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**§1**– Abstract

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*In the current document, we examine – first of all – in brief and then in detail some of the consequences of a new interpretation of the “General Theory of Relativity” by Albert Einstein.*

*These studies ( [1]), in 2014, first have interpreted the plasma fusion as in the high-temperature situation on the stars, and then have studied the electrolytic processes, also called “Cold Fusion”.*

*The result of that work was mainly the finding that the material (such as deuterium in ordinary distilled water: 1 part in 20 million H2O) could be transformed into energy, even at low temperatures, due to the electrolytic process in the open air around 4000 degrees Celsius, which is the temperature at which the tungsten melts, being the electrodes, anode and cathode, tungsten.*

*In “Our Transformation” (*__Cold Fusion Theory__*) therefore not needed exceptional gravitational compression force of the stars, but already as evidenced by the work of ANTONELLA DE NINNO, ANTONIO FRATTOLILLO, ANTONIETTA RIZZO (ENEA Frascati), and also EMILIO DEL GIUDICE (INFN Milano), and even GIULIANO PREPARATA (University of Milan, INFN Sez. Milan), already available on line ( [2]), you get gamma-rays at a low temperature range through the fusion reactions.*

*The experimental conditions of the “group” led by the scientist, whose name is “Preparata”, and others, were different from the one we tested, being the two dissimilar experiments for both the electrodes and also to the use of water in place of heavy water and suction pumps. But both have led to the same consequences of repeatability of the process.*

*“Our transformation” (*__Cold Fusion Theory__*, in 2014), took place in a natural confinement without evaporation of water by electrolysis, while the tungsten was about 4000 degrees Celsius. This was possible because the hydrogen had created a separation between liquid water and the fusion reaction.*

*All this has been pondered for a long time by P. Tufano who has theorized for the formula of Einstein (energy = m0 * c ^ 2) the consequence that the mass does not disappear immediately, but in a gradual process. So, this is not a process of creation, but of transformation.*

*A further consequence of this, is that it is NOT true that the matter cannot reach the speed of light, because this is always from the stars that consume hydrogen and other*

*—*

[1] More info: https://6viola.wordpress.com/associazione-eureka_fusion_2014/

[2] More info: http://www.fusione.enea.it/pubblications/TR/2002/RT-2002-41-FUS.pdf

**pg. 1**

*—*

chemical elements massive, but emerges only energy (via photons) that __travel at the speed of light__*.*

*The present document (*__G’ Theory__*) proposes a change of cosmology, and answer the following questions: *

__As it is possible that an electron, being an entity with negative charge (with mass) does not precipitate on a hydrogen nucleus?__

__Why? .. the proton being something with positive charge (with mass) sees the electron in a stable orbit? __

*Would not be possible any answers to these questions through the implementation of a software based on “Einstein’s geodesic equation Model,” if we hadn’t passed from the study of plasma, as we have briefly exposed.*

*According to the official theory, in fact, even today, 27 February 2017, when we are writing this brief note, the majority of scientists makes the assumption that the behaviour of matter at the atomic scale does not satisfy the usual laws of nature that apply over the atomic scale.*

*It is well known that physics divide theories over and under the scale of the atom, and the science of physics uses a probabilistic theory in models under the atomic scale.*

__As a result of the present document ____it is possible to exit from implementation of probabilistic models____, which remain valid solutions until there is scarcity of information on processes, ____but also DETERMINISTIC descriptions are possible ____under the scale of the atom.__

*Already Albert Einstein have theorized the proper use of study using probabilistic models when there are insufficient data. He had considered this situation caused by “hidden variables”.*

*After reading the actual document you will know where were the famous “hidden variables”.*

*In short, we will show that (under atomic scale) gravitational function is carried out (mainly) by the Coulomb force.*

*The reasons that explain why it has not been possible to implement it so far in the geodesic equations is due to “*__mathematical representation__*” that is not evident immediately.*

*This **mathematical rappresentation **is exposed in the form of a theorem in the discussion that follows. And also we will bring proofs of the theorem and also accompanied by a simulation software.*

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**pg. 2**

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*I thank here those who have allowed and even helped my work as well as the components of the Scientific Association Eureka!, eng. Fabio Sipolino, eng. Maurizio Anselmo, physicist Dr. Daniele Marin, Dr. Michael Balfour, even my brother eng. Diego Tufano.*

