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**Einstein-versus-Heisenberg_GB/USA**
E. B. Christoffel revisited

**Einstein-versus-Heisenberg_GB/USA**

*© Thierry PERIAT : Texts, ideas and photos*

**Introduction**

The
search for unity inside theoretical physics, especially between the general
theory of relativity (GTR) and the quantum approach is soon a hundred years old
fundamental quest. It has occupied many brilliant brains and it does occupy
them yet. Therefore, my tittle on the homepage may sound a little bit
pretentious. Did I really discover the missing path?

I am not
sure because, as Descartes has teach it centuries ago, the doubt is a good
guide for the rationalistic and scientific ways of thinking. If I did, my
presentation is the most simplified and caricatural one. What is the main idea?

W.
Heisenberg has indicated to us that positions and speeds form two separate and
independent sets of observables. He also suggested that energies and lapse of
times were following a similar logic. There is for now, no operator
representing the time, and, at least at a technical level, this absence is
blocking the progression[1].

Therefore,
I decided to consider the simplest transposition of that suggested
interdependence: delta energy. Delta lapse of time must be at least equal to a
fraction of the Planck constant. The situation realizing the exact equality is
labelled as “quantum limit”. After that, considering the physical units involved
in such a relation, I realized that it was possible to inject any force and
especially the Lorentz force density into it. I also understood that that
Heisenberg’s relation was able to yield a polynomial of degree two allowing both,
the simultaneous intervention of my extrinsic method and the one of E. B.
Christoffel’s historical work on the preservation of these polynomials. This is
the central skeleton of my toy-approach.

For
sure, it must be fine tuned and generalized. But if it is the right way
connecting the two main pillars of the modern theoretical physics, this is
already a scoop and an essential stone for future progressions. We may say that
Heisenberg was born a little bit too late. If he could have confronted his
thoughts with the calculations of Christoffel’s, he would certainly have
suggested a similar idea. The preservation of elements of lengths appear to be
a consequence of the preservation of the quantum limit (see definition above in
that text). This conclusion will certainly not receive any positive echo in the
scientific community; just because it is not academic, not politically correct
and contradicting the main stream. Or because it is simply false? You are
deciding. Just let me know your opinion in contacting
me. Thanks.

**The document**

Everybody
knows Einstein's master work (The general theory of relativity - GTR). Only few
specialists remember exactly how it has been built. In that document I exhume
E. B. Christoffel's work [[02] (1869)] which is (i) continuing Riemann's work
(1864) and (ii) one of the mathematical pillars of the GTR. I demonstrate that
that work can be applied either for the preservation of the ds2 (the historical
case) or for the invariance of Planck's limit (see def.4.1) as well, without
being obliged to be in contradiction with the solutions of the GTR. It turns
out that, in doing so, I just preserve the inverse of a non-degenerated 4D
metric. The bonus of that demonstration is a new family of electromagnetic
fields (see equ.22) depending on that metric and on its variations (see further
developments on the next page).

The v5, 16
September 2018 is on www.researchgate.net/profile/Thierry_Periat

The v4 has
been proposed to the review General Relativity and Gravitation but not approved
for publication

© Thierry PERIAT, 02 December 2018.

[1] By the way, you may want to discover
more on this difficult thematic in exploring the GTR2
approach and its diverse consequences step by step (another
exploration extending the GTR).