Jun 23, 2022

^{Image source: exciton’s probability cloud showing where the electron is most likely to be found around the hole. }

Whereas our direct experience with protons in everyday life is not evident at all, our experience with electrons is quite different. Many of us are probably familiar with the phenomenon of static electricity that bristles our skin when we rub certain materials. We are also probably used to the notion of electricity as a current or flow of electrons that can light a bulb, turn on an electrical device, or even electrocute someone if not handled properly. We are probably also aware that matter is composed of atoms, and that atoms are composed mainly of protons and electrons. Most of our daily experience is governed by electrons and their interactions with light. Electrons also govern the physico-chemical properties of atoms. Interestingly, the inference and discovery of the electron predates the discovery of the atom itself.

The first recorded observation of the phenomenon of static electricity is believed to be that of Greek pre-socratic philosopher Thales de Mileto, who noticed it when he rubbed materials such as wood or silk with a piece of amber. This effect became associated with the word *electron*, which allegedly comes from the Greek word for amber, ἤλεκτρον. While electricity and electromagnetism had been widely explored by many visionaries since the 1600s (including William Gilbert, Otto von Guericke, Robert Boyle, Alessandro Volta, Hans Christian Ørsted, André-Marie Ampère, Michael Faraday, Georg Ohm and James Clerk Maxwell, to name the most well-known), it was the Irish physicist George Stoney who first introduced the concept of a fundamental unit of electricity. Then, in 1874, he coined the term Electrine, an atom of electricity. In 1881, Stoney adopted the name “electron” for this unit of charge. He made significant contributions not only to the conception and calculation of this unit, but also to cosmological and gas theory physics. His work laid the foundation for the discovery of an electron outside of matter performed by J.J. Thomson in 1879 at the Cavendish Laboratory in Cambridge University.

^{ George Stoney and his daughters.}

The discovery and description of the electron inside the atom (also called a bounded electron) involved decades of research by many physicists and chemists. But here, we’ll just say that it was a combination of discoveries that brought us the current model of an atom composed of a nucleus (made of protons and neutrons) surrounded by clouds of electrons. These include: 1) the inference of the atom years before by English chemist John Dalton in 1800, through experiments proving a law of multiple proportions; 2) the discovery of radioactivity by Becquerel in 1896, and later, the experiments of Pierre and Marie Curie (along with experiments by Rutherford and Geiger); 3) the discovery of the proton by Rutherford in his famous gold foil experiment in 1909 4) the discovery of the neutron by the physicist James Chadwick in 1932, which defined isotopes as elements whose nuclei have the same number of protons but different numbers of neutrons, among many other studies.

Prior to our current atomic model, the first well-established model for the atom was Niels Bohr’s model, proposed in 1913, and it was the first quantized depiction of the atomic structure. This model evolved progressively into what is now described by quantum mechanics as *wavefunction*, a solution to the famous Schrödinger equation that describes the energy and evolution in time, position, and velocity of fundamental subatomic particles like electrons.

As we have addressed in The Origin of Quantum Mechanics I and II, quantum mechanics emerged gradually from theories that tried to explain observations which could not be reconciled with classical physics.

From the perspective of quantum mechanics, particles are believed to have extremely low mass, so gravity is considered negligible at this scale and all interactions between these particles would be governed either by the strong force (holding quarks together in a proton), the nuclear force (holding protons together in a nuclei of an atom) or the electromagnetic or color force (between charges). The problem of how to include gravity in quantum theory (mainly because the total energy-mass of the sub atomic particle is unacknowledged) makes it impossible for it to resolve the missing link between relativity (the physics of the macroscopical and cosmological scale, in which the mass of the celestial bodies, and hence, their gravity, plays a crucial role) and quantum mechanics. This missing link is quantum gravity.

*The origin of our current Electron model and the atomic spectra of elements*

The electron is considered a fundamental particle in the sense that it has not been shown to have an inner structure. QED (quantum electrodynamics), the field of quantum mechanics describing electrons and their interactions with photons, notoriously describes the electron as a zero-dimensional point particle with no volume, so there is no definitive description of the structure of either electrons or photons. We have a very clear idea of their effects and the interactions between them, but very little is known about their nature.

