Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
9/28/2013 Priza Technologies Inc. 1
Hi To All
Thanks for attending to this seminar
The topics we will cover are:
1. A comp...
9/28/2013 Priza Technologies Inc. 2
Let us start with a BANG (2D, 2 particle case)
Given 2 particles in different directio...
9/28/2013 Priza Technologies Inc. 3
BANG Continued
Then not only the quantities in previous slide are conserved but also f...
9/28/2013 Priza Technologies Inc. 4
BANG Continued
For the case of 2 billiard balls:
9/28/2013 Priza Technologies Inc. 5
BANG Continued
Initially angles are 0, :
Final angles are , :
Where:
1 2( ) 2
( ) 0
( ...
9/28/2013 Priza Technologies Inc. 6
BANG Continued
For conservation momentum seems ok but for energy:
As , if the previous...
9/28/2013 Priza Technologies Inc. 7
BANG Continued
Statement: A matter particle can be represented by 2
photons going in o...
9/28/2013 Priza Technologies Inc. 8
BANG Continued
9/28/2013 Priza Technologies Inc. 9
BANG Continued
9/28/2013 Priza Technologies Inc. 10
Proof 1 Introduction
The derivation is based on looking at conservation of energy
of ...
9/28/2013 Priza Technologies Inc. 11
Prerequisites: None
I will explain and refresh whatever is required
1. Lorentz law of...
9/28/2013 Priza Technologies Inc. 12
Lorentz law of velocity addition
Galilean law is what appeals to intuition.
Relative ...
9/28/2013 Priza Technologies Inc. 13
Lorentz law of velocity addition Cont…
Problem: It is contradictory to the observatio...
9/28/2013 Priza Technologies Inc. 14
Lorentz law of velocity addition Cont…
Lorentz law in one dimension:
Approximates to ...
9/28/2013 Priza Technologies Inc. 15
Lorentz law of velocity addition Cont…
Works well when the object is photon:
object l...
9/28/2013 Priza Technologies Inc. 16
Lorentz law of velocity addition Cont…
It is only valid for the inertial frames of re...
9/28/2013 Priza Technologies Inc. 17
Lorentz law of velocity addition Cont…
Magnitude of observed velocity if the frame of...
9/28/2013 Priza Technologies Inc. 18
Lorentz law of velocity addition Cont…
Magnitude of observed velocity if the frame of...
9/28/2013 Priza Technologies Inc. 19
Lorentz law of velocity addition Cont…
Magnitude of observed velocity if the frame of...
9/28/2013 Priza Technologies Inc. 20
Lorentz law of velocity addition Cont…
Thus the scalar speed function as a transforma...
9/28/2013 Priza Technologies Inc. 21
Taylor Series Expansion in 1D
A function can be written in the form:
If the series su...
9/28/2013 Priza Technologies Inc. 22
Taylor Series Expansion in 1D Cont..
Example:
( , )f x y
2
2
2
2 2
2 2
2
( )
( ) ( ) ...
9/28/2013 Priza Technologies Inc. 23
Taylor Series Expansion chain rule
If there is a function , and itself is a function ...
9/28/2013 Priza Technologies Inc. 24
Now the real proof
( , )f x y
Let us assume there are n particles in a closed system ...
9/28/2013 Priza Technologies Inc. 25
Proof Cont…
( , )f x y
Conservation of energy: Sum of all energy is the closed system...
9/28/2013 Priza Technologies Inc. 26
Proof Cont…
( , )f x y
Writing the total energy in B again:
Assume that the scalar fu...
9/28/2013 Priza Technologies Inc. 27
Proof Cont…
( , )f x y
Then we can write it as the Taylor’s series:
< and higher powe...
9/28/2013 Priza Technologies Inc. 28
Proof Cont…
( , )f x y
Let and be two states of the system both in reference frame A ...
Proof Cont…
Proof Cont…
9/28/2013 Priza Technologies Inc. 31
Proof Cont…
( , )f x y
Also kind note that in the frame of reference B:
As h = 0 mean...
9/28/2013 Priza Technologies Inc. 32
Proof Cont…
( , )f x y
Then the equations simplify to:
< and higher powers>
< and hig...
9/28/2013 Priza Technologies Inc. 33
Proof Cont…
( , )f x y
Similarly in the frame of reference A based on the law of cons...
9/28/2013 Priza Technologies Inc. 34
Proof Cont…
( , )f x y
Divide both sides by and taking limit (remember that the proof...
9/28/2013 Priza Technologies Inc. 35
Proof Cont…
( , )f x y
Now let us look at
at
. (0, , )bk akV V
h
θ∂
∂
( )
2 2 2
2 2 2...
9/28/2013 Priza Technologies Inc. 36
Proof Cont…
( , )f x y
So
is conserved.
This is true for any conserved scalar functio...
9/28/2013 Priza Technologies Inc. 37
Proof Cont…
( , )f x y
So
is conserved.
This is true for any conserved scalar functio...
9/28/2013 Priza Technologies Inc. 38
Proof Cont…
( , )f x y
So
is conserved.
The above is the X component of the relativis...
9/28/2013 Priza Technologies Inc. 39
Proof Cont…
( , )f x y
As is conserved for any choice of conserved function E
If is m...
9/28/2013 Priza Technologies Inc. 40
Proof Cont…
( , )f x y
Let us take . As this is conserved so following sums are also ...
9/28/2013 Priza Technologies Inc. 41
Proof Cont…
( , )f x y
Then
is conserved
Similarly we keep doing it again and again t...
9/28/2013 Priza Technologies Inc. 42
Proof Cont…
( , )f x y
Which means there are infinite such equations. It is easy to p...
9/28/2013 Priza Technologies Inc. 43
Fallacy in Einstein Derivation
( , )f x y
The derivation by Albert Einstein was based...
9/28/2013 Priza Technologies Inc. 44
Fallacy in Einstein Derivation Cont…
( , )f x y
Let us take a simple case of 2 partic...
9/28/2013 Priza Technologies Inc. 45
Fallacy in Einstein Derivation Cont…
( , )f x y
Initial energy equations:
Initial mom...
9/28/2013 Priza Technologies Inc. 46
Fallacy in Einstein Derivation Cont…
( , )f x y
For momentum equations conservation i...
9/28/2013 Priza Technologies Inc. 47
The real fallout
( , )f x y
What Einstein described is a very commonly seen phenomena...
9/28/2013 Priza Technologies Inc. 48
Mass Light Duality
( , )f x y
If there are 2 photons of exactly the same frequency go...
9/28/2013 Priza Technologies Inc. 49
Mass Light Duality
( , )f x y
What is interesting to note is that:
and
A pair of phot...
9/28/2013 Priza Technologies Inc. 50
Mass Light Duality
( , )f x y
If put as we found in earlier slide then 2 wavelengths ...
9/28/2013 Priza Technologies Inc. 51
Mass Light Duality
( , )f x y
With a similar derivation we have proven that space-tim...
9/28/2013 Priza Technologies Inc. 52
Lorentz transformation for V >C
( , )f x y
The modified principle of relativity for V...
9/28/2013 Priza Technologies Inc. 53
Zero energy non zero momentum (ZEN)
( , )f x y
In the case of speed limiting to infin...
9/28/2013 Priza Technologies Inc. 54
Further work not published
( , )f x y
We have modified the Klein Gordon/Dirac equatio...
9/28/2013 Priza Technologies Inc. 55
At last zero point energy
( , )f x y
We have been able to theoretically prove that ze...
9/28/2013 Priza Technologies Inc. 56
Experimental Discussion
( , )f x y
Will only speak about it!.
Upcoming SlideShare
Loading in …5
×

