This presentation discusses using relativistic particles as an energy source based on the variable speed of light theory. It provides theoretical proofs that show as the speed of light slowly decreases over time, the inherent energy of relativistic particles makes them act as an energy source without decreasing their mass. The presentation determines the optimum speed of the particle for maximum power transfer both theoretically by taking the derivative of the power equation and through simulations. It concludes that variable speed of light theory could potentially solve the global energy crisis, though more research is still needed on practical applications.

1. ICEES-2011 : PS010 Presentation on
Relativistic Particle as Energy Source :
Optimum Speed of the Particle for Maximum
Power Transfer
- Dr G V Rangaraj, IEEE Senior Member
AAM Practice Team
HCL Technologies, Chennai, INDIA
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2. Abstract
Variable speed of light (VSL) is an emerging concept in Physics which
states that the speed of light is not constant. Using this theory it is
shown in our earlier work [1], that relativistic particle by itself acts as
an energy source by virtue of variable speed of light. As a continuation
to this work we determine the optimum speed of the particle at which
maximum power transfer takes place.

3. Tutorial Outline:
Introduction
Proof of Relativistic Particle Use As Energy Source
Maximum Power Transfer : Optimum Speed Determination
Using Theoretical Method
Using Simulation Method
Conclusions
Question and Answers
References

4. INTRODUCTION

5. VSL Theory & Our Earlier Contribution
• The Variable Speed of Light (VSL) concept states that
“ The speed of light in a vacuum, usually denoted by c, may
not be constant in some cases”
• In our earlier work we have shown that
“Relativistic particle by virtue of VSL concept posses an
energy which could solve the global energy crisis”
• We have provided a theoretical proof which states that
“Relativistic particle without decrease of mass as in
nuclear reaction is a potential renewable source of energy”

6. PROOF OF RELATIVISTIC PARTICLE
USE AS ENERGY SOURCE

7. Extreme Case Example
• Special theory of relativity for a particle with zero velocity
E = mc2
• It is evident that for a relativistic particle to be used as
energy source either m or c should decrease over time
Relativistic Particle as Energy Source Proof:
• Even if m does not decrease as in nuclear reactions
• It is very evident that as c is slowly decreasing over time
• Hence there is an inherent energy in relativistic particle by
virtue of VSL theory that make it act as an energy source

8. General Case Proof
• Special theory of relativity for a particle with velocity ‘v’
E = mc3/(c2 - v2)1/2
• It has been proved using measurements that the magnitude
of change in ‘c’ is infinitesimal
• Assumption is Special Relativity Theory still holds true &
above equation is valid even if ‘c’ decreases very slowly.
• Let this slow decrease in speed of light be ε. This implies,
dc/dt = – ε (infinitesimal negative constant)

9. General Case Proof
• We assume that the relative velocity between c & v is
constant.
vr = c – v = constant
• Therefore Special Relativity Equation becomes
E = mc3/(c2 – (c - vr) 2)1/2
• For relativistic particle to act as energy source, the power
which is the rate of change of energy dE/dt should be –ve.
P =dE/dt = dE/dc. dc/dt = dE/dc (-ε)

10. General Case Proof
• This implies, for relativistic particle to act as energy source,
dE/dc should be +ve.
• Differentiating E = mc3/(c2 – (c - vr) 2)1/2 with c, we get
dE/dc = m[3c2(c2 – (c-vr) 2)-c3(c- (c-vr))]/(c2 – (c - vr) 2) 3/2
= m[c2(vr)(2c+3v)] /(c2 – (c - vr) 2) 3/2
• Hence dE/dc is always +ve,since vr > 0 as v < c still hold true
• This implies all particles which obey special theory of
relativity is as an energy source.

11. MAXIMUM POWER TRANSFER

12. Power of a relativistic particle
• The next question is at what speed ‘v’ of the particle
corresponds to the situation with maximum power
• Probably if we can have a relativistic particle travelling at
this speed ‘v’ maximum power could be transferred
• The power P of a relativistic particle is given by
P = - ε m[c2(vr)(5c-3vr)] /(c2 – (c - vr) 2)3/2
= - ε m[c2(c-v)(2c+3v)] /(c2–(v)2)3/2
Pabs = ε m[c2(c-v)(2c+3v)] /(c2 –(v)2)3/2

13. Max Power Transfer : Theoretical Method
• Objective: To find the v for which absolute value of P is
maximum
• Since relativistic particle is an energy source, the sign of
P would be negative
• We need to set dPabs/dv should be equal to zero
• A check needs to be done to see if dPabs2/d2v should be
negative at that v.
• It can be shown by derivations that
dPabs/dv = ε m[c2(c-v)( c2+cv+3v2)] /(c2 –(v)2)5/2

14. CONCLUSIONS

15. VSL theory is a solution to energy crisis!
• It has been shown that relativistic particle is an energy
source by virtue of the variable speed of light
• The optimum speed of the particle at which maximum
power transfer happens is when the speed of the particle
approaches the speed of light
• This has been shown using theoretical method and using
simulations
• Thus it has been shown that the VSL concept could be
potentially used to solve the present global energy crisis;
• However the exact pragmatic technique is still an open
area of research

16. QUESTIONS & ANSWERS

17. Biography
Rangaraj received his B.Tech in Electrical Engineering from Indian Institute of Technology (IIT)
Madras, India in 1998, M.S in Electrical and Computer Engineering from Georgia Tech, U.S.A.
in 2000 and PhD in Electrical Engineering from IIT Madras, India in 2005 with specialization in
communication systems. His current areas of interest include design and development of
wireless solutions/ PHY/MAC layer chipsets for future wireless systems involving wireless
personal/body area networks and signal processing algorithms for 4G wireless communication
systems. During his doctoral studies, he also worked as Project Officer for the DECT Wireless
in Local Loop project with the Tenet Group. After graduation, he worked as Technical Lead
Engineer at HCL Technologies, Chennai, where he was developing physical layer of MBOA
UWB wireless system on FPGA platforms and at NXP Semiconductors, Bangalore developing
physical layer for Wireless LAN on embedded vector processors. He then worked as Wireless
Specialist at Tata Elxsi, Chennai in design of Physical layer for LTE wireless systems and other
4G wireless systems on DSP platforms. Currently he is working as Senior Technical Manager at
HCL Technologies, Chennai in design of wireless solutions in medical, automotive and industrial
verticals. He has published more than ten papers in various national and international
conferences and journals and also an active reviewer. He is the recipient of the Philips award
and Seimens award for being the student with best academic record in Electrical Engineering
Department at IIT Madras during 1994–1998. He is also the recipient of the Colonel Oscar
Cleaver award for being the outstanding graduate student in the School of Electrical and
Computer Engineering, Georgia Institute of Technology during 1998–1999.

18. References
• G V Rangaraj, “Relativistic Particle as Energy Source”,
IEEE sponsored Asia Pacific Power and Energy
Engineering Conference (APPEEC), March 2010
• George F R Ellis, "Note on Varying Speed of Light
Cosmologies". General Relativity and Gravitation 39 (4):
511 – 52, April 2007
• A. Montgomery and L. Dolphin, “Is the velocity of light
constant in time”, Galilean Electrodynamics, Vol. 4, no. 5,
Sept/Oct 1993.
• A. Einstein, “Special Theory of Relativity”, 1905.
•

19. Thank You
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