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**pg. 3**

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**§2**– INDEX

Nome | Paragrafo |
PAG. |

Abstract | § 1 |
1-3 |

Index | § 2 |
4 |

G’ Theory | § 3 |
5-14 |

G’ Software | § 4 |
References [11] |

Conclusions | § 5 |
References [12] |

References |
§ 6 |
15 |

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**pg. 4**

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**§3**– G’ Theory

*The following discussion is similar to already published on the Blog of Eng. A. M. P. Tufano on December 1, 2016, and displayed in summary form below ( [3]).*

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# TUFANO’s 3rd theorem (i.e. __G’ Theory__):

__G’ Theory__

—

Hypothesis n.1: Ip.1

*In the hypothesis that the electromagnetic manifestation is an epiphenomenon of electromagnetic forces:*

* *

This type is said: “gravitational force type 1”, or Coulomb force:

**(1) F_cu=(1/4*p*eps)e^2/r^2**

LaTex image:

—

Hypothesis n.2: Ip.2

*In the event that the ordinary gravitational manifestation of Newton is expressed by the following formula*

**(2) F_n=G*m*M/r^2**

LaTex image:

This type is said: “gravitational force type 2”, or Newton force:

—

[3] See for more info: https://6viola.wordpress.com/2016/12/01/deterministic-orbit-of-h-hydrogen-tufanos-3th-theorem-mathematics/

**pg. 5**

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Hypothesis n.3: Ip.3

*The gravitational force of Einstein and Schwarzschild is expressed through geodesic equations. And we want to compute the Schwarzschild radius.*

*In *__MACRO –__

__cosmos____(__macrocosm)

*, we assume:*

Ec = kinetic energy = (1/2)*m*v^2; if v << c

LaTex image:

Eg = gravitational energy = G*m*M/r;

LaTex image:

With Ec = Eg:

1/2v^2=GM/r

*If v -> c the Ec & Eg expressions are modified, but nevertheless Schwarzschild found a solution that puts “rg = 2GM / c ^ 2” as if you could replace v = c & r = rg in the above expression, and thereby you could get a solution of the geodesic equations with:*

*Consequently*

1/2c^2=GM/rg

*From which highlighting rg:*

**(3) rg=2GM/c^2**

*source of confirmation (where rg, is denoted by rs)*

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pg. 6

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https://en.wikipedia.org/wiki/Schwarzschild_radius

*Now you put on sub atomic scale ( micro-*

__cosmos__*:*microcosm

*) the following notation:*

**(3)’ rg’=2*G’*mp/c^2**

where

G’ = you see TH1, Th2, Th3 (below)

mp = mass of the Proton

c^2 = speed of light squared

—

Hypothesis n.4: Ip.4

*In the hypothesis that the manifestation of gravitational field, in the F_t configuration, is an epiphenomenon of electromagnetic forces = F_cu,*

We can write:

** **

**(4) F_t=(G’*mp*me)/r^2=Fcu, you see (1)**

*Where:*

*“gravitational force of type 4, or Tufano’s Force*.**(****[4]****)**

**TH:**

*We can prove that, in the previous hypothesis,*

# TH1: (4.1) rg’=(2*G’*mp)/c^2

LaTex image:

—

[4] F_t, therefore, is not a force in addition to those “classic”, but … a different “reading” of the Coulomb field

pg. 7

—

Where:

*rg’ is the Schwarzschild radius, in geodesic_equations (sub-atomic scale).*

*G ‘ is defined in TH2 following.*

*mp = mass of the Proton.*

*the atom is hydrogen.*

—

*It’s to remember that G will be replaced, on the subatomic scale, with*

# TH2: (4.2) G’=[1/(mp*me)*(4*pi*eps)]*e^2

LaTex image:

*With that G ‘ you get electron’s deterministic orbit:
electron mass, me, around the nucleus of the hydrogen atom, of mass mp.*

—

# TH3: (4.3) F=(G’*me*mp)/r^2

LaTex image:

*The above expression, where G ‘ is given by (4.2), will simulate the gravitational force due to the Coulomb force.*

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**pg. 8**

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# TH4:

(4.4)

*GEODESIC equations (H-23-11-2016-a):*

*The GEODESIC equations can make use of all previous thesis and this will show (in the graph that is obtained from the software):*