Harnessing Zero Point Energy -- Mathematical Physics Perspective

71,767 views

Published on

The topic covered are:

1. A completely mathematical proof of fallacy in Einstein's mass energy derivation.

2. Proof of why classical or quantum mechanical equations cannot even satisfy deflection of billiards balls.

3. The missing factor.

4. Matter Light duality.

5. Speed greater than light.

6. Zero energy non-zero momentum particles.

List of related papers:

-------------------
1. Matter-Light Duality and Speed Greater Than Light: http://www.vixra.org/abs/1309.0167
2. Zero Energy Non-Zero Momentum Particles (Zen Particles): http://www.vixra.org/abs/1309.0168
3. Are All Photon Frequencies a Result of Doppler Effect? : http://www.vixra.org/abs/1309.0169
4. Principle of Super Inertia: http://www.vixra.org/abs/1309.0173
5. Fallacy in Einstein’s 2 blackboard derivation of mass energy: http://www.vixra.org/abs/1309.0172
-----------------

Published in: Technology
  • Light and its nature have caused a lot of ink to flow during these last decades. Its dual behavior is partly explained by (1)Double-slit experiment of Thomas Young - who represents the photon’s motion as a wave - and also by (2)the Photoelectric effect in which the photon is considered as a particle. A Revolution: SALEH THEORY solves this ambiguity and this difficulty presenting a three-dimensional trajectory for the photon's motion and a new formula to calculate its energy. More information on https://youtu.be/mLtpARXuMbM
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here