One of the most precise values we have for the electron is its mass, which is determined using penning traps. These measurements are extremely precise, with a relative uncertainty on the order of 10^{--11}. The standard theoretical value given for the mass of the electron confirms the measured CODATA 2018 value based on the definition of the mass of the electron given by the following expression:

where *R** _{∞}* is the Rydberg constant,

The definition of Eq. (1) shows the combination of fundamental constants that are used to calculate the mass of the electron, and its derivation started with the model for the hydrogen atom (H) proposed by Danish physicist Niels Bohr in 1913. Bohr's atomic model is the result of his studies of the empirical relationships between spectral emission lines (in other words, the light emission at different frequencies or colors) of the H atom, as measured by Balmer and Rydberg. He found that when he multiplied the frequencies of the lines in the hydrogen spectral series (called Balmer series, Figure below) by Planck’s constant *h,* he could calculate the gaps (the scientific term is energy levels) between the various possible frequencies (or colors) of the hydrogen atom. In other words, Bohr found that the lines in the Figure below fall at frequencies that are multiples or integer numbers of Planck’s Constant *h*. The emission spectrum is the digital print of an atom.

The emission spectrum of an element is usually given in terms of wavelength, which is the inverse of the frequency.

^{Figure: Balmer series for Hydrogen, showing the emission spectra of H atom, which is the fingerprint of the atom. Every element in the periodic table has a particular emission spectra. Notice the separation between the lines; Bohr found that these lines fall in frequencies that are multiple or integer numbers of Planck Constant h. }

Based on this information, Bohr proposed an atomic model consisting of the electron with a negative charge which is attracted to the positive charge of the proton in the nucleus because of the electrostatic force defined by Coulomb's law. Instead of falling into the positive charge, the electron is held in orbit by the centrifugal force created by the rotation of the electron around the nucleus. The only assumption he made was that the mass of the electron was much smaller than that of the proton, and he found that the angular momentum (the speed of the electron’s rotation around the nucleus) was also quantized by Planck's constant *h*, producing stable electron orbits, or shells.

In Bohr's model of concentric electron shells, electrons are seen as tiny particles that jump from one orbital to another, as seen in the figure below, where an electron jumps from the third orbital (*n* = 3) to the second orbital (*n* = 2), emitting one photon (red curved arrow) with frequency *f* = *v. *In this model, *n* is always an integer, and it identifies the numerical order of the electron shells, as well as the number of photons exchanged. Hence, the term quantization applies; the energy exchange within the atom or between the electron and light happens in integer numbers of *hf*. For example, the change in energy (written as *ΔE*) of an electron jumping from orbital *n* = 3 to orbital *n* = 2 is *ΔE* = (3-2)*hv . *Since 3-2 = 1, then only one photon is emitted; on the other hand, for the electron to jump from an inner shell (*n* = 2) to an outer shell (*n* = 3), it needs to absorb one photon instead of emitting it. Jumps can be nonlinear (jumps over more than 1 orbital and emitting or absorbing multiple photons), but this requires very intense interaction with light. Such scenarios happen in high-energy situations, like in stars, for instance, or during experiments using laser fields at high intensity. Nonlinear interactions are very important and difficult to describe.

^{Since the atom is neutral (has no net charge), the number of protons (positive charges) in the nuclei, Z, equals the number of electrons (negative charges) in the atom. The electrons are placed in orbitals which are stable. For the H atom, Z = 1, meaning there is only one proton (positive charge +1e) and hence, only one electron with charge -e (the green point). In this figure, an electron jumps from orbital n = 3 to orbital n = 2, emitting one photon (red curved arrow) with frequency f = v. Image from: }^{https://sciencenotes.org/bohr-model-of-the-atom/}^{. }

Bohr's model of the atom predicted a radius for the H atom with the electron in the fundamental state (*n* = 1), and it gained credibility in 1913 with a paper predicting that some anomalous lines in stellar spectra were due to ionized helium, not hydrogen, which astronomy spectroscopist Alfred Fowler quickly confirmed. Thanks to Dirac’s, Heisenberg’s, Schrodinger’s and many other physicists’ developments, Bohr’s model has gone through substantial changes and improvements, refining this semi-classical atom model which is now described entirely by the current quantum mechanics theory that gives the final expression for the electron mass in Eq. 1. Nevertheless, Bohr’s model is a great illustration of the basic principles of the atom structure and its quantization. The **Bohr radius** (*a*_{0}) is considered a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state, and its value is 5.29177210903(80)×10^{−11} m.

The Rydberg constant *R** _{∞}* was first determined empirically in 1888 by the Swedish physicist Johannes Rydberg as an appropriate parameter for the hydrogen spectral series. Later, in 1913, Niels Bohr showed that in the case of lighter atoms, the Rydberg constant value could be calculated from more fundamental first principles by utilizing his Bohr model. For this reason, his model was rapidly adopted.

