Graphene, Emmy NOETHER's Theorem, LINDEMANN–WEIERSTRASS Theorem, and Gravitons: Revisited

Graphene, Emmy NOETHER's Theorem, LINDEMANN–WEIERSTRASS Theorem, and Gravitons: Revisited

by Stefan Geier

This post (these two posts) are of interest by relating to https://www.researchgate.net/.../360897799_ep_GELFOND's...:

Facebook 23. October 2020 ... :

Please, look at the graphene hexagons, nearly circles on the photo above (Hi, provided by Nobel Prize a few hours ago). Please, consider the symmetries by Emmy NOETHER (NOETHER' theorem), and Roger PENROSE (360°/n: n=1,2,3,4,6. In addition by us: LINDEMANN–WEIERSTRASS theorem brings in the #graviton with respect to the breaking of the hexagon-circle symmetry; see the theoretical, and empirical proof by Stefan Geier on facebook).

In honor of Andre GEIM, Konstantin NOVOSELOV, and Roger PENROSE I propose the term "charge black hole" for "π * e^2". This circle is analogous to a black hole: This is because of #Graphenes π*α: π*α (*π^3), and δ(NEWTON’s cradle)=π*(α/π^3) can be transformed into π*e^2 /((h*c*π^3)/2 π).

π * e^2

describes a circle with radius e; this circle is analogous to the opening of a black hole, a charge black hole. Damping energy flows into a charge black hole (Please, compare with GAUSS' law of gravitation, and MAXWELL' equations etc.). This is "correct" for Andre GEIM', and Konstantin K. NOVOSELOV' π * α for #graphene, too (see NOVOSELOV: Nobel Lecture 2010, p117). Please, compare with NEWTON's cradle as a black hole metaphor.

Yours respectfully

Stefan Geier

see facebook 21.Oktober 2020

[1] see facebook Stefan Geier 24.August 2020

Photo: Stefan Geier reading Roger PENROSE' fantastic "The Road to Reality", 2005, Vintage.

charge black hole, black charge hole, charge hole etc.

Arnold Sommerfeld, Paul Dirac, fine-structure constant, Sommerfeld's constant α, and 4πεħcα = e^2, etc.

I can’t find the Facebook posts on Lindemann–Weierstrass theorem, and gravitons. Thus, here a short version:

(i) Physical interaction in time: Rotation (arci) → Translation (ti): ti = f(arci; 1/π), and ti is not transzendental and rational, and π is transzendental and irrational (1/ π thus,too), so:

ti < arci, and arci+1 < ti <arci, and so on.

(see impossibility of squaring the circle, Lindemann–Weierstrass theorem)

Thus: Δ’(momentum; moment of momentum) = f(π) = constant π; (or 1/π).

This is due to NOETHER’s theorem; a circular movement cannot be transformed in translational movement for any given reference point in physics; momentum and moment of momentum are always asymmetric in physics, classical or quantum. (This is no contradiction to spin; spin causes a field to make the asymmetry inducing interaction of particles impossible via field forces.)

(ii) The relation δ(NEWTON’s cradle) ≈ π δ(pendulum) is a confirmation or “empirical proof” of the existence of #gravitons with spin = 2 ħ:

Proof (#theoryandexperiment):

1. Premisses:

1.1 δ(NEWTON’s cradle) ≈ pi * δ(pendulum): δ is equivalent to entropy, and thus to Δenergy by energy = T * entropy.

1.2 Δenergy is quantized for the left side, and the right side, thus:

Left side = Δenergy(NEWTON’s cradle)= m quantum(translation), m an integer

Right side = Δenergy(pendulum) = π * n quantum(rotation), n an integer

1.3 a) NEWTON’s cradle is determined by translation, thus the quanta are related to h: quantum(translation) = l(t) * h, l(t) an integer; b)

pendulum is determined by rotation; thus the quanta are related to ħ: quantum(rotation)= l(r) * ħ, l(r) an integer;

h, ħ: Max PANCK’s h, and Max PLANCK’s ħ (according to Niels BOHR)

1.4 We, and #NOETHER’s theorem distinguish between translation and rotation (see Niels BOHR, too).

2. Algebra in Physics:

2.1 m*l(t)*h = π*n*l(r)*ħ

2.2 ħ = h/(2*pi)

2.3 m*l(t)*h = π*n*l(r)*h/(2*pi)

2.4 a) m*l(t)*h = π*n* l(r)*h/(2*pi) would be true for n = 2m and l(t) = l(r): empirical not possible according to our knowledge till today

2.4. b) equation 2.3 is true for a quantum of rotation = 2 h/(2*pi) = 2 ħ = spin of a graviton by l(t)=1 and l(r)=2: This is in accordance with our knowledge of today, respective string theories (Leonard #SUSSKIND), and the theories of gravity (other values of l(t) and l(r), however possible, are less relevant; see #gravitino, #supersymmetry): q.e.d.

3.Conclusion:

Thus, #NEWTON’s cradle as presented by Caroline Geier and Stephanie Geier with respect to #NOETHER’s theorem at #jufo2019 (Rosenheim, poster presentation, Technische Hochschule Rosenheim) is a conjecture and “empirical proof” of the existence of a spin 2 boson, respective #gravitons with spin = 2 ħ.

I have to care for my family now, again; I will continue later etc. (Additional paper to Nature in preparation).

Yours respectfully

Stefan Geier,

Haidholzen, Gerhart-Hauptmann-Str. 6, 83071 Stephanskirchen, Germany

To:

Nobel Prize

Sir Roger Penrose http://www.penroseinstitute.com/

The Royal Society London

Nationale Akademie der Wissenschaften Leopoldina

Nature

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