**Abstract**

Field torsion models are considered from the experiments realized in electronicdynamical devices and magnetic censoring of a Hall Effect sensor to detect torsion under electrical restricted conditions and space geometry. In this last point, are obtained 2D and 3D-models of torsion energy, which enclose the field theory concepts related with torsion, and open several possibilities of re-interpretations that can be useful in technological applications in the future. Likewise, are considered some measurements that evidence the torsion as field observable. Through geometrical models obtained from theorems and other results are demonstrated the conjectures required to understanding of torsion, as a geometrical and physics invariant most important in the deep study of the Universe. Also, applications in astrophysics and cosmology of these geometrical models are obtained to show Universe phenomena understudy of torsion.

**Keywords:** field torsion models, Hall effect sensor, spectral torsion, torsion detection, torsion energy, magnetic field, spining, spinors

### **1. Introduction**

A deep study of torsion carry us to determine the spectral form of the torsion explored through energy signals that evidence the torsion as an primordial field born from the spins and fermion interaction of the matter-space interaction when the agitation of the space produces the fundamental material particles which create through duality particle/wave the matter in the Universe. This new spectral form that have been defined from the curvature energy concept [1, 2], and expressed as the value of integrals on cycles of a space, come from a generalization of curvature in analysis and integral geometry called integral curvature [3, 4], and obtained through co-cycles (values of the integrals) in a tempered distributions topological space.

After, and applying this new form of curvature to explore and measure several phenomena in the space–time, furthermore of establish a Universe theory through integrals, have been obtained curvature of the space–time in the macroscopic levels as well as microscopic levels, where in this second item, have been obtained results referent to the creation of gravity and matter in the Universe [5], considering the

causes and origin of these and the evolution of the Universe, being the curvature energy κ ωð Þ 1, ω<sup>2</sup> , an theoretical and practical element to consider in all modern Universe studies, and also the technological applications derived of these as corollaries of the great curvature energy theory.

As has been mentioned, the microscopic phenomena in the universe are the causes and are the things that give origin to the gravity and thus to the matter such as is known, through a large process in the Universe development. Likewise, an field observable that result of the microscopic interactions from particles spin level is the field torsion, which let in evidence much other space–time phenomena as the inflation, possibly the role of neutrinos, the baryongenesis, the proliferation of **H**particles and the form of evolution of all sidereal bodies, which in their different steps show mechanism where curvature and torsion are geometrical invariants that give meaning to the evolution of these sidereal objects and possibly to explain the role of the Higgs boson, the meaning of the dark matter and more.

The present chapter will explain and expose some theoretical models, numerically obtained in 2D and 3D-dimensions of torsion and its meaning in field theory and the intrinsic study of torsion as field observable, as geometrical invariant and possible central concept to the new and future technologies that will be required to the human survival.

From a point of view of an electronics study [10] (using a magnetic Hall sensor<sup>1</sup>

was obtained an evidence of the existence of torsion as field observable, where was used a magnetic particle as dilaton [5, 6] moving through of a trajectory whose

*(a). The corresponding solution to the field equation in cylindrical regime is Z = exp(*�*0.5(x + 1))BesselY (0.5x, 8y)sin(7x)BesselJ(0.3y,20). The rotation of cylinder was realized b). (b) Corresponding signals detected in the torsion detection and showed in the wave generator, under electronics measuring conditions: frequency of*

*Numerical Simulations of Detections, Experiments and Magnetic Field Hall Effect Analysis…*

dt <sup>¼</sup> <sup>1</sup> 2π

which belongs to the signals set that evidence the torsion under permanent

*<sup>ω</sup>*<sup>L</sup> , cosh *<sup>ω</sup>*<sup>L</sup> *ω*L

cos*ω*L

b a2 <sup>þ</sup> <sup>b</sup><sup>2</sup> � � 1

<sup>2</sup> The torsion is detected with conditions of movement. Likewise, by the lemma 3. 1 [10], the produced

*<sup>H</sup>* <sup>¼</sup> <sup>I</sup> 2π a2 l 3 ,

�

which is a rectangular signal of conditioning. Here *α*~, is an amplifier factor of the voltage for be

whose magnetic field of the dilaton must be decreasing in the cycles for seconds of the turns for that these are detectable by the Hall type sensor (with low velocity). Then is conditioned the signal the initial

<sup>13</sup> � � <sup>¼</sup> <sup>2</sup>*:*5*<sup>V</sup>* � *<sup>α</sup>* j j*<sup>t</sup>* <sup>≤</sup>0*:*5*<sup>s</sup>*

0 j j*t* ≥0*:*5*s*

,

<sup>l</sup> <sup>¼</sup> Volts ð Þ meter <sup>3</sup> !

� �, <sup>∀</sup><sup>L</sup> <sup>¼</sup> n2π<sup>t</sup>

ð Þ 2*:*5V � α~ b l 3

� � sin 0ð Þ *:*5*<sup>ω</sup>*

Hall. The current deflection detected for the

*:*

torsion is constant in all space [4]. Likewise, was obtained the signal<sup>2</sup>

<sup>τ</sup>ð Þ¼ *<sup>ω</sup>* <sup>1</sup> 2π b l 3

sin*ω*L

<sup>1</sup> **Lemma** [10]. We consider a sensor Hall device <sup>L</sup>*<sup>H</sup>*

magnetic field in the dilaton must be corresponding to

torsion conditions:

constant voltage signal

detectable.

**31**

**Figure 2.**

þ0 ð*:*5s

*235 kHz, wave sample of 13 seconds, voltage of 4 Volts (Figure 3a)).*

*DOI: http://dx.doi.org/10.5772/intechopen.96779*

�0*:*5s

*<sup>ω</sup>*<sup>L</sup> , sinh *<sup>ω</sup>*<sup>L</sup>

Π t 1 � �e�j*ω*<sup>t</sup>

*<sup>ω</sup>*<sup>L</sup> ;

magnetic field change in the sensor produces per volume unit a torsion energy:

<sup>τ</sup> <sup>¼</sup> <sup>V</sup> 2π

*V*<sup>0</sup> ¼ Π

*t*

)

:

<sup>0</sup>*:*5*<sup>ω</sup>* , (1)

*<sup>ω</sup>*<sup>T</sup> , T>0 (2)
