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[Asian Journal of Applied Science and Engineering] Volume 2, Number 1/2013 (Special Issue) ISSN: 2305-915X

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[Asian Journal of Applied Science and Engineering] Volume 2, Number 1/2013 (Special Issue)

ISSN: 2305-915X (Print) ISSN: 2307-9584 (Online)


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ASIAN JOURNAL OF APPLIED SCIENCE AND ENGINEERING International Standard Serial Number: 2305-915X (Print)

International Standard Serial Number: 2307-9584 (Online)

Established: 2012 www.ajase.weebly.com

Review Process: Blind peer-review

Volume 2, Number 1/2013 (Special Issue)

Published by

Asian Business Consortium

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EDITORIAL BOARD

Editor-in-chief

Dr. Asma Ahmad Shariff Center for Foundation Studies in Science, University of Malaya, Malaysia

Managing Editor

Dr. Alim Al Ayub Ahmed

Faculty of Business, ASA University Bangladesh Vice Chairman, Asian Business Consortium

Consulting Editor

Dr. Md. Amin Uddin Mridha

King Saud University, Saudi Arabia (Plant Production)

Dr. Bensafi Abd-El-Hamid Abou Bekr Belkaid University of Tlemcen, Algeria (Chemical Engineering & Polymer Chemistry)

Dr. Iqbal Hossain

ASA University Bamgladesh, Bangladesh (Statistics)

Dr. Vinai K. Singh

Raj Kumar Goel Engineering College, INDIA (Bio mathematics & Remedial Mathematics)

Dr. Shahzad Ali Khan

Quaid-e-Azam University, Pakistan (Health Systems & Policy)

Dr. Hasan Mahmud Reza

North South University, Bangladesh (Pharmacy)

Dr Pankaj

Indus International University, India (Mathematics)

Dr. Mohammad Anwar Hossain

Bangladesh Agricultural University, Bangladesh (Genetics & Plant Breeding)

Dr. Gulzar A. Khuwaja

King Faisal University, Saudi Arabia (Computer Engineering)

Dr. Halenar Igor

Slovak University of Technology in Bratislava, Slovakia (Architecture)

Dr. Mohammad Hadi Dehghani

Tehran University of Medical Sciences, Iran (Environmental Toxicology & Nanotechnology)

Dr. Suresh B. Rana

University of Oklahoma, USA (Medical Physics)

Dr. Osman Goni Talukdar

Varendra University, Bangladesh (Theoretical Physics)

Dr. Lutfar Rahman Rajshahi University Bangladesh (Mathematics)

Dr. Vuda Sreenivasarao

Bahir Dar University, Ethiopia (Electrical Engineering)

Dr. Mojtaba Moradi

University of Guilan, Iran (Stochastic Processes)

Dr. Arun Kumar Gupta

University of Roorkee, India (Computer Programing)

Dr Sudhir K Samantaray

Panjab University, India (Psychology)

Dr. M. Abul Kalam Azad

Rajshahi University, Bangladesh (Applied Mathematics)

Dr. Md. Fazlul Babi

University Sains Malaysia (USM), Malaysia (Material Science)

Dr. Mohammad Ali Shariati

Isfahan University of Technology, Iran (Food Science and Technology)

The Editorial Board assumes no responsibility for the content of the published articles.

http://umexpert.um.edu.my/papar_cv.php?id=AAAJxnAAQAAAF93AAX




AJASE adopt a blinded review policy. Authors are blind to reviewers. Typically, the review period is within 6 weeks. If authors do not receive a decision letter by email in 8 weeks after the submission, the corresponding author may send an email to inquire the status of their submission. If you need a shorter review period due to special circumstances, you may request such along with your explanation of the situation by email; however, AJASE cannot guarantee granting the request because high quality judgment of scientific work in short time is a challenge.




Asian Journal of Applied Science and Engineering

Blind Peer-Reviewed Journal

Volume 2, Number 1/2013 (Special Issue)

