pg. 78

Contents lists available at

Journal homepage: http://twasp.info/journal/home

Research

Mathematical Universe

Prof. Zhu Mao Chun1, Agboifo Edmond Omenonye

1,2, Benjamin Chris Ampimah

1,2

1Faculty of Mathematics, Jiangsu University, Xuefu Road, Zhenjiang, 212013, PR China

2Dept. of Mathematics, Statistics and Computer Studies, Cape Coast Technical University,.

P. O. Box AD 50, Cape Coast, Ghana

*Corresponding Author :

Phone : +8615502426515

Email: eddy4eva007@yahoo.com

Published online : 12 May, 2019

Abstract: Travelling through time is what we do on our everyday world in different means

that could be walking, running sailing, cycling, flying, etc. when we do this we tend not to

notice the effect because it’s on a small scale, since the age of nine down through my

primary, secondary to my present state I have wondered how and why our universe is like

this. The whole idea of my publication is to through lights on the massive doubts of we

humans that time travel is possible through various means, as I will explain on the body of

my presentation.

Keywords: Time, wormhole, time travel, space, universe

Introduction

It has been centuries since the apple fell down from the tree, which gave Sir Isaac Newton a

brilliant idea on knowing the true effect of gravity on objects, similarly here i have always

been curious on the nature of all interpretations, so many questions I would ask myself and

people around but yet their answers aren‟t corresponding to all happenings due to we need

more than understanding to know the true nature‟s secrecy.

My publication is a kind of relief to me because I have always wanted to plunder on issues of

our cosmos, planets, galaxies, stars and other celestial bodies in space. Above Some 13.8

billion years ago we originated from the big bang which gave rise to everything we see today,

But some fascinating question which we all ask on our everyday lives is what was before the

big bang? Was there series of universes? Why did the big bang explode massively? Why are

we forever moving to the future why not to the past?

Firstly, mathematics, which I consider the father of all majors, has made things easy for us all

to research and see the universe in a simplified way. I may not have taken much time to

pg. 79

explain the derivation process of how true our calculations are regarding all measurements on

physical topics like but so as the the laws of mathematical physics are true in small scale it‟s

also a good approach to invest them in larger scale even beyond the cosmos.

1.0 Time travel

Time traveling through time is a path through which you travel from one timeline to another

by different means, some may use wormholes, black holes, tunnels, time travelling machines

and so on. So far, the twin paradox is the most consistent visa method to have pass such test.

Traveling to an arbitrary point in space-time has a limited support in theoretical physics, and

usually only connected with quantum mechanics or wormholes, this is called the Einstein-

Rosen bridges.

1.1 Cosmology view: Physics, mathematics and astrophysics have played a central role in

shaping the understanding of the universe through scientific observation and experiment.

Cosmology (physical) was shaped through both mathematics and observation in an analysis

of the whole universe. The universe is mostly understood to have begun with the Big Bang

some billions of years ago, followed almost instantaneously by cosmic inflation;

an expansion of space from which the universe is thought to have emerged 13.799 ±

0.021 billion years ago. Cosmogony studies the origin of the very Universe,

and cosmography maps the features of the Universe at large scales.

1.2 A look into differential equation to determine the speed of light: A differential

equation is a mathematical equation that relates some function with its derivatives. In

applications, the functions usually represent physical quantities, the derivatives represent

their rates of change, and the equation defines a relationship between the two. Because such

relations are extremely common, differential equations play a prominent role in many

disciplines including engineering, physics, economics, and biology.

