ICEES-2011 : PS010 Presentation on Relativistic Particle as Energy Source : Relativistic Particle as Energy Source : Optimum Speed of the Particle for Maximum Power Transfer

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- Dr G V Rangaraj, IEEE Senior Member

AAM Practice Team

HCL Technologies, Chennai, INDIA

Abstract

Variable speed of light (VSL) is an emerging concept in Physics whichstates that the speed of light is not constant. Using this theory it isshown in our earlier work [1], that relativistic particle by itself acts asan energy source by virtue of variable speed of light. As a continuationto this work we determine the optimum speed of the particle at whichto this work we determine the optimum speed of the particle at whichmaximum power transfer takes place.

Tutorial Outline:

� Introduction

� Proof of Relativistic Particle Use As Energy Source

� Maximum Power Transfer : Optimum Speed Determination

� Using Theoretical Method

� Using Simulation Method� Using Simulation Method

� Conclusions

� Question and Answers

� References

INTRODUCTIONINTRODUCTION

• The Variable Speed of Light (VSL) concept states that“ The speed of light in a vacuum, usually denoted by c, maynot be constant in some cases”

• In our earlier work we have shown that

“Relativistic particle by virtue of VSL concept posses an

VSL Theory & Our Earlier Contribution

“Relativistic particle by virtue of VSL concept posses anenergy which could solve the global energy crisis”

• We have provided a theoretical proof which states that

“Relativistic particle without decrease of mass as innuclear reaction is a potential renewable source of energy”

PROOF OF RELATIVISTIC PARTICLE PROOF OF RELATIVISTIC PARTICLE USE AS ENERGY SOURCE

• Special theory of relativity for a particle with zero velocity

E = mc2

• It is evident that for a relativistic particle to be used asenergy source either m or c should decrease over time

Extreme Case Example

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

• Special theory of relativity for a particle with velocity ‘v’

E = mc3/(c2 - v2)1/2

• It has been proved using measurements that the magnitudeof change in ‘c’ is infinitesimal

General Case Proof

• 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)

• We assume that the relative velocity between c & v isconstant.

vr = c – v = constant

• Therefore Special Relativity Equation becomes

General Case Proof

E = mc3/(c2 – (c - vr) 2)1/2

• For relativistic particle to act as energy source, the powerwhich is the rate of change of energy dE/dt should be –ve.

P =dE/dt = dE/dc. dc/dt = dE/dc (-ε)

• 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

General Case Proof

= m[c (vr)(2c+3v)] /(c – (c - vr) )

• Hence dE/dc is always +ve,since vr > 0 as v < c still hold true

• This implies all particles which obey special theory ofrelativity is as an energy source.

MAXIMUM POWER TRANSFERMAXIMUM POWER TRANSFER

Power of a relativistic particle

• The next question is at what speed ‘v’ of the particlecorresponds to the situation with maximum power

• Probably if we can have a relativistic particle travelling atthis 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

Max Power Transfer : Theoretical Method

• Objective: To find the v for which absolute value of P ismaximum

• Since relativistic particle is an energy source, the sign ofP 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 benegative 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

CONCLUSIONSCONCLUSIONS

VSL theory is a solution to energy crisis!

• It has been shown that relativistic particle is an energysource by virtue of the variable speed of light

• The optimum speed of the particle at which maximumpower transfer happens is when the speed of the particleapproaches the speed of light

• This has been shown using theoretical method and usingsimulations

• Thus it has been shown that the VSL concept could bepotentially used to solve the present global energy crisis;

• However the exact pragmatic technique is still an openarea of research

QUESTIONS & ANSWERSQUESTIONS & ANSWERS

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 incommunication systems. His current areas of interest include design and development ofwireless solutions/ PHY/MAC layer chipsets for future wireless systems involving wirelesspersonal/body area networks and signal processing algorithms for 4G wireless communicationsystems. During his doctoral studies, he also worked as Project Officer for the DECT Wirelessin Local Loop project with the Tenet Group. After graduation, he worked as Technical LeadEngineer at HCL Technologies, Chennai, where he was developing physical layer of MBOAUWB wireless system on FPGA platforms and at NXP Semiconductors, Bangalore developingphysical layer for Wireless LAN on embedded vector processors. He then worked as Wirelessphysical layer for Wireless LAN on embedded vector processors. He then worked as WirelessSpecialist at Tata Elxsi, Chennai in design of Physical layer for LTE wireless systems and other4G wireless systems on DSP platforms. Currently he is working as Senior Technical Manager atHCL Technologies, Chennai in design of wireless solutions in medical, automotive and industrialverticals. He has published more than ten papers in various national and internationalconferences and journals and also an active reviewer. He is the recipient of the Philips awardand Seimens award for being the student with best academic record in Electrical EngineeringDepartment at IIT Madras during 1994–1998. He is also the recipient of the Colonel OscarCleaver award for being the outstanding graduate student in the School of Electrical andComputer Engineering, Georgia Institute of Technology during 1998–1999.

References

• G V Rangaraj, “Relativistic Particle as Energy Source”,IEEE sponsored Asia Pacific Power and EnergyEngineering Conference (APPEEC), March 2010

• George F R Ellis, "Note on Varying Speed of LightCosmologies". General Relativity and Gravitation 39 (4):Cosmologies". General Relativity and Gravitation 39 (4):511 – 52, April 2007

• A. Montgomery and L. Dolphin, “Is the velocity of lightconstant in time”, Galilean Electrodynamics, Vol. 4, no. 5,Sept/Oct 1993.

• A. Einstein, “Special Theory of Relativity”, 1905.•

Thank YouThank You

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