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Beyond Einstein and E =Mc Chapter I Total Chapters 7 Email [email protected] Author : Ajay Sharma Assistant Director 0091 94184 50899

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Beyond Einstein and E =Mc Chapter I Total Chapters 7 Email Ajay.Pqrs@Gmail.Com Author : Ajay Sharma Assistant Director 0091 94184 50899 1 2 Beyond Einstein and E =mc Chapter I Total Chapters 7 Email [email protected] Author : Ajay Sharma Assistant Director 0091 94184 50899 Abstract The ideas of inter-conversion of mass and energy existed in science since inception of mankind. Many scientists contributed to the topic, and it is equally possible that doctrines of many may have not seen the light of the day. In this regard works of Newton, S T Preston, Olinto de Pretto, Poincare , Hasenhorl , Soddi etc form conceptual basis of the mass energy equation. But first of all genuine equation of light energy mass inter-conversion equation is derived by Einstein but only under special or handpicked conditions. Thus Einstein has provided mathematical equation for Newton’s statement [7] that ‘gross bodies and light are inter-convertible to each other’. Einstein had derived mathematical equation for Newton perception , as how light energy is converted to mass as L = mc2 But this derivation as discussed above is only true under special or handpicked conditions. So this derivation may not be regarded as general. Also to obtain equation L = mc2, in the mathematical equations the terms are arbitrarily neglected. Then simply replacing L by E in eq.( 1.31) , L = mc2 is speculated. The derivation of L = mc2 is true under special or handpicked conditions only. The reason is that in the derivation there are four variables and each variable have numerous values. Whereas all possible values of variables are taken then inconsistent results are obtained. E =mc2 is obtained when special values of the parameters are taken. All these aspects are discussed. The generalized equation of mass energy inter-conversion, ∆E =Ac2∆m is also put forth and applied in various physical phenomena. The value of A can be less, equal or more than unity. Thus energy emitted can be equal, less or more than predicted by ∆E =Ac2∆m. This aspect is elaborated in Chapters 3- 5. 2 Chapter 1 Einstein derived L =mc2 For Newton’s Perception First Glimpse Newton stated in 1704 in Opticks "Gross bodies and light are convertible into one another...", S. Tolver Preston(1875), Jules Henri Poincaré (1900) , Olinto De Pretto (1903) Fritz Hasenohrl (1904) etc. developed equations and conceptual basis regarding inter-conversion of mass (E=mc2 or E mc2 ) But the real credit for derivation of mass light energy inter-conversion equation goes to Einstein, who derived equations for Newton’s perception as L =mc2, under arbitrary conditions. The original paper is attached in Appendix 1 From L =mc2 Einstein speculated E=mc2 by replacing E by L which is not justified scientifically. In Einstein’s derivation there are four variables e.g. number of light waves, energy of the light waves, angles at which light waves are emitted and velocity v. These variables have numerous values, but Einstein has taken only special or handpicked values of the variables. If all the values of the variables are taken then result is L mc2 or L =Ac2 m. Thus Einstein’s derivation is not complete. 1 v 2 Einstein derived L =mc2 by retaining term (5.55×10-26, v=0.01cm/s) 2 c 2 compared to unity. In similar equation magnitude 5×10-9 has been neglected (compared to unity), so that mass of the earth in motion and at rest is the same. If the -26 above term(5.55×10 ) is neglected then result is mb=ma. If all values of velocities are considered then energy is given by 3 v2 5 v 4 35 v6 63 v8 E = Δmc2 / (1+ + + + +……..) 4 c2 8 c 4 32 c6 64 v8 This equation is under classical conditions when v<<c. 3 Under general conditions the equation is given by 2L 1 M b M a = 2 [ – 1] v v 2 1 c 2 1.0 Einstein put forth five types of energies (equation relating to mass and energy) Every equation which relates mass and energy does not represent inter-conversion of mass and energy. The equation for mass energy inter-conversion, is written by different authors in different ways. However Einstein has derived mass energy inter-conversion in his September 1905 paper. In this paper change in light energy (ΔL) on emission by luminous body, and corresponding change in mass (Δm) both clearly defined. It implies equation deals with change in light energy ( L ) and change in mass( m ). In the other equations Einstein had not defined there terms (ΔL, Δm) and discussed annihilation of mass to energy. Thus in these equations he did not discuss mass annihilated corresponding to light emitted. Thus the other equations cannot be regarded as mass converted to energy when energy is emitted or vice – versa. Hence only Einstein’s September 1905 derivation may be taken as equation for mass light energy inter-conversion i.e. ΔL = Δmc2. Einstein derived equations relating to various types of masses i.e. rest mass (Mrest), relativistic mass (Mmotion), mass annihilated (Δm ) and mass created (Δm) to various types of energies e.g. (i) ΔL = Δmc2, Light Energy mass inter-conversion equation ΔL : Light energy emitted Δm : Mass annihilated corresponding to emission of energy ΔL (ii) ΔE = Δmc2, Mass energy inter-conversion equation ΔE Energy emitted Δm : Mass annihilated correpoding to emission of energy 2 (iii) KErel = (Mmotion – Mrest)c , Relativistic kinetic energy KErel : The relativistc kinetic energy when body moves with velocity comparble to that of light 2 Emotion = Mmotionc : It is relativistic mass when body moves with speed compare to that of light v ~ c 2 (iv) Emotion = Mmotionc , Relativistic form of energy Emotion : Energy of body when it moves with velocity comparable to that of 4 light. Mmotion : It is relativistic mass when body moves with speed compare to that of light v ~ c 2 (v) Erest = Mrest c , Erest: Rest mass Energy , the energy when body is at rest Mrest: Rest mass , the mass of body at rest In addition there are more equations involving rest mass and energy. 1 2 KE = Mrest v 2 PE = Mrestgh Now the five equations relating mass and energy were derived or speculated by Einstein . 2 2 2 2 These equations ΔL = Δmc , Δ E = Δmc , KErel = (Mmotion – Mrest)c , Erest = Mmotionc and 2 Erest = Mrest c appear to be similar as have same forms, units and dimensions but conceptually are entirely different. Also the dimensions and units of equations of PE and KE are the same. The above equations have following peculiarities. 2 Erme=Mrest c : derived from non-existent equation ∆E=∆mc2 : speculated from ∆L=∆mc2 not derived ∆L=∆mc2 : derived under arbitrary conditions So conceptually ∆L=∆mc2 and ∆E=∆mc2 can be regarded as mass annihilated to energy 2 2 or energy materialized to mass . Thus equations Emotion = Mmotionc , Erme=Mrest c , KE = 2 Mrest v , PE = Mrestgh etc cannot regarded as representing mass annihilated to energy or energy materialized to mass. 1.1 Mass energy inter-conversion before Einstein. The word ‘energy’ derives from energeia which was coined by Aristotle for first time [1]. German Gottfried Wilhelm Leibniz [1646-1716] put forth idea of vis viva (from the latin living force) as mv2 and stated that it is conserved [2-3]. vis viva or living force = mv2 (1.1) where m is mass of body and v is its velocity. In 1807, Thomas Young [1773 -1829] was first to use term ‘energy’ instead of vis viva [4-5]. Energy = mv2 (1.2) French mathematician Gustave Coriolisis [1792-1843] was first to define work as product of force and displacement. 5 W =FScosΦ (1.3) where W is work , Φ is angle between force and displacement S. On eq.(1.3), equations of energy are based. This is the equation given by Coriolisis which predicts that when a coolie takes a head load then does no work (W=FScosΦ =0). 1 In 1829, Coriolisis [4-5] described kinetic energy as mv2 i.e. 2 1 Kinetic Energy = mv2 (1.4) 2 Further mass is quantity of matter contained in the body, the real understanding of mass started when Newton defined second law of motion, F=ma in the Principia. [6]. However in the Principia Newton did not state the second law of motion as we teach now and wrote F = ma. Newton also stated inter conversion of light energy to mass [7], thus initiated important debate on this issue. According to Newton, "Gross bodies and light are convertible into one another...", More specifically Are not gross Bodies and Light convertible into one another, and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition? Newton, Opticks (4 ed. , 1730) Mass energy inter-conversion processes are the oldest in nature and constitute the basis of various phenomena. Further the energies have various forms (e.g. sound energy, heat energy, chemical energy, energy emitted volcanic reactions nuclear energy, magnetic energy, electrical energy, energy emitted in form of invisible radiations, energy emitted in cosmological and astrophysical phenomena energies co-existing in various forms etc.) which are converted into mass. At different times various scientists have studied this significant topic in different ways and study is continuous process even now. 6 Many scientists and philosophers have discussed about inter-conversion of mass to energy at different times. Even an illiterate knew that more the wood or grass he would burn more heat or light energy would be produced. He may not be aware of Einstein’s work but conclusion is obvious, more mass of wood is burnt, more energy is emitted. Before Einstein many scientists contributed to the discussion of inter-conversion of mass to energy.
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