In pure mathematics mostly, differential equations are studied from several different areas

and perspectives, mostly concerned with their solutions “the set of functions that satisfy the

equation”. Only the simplest differential equations are solvable by explicit formulas;

however, some properties made up of the solutions of a given differential equation may be

determined without knowing the initial form

If a self-contained formula for the solution is not available, the solution may be numerically

approximated using computers. The theory of dynamical systems usually puts emphasis

on qualitative analysis of systems described by differential equations; meanwhile

many numerical methods have been made to determine solutions with a given degree of

accuracy.

pg. 80

Application of differential Equation to determine the Speed of Light

,

Note:

1. ε0 = 8.854187817...×10−12

F⋅m−1 (farads per metre)

2. μ0 = 4π×10−7

H/m ≈ 1.2566370614...×10−6

N/A2 or T⋅m/A or Wb/(A⋅m) or V⋅s/(A⋅m)

1.3 Age of the universe: Calculating the age of the universe is one fascinating and consistent

approached. Firstly, we have to pinpoint many galaxies for more accuracy, but because of

space, I limited my calculations to two galaxies (but the further steps for galaxy 3, 4, 5, 6…n

and same format).

When we pinpointed our first galaxy, we determined the speed it is travelling at and also we

determined the distance it has travelled so far, to get these values we have to first determine if

it‟s red shifting or blue shifting this will enable to know if it‟s coming to our direction or

away further from us, after all this when have to use supernova brightness to get the distance

covered and by using Doppler shift to get its distance travelled, then once all known

parameters we them try to use the related formula to isolate all units to years.

1.3 Age of the universe

pg. 81

(By Supernova luminosity and brightness)

(By Doppler shift)

Note:

(By Supernova luminosity and brightness)

(By Doppler shift)

Note:

Average of both galaxies hobbles constant .

Recall :

1.3.1 Brief history of the universe: In 1915, Albert Einstein published the theory of general

relativity and in 1917; he constructed the first cosmological model based on his theory. In

order to remain consistent with a steady state of the universe, Albert Einstein added what was

later called a cosmological constant to his equations. As we know today on our every day

knowledge, for something to be created the designer should be outside to produce it and give

Galaxy 1

Galaxy 2

pg. 82

it a proper shape, our universe was once a single grain of sand initially with a tiny radium and

its weight was as billions of mass, now, theoretically it means that our universe must be

resting on a body which means they must be a space or region that existed before the big

bang which we are calling the multiverse and with this idea we can be able to get proper

findings on our universe.

1.4 Multiverse: The multiverse is a hypothetical groups of many universes existing, this

might be true for all things to remain consistent holding the laws of nature (beyond physics) it

is also called parallel universe, from observation it explains that they are regular big bangs

that must have taken place before our and still taking places as we speak right now.

1.4.1 Brief explanation on multiverse: The physics communities continues to debate the

multiverse hypotheses. Prominent physicists and mathematicians have decided in their

opinions about whether any other universes exist.

Some physicists say the multiverse is not a legitimate topic of scientific inquiry they hope to

discover in the closest future. Concerns have been raised about whether attempts to exempt

the multiverse from experimental verification could erode public confidence in science and

ultimately damage the study of fundamental physics. Some have argued that the multiverse is

a philosophical rather than a scientific hypothesis because it cannot be falsified. The ability to

disprove a theory by means of scientific experiment has always been part of the

accepted scientific method. Paul Steinhardt has famously argued that no experiment can rule

out a theory if the theory provides for all possible outcomes.

In 2007, Nobel laureate Steven Weinberg suggested that if the multiverse existed, "the hope

of finding a rational explanation for the precise values of quark masses and other constants of

the standard model that we observe in our Big Bang is doomed, for their values would be an

accident of the particular part of the multiverse in which we live.

Picture of Multiverses

pg. 83

Figure 1.1: Each universes are billions of light years away from each other with massive size

and masses

1.5 Redshift : In physics, redshift happens when light/electromagnetic radiation from an

object is increased in wavelength,or shifted to a red end of the spectrum. In general, whether

or not the radiation is within the visible spectrum, a "redder" means an increase in

wavelength – equivalent to a lower frequency and a lower photon energy.

