Domain of Relativistic Mechanics

[07PRADEEP]

Title: Domain of Relativistic Mechanics.
Running title: Limits to Special Theory of Relativity.




Einstein's Theory shattered:A 100 year 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 part3 might seem independent,but the formula derived in part1 has a bearing on this.

Part – 1:
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”.

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=100x5=[27²-26²]x5
29²-21²=400=100x4=[27²-26²]x4

28²-22²=300=100x3=[27²-26²]x3
27²-23²=200=100x2=[27²-26²]x2

27²-26²=100=100x1=[27²-26²]x1


At this stage, insight, institution and creativity had been triggered. The pattern, was further checked and studied by extending it to 10-20 range.

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 where N and 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 given A and C, to find B, 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
could be determined.Hence,the only remaining variable,which is the only
unknown now could be found out.In effect,in totality, all the variables can be determined or solved 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”.

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.

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 of the form A² +B² = C²
Hence,
Pythagorean triplets can be generated by using this formula.

Part – 2

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 is required in order to understand this.

Part – 3
Domain of Relativistic Mechanics:
One needs to have ,a great knowledge of Inequalities(part of mathematics-algebra),to scrutinize relativisticmechanics and understand the crux of its deficiency.Let us probe






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.
Since in reality,
( A+B)/2>(A―B)/2 for both A and B greater than 0.
CASE1 GO IN SEQUENCE FROM FROM BOARD,A TO B TO C ie steps 1,2,3,4
BOARD A/PHYSICS
STEP1
(t′)²=(t)²―(tv/c)²,time dialation 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
Equation analogous to
X² = Y²― Z²in which X=squareroot of(AB) or [(k)(k―2 w)].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 involving2 vqariables.
STEP2
Further let Z=w= tv/c above.
Let us introduce w= t v/c
(k)(k―2 tv/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(A-B/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.





CASE 2
Exception to this theory,for values of k less than 2.Note that my above
approach is not valid for time less than 2s,since k(k-2tv/c) will become negative.
The reference equation for the exceptional case is
(t′ c)²=(tc)²-(tv)² ,where the variables have their usual meanings,
and the algebraic equation ,it will be compared will be
4AB= (A+B)² ― ( A ― B)²,and in it
Let A=c,B=(c-tv)We get 4(c) (c-tv)=(2c-tv)²-(tv)²
B>0 gives tv<c
For t′<2 s,tc < 2c units, we obtain t< 2 s
for (tv)less than(c),Maximum of t=2 seconds,minimum of or atmost v=c(nothing prevents v becoming almost c units,maybe t will become equal to one),also t=2 s, t′=2s,


Conclusion:

Maximum of v=c/2 units in Case -1 tv<kc/2 , time in frame S′, t′ element of 2 to k seconds and t<k seconds
Where k stands for any fixed value ,however large in seconds.



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.
Case2
tv<c , t′ in frameS’ element of ( 0 to 2)s , t<2 s and MAXIMUM OF v=c units

In case 2 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.

Conclusion:
In less than or equal to 2 second time interval between events,mass less than 2 kg or length contraction less than 600000km,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 and mass variation.Length contraction,however, could be proved to vary only by 13.3% beyond 600000km.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.

[07PRADEEP]

I have to engage in a minor self-correction ,which in no way affect the grand deductions or conclusion. Case2 has to be ignored since,if units are considered as an issue,which will be, in any case,the statements in Case2 seem to be unsubstantiated.

[07PRADEEP]

CLARIFICATION
[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.Since this was the underlying equation used and we are constrained to obtain positive values,which makes N,(N-2) and (N-1) all to be positive,implies, in net effect k>1.So our consideration of limits to be imposed becomes for: Limit1.Time interval between events less than 1s. Limit 2. mass of particles less than 1kg. Limit 3.Length contraction less than 300000km.Within these specified limits ,special theory of relativity is 100% accurate.Beyond,it could vary only upto half the speed of light.