Contents

1. Reciprocal Symmetric Kinematics and Correspondence between Special Relativity and

Quantum Mechanics

09

Mushfiq Ahmad

2. Correspondence between Reciprocity and Discreteness 10

Mushfiq Ahmad & M.O.G. Talukder

3. Reciprocal Symmetry Quantum Statistics and Spin 11


4. Relativistic Rule of Multiplication of Velocities Consistent with Lorentz – Einstein Law

of Addition and Derivation of the Missing Equations of Special Relativity

12

M.O.G. Talukder & Mushfiq Ahmad

5. Incompatibility between Einstein's Postulate and Special Theory of Relativity 13


6. Non-Associativity of Lorentz Transformation and Associative Reciprocal Symmetric

Transformation

14

Mushfiq Ahmad, Muhammad Shah Alam, & M.O.G. Talukder

7. Derivation of the Missing Equations of Special Relativity from de-Broglie’s Matter Wave

Concept and the Correspondence between Them

15


8. Derivation of Non-Einsteinian Relativistic Equations from Momentum Conservation

Law

16

M.O.G. Talukder

9. Wave Particle Dualism for Both Matter and Wave and Non-Einsteinian View of

Relativity

17


10. Homogeneous Number System and Reciprocal Symmetric Algebra 18

Mushfiq Ahmad

11. Neutrino Traveling Faster than Light and Einsteinian and non-Einsteinian views of

relativity

19


12 International Seminar on Special Relativity – 2012 20

Perspectives




Faster than the speed of light, reciprocal

velocity and quantum mechanics

Planck's hypothesis sets a lower

limit (to energy). Einstein's postulate

sets an upper limit (to speed). If a

particle has velocity v, the

corresponding de Broglie wave has

velocity c2/v. Therefore, de Broglie

wave velocities fulfill Einstein's

reciprocal postulate -- No speed can

be less than the speed of light.

Planck and de Broglie suggest a

reciprocal relation between quantum

mechanics and special relativity.

From velocity v=x/t we can obtain

the reciprocal velocity t/x by

interchanging between x and t.




Reciprocal Symmetric Kinematics and

Correspondence between Special Relativity

and Quantum Mechanics

Mushfiq Ahmad

Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh

Abstract

We have defined reciprocal symmetry and observed its presence in Special

Relativity and quantum mechanics. Therefore, reciprocal symmetry relates

Special Relativity to quantum mechanics. Reciprocal symmetry implies that

there is a boundary value velocity c, which is the limiting value and which is

also constant under addition. We have, then, developed reciprocal symmetric

law of addition of velocities. In case of collinear velocities it agrees with

Lorentz-Einstein law of addition. General reciprocal symmetric transformation

is different from General Lorentz transformation. Reciprocal symmetric

transformation is associative and complex. A comparison between RST and LT

is given.

Keywords: Reciprocal Symmetry; Reciprocal Symmetric

Transformation; Lorentz Transformation; Associativity

PACS No.: 03.30.+p, 03.65.-w




Correspondence between Reciprocity and

Discreteness

Mushfiq Ahmad1 & M.O.G. Talukder2 1Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh 2Varendra University, Rajshahi-6204, Bangladesh

Abstract

We have represented physical quantities (velocity and distance) in hyperbolic

space. In hyperbolic space velocities obey Einstein's law of addition. We have

found the expression for the distance traveled in hyperbolic space. The same

motion has been described in terms velocity and reciprocal velocity. In case of

reciprocal velocity, distance and time of travel become discrete.




Reciprocal Symmetry Quantum Statistics and

Spin

Mushfiq Ahmad & M.O.G. Talukder 1Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh 2Varendra University, Rajshahi-6204, Bangladesh

Abstract

We have shown that a reciprocal transformation relates Bose-Einstein statistics to

Fermi-Dirac statistics. We have also shown that a reciprocal inversion produces a

spin change by a half integral spin.

Key Words: Reciprocal; Reciprocity; Reciprocal Symmetry; Fermi-Dirac

Statistics; Continuity; Discreteness; Boltzmann’s function; Finite

difference equation

PACS: 03.65.-w, 03.30.+p




Relativistic Rule of Multiplication of Velocities

Consistent with Lorentz – Einstein Law of

Addition and Derivation of the Missing

Equations of Special Relativity

M.O.G. Talukder1 and Mushfiq Ahmad2 1Varendra University, Rajshahi-6204, Bangladesh 2Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh

Abstract

In this paper, we present the rule for relativistic multiplication of a velocity by a number.

We have reasoned on the basis of a thought experiment and we have taken into consideration

the L-E law of addition of velocities. The formalism gives the result of repeated L-E addition

just as ordinary multiplication gives the effect of repeated Galilean addition. In the classical

limit, it complies with the Galilean law of multiplication. The formalism presented here can

extend the horizon of relativity. The thought experiment also reveals the values of both the

relative length and time in the longitudinal direction. Further, it has been demonstrated, as

implications, that each relative quantity has two values - one in the longitudinal and the

other in the transverse directions. As a consequence, we have found out the missing

equations which are necessary to make Einstein’s theory of special relativity self-consistent

and complete. Moreover, we use the geometric mean to get the mean value of the relative

quantities. The justification of doing so is also demonstrated in this paper. Finally, in the

appendix, we present the relativistic multiplication rules for the relative quantities like

velocity, mass, time and length by a number. We also present the general rules for the

product of two relative quantities of the same entity.

