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Transactions on Engineering and Computing Sciences - Vol. 12, No. 6

Publication Date: December 25, 2024

DOI:10.14738/tecs.126.17963.

Negulescu, V. L. (2024). A New Hypothesis Concerning the Big Bang. Transactions on Engineering and Computing Sciences, 12(6).

14-20.

Services for Science and Education – United Kingdom

A New Hypothesis Concerning the Big Bang

Vlad L. Negulescu

ABSTRACT

Using the fact that the power Pg is a tangent function, this paper develops a

hypothesis concerning the beginning of the Universe and the Big Bang. Everything

starts from an initial singularity which contains infinite power. Further the mass

and the diameter of the whole Universe is also calculated.

INTRODUCTION

A Vector-Hyper-Complex Number, representing an ideal particle, can be written as1:

p = t

g + iz + jȳ+ kx̄ (1.1)

Where, t

g + iz is the scalar part of this number, and jȳ + kx̄represents the vector part. The

symbols 1, i, j and k are fundamental units of H-numbers as defined in the reference paper2. The

Table 1 shows the multiplication rules of the fundamental units.

Table1: Units’ Multiplication Table

The four parameters of the particle’s representation are time (tg), mass (z), the momentum (y̅)

and the space (x̅). The space and momentum are vectors in the 3d Euclidean space. The

geometrized system of units3 (GU) enables to express all these parameters using a common

unit, meter, as shown below in the Table 2.

Table 2: The conversion of international system of units (SI) to geometrized system of

units (GU); c is the velocity of light and G gravitational constant, as seen in reference4.

z GU SI Conversion

symbol unit symbol unit SI↔GU

Length x m l m 1↔1

Time t

g m t s c↔c-1

2.998x108↔3.335x10-9

Velocity v

g none v ms-1 c

-1↔c

3.335x10-9↔2.998x108

Mass z m m Kg Gc-2↔G-1c

2

7.424x10-28↔1.347x1027

Momentum y m p Kgms-1 Gc-3↔G-1c

3

2.477x10-36↔4.037x1035

Force Fg none F N Gc-4↔G-1c

4

8.257x10-45↔1.211x1044

x 1 i j k

1 1 i j k

i i -1 -k j

j j -k -1 i

k k j i 1

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Negulescu, V. L. (2024). A New Hypothesis Concerning the Big Bang. Transactions on Engineering and Computing Sciences, 12(6). 14-20.

URL: http://dx.doi.org/10.14738/tecs.126.17963

Power Pg none P W Gc-5↔G-1c

5

2.755x10-53↔3.629x1052

As can be easily seen the velocity (v

g

), force (F

g

) and power (Pg) are dimensionless.

The Power, as defined in GU, is in fact the mass flow. The mass flow (μ), is expressed in SI in

Kgs-1, when refers only to displacement of masses. Simultaneously any mass flow is

representing power in the classical sense, because the mass is equivalent to energy. If we

consider a mass flow μ=1 kgs-1, then this represents also a power P= 8.988x1016 W. Both values

correspond to a unique Pg of 2.477x10-36. The conversion coefficients to GU for mass flow and

power are Kμ = 2.477x10−36and Kp = 2.755x10−53

.

THE POWER OF PARTICLES

The Coordinate Transformations

A particle in the “space-rest frame” has an evolution line which remains in the complex plane1,

C. The time measured by an observer attached to this frame, is called the proper time. The mass

of the particle represents evidently the rest mass. The corresponding H-number has the

following expression:

p0 = t0

g + iz0 (2.1)

The coordinate transformations of this H-numbers occur by multiplication with unit

multipliers5 as it follows:

a. The rotor with imaginary argument is, by definition, a pure scalar

e

iα = cos α + i sin α

b. The rotor with co-imaginary argument contains a vector part:

e

jβ̄ = cos β + ju̅ sin β

c. The pseudo-rotor with co-real argument contains a vector part, too:

e

kχ̄ = cosh χ + ku̅ sinh χ

Where u̅ is an arbitrary unit vector in the tridimensional Euclidean space. For particle with the

constant rest mass, it obtains5:

P

g = tanα; F̅g = u̅tanβ; v̅

g = u̅tanhγ (2.2)

Addition of Powers

As it shown in the equations (2.2) the mass flow, or the power of a particle, may be written as

P

g = tanα (2.3)

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Transactions on Engineering and Computing Sciences (TECS) Vol 12, Issue 6, December - 2024

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Let us consider a set of different powers:

P1

g = tanα1 ; P2

g = tanα2 ; ... ... ... ... ... ... Pn

g = tanαn (2.4)

The superposition of the powers above, means the addition of the imaginary arguments:

α = ∑ αi

n

i=1

(2.5)

Consequently, the resulting power can be written as it follows:

Ptotal

g = tanα = tan(∑ arctanPi

g

)

n

i=1

(2.6)

Because the value of Pg

is usually verry small, the expression (2.6) reduces to an algebraical

addition, in most of the cases, i.e.

Ptotal

g ≈ ∑ Pi

n g

i=1

(2.7)

In order to have an idea about how awfully small is the power expressed in GU, even for cosmic

objects, let’s calculate the power (Pg) of a quasar. The quasar represents the ultimate sources

of power in the universe. This power6 is in the range of 1037 W to 1039 W.

The corresponding quasar’s power expressed in GU is obtained multiplying by the factor KP,

mentioned above in the chapter Introduction, and lies within the range of 10-16 to 10-14.

In the particular case involving the superposition of only two powers, the equation (2.6)

becoms5

Ptotal

g =

P1

g

+P2

g

1−P1

g

P2

g (2.8)

If the denominator of the expression shown above is zero, then the resulting power Pg becomes

an infinite number. Reciprocally, the infinite power could split, for example, in two finite

powers P1

g = P2

g = 1 .

In general, there is possible that a superposition of a set of finite powers result in an infinite

total power. This happens when the resulting α, shown in the equation (2.5), becomes: π

2

=

1.571 Rad.

It is also possible that an infinite power transforms in a set of finite powers.

Hypothetically, the infinite power is contained in a kernel which has no proper time flow:

dz

dt

= tan π

2

= ±∞ i.e. dt = 0 .