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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.

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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<

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 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

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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.

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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.

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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. It is equally possible that there may be many more scientists whose contributions are not recorded or may have been destroyed or purposely annihilated, hence their names are not in this list of contributors. Aristotle [384-322 BC] believed that all matter on earth consisted of four pure substances or elements, which were earth, air, fire, and water [1]. Here fire may be regarded as energy. Antoine Lavoisier [1743-1794] French Chemist was the first to formulate a law of conservation of matter in chemical reactions i.e. matter can neither be created nor be destroyed but can be transformed from one form to other form [8]. Newton [7] has quoted in his book ‘Opticks’ in 1704 that "Gross bodies and light are convertible into one another...", No immediate reason is known for Newton’s intuition. It implies that energy is other form of mass. Neither Lavoisier nor Newton gave any mathematical equation relating to mass- energy inter-conversion, hence the deduction is qualitative only. Had any equation been given by any of two, then situation would have been entirely different. The speed of light c (3×109 m/s) was not defined in Newton’s time, however now c plays a significant role in such cases. S T Preston [9], An English scientist Samuel Tolver Preston (born 1844) had speculated first of all conversion of mass to energy which may be similar to E = mc2. Preston in his book Physics of the Ether proposed in 1875 that vast amounts of energy can be produced from matter

an English scientist in his book Physics of the Ether in 1875, gave and applied equation ΔE  Δmc2 (proportionality form) apparently. In one example, Preston speculated that one grain could lift a 100,000-ton object up to a height of 1.9 miles. Mathematically, if the calculations are based upon E = mc2 then mass of one grain (64.79891 milligram) emits energy equal to 5.832×1012 J, if completely annihilated. Also energy required to lift (mgh) one hundred thousand ton (9.0718×107 kg ) to height of 1.9 miles ( 3.0577 ×103 m) is 2.7006×1012 J i.e.

E= mgh = 2.7006×1012 J

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The calculations imply that Preston used equation E = mc2 in form E  mc2. It is work of the rarest or exceptional scientific perspicacity. Now Preston’s 137 years old book is in the category of the rare books. This book was published by E & F N SPON , 48 Charing Cross from New York in 1875. Now it is also available online.

Jules Henri Poincaré [10,11] in 1900 applied the calculations in a recoil process and  E  reached at the conclusion in the form, mv = c. From the viewpoint of dimensional c 2  E analysis, takes on the role of ‘mass’ associated with radiation, which yields E=mc2. c 2

Olinto De Pretto [12] An Italian Industrialist Olinto De Pretto speculated E =mc2 without any derivation. Firstly, this article was published on June 16, 1903. Second time the same was published in the Atti of the Reale Instituto Veneto di Scienze on February 27, 1904. In 1921, De Pretto was shot dead by a woman over a business dispute. When De Pretto was killed, he was trying to publish the complete book of his scientific ideas. This paper is in Italian; hence it remained away from accessibility of wider scientific community.

Pretto speculated E=mc2, implying that when v = c, then E= mv2 (Leibniz’s vis viva) becomes E=mc2, in 1903-04. Few years back some Italian scientists and philosophors logically sought priority of innovation of E=mc2 as they claimed E=mc2 is Italian idea before Einstein. Just possible Einstein may have been prompted to obtain E=mc2 by replacing L by E in L=mc2. Bartocci [13] and Bjerknes[14] argued that Einstein knew exsiting work of scientists then speculated E=mc2. However Einstein pretended he was ignorant of the existing knowldge. Fritz Hasenohrl [15, 16] in 1904, concluded “to the mechanical mass of our system must be added an apparent mass which is given by, 8E m= where E is the energy of the radiation.” 3c 2 3mc2 It implies, E = 8 4E In a later paper he further improved result that mass exchanged is, m= . Thus in this case 3c 2

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also E  mc2 Ebenezer Cunningham [17] has further improved Hasenohrl’s equation as E =mc2, but much later than Einstein’s equations. Frederick Soddi [18] in 1904 and M. Henri Becquerel both have predicted that in radioactive emissions the mass of body decreases i.e. energy of radiations is at the cost of mass. Thus higher the decrease in mass more radiations (hence energy) will be emitted. But no conversion factor was given between ‘decrease in mass’ and ‘energy emitted.’ More energy emitted: More decrease in mass It also corresponds to E  m. Hence more radiations are emitted, more mass of radioactive sample or mass of source will decrease. More radiations emitted: More decrease in mass Conceptually it would be one method to experimentally confirm the E =mc2, by measuring the energy of radiations emitted and decrease in mass of body. But no conversion factor between decrease in mass of radioactive sample and energy of radioactive radiations, was given by Frederick Soddi, like Lavoisier, Newton and others. This deduction can be qualitatively experimentally verified. It is believed that Einstein was influenced by radioactivity while he derived mass energy inter-conversion equation. In September 1905 Einstein has written It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.

