Origin of Quantum Mechanics III: The Atomic Structure and the Electron

^{Source of Image here.}  

^{By Dr. Inés Urdaneta  / Physicist at  Resonance Science Foundation}

In our previous article entitled Origin of Quantum Mechanics II: Black Body Radiation and Quantization of the Electromagnetic Field we saw that quantum mechanics started from the combined results of two experiments called black body radiation and photoelectric effect, which indicated that matter could only exchange energy -absorb or emit- through discrete packets, quanta of energy that were called photons, which gave a corpuscular aspect to light. Light, which is observed macroscopically as a continuous wave, must then be composed of these discrete packets of energy called photons. This allowed light and matter to exchange photons, i.e., integer units of energy.

The main interlocutor between light and atoms are the electrons that make up the atom. Roughly speaking, it is the electron inside the atom that absorbs or emits electromagnetic radiation in the material, which, as we have pointed out before, must come in discrete packets, or whole numbers. That is to say that the electron is only allowed to absorb or emit one photon, two photons, etc, and not half a photon, three quarters of a photon, etc. The energy exchange between light and matter was quantized.

Now, what does this tell us about the nature of matter, the atom, and its internal structure?

Before our current atomic model, the first well-established model for the atom was that of the Danish physicist Niels Bohr, proposed in 1913, and it was the first quantized representation of the atomic structure. This model progressively evolved into what is now described by quantum mechanics as the wave function, a solution to the famous Schrödinger equation that describes the energy and time evolution - the position and velocity - of fundamental subatomic particles such as electrons. As we have discussed in Origin of Quantum Mechanics I and II, quantum mechanics emerged gradually from theories that attempted to explain observations that could not be reconciled with classical physics.

^{Niels Bohr}

Bohr's atomic model is the result of his studies of the empirical relationships between the spectral emission lines (in other words, the emission of light at different frequencies or colors) of the hydrogen (H) atom, measured by Balmer and Rydberg.  Bohr discovered that when he multiplied the frequencies of the hydrogen spectral series lines (called the Balmer series, see figure below) by Planck's constant h, he could calculate the gaps (the scientific term is energy levels) between the different possible frequencies (or colors) of the hydrogen atom. In other words, Bohr discovered that the lines in the figure below fall at frequencies that are multiples or integers of Planck's constant h.

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

^{Figure: Balmer series for hydrogen, showing the emission spectrum of the H atom, which is the fingerprint of the atom. Each element in the periodic table has a particular emission spectrum. Note the spacing between the lines; Bohr found that these lines fall at frequencies that are multiples or integers of Planck's 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. Nevertheless, Bohr’s model is a great illustration of the basic principles of the atom structure and its quantization. The Bohr radius (a₀) 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 discovery of the electron as a subatomic particle is closely related to the history of atomic structure as such. If you want to know more in depth about the history of the electron, go to this RSF article, A Brief History of the Electron.

RSF in Perspective

From modern physics, this would be the end of the story about the origin of quantisation, and hence of quantum mechanics.  But there is a fundamental limitation, a problem still unanswered in that paradigm: how to include gravity in quantum theory?

To answer this question, we must delve deeper into the origin of quantisation. Not only matter and light are quantized, or rather, for them to be quantized - for them to have a quantum nature - there must be an even finer quantization, in the structure of space. That is, space itself must be quantized into particles or energy units, or volumes of space!

And that is what Nassim Haramein discovers, by finding a structure and a volume with which to voxel the apparently empty space at the macroscopic scale, but filled with ever greater energy as we dive into the smaller, quantum and subquantum scales. By defining a very tiny fundamental unit for that space; a spherical volume with Planck radius, called the Planck Spherical Unit PSU, Haramein finds the true origin of quantization ... space itself is organized into discrete units of energy, the PSUs, which by organizing and interacting with each other, create the reality we perceive. The clue is to find the appropriate thermodynamics of such novel particles of space. 

Just as water appears liquid - a continuous flow - but upon close inspection, we see that it is composed of tiny water molecules, which in turn are composed of hydrogen and oxygen atoms, which are energetic units (or vibrations) confined in very small spherical shapes, so space appears continuous and "fluid", when in reality it is composed of incredibly fast vibrations, because they are resonances confined in infinitely small volumes, which could even be considered singularities. 

As Haramein explains, it makes no sense to look for the smallest particle, because there will always be smaller ones ... the important thing is to find the pattern of division, or quantization, of space. On that pattern of division is based his generalized holofractographic model, from which we will soon know how particles, fields, and forces emerge from the plasma of the quantum vacuum. 

PSUs represent the shape and structure of the fluctuations of the quantum vacuum, and the splitting pattern does not stop there, it can go deeper, because it is a fractal pattern.