Keywords: Relativistic addition and multiplication, velocity, mass, time,

length, special relativity, missing equations, geometric mean.




Incompatibility between Einstein's Postulate

and Special Theory of Relativity

Mushfiq Ahmad1 & M.O.G. Talukder

2

1Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh 2Varendra University, Rajshahi-6204, Bangladesh

Abstract

A hyperbolic transformation relates relativistic velocities to corresponding

Galilean velocity or rapidity. Comparison shows that usual definition of

velocity is valid in Euclidian space but not valid in relativistic hyperbolic

space. It also reveals that Einstein's postulate -- that the speed of light is the

same in all inertial frames of reference -- is equivalent to the trivial statement

that infinite velocity is the same in all inertial frames of reference.

Key Words: Galilean; Relativistic; Hyperbolic transformation; Lorentz

transformation; Einstein's postulates; Einstein's addition; Velocity.

PACS: 03.30.+p




Non-Associativity of Lorentz Transformation

and Associative Reciprocal Symmetric

Transformation

Mushfiq Ahmad1, Muhammad Shah Alam

2, & M.O.G. Talukder

3

1Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh 2Department of Physics, Shahjalal Universit, Sylhet, Bangladesh

3Varendra University, Rajshahi-6204, Bangladesh

Abstract

We have shown that Lorentz transformation is not associative. The non-

associativity makes it frame dependent; and it does not fulfill relativistic

requirement. We have proposed an associative Reciprocal Symmetric

Transformation (RST) to replace Lorentz transformation. RST is complex and

is compatible with Pauli and Dirac algebra.

Keywords: Lorentz boost; Non-associativity; Reciprocity Principle;

Reciprocal Symmetric Transformation; Thomas Precession;

Quaternionic transformation; Pauli quaternion; Spin; Clifford algebra.

PACS: 03.30.+p, 03.65.-w




Derivation of the Missing Equations of Special

Relativity from de-Broglie’s Matter Wave

Concept and the Correspondence between Them

M.O.G. Talukder1 & Mushfiq Ahmad

2 1Varendra University, Rajshahi-6204, Bangladesh 2Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh

Abstract

In this paper, we have considered that the particle velocity in the matter wave concept of

de Broglie is relative. It reveals that matter wave associated with a moving particle is a

photon wave which has longitudinal and transverse values. The conventional de-

Broglie’s wavelength-momentum relation corresponds to the longitudinal wave. As a

consequence, we have found the longitudinal and transverse relative values of the mass,

time, length and velocity including the missing equations of Einstein’s theory of special

relativity. It also reveals that momentum and energy are relative quantities and the

corresponding expressions for the longitudinal and transverse values for both of them

have been presented. Moreover, the addition rules, with a general expression, for all the

relative quantities based on Lorentz-Einstein transformation law for the addition of

velocities have been given. Finally, the maximum and minimum values of the relative

quantities have been expressed in terms of Plank’s constant and the speed of light. Their

numerical values have also been calculated and presented in this paper.

Keywords: Matter wave, Photon, Wavelength, Momentum, Relative mass,

Time, Length and velocity, Transverse, Longitudinal and Plank’s constant.




Derivation of Non-Einsteinian Relativistic

Equations from Momentum Conservation Law

M.O.G. Talukder

Varendra University, Rajshahi–6204, Bangladesh.

Abstract

In this paper, we present a relativistic expression for the momentum

conservation law using a formalism derived from the Lorentz-Einstein law for

the addition of velocities. It demonstrates that a mass-less particle can move

only at the speed of light and it has momentum like a photon. Hence,

consideration of relativistic momentum conservation of a photon-gun system

reveals that the mass of the gun and the time period, amplitude and the speed

of photon vary with the speed of the gun. That is the mass, time, length and

velocity are relative quantities. However, the corresponding expressions are

different from those in Einstein’s theory of special relativity. Hence, we call

those as Non-Einsteinian relativistic expressions. Moreover, each relative

quantity has been found to have two values – one in the longitudinal and the

other in the transverse directions, such that the product of the two remains

invariant. Nevertheless, the longitudinal and transverse values have been

denoted by the suffixes NL and NT respectively. It should be pointed here that,

in the previous papers, the corresponding expressions in Einsteinian

relativistic case have been denoted by the suffixes EL and ET respectively.