The radium is over one million times more radioactive than uranium. It decays 3.7 10 × 10 disintegrations per second, its salts like RaF2, RaCl2, RaI2 etc are also extremely radioactive. After or during radioactive decay, the sample remains at rest. The energy content of radium is highly variable i.e. emits radiations (hence energy) far more intensely than other radioactive samples. Thus equation nearly similar to E =∆mc2 were suggested by some intellectuals. Einstein derived under special conditions L =∆mc2 (as discussed in the forth coming discussions), and speculated without mathematical proof E =∆mc2 (may have taken hint from existing discussions as a section of thinkers believe). Further Einstein in September 1905 paper did not write E= ∆mc2. Consequently various scientists used equation E =∆mc2 and now it is generalized as E = Ac2M, is suggested. So science progresses steadily and continuously. 1.2 What was in Einstein’s mind while deriving ∆L =∆mc2 ?

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Radioactivity was discovered in 1896 by the French scientist Henri Becquerel, while working on phosphorescent materials. Frederick Soddi [18] in 1904 and M. Henri Becquerel both have predicted that in radioactive emissions the mass of body decreases i.e. energy of radiations is at the cost of mass. Thus higher the decrease in mass more would be energy of radiation and no conversion factor was given, this inference is like above one. It appears that Einstein has in his mind Frederick Soddi’s perception, as he has written in September 1905 paper. “If this theory agrees with facts, then it will imply that radiation is also associated with inertia (mass).” Radiations  Radioactive emission = Energy Inertia  Mass A similar conclusion had been drawn earlier in 1904 by F Soddy [18] about radioactivity process. In addition, Pais [19] has mentioned that while deducing and interpreting E = mc2 Einstein had in his mind about loss of mass in radioactive phenomena. In fact while interpreting the equation ΔL = Δmc2, Einstein had in his mind the energetic radiations emitted by radioactive samples. It is also supported by contents of the paper.

In September 1905 paper Einstein [20] stated “It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test. If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.” So Einstein did not write anything about chemical reaction and nuclear reactions as possible phenomena for confirmation of E = mc2 . It means these reactions were beyond consideration of Einstein and he was mainly interested in radioactivity which was discovered few years before. The radium is over one million times radioactive than uranium. It decays 3.7 × 1010 disintegrations per second, its salts like RaF2, RaCl2, RaI2 etc are also extremely radioactive. After radioactive decay the sample remains at rest. The energy content of radium is highly variable i.e. emits radiations (hence energy) far more intensely than other radioactive samples. Before this Frederick Soddi in his book Radioactivity: an Elementary Treatise [18] published in 1904, has indicated that mass of radioactive sample decreases when it emits radiations. So there is direct evidence that this aspect was in Einstein’s mind when he derived ΔL = Δmc2 and speculated (as E=mc2 was already existing earlier) ΔE = Δmc2 as he has mentioned about radium in Sep. 1905 paper. Thus Einstein had two aspects in mind,

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(i) When radiations are emitted mass decreases, thus ΔL = Δmc2 is feasible (ii) At that time E=mc2 was existing in scientific literature, so replacing L by E (without mathematical derivation), Einstein obtained ΔE = Δmc2. There are no hints in the paper [20] that Einstein was concerned at that time about energy emitted in burning of fuel or energy emitted by the Sun etc. These were two most familiar sources of energy since beginning of humankind. The nuclear fission and fusion was out of question at that time. The chemical reactions are the most ancient reactions. It is author’s opinion that Einstein should have mentioned these reactions (source of energy) in applications of E = mc2.

