Domain of Relativistic Mechanics.

Pradeep Koshy

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1.Introduction

Einstein's Theory undermined.

A century old theory is being

investigated by a mind for 20 years.

The result in this case, Einstein’s

theory seems to be shattered.

We will prove it in 3 parts.

PART1: A three way related algebraic

formula developed by me and its

significance like number theory could

be the basis of even a theory like

Special theory of Relativity.

PART2: In the shadow of Einstein.

PART3:Relativistic Mechanics

probed to find the domain of it.Note

that , part3 might seem independent,

but the formula derived in part1 has a

bearing on this. International Journal of Scientific & EngineeringResearch, Volume 4,Issue 4,April‐2013 561

ISSN 2229‐5518

IJSER © 2013

Part – 1:

2.Lord Kelvin’s Statement

“I often say, if you can express what

you know of something, in numbers,

you know something about it.

Otherwise, your knowledge is of a

meager and unsatisfactory kind. It

may be the beginning of knowledge,

but you have scarcely in your

thoughts advanced to the stage of

science, whatever the matter may be”.

3.The bombshell of the 21st century:

An algebraic formula developed by

me

I was preparing for SAT almost 2

decades back. I studied and observed

squares of numbers.

20²=400

21²=441

22²=484

23²=529

24²=576

25²=625

26²=676

27²=729

28²=784

29²=841

30²=900

The difference between the first and

last numbers, second and second last

numbers and so on are as follows:

500, 400, 300, 200 and 100. This

difference looked unbelievable to me.

To my observation, it was stunning to

observe that the squares of the

difference of numbers was falling into

a definite pattern.

30² ― 20²= 500 = [26² ― 24²] x 5

29² ― 21²= 400 = [26² ― 24²] x 4

28² ― 22²= 300 = [26² ― 24²] x 3

27² ― 23²= 200 = [26² ― 24²] x2

26² ― 24²= 100 = [26² ― 24²] x1International Journal of Scientific & EngineeringResearch, Volume 4,Issue 4,April‐2013 562

ISSN 2229‐5518

IJSER © 2013

At this stage, insight, institution

and creativity had been

triggered. The pattern, was

further checked and studied by

extending itto10‐20range.

10² =100

11²=121

12²=144

13²=169

14²=196

15²=225

16²=256

17²=289

18²=324

19²=361

20²=400

20²―10²=300=60x5

19²―11²=240=60x4

18²―12²=180=60x3

17²―13²=120=60x2

16²―14²=60=60x1

These observations, were further

extensively checked and it led me to the

formula.

[N² ― (N―2)² ]X=4(N‐

1)X=[N―(1―X)]²―[N―(1+X)]² whereNand

X are are two variables.

Now, it is the triumph of creativity.It is a

three way related formulae and

hence ,can be used to pose a question like

given an equation,

[A² ― B²] C = D= E²― F² where given E and

F

to findA,B,C and D. or alternatively posed

as givenAand C,to findB, D,E and F.where

the

Capital letters denote numbers, either

Real or Complex.This is a formula so

revolutionary

that I would call it miracle equation.It is

God’s gift to me.Note,that my formula is

capable

of solving 2 variables in a single

equation,which is conventionally

impossible from a mathematical

point of view.Also,understand that the

modified form of special theory of

relativity equations

contain 3 variables.For instance(t′)²=(t)²―(

tv/c)².Using my formula,2 of the variables

are determinate. Hence, the only

remaining variable, which is the only

unknown now could be found out.In

effect,in totality,in reality, all the variables

can be determined orsolved ie meaningful

interpretation of the same an be

made.From,hereon,we proceed keeping

,this in mind.No longer,is the Special

Theory of Relativity Equations

mysterious,inscrutable or

perplexing.Armed with a formula like the

above,we will pursue the same.

Pythagoreans believed that the number 4

governs the world. It is there in my

formula.

Number theory can be the key to the

understanding or unlocking the limits of

the special theory of Relativity. It

reinforces the maxim “Mathematics is the

Mother of all sciences”.

4.VITAL DEDUCTION: The formula

developed by me, serves as a way of

solving two variables minimum or upto 3,

maximum in a single equation relating two

sets of difference of squares of numbers.

Hence, it is a paradox from mathematical

point of view, although ,it is only a

particular solution. That can be

miraculous, in nature, will be proved later,

when considered it is analogous to special

relativity equations in number theory

form. Something of trivial significance, is

mentioned below.

5.Deviation Formula has one more use)

Let me rearrange the formula:

[√[ {N²―(N―2)²}X]²

+[N―(1+X)]²=[N―(1―X)]²ie ofthe form A²

+B² = C²

Hence,

Pythagorean triplets can be generated by

using this formula.International Journal of Scientific & EngineeringResearch, Volume 4,Issue 4,April‐2013 564

ISSN 2229‐5518

IJSER © 2013

6.IN THE SHADOW OF EINSTEIN –

Applications in Special Theory of Relativity

The formula was invented 2 decades back. It

was rejected, or considered trivial among

most people I met or submitted, in India.