Keywords: Momentum conservation, Lorentz – Einstein law, Non-

Einsteinian relativity, photon, relative mass, time, length and velocity.




Wave Particle Dualism for Both Matter and

Wave and Non-Einsteinian View of Relativity


2

1Varendra University, Rajshahi–6204, Bangladesh. 2Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh

Abstract

In this paper, we demonstrate the significance of Non-Einsteinian view of

relativity in relation to wave model of particle and particle model of wave. To

accommodate wave-particle dualism, we have considered de-Broglie’s matter

wave concept and Compton Effect. The kinematics of the photon and the

photon emitter particle (photon-gun) are taken into consideration. Then, we

have correlated the motion related parameters of the gun with the

characteristics of the photon. This provides a correlation between wave aspect

of particle (matter wave) and particle aspect of wave.

Keywords: Wave, particle, matter wave, photon, wavelength, momentum

and Compton wave.




Homogeneous Number System and Reciprocal

Symmetric Algebra

Mushfiq Ahmad

Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh

Abstract

We have shown that an isomorphic transformation relates the set R of real

numbers extending from to , to the set S of numbers between

arbitrarily chosen numbers c and c . Any set of physical quantities which

can be represented by R can also be represented by S and vise versa. c

corresponds to , and invariance of c under Einstein addition corresponds to

invariance of under ordinary addition .

Keywords: Real numbers; Isomorphism; Neutral number; Infinity;

Invariant under addition; Einstein law of addition; Reciprocal

symmetry

PACS: 03.30.+p, 03.65.-w




Neutrino Traveling Faster than Light and

Einsteinian and non-Einsteinian views of

relativity


2

1Varendra University, Rajshahi – 6204, Bangladesh. 2Department of Physics, Rajshahi University, Rajshahi-6205, Bangladesh

Abstract

In this paper, we classify the velocity as Galilean and relative. The Galilean

velocity can have any value between 0 and ∞ as in Newtonian/classical mechanics,

whereas, the relative velocity follows Lorentz – Einstein (L-E) transformation law

for addition and cannot exceed the speed of light c. We present the transformation

law from Galilean to relative velocity and vise versa. We consider that the velocity

in the relativity factor of non-Einsteinian relativistic case is Galilean, since it does

not put any restriction on any particle’s velocity being equal to or greater than

that of light. On the other hand, using the relativistic multiplication rule of

velocities, we demonstrate that the velocity in the relativity factor of Einsteinian

relativistic case is relative. Hence, it will remain within the limit of c, even if the

corresponding Galilean velocity is much higher than c. We believe that CERN

scientists have measured the Galilean velocity of neutrino being slightly higher

than c. We demonstrate that the transverse relative mass of neutrino traveling at

that speed remains finite in both views of relativity. Thus, in this paper, the

dilemma concerning neutrinos traveling faster than light has been resolved.

Keywords: Galilean velocity, relative velocity, transformation law,

neutrino speed, light speed and transverse mass.




International Seminar on Special Relativity-2012 NEUTRINO TRAVELING FASTER THAN LIGHT AND EINSTEIN'S VIEW OF RELATIVITY CERN researchers have observed that neutrinos can travel faster than light. Their finding agrees with our prediction (quoted below), which appeared in the daily newspaper "The Observer" on 5 June 2001. The statement was made on 4 June 2001 on the occasion of the inauguration of the book "An Alternative Approach to the Relativity" published by Grontho Procation, Rajshahi, Bangladesh. However, recently, we have found that Einstein's theory of special relativity is incomplete. It needs three more equations to make it complete. We have found those missing equations. Some of our findings have already been published in scientific journals and some others are in the process of publication. We hope to disclose all our results (published and unpublished) in a forth coming international conference to be organized by Rajshahi University. With the help of the completed form of the concept of relativity and the introduction of the concept of Reciprocal Symmetry, we have seen that there is no restriction on any particle's speed being equal to or greater than that of light. Therefore, we would like to convey our heartiest congratulations to the researchers of CERN lab. Their recent finding will, we hope, help achieve completeness and perfection of the development of relativity; just as Michelson-Morley's result of 1887 launched it. Quotation from "The Observer" of 5 June 2001, Dhaka: "According to Einstein's Relativity Theory, no particle can achieve the speed of light. This is a consequence of Einstein's Relativity Theory that when the speed of a particle approaches that of light, its mass becomes infinite which is absurd. It should be pointed here that it was experimentally found that a neutrino has a finite mass but it moves at the speed of light in contradiction with Einstein's Theory. On the contrary, according to the alternative approach, there is no such restriction on any particle's speed being equal to or greater than that of light. When the speed of a particle approaches that of light its mass becomes half which is reasonable and consistent with the experimental evidence". PLEASE NOTE: For your kind information, the proceedings of the seminar will be published in a special issue of the journal of Rajshahi University