Einstein’s deduction was earlier stated by the Newton [7] about 200 years before in his book ‘Opticks’ in 1704 that

"Gross bodies and light are convertible into one another"

After about 200 years Einstein [20] derived mathematical equation for Newton’s perception i.e. ∆L = ∆mc2 where ∆L is light energy emitted when mass ∆m is annihilated and c is speed of light. It is the rarest coincidence in between Newton’s hypothesis and Einstein’s mathematical derivation. When the paper was published, Einstein was obviously optimistic about the response (criticism or appreciation from the scientists). Nevertheless, it took considerable time for idea to be fully appreciated by scientific community. In 1910 Einstein himself wrote

“There is no hope whatsoever.”

Even title of Einstein’s paper is, “Does inertia of body depends upon Energy content?”

The title suggests that Einstein was not confident about what he was proposing at that time, which is natural. But there are plenty of evidences that Einstein had in his mind that the energy emitted in radioactive radiations and corresponding loss in mass of source. When radioactive radiations are emitted then source remain at rest. This is main condition in Einstein’s derivation. In the derivation Einstein used plane light waves and used eq.(1.5), which he had given in the June 1905 paper. But in the concluding remarks Einstein while discussing experimental verification of equation, he mentioned about highly energetic radioactive sources i.e. radium salts. The radium is over one million times radioactive than 10 uranium. It decays 3.7 × 10 disintegrations per second, its salts like RaF2, RaCl2, RaI2 etc are also extremely radioactive.

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1.3 Existing Experimental observations where ∆E = ∆mc2 is not verified

Before we proceed towards the theoretical understanding of Einstein mass energy equation ∆E = ∆mc2, let us quote from the existing literature the results where the equation leads to inconsistent results. ∆E = ∆mc2 is regarded as experimentally confirmed initially in two reactions. These reactions are disintegration of Li7 by swift protons in 1932 and fission of uranium 235 by neutrons in 1938. If available experimental data is critically analyzed then none of the equations, confirm the mass energy inter conversion equation ∆E = ∆mc2, proposed by Einstein. It would be better to consult the original papers of the topmost nuclear physicists in 1930s. It that time there was no hype of Einstein’s ∆E = ∆mc2 and results may be regarded as unbiased comparatively. To set the stone rolling available data from the authentic sources is quoted.

First Experiment (i) John D Cockcroft‘s Nobel Lecture of 11 Dec 1951, if completely analyzed it contradicts E=mc2. or Nuclear reaction without hype of E=mc2

In 1917, Ernest Rutherford, at university of Manchester, converted nitrogen to oxygen. In 1932 John Cockcroft and Ernest Walton accomplished fully artificial nuclear reaction ( accelerating protons against lithium-7 , to split the nucleus into two alpha particles). Cockcroft and Walton examined a variety of reactions where different atomic nuclei are bombarded by protons [21 ]. The theme of the paper was also quoted in the Nobel Lecture on 11 Dec. 1951, available at [22] http://www.nobelprize.org/nobel_prizes/physics/laureates/1951/cockcroft-lecture.pdf

The title of lecture is Experiments on the interaction of high-speed nucleon with atomic nuclei

In the Nobel Lecture Cockcroft explained about the reaction p +Li7= + α In 1932, they experimentally concluded that when lithium is disintegrated into two α-particles

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with a total energy release of 17.2 MeV energy is released. According to E=mc2, this energy must be equal to mass defect 0.018465 amu. It means difference in mass between reactants (p + 7Li ) and products ( two alpha particles) must be 0.018465 amu. As theoretical and experimental techniques vary results are interpreted accordingly.