Subsconsciously, feeling always, analogous

to Special Relativity-- those issues, were

boiling in my mind, for more

than a decade, when at last, it was serving as

a catapult to my long standing cherished

view, that it could be applied to Special

Relativity equations and the domain of

Relativistic Mechanics could be identified. I

was awestruck at how ,I arrived at it.

The sequence of events:

Knowledge of inequalities(Algebra branch)

is required in order to understand this.

TIME DILATON EQUATION

t = t′

√ (1― v²/c²)

where t is the time measured in S

frame is slower than the time t′

measured in inertial frame S′ by time

dilation equations.In all these cases, c

stands for velocity of light and equal

to it,whereas v is the velocity of the

frame S′ with respect to S.

On rearranging the relativistic

equation ,simplifies to( t′c)²=(tc

)²―(tv)²,which finally leads to

(t′)²=(t)²―( tv/c)²

We proceed like this:At this stage,my

invented formula’s most simplified

form will be adequate in proving my

contention. A simpler form of my

formula could be treated as ,the

formula 4AB= (A+B)² ―

(A―B)²,when we apply(N-1)=A and

X=B which on further simplification

leads to

AB=[(A+B)/2 ]² ― [ ( A ― B)/2]² by

rearranging.,will thereby have the

merits and advantages of my formula ,

which is worth mentioning.

Please note also, in reality,

( A+B)/2 > (A―B)/2 for both A and B greater

than 0.

. 8.CASE1

BOARD A/PHYSICS

STEP1

(t′)²=(t)²―(tv/c)²,time

dilation equation

modified form involving

3 variables,which have

their usual meanings.

STEP2

Note,that each term of

the above equation has

the same unit.(second

squared)

STEP3

But t>0 and t′ >0 and

t < k,hence maximum of

t=k,comparing physics

equation divested of its

units,with mathematics

equation

BOARD B/NUMBER

THEORY

STEP1

AB=[(A+B)/2 ]² ― [ ( A ―

B)/2]² is true and has the

properties of miracle

equation

STEP2

All Equations are

analogous to

X² = Y²― Z²,in which X

equals squareroot of(AB) or

[k(k― 2w)].This is the

instance when physics and

mathematics are

identical.STEP3

Maximum of tv/c=kv/c is

the first value of w.

STEP4

Equating first value of w

with second value,we get

kv/c=k/2.Cancelling out k

from both sides in it and

rearranging,we get

maximum of v=c/2 units.

BOARD C

\MATHEMATICS

STEP1

(k)(k―2 w)=(k―w)²― (w)² is an

algebraic identity involving 2

vqariables.

STEP2

Furtherlet Z=w= tv/c above.

Let usintroduce w= t v/c,then

(k)(k―2tv/c)=(k―tv/c)²― (tv/c)²

SinceA>0 , B>0&

A>B,we get (tv < ck/2) ,

Also(A+B/2)>0

gives(tv<ck),

ergo,tv<ck/2 is the

deduction.Hence,the

maximum value of

tv= ck/2,since even(AB/2)>0

STEP3

It follows since max. of

tv= ck/2,therefore ,max.

of tv/c=k/2.This is the

second value of w.

VERY IMPORTANT

In the basic equation [N²―

(N―2)² ]X=4(N-

1)X=[N―(1―X)]²―[N―(1+X)]²

where N and X are are two

variables.,N,(N ― 1) and

(N ― 2) ought to be

positive which implies k

has to be greater than1.

9.CASE2

For values of k<1,

the valid equation is

t = t′

√ (1― v²/c²)

,where Einstein’s special

theory of relativity be valid

and the limitations,I tried

to impose upon

invalid.Hence v almost

could be equal to c

,implies t< 1,which also

implies t′ <1.

.

10.Conclusion:

Yes, we can reduce a two dimensional multiplication to a squaring operation in a single

dimension (though this can raise the question of whether or not higher dimensional spaces

can inversely be constructed by operations performed within a single dimension! I think this

is true and that the dimensionality of a space arises from quantities and the inherent

diversity of qualities in the context of which information is presented)

CASE1

Maximum of v=c/2

units in tv<kc/2 , time in frame S′, t′, element of 1to k seconds

and also t<k seconds,where k stands for any fixed value ,however large in

seconds,greater than 1.

In case 1 not only numerical verification is done by number theory developed by

me, even if ,units and dimensions are considered as issues,will not hamper the

conclusion.

In less than or equal to 1 second time interval between events,mass less than 1 kg

or length contraction less than 300000km,Einstein’s special theory of relativity is

100% accurate.Beyond the same,it is only accurate upto half the speed of light,for

Time dilation , mass variation and Length contraction .Also, Special Relativity is

absurd in momentum and energy considerations also in this affected domain.

Ergo, my theory serves to destroy, a century's unabashed approval of Special

Theory of Relativity by world's leading scientists , of much, of its miraculous

nature. Einstein's view “The distinction between past, present and future is illusory,

however tenacious, it may appear to be” does not seem vindicated.

Cosmic speed or speed barrier for particles above 1kg is proved to be half the

speed of light.There is no Theory of Everything.