On the other hand, the nature of fine structure *α* constant found in Eq. (1) is a mystery. We could even say it is the most fundamental constant as it doesn’t depend on the units used; on the contrary, it seems like all physical properties depend on it. Its value is very close to 1/137 and it can be derived in different contexts. An interesting derivation of *α* in the context of studying unified physics is that of the electron charge *e* divided by the Planck charge *q*_{l}__:__

Physics Nobel laureate Richard Feynman says about the fine structure:

^{"... It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number for a coupling comes from: is it related to Pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!" }^{― Richard P. Feynman, }^{QED: The Strange Theory of Light and Matter}^{ }

^{Richard Feynman at Caltech. Image courtesy of the }^{American Institute of Physics}

From all the above, we can appreciate how the exploration and discovery of the atomic structure and its interaction with light has led the way to what is considered one of the most precise theoretical equations encountered in physics. However, Eq (1) is not entirely derived from first principle notions, and thus it provides little to no insight into what the electron is.

Also, in the standard approach, quantum chromodynamics (QCD), nuclear masses like the proton are calculated by considering not only the quark masses but, more importantly, the dynamics of the system. These dynamics are complex to describe due to the number of different interactions involved, which results in a non-linear description of both the nuclear force and the confining force or color force (the forces that hold the protons and its constituents together). For this reason, exact calculations of the properties of nucleons and of their constituent parts are extremely difficult and thus rely on computational techniques in which probability amplitudes are assigned to each Feynman diagram (interactions diagrams) and Monte Carlo simulations (or other similar iterative perturbative methods) determine the best fit. Also, the equations from QCD and QED use at least 17 free-adjusting parameters. The absence of a complete analytical solution required the development of sophisticated computational techniques to attempt a precise description of interactions in the nucleon. However, despite the development of ever faster supercomputers, QCD calculations have been unable to successfully predict the mass of the proton and the Higgs mechanism can only account for some 2% of the total mass.

Nassim Haramein’s Generalized Holographic Model [1,2] proves from first principles and without free parameters, that the remaining 98% of mass is accounted for by the energy of quantum vacuum fluctuations. The Generalized Holographic Model is a solution to quantum gravity that is based on a fundamental surface-to-volume holographic ratio *ɸ* that explains the origin of mass and its connection to energy and forces.

“Defining the fundamental characteristics of particles from first principles is of great importance because it provides information not only about the structure of subatomic particles but also about the source of mass and the nature of spacetime itself.”– Dr. Amira Val Baker

Starting with the premise that an electron cloud can be considered an ‘electron’ coherent field of information, we must look at the microstructure of the electron system from a generalized holographic approach, which, in previous work, successfully computes the mass of the proton and the precise charge radius of the proton [1,2] in agreement with the latest electronic measurements [3].

Utilizing the generalized holographic approach, Val Baker et al. demonstrate the electron mass solution in terms of the surface-to-volume entropy measured as Planck oscillator information bits. The value obtained agrees with the measured CODATA 2018 value. In this novel first principles derivation of the mass of the electron, the mass is defined in terms of its holographic surface-to-volume ratio 𝛷 and the relationship between the electric charge at the Planck scale and that at the electron scale.

The new derivation for the mass of the electron extends the holographic mass solution to the hydrogen Bohr atom and to all known elements. As a result, we can now see that atomic structure, mass, and charge emerge from the electromagnetic fluctuations of the Planck quantum vacuum. This new approach generates an accurate value of the mass of the electron and offers an understanding of the physical structure of spacetime at the quantum scale, yielding significant insights into the formation and source of the material world.

Very important parameters of the atom like the fine structure constant, Rydberg constant and the proton to electron mass ratio, are also outputted from the model.

References:

**[1]** N. Haramein, Phys. Rev. Res. Int. 3, 270 (2013)

**[2]** N. Haramein, e-print https://doi.org/10.31219/osf.io/4uhwp (2013)

**[3]** A. Antognini, F. Nez, K. Schuhmann, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, M. Diepold, L. M. P. Fernandes, A. Giesen, A. L. Gouvea, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C-Y. Kao, P. Knowles, F. Kottmann, E-O. Le Bigot, Y-.W Liu, J. A. M. Lopes, L. Ludhova, C. M. B. Monteiro, F. Mulhauser, T. Nebel, P. Rabinowitz, J. M. F. dos Santos, L. A. Schaller, C. Schwob, D. Taqqu, J. F. C. A. Veloso, J. Vogelsang, and R. Pohl, Science 339, 417 (2013)

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