(i) Cockcroft and Walton’s measurements “ Soon after this, we resumed our experiments on lithium, but this time, instead of looking for gamma rays, we set out to look for α-particles from the disintegration of lithium. A mica window was provided to allow the alpha-particles to escape, and opposite the mica window we placed the well-tried-tool of Rutherford - the zinc sulphide screen . Almost at once, at energy of 125 kilovolts, Dr. Walton saw the bright scintillations characteristic of α-particles, and a first primitive absorption experiment showed that they had a range of about 8.4 cm. We then confirmed by a primitive coincidence experiment, carried out with two zinc sulphide screens and two observers tapping keys , that the α-particles were emitted in pairs. Our resolving time was a second or so - somewhat longer than the resolving time of modern coincidence circuits which operate in units of milli microseconds. More refined experiments showed that the energy of the α-particles was 8.6million volts. It was obvious then that lithium was being disintegrated into two α-particles with a total energy release of 17.2 million volts. This energy could be provided by a diminution of mass of 0.018465 mass units (0.018465 amu, based upon E=mc2). The mass balance of the reaction at that time was 7Li =7.010 4 (Costa) 1H = 1.0072 Mass of reactants = 8.0176amu 2 4He = 8.002 2amu Mass decrease = 8.002 2amu -8.0176amu= 0.0154 amu (1.5) Energy equivalent = 14.3449 MeV Now from both the energies we can write %age difference = 16.594 ’’ (1.6) Hence the first reaction which is regarded as proof for confirmation of E=mc2. Moreover this experiment was conducted and interpreted when there was no hype for E=mc2. A little later Bainbridge re determined the mass of 7Li to be 7.0130 amu. This changed the

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mass decrease to 0.0180 mass units, in very good agreement with the observations.” In realistic calculations mass decrease is 0.018465amu not 0.0180amu The mass equal to 0.018 amu is equivalent to energy, 16.76682MeV. Thus difference experimental energy and expected energy is 0.43318 MeV which is nearly 2.518%. (ii) Bainbridge’s new estimation of mass of Li7 The research and post-search continue. Similar is the example of measurement of mass of Li7. After sometimes Bainbridge redetermined the mass of Li7 equal to 7.0130 amu, whereas Cockcroft and Walton has taken mass equal to 7.0104 amu. ( difference of 0.0026amu or 2.4218MeV). Thus the deductions of experiments vary. This fact was stated by Cockcroft in his Nobel Lecture on 11 December 1951. Now the equation of mass defect and energy varies. Now with new measurement of mass of Li7 the energy considerations are: For reactants p +Li7= 1.0072 + 7.0130 = 8.0202 amu For products  + α = 8.0022 amu Difference =0.018 amu (1.7) Energy = 16.76682 MeV (1.8) %age difference = 2.491 (1.9) So there is considerable difference in results with data taken by Crockcroft and Walton , and latest findings of Bainbridge. Moreover this experiment was conducted and interpreted when there was no hype of E=mc2.

7 (iii) Latest Observations about masses of Li , alpha particles and protons. Further, search, research and re-research continue, and currently mass of lithium, proton and alpha particle are regarded as 7.01600455amu, 1.0072764 amu and 4.0015061amu. For reactants p + 7Li =7.01600455 +1.0072764 =8.02328095amu α + α =24.0015061 = 8.0030122 amu Mass Defect =8.02328095amu- 8.0030122 amu= 0.0202687amu (1.10) Energy emitted =18.88 MeV (1.11) %age difference =9.768 MeV (1.12) Thus we find that the first experimental confirmation of ΔE = Δmc2 by Cockcroft and Walton ( students of Rutherford) only justifies that mass is converted into energy. It does not

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confirm mass is converted to energy according to ΔE = Δmc2. The nearest confirmation is found in eq.(1.9 ), where energy required to disintegrate the Lithium-7 is 17.2MeV . The percentage difference between both the energies is 2.491MeV. Whereas in the reported experiments by Cockcroft and Walton the energy difference is quiet large. In the case calculated energy is 14.3449MeV and %age difference 16.59. Whereas currently mass of the Li7 and proton are regarded as much higher and %age deviation is 9.768 MeV. Moreover this experiment was conducted and interpreted when there was no hype of E=mc2. Table 1 Variations in values of energy (ΔE = Δmc2 ) in disintegration of Lithium by swift protons in Crockcroft & Walton experiment in 1932.

Sr.No. Scientist Mass Mass Energy Energy %age (amu) Difference Theoretical Observed difference (amu) (MeV) (MeV) Cockcroft Li = 7.0104 0.0154 14.3449 17.2 16.594 & p = 1.0072 1 Walton 2 =8.0022 Cockcroft Li = 7.0130 0.018 16.76682 17.2 2.491 & p = 1.0072 2 Walton 2 =8.0202 (Bainbridge) Latest values Li =7.01600455 0.0202687 18.88 17.2 9.768 of mass p=1.0072764 3 2 =8.0030122

Note: In view of the variation in values of variable this classical experiment Cockcroft & Walton may be conducted again.