Harnessing Zero Point Energy -- Mathematical Physics Perspective

  1. 1. 9/28/2013 Priza Technologies Inc. 1 Hi To All Thanks for attending to this seminar The topics we will cover are: 1. A completely mathematical proof of fallacy in Einstein's mass energy derivation. 2. Why classical equations cannot even satisfy deflection of billiards balls. 3. The missing factor. 4. Matter Light duality, Speed greater than light. 5. Zero energy non-zero momentum particles.
  2. 2. 9/28/2013 Priza Technologies Inc. 2 Let us start with a BANG (2D, 2 particle case) Given 2 particles in different directions and , if the total energy of them is conserved then it implies that momentum is conserved, which means is conserved and is conserved. 1θ 1 2E E E= + 1 1 2 2cos cosxP P Pθ θ= + 1 1 2 2sin sinyP P Pθ θ= + 2θ
  3. 3. 9/28/2013 Priza Technologies Inc. 3 BANG Continued Then not only the quantities in previous slide are conserved but also following are conserved: Shocking but true! We will see proof after some time. 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 ( ) cos(2 ) cos(2 ) ( ) sin(2 ) sin(2 ) ( ) cos((2 1) ) cos((2 1) ) ( ) sin((2 1) ) sin((2 1) ) x y x y E r E r E r E r E r E r P r P r P r P r P r P r θ θ θ θ θ θ θ θ = + = + = + + + = + + +
  4. 4. 9/28/2013 Priza Technologies Inc. 4 BANG Continued For the case of 2 billiard balls:
  5. 5. 9/28/2013 Priza Technologies Inc. 5 BANG Continued Initially angles are 0, : Final angles are , : Where: 1 2( ) 2 ( ) 0 ( ) 0 ( ) 0 x y x y E r E E E E r P r P r = + = = = = π π θ+θ 1 2 1 2 1 2 1 2 ( ) cos(2 ) cos(2 ( )) cos(2 )(2 ) ( ) sin(2 ) sin(2 ( )) sin(2 )(2 ) ( ) cos((2 1) ) cos((2 1)( )) 0 ( ) sin((2 1) ) sin((2 1)( )) 0 x y x y E r E r E r r E E r E r E r r E P r P r P r P r P r P r θ θ π θ θ θ π θ θ θ π θ θ π = + += = + += = + + + += = + + + += 1 2 1 2 E E E P P P = = = =
  6. 6. 9/28/2013 Priza Technologies Inc. 6 BANG Continued For conservation momentum seems ok but for energy: As , if the previous given results are true then the difference is be staggering. 2 cos(2 )(2 ) 0 sin(2 )(2 ) E r E r E θ θ ≠ ≠ 2 E mc γ=
  7. 7. 9/28/2013 Priza Technologies Inc. 7 BANG Continued Statement: A matter particle can be represented by 2 photons going in opposite directions. A photon can be represented by 2 electrons, one going below the speed of light = u, other going above the speed of light = v with uv = 2 c
  8. 8. 9/28/2013 Priza Technologies Inc. 8 BANG Continued
  9. 9. 9/28/2013 Priza Technologies Inc. 9 BANG Continued
  10. 10. 9/28/2013 Priza Technologies Inc. 10 Proof 1 Introduction The derivation is based on looking at conservation of energy of particles from 2 reference frames, one moving at an infinitesimally small speed with respect to the other frame of reference. For the simplicity of equations the derivation is given for the 2D space. The same derivation works well for the 3D or N dimensions as well.
  11. 11. 9/28/2013 Priza Technologies Inc. 11 Prerequisites: None I will explain and refresh whatever is required 1. Lorentz law of velocity addition. 2. Taylor series expansion. 3. Relativistic energy equation. 4. Doppler effect.
  12. 12. 9/28/2013 Priza Technologies Inc. 12 Lorentz law of velocity addition Galilean law is what appeals to intuition. Relative Speed = Speed of the frame of reference + Speed of the particle
  13. 13. 9/28/2013 Priza Technologies Inc. 13 Lorentz law of velocity addition Cont… Problem: It is contradictory to the observation that the speed of light is same in all frames of reference. Example: If a train is moving at the speed of 100 miles per hour the speed of light as observed by a observer on the ground is 100 mph + speed of light. This is contradiction.
