Tribute to Einstein as Icon of Modern Physics

After his death Einstein was chosen as the icon of modern physics as the creator of both the Special Theory of Relativity SR (1905) and the General Theory of Relativity GR (1915) forming the foundation of modern physics together with Quantum Mechanics QM in the form of Schrödinger's Equation SE (1925) without SR/GR. 

This looks great, but looking closer we find that (i) GR and QM are incompatible, and (ii) SR and QM/SE do not connect, which is a root cause to the present crisis of modern physics. 

To at least save something Dirac (1928) invented an SR relativistic model to replace SE named Dirac's Equation DE.  

Both SE and DE are multi-dimensional models without physical meaning invented on formalistic grounds and are uncomputable without drastic dimensional reduction with unknown effects. In any case SE/DE are the basic models of QM. 

As a tribute to Einstein and to create some form of unity between SR/GR and QM, physicist have decided to attribute relativistic effects not only to fast moving trains but also to the inner workings of an atom although nothing there is actually moving. 

So it is claimed that: 

• The single electron of a Hydrogen atom has an effective velocity $v\approx 0.0073\times c\approx 2.19\times 10^3$ km/s.
• A first shell electron of Gold has a effective velocity $v\approx 0.58\times c\approx 1.73\times 10^5$ km/s with $c$ the speed of light $c$. Very fast indeed! Relativistic effects must be added!

The very high speed of the 1st shell electrons of Gold is then used to explain observed electron structure of Gold, which does not fit with SE without SR. Very useful.

But how is it possible that the inner electrons of Gold move with a speed close to the speed of light, when in fact the electron charge distribution does not move at all?

Of course this does not make sense and let us then seek the origin of this strange idea. It comes from the formalistic derivation of SE where classical kinetic energy $m\frac{v^2}{2}=\frac{p^2}{2m}$ with $p=mv$ momentum, $m$ mass and $v$ velocity is formally replaced by

• $KE=\frac{1}{2m}\int\vert\nabla\psi (x)\vert^2dx$  

where $\psi (x)$ is a wave function depending on a 3d space variable $x$. The formal connection is thus:

1. Replace momentum $p=mv$ by the operator $i\nabla$.
2. Connect KE to $\frac{1}{2m}p^2=\frac{1}{2}mv^2$ thus connect KE to "effective velocity" $v$. 
3. Claim that the effective velocity of inner electrons of Gold is close to the speed of light.
4. Conclude that Gold carries large relativistic effects and explain observations as the result of increase of relativistic mass of inner electrons.

Here 1 is the key: Pure formalism as a form of voodoo physics is used to attribute relativistic effects in the inner working of an atom as if charges are moving with speed close to the speed of light with then a time scale of about $10^{-21}$ s or frequency $10^{21}$ in the range of gamma rays. It is hard to believe this to be any reality at all.

You may compare with RealQM directly based on real physics without relativity including an analysis of weak reactivity of Gold.

The big trouble with SE is that a derivation based on physics is missing. The derivation is based on identification of classical momentum $p=mv$ with the operator $i\nabla$ as pure formalism without physics. 

The further step to attribute relativistic effects also comes from this identification connecting $\nabla\psi (x)$ to velocity $v$ coming out as being very large suggesting presence of relativistic effects inside atoms. 

So all this can be seen as a tribute to an Einstein, who never accepted QM in its standard multi-dimensional non-physical form as one of the many paradoxes of modern physics behind the crisis.

Lorentz long before 1905 noted the fact that a wave equation in space-time coordinates $(x,t)$ formally reads the same under a certain simple linear transformation into new coordinates $(x^\prime , t^\prime )$ later named Lorentz transformation LT. Lorentz very carefully remarked that there was no underlying physics for this invariance and that accordingly the new primed coordinates $(x^\prime , t^\prime )$ had no physical meaning as space-time coordinates. 

Einstein as patent clerk in Bern must have met this idea and picked it up to rebrand it as Lorentz invariance now giving the transformed primed coordinates $(x^\prime , t^\prime )$ a physical meaning in direct confrontation with Lorentz, which became the trade mark of SR identified with LT with physicial meaning. 

Relativistic velocities in atoms thus have a doubly questionable physical nature: (i) SE is formally without physics connected to SR by connecting $p=mv$ to $i\nabla$, and (ii) SR is born from Lorentz invariance without physics. 

What Is the Shape of an Atom?

Standard Quantum Mechanics StdQM presents a picture of an atom as being built from electron configurations/orbitals represented by the eigenfunctions for the Hydrogen atom H as the excited states of its one and only electron according to the following partial list:

There is no real rationale for this choice of representation for the electron configuration of an atom with many electrons, other than the completeness of the set of Hydrogen eigenfunctions like any other set. 

The idea is thus to build many-electron configurations as combinations of the above list. Is it a good idea? Does it appear to be complicated? Is it likely that real physics is built this way from some storage of Hydrogen eigenfunctions? It has the same ad hoc character as the Linne's Sexual System classifying  plants into groups based on the arrangement of stamens and pistils, today completed in the Standard Model of particle physics.

We see in the above collection a presence of a shell structure which connects to a different representation of a many-electron configuration as organized in an expanding sequence of shells with at most $2*n^2$ electrons in shell $n=1,2,,$. Here is this shell structure for Iron complemented by electron orbitals below

RealQM is based on a new form of Schrödinger equation for a collection of one-electron wave functions with non-overlapping supports meeting at a Bernoulli free boundary, which for an atom has a shell structure carrying the supports and where the actual electron distribution comes out as a packing problem under energy minimisation. You can inspect the representation of a Gold atom in this code by pressing start.   

The basic shape of an atom in RealQM in spherical symmetry thus consists of a sequence of non-overlapping spherical shells with a certain number of equally distributed electrons in each shell, like a spherical onion built from spherical shells:

In this model there is no need of complicated Hydrogen electron orbitals from the above lists. Using Ockham's razor we can thus leave these out and make life much simpler as concerns mathematical modeling of atoms. This model meets the requirement of Anschaulichkeit demanded by Schrödinger, but not met by StdQM.

For molecules, RealQM offers a richer set of shapes formed by shell interaction of outermost shells of several atoms. See label RealQM Quantum Chemistry.