__model n.1: model in perihelion:__*the position at perihelion means that the body of lesser weight, m, is closer to the body of greater weight, M, (in our case the Proton). This first model is needed for us because we want study the actual orbit when the system is left to his “free evolution”. And this can be achieved by placing in the initial conditions with rpunto0 = 0. This means radial velocity = 0. Use of this orbit it will be elliptical, to improve our second model, which we call in Aphelion. In Aphelion: distance will be at its highest point. The method of calculating so will (in Aphelion) using areal velocity and more accurate results.*__model n.2: model in aphelion:__*With an eccentricity of about 0.0022 inferred from the number one model, and after about 25600 calculation iterations we’ll see (by software) the velocity v > c (c=the velocity of light)**.**This of course means only that to v > c the model is unreliable.**But this situation (v = c) gives us also a boundary condition of saturation, which is reached with rg as minimum radius, beyond which the electron cannot “further to fall”*. // pg.9 //__model n.3: rg’ di Schwarzschild:__*We know the true value of rg is not only from the previous model, but also from the Schwarzschild formula indicating the subatomic situation. From which we can immediately evaluate this model “number 2” as insufficient.**We will expand the software model with a faster sampling and associated considerations in step 4 below. Now let’s see how do you calculate rg is not by software, but by the Schwarzschild radius.**Calculating how much is rg ‘, in fact, is given by the following formula*__rg’____=2*____G’____*____mp____/____c^2__*. That from the same value as the following formula expressing***rg’**__-> (½)*me*____c^2____=[1/(4*pi*eps)]e^2/____rg__**’.****rg’****=2(****15*10^28****)(****6*10^-27****)/(****8.9*10^16****)= 5.6*10^-15 [m];**__1/2*me*c^2____=[1/(4*pi*eps)]e^2/rg with “me”=9.1*10^-31 kg; c^2=8.9*10^16; pi=3.14; eps=8.8*10^-12; e=-1.6*10^-19 C;____model n.4: zoom of the film:__*Further higher order orbit due to the increasing frequency of sampling.**Such activity by reducing the angle 1° sampling instance (of 360° degrees total) to 1° degree divided 60 * 60 = 3600. This will expand the latest list of photos (now with higher frequency) that show the transient. This increased sampling will provide, if repeated, zooming of the film. More info on part 5 of the mathematical proof..(***[5]**)

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**pg. 9**

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# Mathematical Proof:

*In reference to “historical” mathematical proof, that you can view at the link in note, I will show here a synthetic version.*

**First Part:**

__Demonstration of the consistency of the hypothesis 4:__

*It is necessary to prove, first, that it is true*

(4) F_t=(G’*mp*me)/r^2

This is immediate, since the (4) is equal to

(4)bis F_t=F_cu.

*If we explain “(4)bis” formula in more terms:*

(4)tris F_t=(G’*mp*me)/r^2=F_cu=(1/4*p*eps)e^2/r^2

*From which one has the equality if and only if: *

(4.2) G’=[1/(mp*me)*(4*p*eps)]*e^2

—

[5] We will see that the Einstein geodesic_equation (also in the subatomic space) make (unlike Kepler) open curves.

**pg.10**

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Q.E.D.

(quod erat demostrandum)

(written or said after an argument to show that you have proved something that you wanted to prove)

—

**Second Part:**

** **

__Why the electron does not precipitate on the Proton?__

*Therefore, you can use the Coulomb force by giving it a form compatible with the gravity, thanks to expression G’, by Tufano’s formula: (4.2).*

*The principal importance of the 4.2 formula is not for the equivalence that highlights two masses that are “the official masses” when the orbital speed is in “input into the orbit”!*

*Because this calculation already exists in literature and confirms the following three values: *

(me0, re0, v0)

re0 = 0.528*10^-10 m (approximately)

v0 = 2000 km/s (approximately)

me0 = 9*10^(-31) kg (approximately)

*.. but that allows you to define a “new cosmology” in which the laws of physics don’t see classical gravity, Newton/Einstein, to play the force of orbital link, but electromagnetic fields (for the electrostatic part).*

*.. However, if you leave in the form of Coulomb, you can’t highlight G’, and consequently cannot use typical structuralism of the geodesic equations*!([6])

*When we create an abstract space S2, (subatomic space), where G is replaced by G’ and rg is replaced by rg ‘ ( [7]), we don’t care “who” (Newton or Coulomb) is that got the force, but only the “structure”*!

*The design proposed becomes the same structure of Einstein if we give the same structuralism of Einstein/Newton: where we must make explicit:
*

—

[6] See the simulation software later in this article for that clarification.

[7] See also the Th4: (4.4) subparagraph 3.