  14. 14. 9/28/2013 Priza Technologies Inc. 14 Lorentz law of velocity addition Cont… Lorentz law in one dimension: Approximates to Galilean Law when speeds are small in comparison to the speed of light: 2 ( ) / (1 / )observed frame object frame object lightV V V V V V= + + × Correction 2 1 / 1 ( )/ (1) frame object light observer frame light observer frame light V V V V V V V V V + × ≈ ⇒ = + ⇒ = +
  15. 15. 9/28/2013 Priza Technologies Inc. 15 Lorentz law of velocity addition Cont… Works well when the object is photon: object lightV V= 2 ( ) / (1 / ) ( ) / (1 / ) ( / 1) / (1 / ) observed frame light frame light light observed frame light frame light observed light frame light frame light observed light V V V V V V V V V V V V V V V V V V V = + + × ⇒ = + + ⇒= + + ⇒ =
  16. 16. 9/28/2013 Priza Technologies Inc. 16 Lorentz law of velocity addition Cont… It is only valid for the inertial frames of reference Lorentz Law for 3D/ND velocity addition Where is the velocity of frame of reference ( )2 2 ( ) ( ) 2 1 / (1 / ) object parallel object perpendicular observed object V h h c V V V h c + + − = + ⋅     h 
  17. 17. 9/28/2013 Priza Technologies Inc. 17 Lorentz law of velocity addition Cont… Magnitude of observed velocity if the frame of reference is moving in x direction and the object is moving in 2D with angle ( ) ( ) ( ) 2 2 cos sin cos sin cos cos 1 / sin (1 cos / object object object object parallel object object perpendicular object object object object object observed object h hi V V i V j V V i V V j V h V h V i hi h c V j V V h θ θ θ θ θ θ θ θ = = + = = = + + − = +                2 )c θ
  18. 18. 9/28/2013 Priza Technologies Inc. 18 Lorentz law of velocity addition Cont… Magnitude of observed velocity if the frame of reference is moving in x direction and the object is moving in 2D with angle ( ) ( ) ( ) ( ) 2 2 2 22 2 2 2 2 2 2 2 2 2 ( cos ) 1 / sin (1 cos / ) cos 1 / sin (1 cos / ) cos 1 sin / 2 cos (1 object object observed object object object observed object object object object o V h i h c V j V V h c V h h c V Speed V V h c V h V c V h Speed V θ θ θ θ θ θ θ θ θ + + − ⇒ = + + + − ⇒ = = + + − + ⇒ = +     2 cos / )bjecth cθ θ
  19. 19. 9/28/2013 Priza Technologies Inc. 19 Lorentz law of velocity addition Cont… Magnitude of observed velocity if the frame of reference is moving in x direction and the object is moving in 2D with angle ( ) ( ) ( ) ( ) 2 2 2 22 2 2 2 2 2 2 2 2 2 ( cos ) 1 / sin (1 cos / ) cos 1 / sin (1 cos / ) cos 1 sin / 2 c object object observed object object object observed observed object object object object observed V h i h c V j V V h c V h h c V V V V h c V h V c hV V θ θ θ θ θ θ θ θ + + − ⇒ = + + + − ⇒ = = + + − + ⇒ =     2 os (1 cos / )objectV h c θ θ+ θ
  20. 20. 9/28/2013 Priza Technologies Inc. 20 Lorentz law of velocity addition Cont… Thus the scalar speed function as a transformation is: ( ) ( )2 2 2 2 2 2 2 cos 1 sin / 2 cos , , (1 cos / ) object object object observed object object V h V c hV V V h V h c θ θ θ θ θ + − + = +
  21. 21. 9/28/2013 Priza Technologies Inc. 21 Taylor Series Expansion in 1D A function can be written in the form: If the series sum converges. ( )f x h+ ( , )f x y 2 3 2 3 ( ) 1 ( ) 1 ( ) ( ) ( ) ... 2! 3! df x d f x d f x f x h f x h h h dx dx dx + = + + + +
  22. 22. 9/28/2013 Priza Technologies Inc. 22 Taylor Series Expansion in 1D Cont.. Example: ( , )f x y 2 2 2 2 2 2 2 2 ( ) ( ) ( ) ( , ) 2 , 2, 0 3 ( ) 2 2 / 2! ( ) 2 ( ) ( ) n n f x x df x d f x d f x y x n dx dx dx f x h x h x h f x h x xh h f x h x h = = = = ∀ ≥ ⇒ + = + + ⇒ + = + + ⇒ + = +
  23. 23. 9/28/2013 Priza Technologies Inc. 23 Taylor Series Expansion chain rule If there is a function , and itself is a function of some other variables Then the Taylor series can be written in the form: < and higher powers > ( , )f x y 1 2 3 1 2 3 1 2 3 1 g( , , ) ( ) (g( , , )) (g( , , )) y y y df x f y h y y f y y y h y dx ∂ + = + + ∂ ( )f x x 1 2 3( , , )x g y y y= 2 h