SCOPE Special Relativity

TITLE Neutrino Traveling Faster than Light and Einstein's View of Relativity

DATE 11-12 February, 2012

VENUE Senate Building, University of Rajshahi, Bangladesh

http://ru.ac.bd/issr-12/index.php




ORGANIZING COMMITTEE Chair Prof. M. Abdus Sobhan, Honourable Vice Chancellor, University of Rajshahi Co-Chair

Prof. Muhammad Nurullah, Honourable Pro-vice Chancellor, University of Rajshahi Secretary Prof. Abu Bakar Md. Ismail, Chairman, Dept. of Applied Physics & Electronic Engineering, University of Rajshahi International Advisory Committee Chief Advisor

H.E. Prof. M. Sayeedur Rahman Khan, The High Commissioner of Bangladesh in UK Advisor Prof. Hurtmut Baerwolff, Chairman, Dept. of Analog & Opto-Electronics, University of Applied Science, Colongne, Germany Prof. Dinnath Saha, Chairman, Dept. of Physics, IIT Kharagpur, Kharagpur, India Local Advisory Committee Chief Advisor Prof. M. Aminul Islam, Dept. of Physics, University of Rajshahi Advisors Prof. Shahida Rafique, Dept. of Applied Physics, Dhaka University, Dhaka Prof. Jiban Podder, Dept. of Physics, Bangladesh University of Engineering & Technology (BUET), Dhaka Prof. M. Abul Mansur Chowdhury, Research Center for Mathematical and Physical Sciences(RCMPS), University of Chittagong, Chittagong Abu Sayeed Mohammad Firoz, Chairman, Bangladesh Atomic Energy Corporation, Dhaka Treasurer Prof. M. O. G. Talukder, Vice Chancellor, Barendra University, Rajshahi, Bangladesh Members Prof. Tofazzal Hossain Tarafder, Dean, Faculty of Science, University of Rajshahi Prof. M. Rostom Ali, Dean, Faculty of Engineering, University of Rajshahi Prof. Raquib Ahmed, Director, Institute of Environmental Science, University of Rajshahi Prof. Chitto Ranjan Misra, Administrator, Public Relation Office, University of Rajshahi Prof. Shaikh Enaetullah, Chairman, Dept. of Information & Communication Engineering, University of Rajshahi Dilruba Akhter Banu, Associate Professor, Dept. of Physics, University of Rajshahi Dr. A. K. Fazlul Haque, Associate Professor, Dept. of Physics, University of Rajshahi Dr. Babul Islam, Assistant Professor, Dept. of Applied Physics & Electronic Engineering, University of Rajshahi Mahboob Qaosar, Lecturer, Dept. of Computer Science & Engineering, University of Rajshahi S. N. M. Akhtaruzzaman, National Consultant for ICT, NATP, World Bank Project, Ministry of Agriculture, Dhaka, Bangladesh Mr. Sirajur Rahman, Executive Officer, Barendra University Trust




MAIN GOALS

disclose some issues related to Special Theory of relativity

present views developed during the past years

complete the theory of relativity by including three more equations

to introduce a new concept of Reciprocal Symmetry as an alternative to that of Special Relativity

SPEAKERS

Ten papers will be presented by the following scholars:

Dr. M. O. G Talukder Former Professor, Dept. of Applied Physics, Rajshahi University, Vice Chancellor, Barendra University, Rajshahi Dr. Mushfiq Ahmad Former Associate Professor, Dept. of Physics, Rajshahi University

ORGANIZED BY

University of Rajshahi, Rajshahi, Bangladesh

SPONSORED BY Barendra University Trust Brac Bank Ltd. Engg. Md. Enamul Haque, MP, Rajshahi-4 Md. Abdul Wadud Dara, MP, Rajshahi-5 Shahriar Alam, MP, Rajshahi-6

In association with

and Media partner




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