Some of the redshifts are an example of the Doppler Effect, familiar in the change of

apparent pitches of bell/sirens and frequency of the sound waves emitted by speeding

vehicles. A redshift occurs when a light source moves away from the observer. An example

of this is the cosmological redshift, which is due to the expansion of the universe, and distant

light sources (generally more than a few millions of light years away) show redshift

corresponding to the rate of increase in their distance from Earth. In conclusion, gravitational

redshift is a relativistic effect that is observed in electromagnetic radiation moving out of a

field of gravity. Conversely, a decrease in wavelength is called blue shift and is mostly seen

when a light-emitting object moves toward an observer or when electromagnetic radiation

moves into a gravitational field. However, redshift is a more common term and sometimes

blue shift is referred to as negative redshift and they both apparently does not change the

output of the result.

Knowledge of redshifts and blue shifts have been applied to develop several terrestrial

technologies such as Doppler radar and radar guns. Redshifts are also seen in

the spectroscopic observations of astronomical objects. Its value is represented by the letter z.

A special relativistic redshift formula (and its classical approximation) can be used to

calculate the redshift of a nearby object when spacetime is flat. However, in many contexts,

such as black holes and Big Bang cosmology, redshifts must be calculated using general

relativity. Special relativistic, gravitational, and cosmological redshifts can be understood

under the umbrella of frame transformation laws.

pg. 84

Figure 1.2: wavelength of shifts

Here is a pure example of redshift and blue shift describing how different observers could see

it, the right observer sees an extended (longer) wavelength while the left observer sees a

squeezed wavelength

Figure 1.3: Example of Red shift picture

2.0 Worm holes

A wormhole is a theoretical travelling route or passage through space-time that could create

shortcuts for long journeys across huge distances to distant locations, galaxies, universes etc.

Wormholes are predicted by the theory of general relativity. However, wormholes comes

with sudden closures, high radiation and dangerous contact with exotic matter.

Figure 2.1: Wormhole connecting two points in space

2.1 Tips of Wormholes

1. Wormholes wrap space together by causing a space time travel

2. Wormholes keep its both end opened with negative energy

3. Worm holes are negative energies driven

4. They are generally visible in space where there is likely to be some negative

matters/energies

pg. 85

5. It has a structure of a funnel and at the middle of the passage is very thin, known as

the pinch point

Figure 2.2: A simple worm home structure with bent space causing dilation of time

Though wormholes have never been proven to exist, these theoretical passageways through

space-time are predicted by Einstein's general theory of relativity.

2.1.1 Calculations of a Wormhole

Then, . This equation holds if time travel is possible through the medium of

wormhole by us investigating from P to Q through as the longest path and P to Q as the

shortest path. If our investigation gives us, a value equal to one or more, then it holds.

C

y

s

Q

x O

P 𝐱

∆𝐱

pg. 86

Remember where an imaginary unit is.

(This equation is for complex plane)

, by approximation

=

Eq 1. Integration rules

As then

Eq 2. By fractionalization

From this

Finally, the major idea is that, as P gets closer to Q, then which was the shortest path from

P to Q is 6% shorter than , which means time travel through the wormhole is possible,

although negative energy is required.

3.0 Speed of Light

The primary concept behind both events involves the speed of light and all other forms of

electromagnetic radiation, which scientists have thoroughly examined, and expressed as a

constant value denoted in equations by the symbol c. Not truly, a constant, but rather the

maximum speed in a vacuum, the speed of light, which is almost 300,000 kilometres per

second, can be manipulated by changing media or with quantum interferences.

pg. 87

Table 3a: Speed of light at different substances

The measurements of the Speed of Light by different, astronomer’s and scientist

Date Researchers Respective methods Estimated

Kilometers

/Seconds

1667 Galileo Galilei Covered Lanterns 333.5

1862 Leon Foucault Rotating Mirror 298,000

1868 James Clerk Maxwell Theoretical Calculations 284,000

1875 Marie-Alfred Cornu Rotating Mirror 299,990

1879 Albert Michelson Rotating Mirror 299,910

1888 Heinrich Rudolf

Hertz

Electromagnetic Radiation 300,000

1889 Edward Bennett Rosa Electrical Measurements 300,000

1890s Henry Rowland Spectroscopy 301,800

1907 Edward Bennett Rosa

and Noah Dorsey

Electrical Measurements 299,788

1923 Andre Mercier Electrical Measurements 299,795

1926 Albert Michelson Rotating Mirror

(Interferometer)