  24. 24. 9/28/2013 Priza Technologies Inc. 24 Now the real proof ( , )f x y Let us assume there are n particles in a closed system and there exists a scalar conservation function energy E, which solely depends on the speed of the particles. Let the velocities of the particles be in a reference frame A. Let us take another frame of reference B which has a velocity w.r.t. to A. Let the resultant velocity of the particles in frame of reference B be . 1 2{ , ,..., }a a anV V V    h hi=   1 2{ , ,..., }b b bnV V V   
  25. 25. 9/28/2013 Priza Technologies Inc. 25 Proof Cont… ( , )f x y Conservation of energy: Sum of all energy is the closed system remains constant Looking from the frame of reference A Looking from the frame of reference B . ( ) ( ) 1 1 (B) . C n n bk bk b k k TotalEnergy E V E V const = = = = = =∑ ∑  ( ) ( ) 1 1 (A) . C n n ak ak a k k TotalEnergy E V E V const = = = = = =∑ ∑ 
  26. 26. 9/28/2013 Priza Technologies Inc. 26 Proof Cont… ( , )f x y Writing the total energy in B again: Assume that the scalar function E can be represented as a Taylor series. (This is can easily demonstrated for the Relativistic energy scalar function). . ( ) ( ) 1 1 (B) ( , , ) n bk k n bk ak k TotalEnergy E V E V h V θ = = = = ∑ ∑
  27. 27. 9/28/2013 Priza Technologies Inc. 27 Proof Cont… ( , )f x y Then we can write it as the Taylor’s series: < and higher powers> . ( ) ( ) 1 1 (B) ( , , ) (0, , ) ( ) (0, , ) n bk ak k n bk ak ak bk ak k ak TotalEnergy E V h V V V dE V E V V h h dV θ θ θ = = = ∂ = + + ∂ ∑ ∑ 2 h . bConst C= =
  28. 28. 9/28/2013 Priza Technologies Inc. 28 Proof Cont… ( , )f x y Let and be two states of the system both in reference frame A & B. Then based on the law of conservation of energy in the frame of reference B: < and higher powers> < and higher powers> . ( ) ( ) 1 1 (B) ( , , ) (0, , ) ( ) (0, , ) n bk ak k n bk ak ak bk ak k ak TotalEnergy E V h V V V dE V E V V h h dV α α α α α α α α θ θ θ = = = ∂ = + + ∂ ∑ ∑ 2 h α β ( ) ( ) 1 1 ( , , ) (0, , ) ( ) (0, , ) n bk ak k n bk ak ak bk ak k ak E V h V V V dE V E V V h h dV β β β β β β β β θ θ θ = = = ∂ = + + ∂ ∑ ∑ 2 h
  29. 29. Proof Cont…
  30. 30. Proof Cont…
  31. 31. 9/28/2013 Priza Technologies Inc. 31 Proof Cont… ( , )f x y Also kind note that in the frame of reference B: As h = 0 means there relative speed between A and B is zero, which means no transformation of the speed. . ( ) ( ) ( ) ( ) 1 1 1 1 (0, , ) (0, , ) n n bk ak ak k k n n bk ak ak k k E V V E V E V V E V α α α α β β θ θ = = = = ∑ ∑ ∑ ∑
  32. 32. 9/28/2013 Priza Technologies Inc. 32 Proof Cont… ( , )f x y Then the equations simplify to: < and higher powers> < and higher powers> . ( ) ( ) 1 1 (B) ( , , ) (0, , ) ( ) n bk ak k n bk ak ak ak k ak TotalEnergy E V h V V V dE V E V h h dV α α α α α α α θ θ = = = ∂ =+ + ∂ ∑ ∑ 2 h ( ) ( ) 1 1 ( , , ) (0, , ) ( ) n bk ak k n bk ak ak ak k ak E V h V V V dE V E V h h dV β β β β β β β θ θ = = = ∂ =+ + ∂ ∑ ∑ 2 h
  33. 33. 9/28/2013 Priza Technologies Inc. 33 Proof Cont… ( , )f x y Similarly in the frame of reference A based on the law of conservation of energy: Subtracting the this equation from earlier equation: < and higher powers> < and higher powers> . ( ) ( ) 1 1 (A) n n ak ak k k TotalEnergy E V E Vα β = = = =∑ ∑ 2 h 2 h 1 (0, , ) ( )n bk ak ak k ak V V dE V h h dV α α α α θ = ∂ + ∂ ∑ 1 (0, , ) ( )n bk ak ak k ak V V dE V h h dV β β β β θ = ∂ + ∂ ∑
  34. 34. 9/28/2013 Priza Technologies Inc. 34 Proof Cont… ( , )f x y Divide both sides by and taking limit (remember that the proof is based on 2 frames of reference, one moving at infinitesimal with respect to the other) This means is conserved for transition from any state to . 1 1 (0, , ) ( )(0, , ) ( )n n bk ak akbk ak ak k kak ak V V dE VV V dE V h dV h dV β β βα α α α β θθ = ∂∂ = ∂ ∂ ∑ ∑ 0h → 1 (0, , ) ( )n bk ak ak k ak V V dE V h dV θ = ∂ ∂ ∑ α β h