[07PRADEEP]

Further slight clarification and revisioning,
In (k)(k―2 tv/c)=(k―tv/c)²― (tv/c)²,let k=1, equation becomes
(1)(1―2 tv/c)=(1―tv/c)²― (tv/c)², the implication being if t’ <1 and t<1/2,nothing prevents from
v being equal to c units,which I strongly believe is Einstein’s special theory of relativity domain ,where
it is 100% acceptable and accurate.Hence, considered mass has to be less than ½ kg and length contraction considered in one frame, less than1,50000km. The above views further stongly prove my claim.

[07PRADEEP]

Further slight clarification and revisioning,
In (k)(k―2 tv/c)=(k―tv/c)²― (tv/c)²,let k=1, equation becomes
(1)(1―2 tv/c)=(1―tv/c)²― (tv/c)², the implication being if t’ <1 and t<1/2,nothing prevents from
v being equal to c units,which I strongly believe is Einstein’s special theory of relativity domain ,where
it is 100% acceptable and accurate.Hence, considered mass has to be less than ½ kg and length contraction considered in one frame, less than1,50000km. The above views further stongly prove my claim.

Concrete Deduction.:These views are valid for t < 1/2 s and hence t’ < 1 s.Presently,no scientific proof exists to defy these limits,imposed from or derived by my theory.

[07PRADEEP]

.It is astonishing to note that ,Special Relativity Theory Equations are incongruous beyond half the speed of light, by mere Number Theory considerations ,specifically ‘time dilation’ and ‘length contraction’ equations. Nevertheless, there is an exception to this theory,for particles of masses less than 1kg, or time intervals between events which are less than 1s or length contraction less than 300000km ,where it could be absolutely accurate as Einstein predicted and therefore it implies,these could change upto only 13.3%.

[07PRADEEP]

.It is astonishing to note that ,Special Relativity Theory Equations are incongruous beyond half the speed of light, by mere Number Theory considerations ,specifically ‘time dilation’ and ‘length contraction’ equations. Nevertheless, there is an exception to this theory,for particles of masses less than 1kg, or time intervals between events which are less than 1s or length contraction less than 300000km ,where it could be absolutely accurate as Einstein predicted and therefore it implies,these could change upto only 13.3%.

Further slight clarification and revisioning,
In (k)(k―2 tv/c)=(k―tv/c)²― (tv/c)²,let k=1, equation becomes
(1)(1―2 tv/c)=(1―tv/c)²― (tv/c)²,B>0 IMPLIES(1―2 tv/c)> 0 IMPLIES (tv/c) <1/2.Please note the gigantic implication or consequence of the same.Assuming t<1/2 in the AFOREMENTIONED condition,v/c amounts to a positive real number greater than1. This unambiguously exemplifies,the bizarre observations,scientists obtained as regards neutrinos,the behaviour of them is very real and all my observations is absolutely verified.The implication being if t’ <1 and if t<1/2,nothing prevents from
v being equal to or greater than c units,which I strongly believe is beyond Einstein’s special theory of relativity domain .

[Brent]

Pradeep. I am not going to pretend to follow all of your math. I can see where your equation comes from and it looks OK to me but I am not qualified to provide any feedback

As for special relativity not being accurate after 50% of C, I assume that you mean that your equation provides different results above 50% of C.

As far as I can tell the velocity of an accelerating mass, when graphed velocity relative to time, will produce an exponential curve. The first half of the curve is pretty much linear and begins to arch more and more as the velocity increases.

Your equation is similar to SR when the graph is linear but differs when it curves.

The whole point of SR is that the graph curves. If the graph doesn't curve and is a straight line, regular math will get the job done.

Does your line curve less than an exponential curve or more or is it a straight line.

According to experts, electrons have mass. When electrons are accelerated through an electrical conductor from zero to C, they will follow an exponential curve.

I believe this holds true for all masses which are accelerated.(disclaimer: I am an idiot who makes stuff up.)

