
Author(s):  
Shlomo Barak
Keyword(s):  
Fine Structure ◽  
Electric Charge ◽  
Structure Constant ◽  
Electromagnetic Theory ◽  
The Other ◽  
Fine Structure Constant ◽  
Electric Charge Density ◽  
Electron Positron ◽  
Simple Equations ◽  
First Time

The essence of electric charge has been a mystery. So far, no theory has been able to derive the attributes of electric charge, which are: bivalency, stability, quantization, equality of the absolute values of the bivalent charges, the electric field it creates and the radii of the bivalent charges. Our model of the electric charge and its field (this paper) enables us (in additional papers), for the first time, to derive simple equations for the radii and masses of the electron/positron muon/anti-muon and quarks/anti-quarks. These equations contain only the constants G, c, ℏ  and α (the fine structure constant). The calculated results based on these equations comply accurately with the experimental results. In this paper, which serves as a basis for the other papers, we define electric charge density, based on space density. This definition alone, without any phenomenology, yields the theory of Electrostatics. Electrostatics together with Lorentz Transformation is known to yield the entire Maxwell Electromagnetic theory.

scholarly journals Fine-Structure Constant from Golden Ratio Geometry

2018 ◽  
Author(s):  
Michael A. Sherbon
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Exponential Function ◽  
Golden Ratio ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Electron Mass ◽  
Mass Ratio ◽  
Mathematical Constants

After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients.

scholarly journals The quantum theory of the neutron

1934 ◽  
Vol 145 (854) ◽  
pp. 344-358 ◽  
Keyword(s):  
Wave Equation ◽  
Fine Structure ◽  
Quantum Theory ◽  
Hydrogen Atom ◽  
Ad Hoc ◽  
Structure Constant ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
Second Order Wave Equation ◽  
Plausible Theory

The object of this paper is to show that a plausible theory of the neutron can be developed from Dirac's wave equation without the use of any ad hoc assumptions. It is shown that the second order wave equation of the hydrogen atom, which exhibits the relativistic and spin corrections, possesses two sets of solutions "H" and "N" distinguished by their behaviour as r →0 ( r being the distance of the electron from the proton). The H-solutions are the accepted wave functions of the hydrogen atom. As r →0 these solutions tend to zero if the serial quantum number l differs from zero, and they become infinite of order r [(1 - a 2 ) 1/2 - 1] if l = 0 (α is the fine structure constant).

scholarly journals Numerical task for orbital electron in transition subatomic structure

2021 ◽  
Author(s):  
Mikhail Ivantsov
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Ground State ◽  
Lamb Shift ◽  
Electroweak Interaction ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Multiply Charged ◽  
Electric Interaction ◽  
Orbital Electron

Abstract The present work as part of a known task of single-electron atom has been carried out, wherein one mathematical theorem is proved. Herewith an orbital electron was modeled, for which a certain parallelism exists between the highlighted ground state of the atom and special transition states in subatomic structure. Moreover, the ground state in unambiguous solution of fine-structure constant is obtained, where first transition state at the exceptional accordance with proton nucleus can be founded. For here, it is possible to relate the hyper-fine nuclear structure like the Lamb shift of hydrogen atom. In this substantiation of the task, multiply charged states were predicted for a hypothetical nucleus, as in the higher order of meson-boson transitions. The specified approach, in the terms of electric interaction, may be beyond a scope of the existing boson classification, supposedly for the carriers of electroweak interaction.

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