  35. 35. 9/28/2013 Priza Technologies Inc. 35 Proof Cont… ( , )f x y Now let us look at at . (0, , )bk akV V h θ∂ ∂ ( ) 2 2 2 2 2 2 2 2 2 1 (2 (1 / sin ) 2 cos )( , , ) 2 1 cos / (1 / sin ) 2 cos ak k ak k bk ak ak k ak ak k ak k h V c VV h V h hV c V h V c hV θ θθ θ θ θ − +∂ = ∂ + + − + ( ) 2 2 2 2 2 2 22 (1 / sin ) 2 cos ( cos / ) 1 cos / ak ak k ak k ak k ak k V h V c hV V c hV c θ θ θ θ + − + − + 0h = ( ) 2 2 2 2 (0, , ) cos / cos / (0, , ) cos 1 / bk ak ak k ak ak k bk ak k ak V V V V V c h V V V c h θ θ θ θ θ ∂ = − ∂ ∂ ⇒ = − ∂
  36. 36. 9/28/2013 Priza Technologies Inc. 36 Proof Cont… ( , )f x y So is conserved. This is true for any conserved scalar function Let us take relativistic energy function Then . ( ) 1 2 2 1 (0, , ) ( ) ( ) cos 1 / n bk ak ak k ak n ak k ak k ak V V dE V h dV dE V V c dV θ θ = = ∂ ∂ − ∑ ∑ 2 2 2 ( ) 1 / mc E v v c = − 2 2 2 2 3/2 2 2 3/2 ( ) 2 /1 2 (1 / ) (1 / ) ak ak ak ak ak ak dE V mc V c mV dV V c V c − =− = − −
  37. 37. 9/28/2013 Priza Technologies Inc. 37 Proof Cont… ( , )f x y So is conserved. This is true for any conserved scalar function Let us take relativistic energy function Then . ( ) 1 2 2 1 (0, , ) ( ) ( ) cos 1 / n bk ak ak k ak n ak k ak k ak V V dE V h dV dE V V c dV θ θ = = ∂ ∂ − ∑ ∑ 2 2 2 ( ) 1 / mc E v v c = − 2 2 2 2 3/2 2 2 3/2 ( ) 2 /1 2 (1 / ) (1 / ) ak ak ak ak ak ak dE V mc V c mV dV V c V c − =− = − −
  38. 38. 9/28/2013 Priza Technologies Inc. 38 Proof Cont… ( , )f x y So is conserved. The above is the X component of the relativistic momentum! Similarly if we take we can prove that Y component of relativistic momentum is conserved. So conservation of energy implies conservation of momentum. . ( ) ( ) 2 2 1 2 2 2 2 3/2 1 2 2 1 ( ) cos 1 / cos 1 / (1 / ) cos 1 / n ak k ak k ak n ak k ak k ak n ak k k ak dE V V c dV mV V c V c mV V c θ θ θ = = = − − − = − ∑ ∑ ∑ h hj=  
  39. 39. 9/28/2013 Priza Technologies Inc. 39 Proof Cont… ( , )f x y As is conserved for any choice of conserved function E If is magnitude of the momentum then: Take Both are conserved as a sum of conserved quantities. So . ( )2 2 1 ( ) cos 1 / n ak k ak k ak dE V V c dV θ = −∑ ( ) cos ( ) sin akx ak k ak aky ak k ak P V P P V P θ θ = =akP ( ) ( ) i ak ak akx aky ak i ak ak akx aky ak P V P iP P e P V P iP P e θ θ + − − = + = = − = 1 1 ( ), ( ) n n ak ak ak ak k k P V P V+ − = ∑ ∑ ( ) ( )2 2 2 2 1 1 ( ) ( ) cos 1 / , sin 1 / n n ak ak ak ak k ak k ak k kak ak dP V dP V V c V c dV dV θ θ+ + = − −∑ ∑
  40. 40. 9/28/2013 Priza Technologies Inc. 40 Proof Cont… ( , )f x y Let us take . As this is conserved so following sums are also conserved: Take , , which is also conserved. is also conserved . ( )2 2 1 ( ) 1 / n iak ak ak k ak dP V S V c e dV θ+ = ⇒ = −∑ ( )ak akP V+ 2 1 2( )S c S iS= + ( ) ( )2 2 2 2 1 2 1 1 ( ) ( ) cos 1 / , sin 1 / n n ak ak ak ak k ak k ak k kak ak dP V dP V S V c S V c dV dV θ θ+ + = = − =−∑ ∑ 2 2 ( ) 1 / i iak ak ak ak ak mV P V P e e V c θ θ + = = −
  41. 41. 9/28/2013 Priza Technologies Inc. 41 Proof Cont… ( , )f x y Then is conserved Similarly we keep doing it again and again to prove that: is conserved for integer r. Similarly is conserved for any integer r . ( ) ( ) 2 3/2 3/22 2 2 2 2 2 2 2 ( ) 2 /1 1 21 / 1 / 1 / 1 / i i iak ak ak ak ak ak ak ak ak ak ak dP V mV V cd e m e e m V dV dV V c V c V c V c θ θ θ+     −   = = − =     − − − −     ( ) ( ) 2 2 22 2 2 3/2 2 22 2 1 1 1 1 / 1 /1 / k k k k i in n n i i ak ak k k k akak e m e mc S c V c e E e V cV c θ θ θ θ = =    =− ==   −−  ∑ ∑ ∑ 2 1 k n i r ak k E e θ = ∑ (2 1) 1 k n i r ak k P e θ+ = ∑
  42. 42. 9/28/2013 Priza Technologies Inc. 42 Proof Cont… ( , )f x y Which means there are infinite such equations. It is easy to prove that these are all independent equations. This leads to a very strict form of change of energy and momentum, which we name as: Principle of Super Inertia. We need to revisit all our earlier derivations which were relying on and using conservation of energy and momentum. .