299,798

1928 August Karolus and

Otto Mittelstaedt

Kerr Cell Shutter 299,778

1932 to

1935

Michelson and Pease Rotating Mirror

(Interferometer)

299,774

1947 Louis Essen Cavity Resonator 299,792

1949 Carl I. Aslakson Shoran Radar 299,792.4

pg. 88

1951 Keith Davy Froome Radio Interferometer 299,792.75

1973 Kenneth M. Evenson Laser 299,792.457

1978 Peter Woods and

Colleagues

Laser 299,792.4588

Table 3b: Different calculations on the speed of light in the early years, the average of all

these values was what gave the specific values we use today and they are consistent

Speed of light calculations

Using Maxwell‟s Equation to derive the speed of light

In addition, God said,

, magnetic field is enclosed to it should give „0‟ output

, faradays law

, and hence

there was light.

ε0 = 8.854187817...×10−12

F⋅m−1 (farads per metre)

μ0 = 4π×10−7

H/m ≈ 1.2566370614...×10−6

N/A2 or T⋅m/A or Wb/(A⋅m) or V⋅s/(A⋅m)

this has shown that the combination of magnetic flux and the electric field must be

the speed of light

3.1 A glance on Sunlight: Sunlight is a key factor that makes the universe work, it is very

essential for all living things because its radiation, energy, light, are one of the more

important key factor to the human existence.

It takes about 8 Minute for the suns light to travel to us here on earth which means that for

every time we look upon the sky we are seeing an illusion of the sun because that light hitting

our face was what radiated 8 minutes ago. Below is an illustrated picture from the sun to the

earth.

pg. 89

Figure 3.1: Sunlight takes about 8 minutes 17 seconds to travel the average distance from the

surface of the Sun to the Earth. Meters per second : 299792458

3.2 Composition of the sun: The Sun is made up mostly on chemical

elements hydrogen and helium. Our suns life presently, it accounts for 74.9% and 23.8% of

the mass of the Sun in the photosphere(s) respectively. All the heavier elements,

called metals in astronomical language, account for less than 2% of the mass, with oxygen

(about 1% of the Sun's mass), carbon is (0.3%), neon (0.2%), and iron (0.2%) being the most

abundant.

The Sun's original chemical composition was inherited from the interstellar medium out of

which it formed. Originally, it would have contained about 71.1% hydrogen, 27.4% helium,

and 1.5% heavier elements.

The hydrogen and most of the helium gas in the Sun would have been produced by Big Bang

nucleosynthesis in the first 20 minutes of the universe, and the heavier elements

were produced by previous generations of stars before the Sun was formed, and spread into

the interstellar medium during the final stages of stellar life and by events such

as supernovae. Since the Sun formed, the main fusion process has involved fusing hydrogen

into helium. Over the past 4.6 billion years, the amount of helium and its location within the

Sun has gradually changed. Within the core, the proportion of helium has increased from

about 24% to about 60% due to fusion, and some of the helium and heavy elements have

settled from the photosphere towards the center of the Sun because of gravity.

Mass of the Sun simplified calculations

Recall,

pg. 90

All units are standard, and this is the estimated mass of our sun it is consistent and accurate

with high %certainty

4.0 Black Hole

Black holes of stellar mass are formed when a small massive stars collapse at the end of their

life span. After a black hole has formed, it can continue to grow by absorbing mass from its

surroundings and keep merging with other black holes.