Experiment No 2 Did Hiroshima and Nagasaki atomic bomb explosions on Japan absolutely confirm E=Δmc2 ?

The Atomic Bomb explosions on Hiroshima and Nagasaki did not confirm E=Δmc2 quantitatively. These explosions simply confirmed ΔE  c2Δm or ΔE =Ac2Δm (mass is

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converted to energy). It is justified from report of the first American team which visited the affected places in August 1945.

The efficiency of the nuclear weapons as well as nuclear reactors is far less than the theoretical value predicted by E=Δmc2. Robert Serber (member of first American team entered Hiroshima and Nagasaki in September 1945 to assess loses), has mentioned [23] that the efficiency of “Little Boy” atom bomb [U235, 49kg] that was used against Hiroshima was about 2% only. Where the 98% energy is gone? It is not investigated. It is assumed that all the atoms do not undergo fission, thus material is wasted. However, no such waste material is specifically measured quantitatively.

Until such calculations are not precisely confirmed experimentally; it is equally feasible to assume that the energy emitted may be less than predicted by ΔE = Δmc2 (or ΔE  Δmc2 is feasible). When reactants are in bulk amount and various types of energies are simultaneously emitted (or energies co-exist in the various forms). Thus, both the possibilities are equally probable until one is not specifically ruled out. So in the uncontrolled fission reaction the proportionality ΔE  Δmc2, cannot be denied. Experiment No 3 Particle of lesser mass than predicted by E  mc2 Babar [24] Stanford Linear Accelerator Center (Slac) in the US. The discovery was made by the BaBar international consortium, which operates a detector at Slac that analyses debris from subatomic particle collisions.

The BaBar experiment at Stanford in the US has identified a new sub-atomic particle called the Ds(2317) . " Congratulations to BaBar. The existence of the particle is not a surprise, but its mass is lower than expected. This result will send theorists back to their drawing boards. " said Slac's director, Jonathan Dorfan The anomalous observations of less mass of Ds(2317) had been found. The mass of the particle is found to be less than predictions. All the energies and masses are measured with help of Δ . Thus in this case also Δ is not justified, hence ΔE  c2Δm is equally possible. Experiment No 4

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(iv)The total kinetic energy (TKE) of fission fragments of U235 or Pu239 Is 20-60 Mev less than predicted by E =mc2.

The familiar fission reaction is 235 1 141 92 1 92U + 0n → 56Ba + 36Kr + 3 0n + Q The value of Q-value is nearly 200MeV. The Q value is quoted by different scientists in different ways. But Q value as obtained by Otto Hahn and Fritz Strassmann must be quoted along with masses of reactants and products, as experimental data of Cockcroft and Walton is quoted. In laboratory [25-28] it has been experimentally confirmed that using thermal neutrons the total kinetic energy of fission fragments that result from U235 or Pu239 is 20-60 MeV less than the Q value of the reaction predicted by ΔE =mc2. These observations are over 40 years old. This limitation has been confirmed and scientists tried to explain it in number of ways. This observation implies that ΔE  c2Δm (ΔE =mc2). However it is believed that above equation confirms ΔE =mc2 which is far from the reality. Actually the paper in which Otto Hahn and Fritz Strassman has quoted the fission reaction would be interesting to critically analyze. 5. Prospective experiment relating to chemical reactions E=mc2 is not verified in the oldest existing reactions. Let wood or straw of mass 1kg is burnt under controlled conditions, consequently ashes and gases are emitted. The magnitude of ashes and masses are to be measured. Consider the wood of mass equal to 1kg is burnt under controlled conditions. Let the mass equal to 10-9 kg is annihilated, and equivalent amount of energy is emitted. If 10-9 kg of matter is annihilated then theoretically energy equal to 9×107J will be produced i.e. E = ∆mc2 = 10-9 ×9×1016 kg m2/s2 = 9×107 J (1.13)

This energy can derive a truck of mass 1,000 kg to distance of 90 km. Such or similar predictions are not experimentally confirmed in specific experimentation, even at lower level. Only then final conclusions about applicability of E = mc2 in such cases can be confirmed.