**pg. 11**

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- the masses that are present in the experiment
- the distance between the masses
- G’

*It is therefore a change of cosmology.*

*This change seems to separate the laws of macro_cosmos, from those of the micro_cosmos, but this is not true!*

*The force of F_n Newton, is negligible, as deformation, until is v << c! … and also, it is negligible, as entity, for v-> c*

*In particular, as you can verify by my study of the plasma-stroboscopy, it should not be thought that a mass become more heavy for the speed increase.*

*But, against the common sense, the measurability of the mass, of any mass, it acts as a “sail of a ship that becomes more small, as sail”. More small sail if velocity is increasing.*

*The wind on the sail simulates, in the example, the ability of a force to push the ship out of a smaller area, when the force is (at the point of application) from our universe (U1). *

*This means that the mass does not expand, but what is expanded is the kinetic energy applied for give more velocity. But is less the surface on the sail until zero when v=c.*

*When v = c, if we see from U1, there is no longer any mass that can be pushed, because m0 = 0, if measured by U1, indicating, with m0, the electron mass, before the transformation.*

Ec=[m0/rad(1-v^2/c^2)]*c^2;

*Ec is thus a kinetic energy that increases in value with v -> c.*

.. *but the mass, measured by U1, m’, is*

m’=m0*rad(1-v^2/c^2)

*that then becomes zero when v = c.*

*Its function (to attract) when v = approx 2000 km/s is carried out very well by the Coulomb force, but the Coulomb force would not be able to describe relativistic dynamics that instead, we describe with “abstract space = sub_atomic_space”* ([8])

*What information shows the mathematical experimentation?*

—

[8] In sub_atomic_space G you must replace by G’ and rg with rg’. Exactly rg’=2G’mp/c^2

**pg.12**

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*It happens that the electron has an orbit in stationary conditions of input/output (i/o to the orbital motion) in ordinary measures ..*

*But what happens immediately after the electron is stationary in its orbit around 2000 km/s velocity and the RADIUS 0.5 * 10 ^ -10 re0 = m?*

*As it is shown in the simulation software, a slight alteration *([9])* of the parameters of the orbit and ..*

*elector is easily removable from the ordinary orbit**or … the electron “tends to precipitate on the Proton”.*

*On point (1) above:*

*The evidence that an electron can absorb a photon and switch to a higher orbit is well known in literature, and also that the preferential status is to expel the photon, after this situation. Thus, the moving is later in direction to the previous orbit, more near to the nucleus.*

*On point (2) above:*

*The simulation software shows that if the electron falls, quickly falls on the core. The mode is vortex mode. The minimal distance is called re(new), or re_new, or rg in the later discussion.*

*HOWEVER, the stability of the orbit of an electron is well known fact, although some authors theorize a minor stable distance of orbit,
instead of the official orbit 0.528*10^-10 [m] (approximately).*

__(@)__*We will demonstrate that the stable orbit is at value 5.6*10^-15 [m] (approximately) as consequence of physics and mathematics, in more manner.*

**(@)**this is evident with formula

R (Schwarzschild)=(2*G’*M)/c^2

And also with software:

[…]

—

[9] On the concept of “slight alteration”: We observe evolution with rpunto0=0. This is for measure the free response of the system.

**pg. 13**

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QED

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**pg. 14**

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- 6 – References

[1] Albert Einstein:

http://scienzapertutti.lnf.infn.it/newslettersxt/immagini/relativita_einstein_italiano.pdf

[2] Preparata et altri:

http://www.fusione.enea.it/pubblications/TR/2002/RT-2002-41-FUS.pdf

[3] geodesic_equation – Amadori Lussardi:

https://www.matematicamente.it/appunti/relativita/

[4] Cold Fusion – Fleischmann et altri:

M. Fleischmann, S.J. Pons, J. of Electroanal. Chem. 261, 301 (1989)

[5] software php:

https://secure.php.net/manual/it/

[6] calcolo differenziale assoluto:

http://mathematica.sns.it/media/volumi/411/Levi-Civita_Calcolo_differenziale_assoluto.pdf

[7] my web space, rif. a G’:

https://6viola.wordpress.com/2016/12/01/deterministic-orbit-of-h-hydrogen-tufanos-3th-theorem-mathematics/

[8] Cold Fusion:

https://6viola.wordpress.com/associazione-eureka_fusion_2014/

[9] *new-H@ Deterministic Orbit of H (Hydrogen): TH-16
*https://6viola.wordpress.com/2017/07/07/new-h-deterministic-orbit-of-h-hydrogen-th-16/

[10] *k_Fermat’s geodesic_equations: [mathematical proof: 6° & 7°]
*https://6viola.wordpress.com/2017/07/23/k_fermats-geodesic_equations-mathematical-proof-6-7/

[11] *Deterministic Orbit of H (Hydrogen): TUFANO’s 3rd theorem [*Mathematics*] (software and italian version)*

https://6viola.wordpress.com/2016/12/01/deterministic-orbit-of-h-hydrogen-tufanos-3th-theorem-mathematics/

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**pg. 15**

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versione in formato “pdf”:

new_G-micro_cosmos.pdf