  43. 43. 9/28/2013 Priza Technologies Inc. 43 Fallacy in Einstein Derivation ( , )f x y The derivation by Albert Einstein was based on elastic collision of two particles, which approach each other head on and then divert at some angle. It was shown in the derivation that if this phenomena was observed from any other frame reference, the conservation still was true. Here we prove using the infinite conservation equations that such an elastic collision is not at all possible thus the derivation is wrong. r .
  44. 44. 9/28/2013 Priza Technologies Inc. 44 Fallacy in Einstein Derivation Cont… ( , )f x y Let us take a simple case of 2 particles as in the Einstein’s 1934 2 black board derivation: r .
  45. 45. 9/28/2013 Priza Technologies Inc. 45 Fallacy in Einstein Derivation Cont… ( , )f x y Initial energy equations: Initial momentum equations: Final energy equations: Final momentum equations: . 22 2 2 ( ) 2 2 2 1 (1 ) 2 1 / ki rn i r k ak mc e mc e mc V r c θ π γ γ = = ∈+ = − ∀∑   (2 1) (2 1) 2 2 1 (1 ) 0 1 / ki rn i rak k ak mV e mV e r V c θ π + + = = + = ∀ ∈ − ∑  22 2 2 2 ( ) 2 2 2 2 1 ( ) 2 1 / ki rn i r i r i r k ak mc e mc e e mc e r V c θ θ θ π θ γ γ+ = = + = ∀ ∈ − ∑   (2 1) (2 1) (2 1) 2 2 1 (1 ) 0 1 / ki rn i r i rak k ak mV e mVe e r V c θ θ π + + + = = + = ∀ ∈ − ∑ 
  46. 46. 9/28/2013 Priza Technologies Inc. 46 Fallacy in Einstein Derivation Cont… ( , )f x y For momentum equations conservation is satisfied. Energy equations should satisfy: BUT IT CANNOT SATISFY ABOVE EQUATION FOR ANY GENERAL ANGLE Which means there is a fallacy in the derivation. . 2 2 2 2 2 i r mc mc e rθ γ γ= ∀ ∈ θ
  47. 47. 9/28/2013 Priza Technologies Inc. 47 The real fallout ( , )f x y What Einstein described is a very commonly seen phenomena of life, an almost elastic collision of billiards ball going away at an angle. For our conservation equations to be satisfied, there is a correction needed of the order of , which is complete mass energy! So how does it happen that equations are not satisfied but the first order equations still hold true? What provides the energy compensation of the higher order? . 2 mc
  48. 48. 9/28/2013 Priza Technologies Inc. 48 Mass Light Duality ( , )f x y If there are 2 photons of exactly the same frequency going in exactly the opposite directions. The total energy of the photon pair is: Total Momentum of the photon pair is: Looking from a frame of reference moving at speed u wrt the stationary frame then: The total energy of the photon pair is: Total Momentum of the photon pair is: . 2bE ω ω ω= + =   0bE ω ω= − =  1 2 2 2 2 2 1 / 1 / 1 / c 1 / c 1 2 1 / 1 / 1 / 1 / a v c v c v v E E E v c v c v c v c ω ω ω ω    + − + + − = + = + = =    − + − −        1 2 2 2 2 2 1 / 1 / 1 / c 1 / c / / / / 2 / 1 / 1 / 1 / 1 / a v c v c v v v c P P P c c c c v c v c v c v c ω ω ω ω    + − + − + = + = − = =    − + − −       
  49. 49. 9/28/2013 Priza Technologies Inc. 49 Mass Light Duality ( , )f x y What is interesting to note is that: and A pair of photons going in opposite directions transform energy and momentum as matter with mass Furthermore the frequencies of their interference are: . 2 2 1 / b a E E v c = − 2 2 1 / b a P P v c = − 1 1 / 1 / 2 1 / 1 / v c v c v c v c ω ω γω  + − = + =  − +  2 1 / 1 / 2 / 1 / 1 / v c v c v c v c v c ω ω γω  + − = − =×  − +  2 2 /m cω= 
  50. 50. 9/28/2013 Priza Technologies Inc. 50 Mass Light Duality ( , )f x y If put as we found in earlier slide then 2 wavelengths are: De-Broglie wavelength The other wavelength So the model of a particle as 2 photons going in opposite directions not only works perfectly for momentum and energy but also for matter wave model. Further in case of v = 0 De Broglie hypothesis fails but we have the correct answer that at v = 0 only one frequency exists with wavelength: hc/E . 2 / 2mcω =  2 2 2 2 2 / 2 / c c h c v c m vc P π π λ π ω γω γ = = = = ×  1 1 2 2 2 2 / 2 c c hc c m c E π π λ π ω γω γ = = = = 