When such phenomena were discovered, scientists used E = mc2 in absence of any alternative. At that time scientists may not be aware of Preston’s equation which gives E  Δmc2, this perception was published in 1875. Scientists accepted Cockcroft and Walton experiments of splitting of Li7 by protons and a pair of alpha particles, as proof for

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confirmation of E = mc2. In the most famous reaction of splitting of U235 by thermal neutrons conducted by Otto Hahn and Fritz Strassmann [29] 235 1 141 92 1 92U + 0n → 56Ba + 36Kr + 3 0n + Q the total kinetic energy is found 20-40MeV less experimentally. Scientists tried to explain these by other methods. These are experimental observation over five decades but these are ignored. These are being overlooked in view of qualitative observations of nuclear reactions. Einstein’s E = mc2 is regarded as to hold good in such cases. It is the irony of scientific analysis. Then it was used as standard in nuclear physics, as there are 7 days in week not 10, there are 12 months in a year not 10, there are 60 minutes in an hour not 50. The basic units of mass energy were defined in terms of it, the date which was consistent with E = mc2 was retained and other neglected. It is being assumed that predictions of E = mc2 are God’s will and is absolute reality. It must be noted in chemical reactions, cosmological, astrophysical reaction no specific observations are there that E = mc2 is justified. In some sense Einstein speculated E = mc2 in his September 1905 paper. The theoretical critical analysis of the derivation implies that it is also mathematically inconsistent. This aspect is discussed below.

2.0 Einstein’s approach in September 1905 paper in which ∆L =∆mc2 was derived and E =∆mc2 was speculated? Or

Description and Critical Analysis of Einstein’s Thought Experiment In Einstein’s derivation [20] basic equation is  v  1 cos  c       (1.14) v 2 1 c 2 where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. This equation was given in Einstein’s June 1905 paper in Section 7 and is called Doppler principle for any velocity whatever [30]. But there is no specific derivation to the equation in paper.

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Also there are no references in the paper so that its origin may be quantitatively understood. Then this equation is used in derivation which is basically equation of conservation of energy, as light energy is inter-converted into mass. Einstein derived L = ∆mc2 from this equation under special conditions and speculated E = ∆mc2 under all circumstances. Thus we find that E = ∆mc2 is speculated from L = ∆mc2 which is based upon eq.(1.14) and eq.(1.14) is not derived as in Einstein’s June 1905 paper. It is really a strange situation about origin of E=∆mc2 and from equations it is derived. Obviously many possibilities exist. Imagination of peculiar luminous body. Einstein perceived a peculiar body which emits two light waves. The perceived body emits light waves of equal energy and exactly opposite directions. Theoretically such body can be imagined but may be difficult to construct it practically. Hence it may be called thought experiment.

Einstein’s perception: Let a system of plane waves of light, referred to the system of coordinates (x, y, z), possesses the energy  , let the direction of the ray (the wave-normal) makes an angle ɸ with the axis of x of the system.

If we introduce a new system of co-ordinates (ξ, η, ζ ) moving in uniform parallel translation with respect to the system (x, y, z), and having its origin of coordinates in motion along the axis of x with the velocity v. Thus v is the relative velocity between system (x, y, z) and system (ξ, η, ζ ) . The body which emits light energy is considered stationary in the system (x,y,z) and also remains stationary after emission of light energy in the system (xy,z).

Let E 0 and H 0 are energies in coordinate system (x, y, z) and system (ξ, η, ζ

) before emission of light energy, further E1 and H 1 are the energies of body in the both systems after it emits light energy. Ei and Hi include all the energies possessed by body in two systems. The various values of Ei’s and Hi’s are shown in Table I.

Table I. Energies emitted before and after emission by body in Einstein’s Sep. 1905 derivation.

Sr No System (x,y,z) System(ξ, η, ζ )

1 Before Emission E0 Before Emission H0

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2 After Emission E1 After Emission H1

Thus Einstein wrote various equations as energy of body in system ( x,y,z ). Then Einstein concluded that body emits two light waves of energy 0.5L each in system (x,y,z) where energy is E0. Energy before Emission = Energy after emission +0.5L + 0.5L

E 0 = E1 + 0.5L + = E1 + L (1.15) Hence Einstein took all possible energies in account in the derivation. Energy of body in system (ξ, η, ζ )

v v H = H + 0.5  {(1 – cos ) + (1+ cos ) } (1.16) 0 1 c c 1   (1.17) v 2 1 c 2

= + L (1.18) Subtracting eq.(1.15) from eq.(1.18)