Figure 4.1: Structure of a black hole

4.1 Supermassive Black Hole: A supermassive black hole (SMBH) is the biggest and largest

type of black hole, on the orders of billions of solar masses, and it is theorized at the centre of

most big galaxies that is existing . Unambiguous dynamical evidence for SMBHs exists only

in a handful of galaxies, these include the , the Local Group galaxies M31 and M32,Milky

Way and a fewer galaxies beyond the Local Group for example NGC 4395.

4.1.1 Creation of black holes: Black holes are created by the death of a star, this is as a

result of when a star uses most of its energy its helium gas and other constituted fuel finishes

and it then forces itself into its very self and then its weight becomes so large in itself by

making an irregular path on space-time and when all this finishes it implodes in itself and a

new black hole is born

Black hole thermodynamics Hawking Radiation, specific heat And Entropy Calculations-

More simplified.

Temperature of a Black body Radiation is defined by

o m=mass of black hole

o G=gravitational constant

o C=speed of light

pg. 91

= Boltzmann‟s constant

From ,

Specific heat

To calculate the entropy of the black hole use these identities are as follows:

,

Some notable facts about BH based on the calculations

1. Black hole mechanics says that the surface area of the event horizon always increases

and never decreases

2. The temperature of a black hole is inversely proportional to its mass

3. When two black hole surface horizons combine, the combination of horizons are far

greater than the initial sum.

Figure 4.2: Simulated black hole in front of the Milky Way

Source: Space Time Travel

Results

The speed of light is same for all observers, which makes things good here, After much

research I came to realize that time travel is possible under the below calculations

pg. 92

t= earth time before travel=50 years

vel =velocity=98% of the speed of light

c= speed of light

If you travel with 98% of the speed of light in space and you spend 50 years on the total trip

then you will arrive in earth after 250 years, which means if you leave in the year 2019 upon

your arrival on earth you would have aged by only 50 years, your hope is to meet earth‟s

time in 2069, but eventually you will arrive in the year 2269, which means you would be a

living ancestors to your great great great grandchildren, below if the calculation with the

inputs of the parameters,

Note Edmond correction factor was specially designed by myself for more accuracy of the

result due to lags and leads of the rest parameters in the equation.

On the nutshell, I have been able to prove in my ways that time travel is very possible and our

only challenge is to get our space ship to attain the speed of light, which by more researches I

hope to get it published in the future.

Conclusion

In presiding the fate of our universe all physical quantities should be involved from the

theory of general relativity at large scale through quantum mechanics to the very last sub

atomic particles. Time travel is a very interesting topic that triggers everyone‟s thought, as it

is not visible to our naked eyes so far the laws of mathematics are consistent to interprets the

language of the universe in small scale(on our everyday lives computer coding and so on)

pg. 93

then it should hold consistency in all areas of knowledge if applied in the right direction. The

four chapters, I explained Time Travel, wormholes, Speed of light and Black holes. I focus

mainly on the possibilities of Time travel, how mathematics works on different areas of

theoretical physics and some universal findings (black hole) beyond our solar system all

chapters discussed are branches of one another. Over centuries (100 years more), we humans

have tried to find the ultimate ways of long human life expectancy but to no fact yet. The

speed of light which is the fastest on our universe is much more a fascinating approach

because stars which are millions and millions of light years away from us, their lights are still

travelling towards our direction which practically means all Night sky stars we see are just an

illusion of its appearance (rather travelling photons) because they are not there anymore (or

rather long time dead).

I tried to make all mathematics calculations in my publication simple to make it flexible for

readers and I tried to avoid some mathematical proving theorems as well. The beauty of

mathematics either pure or applied is truly the language of our universe.

Acknowledge

I hope to throw lights on much publication in the future, especially how we can achieve the

speed of light and its applications to give us humans the ability to increase our lives

expectancy in the future. Special thanks goes to my supervisor Prof.Zhu Mao Chun, my

family, Jiangsu University in general and to all those who stood by me to make this a dream

come true.

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