Part 3

Spacetime Model



Niels Bohr (Nobel Prize - 1922) thought that electrons were continually moving around the nucleus inside the atom.

In the 1930s, Schrödinger (Nobel Prize - 1933) and Max Born (Nobel Prize - 1954) created the concept of "probability density". The third postulate of quantum mechanics states: "the probability of locating the particle is described by the wavefunction...". The word "particle" is not ambiguous and does not mean a wave.

The concept of "probability" is an improvement on Bohr's theory but does not explain why orbitals are quantified (remember that Einstein was opposed to this concept of "probability").

Here we try to bring logical and rational answers to some questions that are mathematically verified but, so far, remain unexplained.

This webpage is the third part of the website
It is strongly suggested to also read the first two pages.


Wave or Particle?

Contrary to preconceived ideas, electrons are moving around the nucleus as punctual particles, as the third postulate of quantum mechanics indicates, but are stationary waves. In reality, atoms are built according to the "wave model" described in the previous webpage. This is a consequence of the explanation of the wave-particle duality given in our website


Energy levels of orbitals

The Schrödinger Equation gives mathematical solutions to orbitals with great accuracy but does not rationally explain why electrons follow predifined orbits. We can take the example of satellites orbiting around Earth. Many satellites may share the same orbit. Why, in quantum mechanics, would it be different? If the electron is a particle moving in all directions around the nucleus, like satellites, there is no reason that orbitals are quantified.

Moreover, if the electron is a punctual particle, the Pauli Principle also can not be explained. Why do orbitals accept a maximum of electrons on each layer (2, 8, 18...)?

If the charge of the electron is distributed in several sCells (see the previous webpages) around the nucleus, according to our "Wave Model", the quantification of orbitals becomes clear and obvious. The following example explains the principle.

Let's place five magnets, all oriented in the same direction. Each magnet is subject to gravity, which attracts it toward Earth, and to a repulsive force due to the adjacent magnets. The lower magnets carry the total weight of the upper ones. This is why spaces between magnets are not equally drawn. So, the levels E1, E2, E3... are dynamically built.

By repeating the same experiment any number of times and under the same conditions, we will always find the same spaces E1, E2, E3... We could think that these magnets are systematically placed on imaginary rails, or "quantum rails", E1, E2, E3... In other words, we could think that the position of each magnet E1, E2, E3... is "quantified". Of course, the explanation is somewhere else.

level_orbitals.gif - Atoms

The above example explains the construction of orbitals inside atoms. Quantum levels are not "predefined" as we think, but are dynamically built.

In the following example, if the magnet E1 is removed, the magnet E2 drops down and takes the empty place of the removed magnet. Other magnets also drop down one level. A dynamic organization is done every time an electron is moved from one place to another. This also explains why electrons goes always on the last layer.

level_atoms.gif - Atoms

The following figure shows energy levels in atoms. The principle is equivalent to the example of magnets. The only difference is that the Coulomb force replaces the magnetic force of magnets.

orbitals.gif - Atoms

Note1: Spin has been intentionally omitted. It is covered in Part 4.
Note 2: In quantum mechanics, there is often confusion between "discrete" and "quantified". In the Schrödinger Equation, we have both definitions. On one hand, the Laguerre Polynomials (or other polynomials), i.e. eigenvalues, which are solutions of the Schrödinger Equation, are discrete. On the other hand, the Planck Constant is a quantified quantity. In all websites of the Spacetime Model, when the two concepts are simultaneously present, we will use the qualifier of "quantified", even if this word is not entirely correct.



To summarize, we can say:

  • Levels are dynamically built, one after the other.
  • An atom cannot have high-level orbitals if low-level ones do not exist. There are, however, a few exceptions (note 1).
  • Since the levels are dynamically built, electrons always tend to fill lower empty layers.
  • If an external disturbance occurs, it modifies the overall magnetic field. In such a case, all the levels may be displaced (level degeneration).

To sum up, the solution of the Schrödinger Equation is not a quantification as in Max Plank's view, but a discrete suite of terms (note 2). Orbitals are dynamically built, taking into account electrons already in place. They also take into account spin (see Part 4). New electrons are distributed in sCells around the nucleus in a wave form, and take their natural place on orbitals having the most favourable Coulomb Force.

Note 1:Sometimes, some orbitals are far from each other. This is the case of the "p" layer orbitals. We can also have coinciding energy levels of layers, like "s" and "p" for example (layers known as "sp").
Note 2: Similar situations also exist on Earth. For example, the propagation of the waves on the membrane of a drum is described by the Bessel Functions, which are similar to Laguerre Polynomials (both are solutions to the Hypergeometric Gauss Function). We do not deduct for all that the membrane of a drum is quantified...


E0 Energy Level

In quantum mechanics, we have another enigma regarding the atom: why, the electron, does not drop on the nucleus yielding its energy? If the electron was a punctual particle moving around the nucleus, this enigma can not be solved.

The E0 energy level was imagined to solve such a phenomenon, but this explanation is only a theory, nothing more. Here we give another explanation which is much more rational.

Since the charge is distributed in sCells, the overall charge surrounding the nucleus is stable. The electron, in its wave form, does not drop because the forces are equipotential around the nucleus. Therefore, this problem does not exist in the Spacetime Model and the E0 energy level has no reason to be.


Schrödinger Equation

The Schrödinger Equation introduces another enigma: the probability of the presence of electrons is maximal at the center of the nucleus. The solution to this enigma is very simple.

The Spacetime Model does not relate to a probability but to a part of the overall charge. Since the nucleus (the main charge) is precisely located in the center of the atom, the maximum charge is obviously focused in the center.


Pauli Principle

The Pauli Principle is fully demonstrated but no one can explain it. Indeed, if electrons are those punctual particles moving around the nucleus, the Pauli Principle remains a true enigma.

For example, it is obvious that two or more satellites moving around the Earth may share the same orbit. In quantum mechanics, we can not exceed a maximum of two electrons by layer. Why?

The following figure shows the simplest case: layer n = 1 filled with one and two electrons. However, the principle can be extended to other layers.

Electrons are distributed in several sCells in their wave form (not as punctual particles). If two electrons fill the same orbital, the spin locks them up. This is due to the polarization of spin (see Part 4).

spin_orbitals.gif - Atoms

The charge of two electrons is different of the charge of only one. So, orbitals are necessary different.

When one electron is ejected from (B), the remaining electron takes another orbital (A) with a different energy level. This is why spin produces multiple lines.

So, this view, which is only a suggestion, solves both the Exclusion Pauli principle and the multiple lines due to spin in atomic spectroscopy.