  51. 51. 9/28/2013 Priza Technologies Inc. 51 Mass Light Duality ( , )f x y With a similar derivation we have proven that space-time also transforms as if each point is composed of 2 light rays going in opposite directions. A more interesting part in the paper is the proof that a photon can also be modeled as 2 non-zero rest mass particles, one going below the speed of light and the other above the speed of light. We have also formulated and proven the energy and momentum of above the speed of light as: . 2 2 2 / / 1aE mc v c=− − 2 2 / / 1aP mv v c=− −
  52. 52. 9/28/2013 Priza Technologies Inc. 52 Lorentz transformation for V >C ( , )f x y The modified principle of relativity for V > C: The set of “pure measurements” is same if they are done from a frame of reference A into B or B into A. At speed greater than light a single event appears 2 different events. It is light looking into 2 different mirrors. We have given the modified Lorentz transformation with the new principle of relativity in 1D as: Where are 2 different space-time points in the frame of reference B given a single point in the frame of reference A. This is like seeing the world in mirror but 2 different mirrors. . 1 1 1 12 2 2 2 2 2 0 0 1 / 0 0 / c 1 1/ / 1 1 / 0 0 / 1 0 0 b a b a b a b a x xv c ct ctv v c x xv c ct ctv c −          −    = −     −      −     1 1 2 2( , ),( , )b b b bx t x t
  53. 53. 9/28/2013 Priza Technologies Inc. 53 Zero energy non zero momentum (ZEN) ( , )f x y In the case of speed limiting to infinity These are in-fact zero energy and finite momentum particles! As they have infinite speed they exist only for a single instant of time, where they are omnipresent. These particles when present in any system can take away or add momentum without taking away or adding energy to the system. When these take away momentum, they lead to conversion of kinetic energy to mass. When these particles add momentum they lead to conversion of mass to kinetic energy. We conjecture that these particles form space component of space time and also the binding force in the atom nucleus. . 2 2 2 lim / / 1 0a v E mc v c →∞ =− − = 2 2 lim / / 1a v P mv v c mc →∞ =− − =−
  54. 54. 9/28/2013 Priza Technologies Inc. 54 Further work not published ( , )f x y We have modified the Klein Gordon/Dirac equation for the In the case of speed greater than light and proven that there are states of electrons in an atom called as negative excited states, which can be achieve only when an atom gets negative energy photon. From the quantum time evolution point of view, these negative excited states have lower energy but still are not the most probable states BUT to bring an electron from the negative excited state to the ground state positive energy photon is required. We have also proven that an positron is an electron going at a speed greater than light, which manifests as going into past. .
  55. 55. 9/28/2013 Priza Technologies Inc. 55 At last zero point energy ( , )f x y We have been able to theoretically prove that zero point energy or free energy can only be harnessed if the particles are tunneled from speed below light to above light (patent pending). We have also found a very simple way of tunneling particles from speed below the speed of light to above the speed of light. CERN cannot do it because they do not have the complete theory. Particles cannot be accelerated to beyond the speed of light but can be tunneled. The easiest way to tunnel the particles/electrons across the speed of light is through solid state devices. Solid state devices/semi-conductors are the place where electrons really move in space. With our theory there are 100s of ways to build devices to harness zero point energy and in all form factors (nano-scales)! .
  56. 56. 9/28/2013 Priza Technologies Inc. 56 Experimental Discussion ( , )f x y Will only speak about it!.

×