## lördag 26 september 2015

### Volkswagen Emission Scandal vs German Political Correctness Leadership

Germany with Angela Merkel is actively seeking to take the leading role in a giant transformation of the world economy into a new green economy with reductions of CO2 emissions to preindustrial levels as prime goal.  In this giant transformation German car industry has promoted the diesel engine as being more fuel efficient with less CO2 emission than the gasoline engine under strong support from German governmental political correctness.

The Volkswagen emission scandal shows the hollowness and hypocrisy of this grand scale religion: To meet the strict demands of political correctness and moral leadership set by Germany, grand scale cheating is necessary and is accordingly delivered by Germany.

The world is watching with amazement. And in China a new coal power plant is opened every day.

## torsdag 24 september 2015

### Finite Element Quantum Mechanics 6: Basic Analysis vs Observation

Let us now inspect the basics of the atomic model considered in this sequence of posts.

Consider then a neutral atom of kernel charge $Z$ with $N=Z$ electrons occupying non-overlapping domains in space. Assume that the electrons are partitioned into a sequence of shells $S_m$ of increasing radius $r_m$ with corresponding widths $d_m$ each shell being filled by $2m^2$ electrons, for $m=1,...,M,$ with $M$ the number of shells. We consider a hypothetic atom with all shells fully filled with $2, 8, 18, 32, 50,...,$ electrons in successive shells displaying a basic aspect of the periodicity of the periodic table of elements.

Consider now the case $d_m\sim m$ with $r_m\sim m^2$, and assume $r_1=d_1\sim\frac{1}{Z}$. The electron density $\rho_m$ in $S_m$, assumed to be spherically symmetric,  then satisfies
• $\rho_mr_m^2d_m\sim m^2$
from which follows that
• $\rho_m\sim \frac{m^3}{r_m^3}$.                            (1)
We now compute the following characteristics of this model:
1. $M^3\sim Z$, that is $M\sim Z^{\frac{1}{3}}$
2. potential energy in $S_1\sim Z^2$
3. potential energy in $S_m\sim m^2Z/r_m\sim Z/d_1\sim Z^2$
4. total potential energy and thus total energy $\sim Z^{\frac{7}{3}}$.                             (2)
We check that indeed there is room for $m^2$ electrons in shell $S_m$, because the volume of $S_m$ is $r_m^2d_m\sim m^5$, while the volume of an electron $\sim d_m^3\sim m^3$.

We observe that (2) fits with observations. We understand that the electronic density is distributed so that the potential energy and thus total energy in each full shell is basically the same, which may be viewed to be a heavenly socialistic organization of the shell structure of an atom.

Numerical computation seeking the ground state energy by relaxation in the Schrödinger model of post 5 starting from an initial density distribution according to (1), shows good correspondence with observation, supporting the basic analysis of this post. Numbers will be presented in an upcoming post.

The basic aspect of this model as a form of electron density model, is that electrons (or shells in the present spherically symmetric case) keep individuality by occupying different domains of space, which makes it possible to accurately represent electron-electron repulsion.

This feature is not present in standard density models such as Thomas-Fermi and Density Functional Theory. In these models electrons lack individuality as parts of electron clouds, which makes it difficult to represent electron-electron repulsion ab ibnitio.

Recall also that in the standard Schrödinger equations wave functions appear as multi-dimensional linear combinations of products of one-electron wave functions defined in all of space by separate spatial variables, thus with each electron "both nowhere and everywhere" without individuality, which requires a statistical interpretation of the wave function as a multi-dimensional uncomputable monster.

Another basic aspect of the presented model is continuity of electron density across inter-electron or inter-shell boundaries for the electron configuration of ground states. This allows atoms to have stable ground states as non-dissipative periodic states of minimal energy.

Notice further that the size of the atom as $r_M\sim Z^{-\frac{1}{3}}$ with decreasing size as $Z$ increases, corresponds to the observed decrease of size moving to the right in each row of the periodic table:

## fredag 18 september 2015

### Ripples in the Fabric of Space and Time?

The code word of modern physics is:
• fabric of space and time
• observe gravitational waves—ripples in the fabric of space and time.
If we dare to ask what the meaning of "fabric of space and time" may be, we get the following illuminating lesson by leading physicists:
• First of all, space-time is not a fabric. Space and time are not tangible 'things' in the same way that water and air are. It is incorrect to think of them as a 'medium' at all.
• No physicist or astronomer versed in these issues considers space-time to be a truly physical medium, however, that is the way in which our minds prefer to conceptualize this concept, and has done so since the 19th century.
• We really do not know what space-time is, other than two clues afforded by quantum mechanics and general relativity.
• Space-time does not claim existence in its own right, but only as a structural quality of the [gravitational] field. (Einstein)
• Space and time coordinates are just four out of many degrees of freedom we need, to specify a self-consistent theory. What we are going to have [in any future Theory of Everything] is not so much a new view of space and time, but a de-emphasis of space and time. (Steven Weinberg)
• In the theory of gravity, you can't really separate the structure of space and time from the particles which are associated with the force of gravity [ such as gravitons]. The notion of a string is inseparable from the space and time in which it moves. (Michael Greene)
The punch line of this educational experience is presented in this way:
• So, the question about what happens to space-time when a particle moves through it at near the speed of light is answered by saying that this is the wrong question to ask. Just because the brain can construct a question doesn't mean that the question has a physical answer!
We understand that LIGO in its search for "ripples in the fabric of space and time" is studying "the wrong question" and thus can be viewed as a study into the ""fabric of fantasy" which has become such a fundamental part of modern physics demanding full devotion by the sharpest brains of modern physicists (see also here ):