Therefore your equation should follow a basic exponential curve if it is accurately describing nature according to what I made up.

If your equation accurately describes nature, what does it mean in words.

Lord Calvin may be the result of inbreeding. To understand something you must figure out how it works logically and explain it in words. Equations and numbers should be used to engineer something from what you figured out with logic and words.

If you use math to describe words, sense is made. When you use words to describe a mathematical equation, nonsense is made.

When are you moving to Brampton?

Brent

[07PRADEEP]

Pradeep. I am not going to pretend to follow all of your math. I can see where your equation comes from and it looks OK to me but I am not qualified to provide any feedback

As for special relativity not being accurate after 50% of C, I assume that you mean that your equation provides different results above 50% of C.

As far as I can tell the velocity of an accelerating mass, when graphed velocity relative to time, will produce an exponential curve. The first half of the curve is pretty much linear and begins to arch more and more as the velocity increases.

Your equation is similar to SR when the graph is linear but differs when it curves.

The whole point of SR is that the graph curves. If the graph doesn't curve and is a straight line, regular math will get the job done.

Does your line curve less than an exponential curve or more or is it a straight line.

According to experts, electrons have mass. When electrons are accelerated through an electrical conductor from zero to C, they will follow an exponential curve.

I believe this holds true for all masses which are accelerated.(disclaimer: I am an idiot who makes stuff up.)

Therefore your equation should follow a basic exponential curve if it is accurately describing nature according to what I made up.

If your equation accurately describes nature, what does it mean in words.

Lord Calvin may be the result of inbreeding. To understand something you must figure out how it works logically and explain it in words. Equations and numbers should be used to engineer something from what you figured out with logic and words.

If you use math to describe words, sense is made. When you use words to describe a mathematical equation, nonsense is made.

When are you moving to Brampton?

Brent

Dear Brent,
You,raise the issue of electrons,travelling almost the speed of light to contradict or refute my theory.For masses,less than 1 kg,here when we are considering subatomic particles,my theory substantiates,if t<0.5 second,it can even travel faster than the speed of light.Now,if my equations work or explain, even in the case of neutrinoes that can travel faster than the speed of light.Then it is authentic,real and genuine.On the contrary,my theory states,if masses are greater than 1kg,beyond half the speed of light is unattainble speed for particles.STR thereby will be constrained by mathematics or number theory,which has greater significance and impunity.

[Brent]

Dear Brent,
You,raise the issue of electrons,travelling almost the speed of light to contradict or refute my theory.For masses,less than 1 kg,here when we are considering subatomic particles,my theory substantiates,if t<0.5 second,it can even travel faster than the speed of light.Now,if my equations work or explain, even in the case of neutrinoes that can travel faster than the speed of light.Then it is authentic,real and genuine.On the contrary,my theory states,if masses are greater than 1kg,beyond half the speed of light is unattainble speed for particles.STR thereby will be constrained by mathematics or number theory,which has greater significance and impunity.

If you are relying on neutrinos to authenticate your theory, you will be waiting a long time because neutrinos do not exist in reality, only in peoples minds.

Why do small mass objects behave differently than large mass objects. Large mass objects are made of lots of little mass objects. How close together do small mass objects have to be before their behaviour changes.

I have a small mass attached to a rocket that will accelerate the small mass to C. Suppose I have small masses with rockets and all the small masses add up to more than 1kg but individually they are all less tan 1kg. If these rockets are ignited, according to you and STR, the small masses will all individually accelerate to C. But if I space them out and tie them all to a stick and ignite them, according to you they can only reach 50% of C. What difference could tying them to a stick make?

Your theory matches STR up to 50% of C. So does conventional math. The first half is pretty much linear.

Does your theory predict a mass will accelerate until 50% of C and then suddenly stop accelerating?

You don't have to move to Brampton, your Canadian Citizenship is in the mail.

Resistance is futile
You will be assimilated.