Or ( – ) – ( – ) = L [  –1] (1.19) 1 Or ( – ) – ( – ) = [ –1] (1.20) v 2 1 c 2 Einstein calculated as

1 2 ( – ) = K +C = M v + C (1.21) 0 2 b

1 2 ( – ) = K1 +C = M v + C (1.22) 2 a

Einstein defined C as additive constant which depends on the choice of the arbitrary additive constants of the energies H and E. The arbitrary additive constant C is regarded as equal in both the cases. Thus value of C is purely arbitrary, it is same in both the terms i.e. ( –

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) and ( H 1 – E1 ). Basically it is constant of proportionality. Arbitrary assumptions are not allowed in science. The reason is that if arbitrary assumption is valid for one equation then it is equally possible for other equations as well. Like this constant of proportionality can be introduced in Newton’s second law of motion, law of gravitation and in other laws. Kinetic 1 energy of body before emission of light energy, K ( M v2 ) and kinetic energy of body 0 2 b

1 2 after emission of light energy, K1 ( M v ). 2 a

1 – K1= L { – 1} (1.23) v 2 1 c 2 Einstein’s approach in September. 1905 paper Equation of mass energy inter-conversion for velocities under classical conditions. So far we have assumed that system (x,y,z) is at rest and body is placed in it , which remain at rest before and after emission of light energy. The system (ξ, η, ζ ) is moving with uniform velocity v w.r.t system (x,y,z). Einstein did not distinguish whether velocity v is in classical or relativistic region. In fact as eq.(1.14) is used, which gives significant results when velocity is in relativistic region , like other relativistic equations. However starting from relativistic equation Einstein interpreted the equation under classical region. It may be due to two reasons to attain mathematical simplicity in equations. (a) The equation for relativistic variation of mass i.e.

M rest Mmotion = (1.24) v 2 1 c 2 reduces to classical mass when interpreted under classical conditions i.e. v<

 v2 v4 5 v6 35 v8 63 v10  M = M 1  3   .  . .  ......  (1.25) motion rest  2 4 6 8 10   2c 8c 16 c 128 c 256 c 

v2 v4 5 v6 35 v8 Under classical conditions then terms , 3 , , …… can be neglected . 2c2 8c4 16 c6 128 c8 Thus

Mmotion = Mrest (1.26)

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v2 (b) Secondly in the derivation by retaining only term , Einstein was eliminated the 2c2 variable (v) from the final equation. Also it simplified equations.

Now eq.( 1.23) can be expanded by applying Binomial Theorem if v<

 v2 v4 5 v6 35 v8 63 v10  K – K = L 1  3   .  . . ...... 1 (1.23) 0  2 4 6 8 10   2c 8c 16 c 128 c 256 c 

Lv2 – = (1.27) 2c 2 However Einstein even did not expand terms with Binomial Theorem, in eq.(1.13) and solved equation but lead to direct conclusion and directly wrote above equation (1.31 ). Further Einstein drew conclusion about mass energy inter-conversion equation by text description only. Einstein did not drew conclusion by mathematical equation. Einstein interpreted eq.(1.14 ) .17, as when m is annihilated then energy emitted is mass multiplied by c2. However in the derivation Einstein never wrote equations ∆L= mc2 or ∆E= or E, it is also independently and correctly concluded by Fadner [31] in American Journal of Physics. According to Hetch [32], Einstein never constructed a general proof for ∆E= and rigorous proof of the mass-energy equivalence is probably beyond the purview of the special theory. So scientists are critical about theoretical derivation of ∆E= , but it is used as standard in experimental physics. Even then theoretical analysis must continue, and may lead to novel findings because science is open body not closed one. It is obvious that Einstein hurriedly wrote the paper, as it is just of less than two and half pages, it contains no section or sub-section, equation number and acknowledgement. In addition Einstein never wrote equations ∆L= or ∆E= or E. Why Einstein did did not elaborate it in paper? Just possible he may not be sure of the importance of the paper. Here L is light energy emitted. If initially light energy is regarded as zero and after sometime light energy emitted is L . The light energy emitted ∆L (L-0) is L, thus ∆L=L. Einstein neither meant nor interpreted the derivation for non-classical velocities. If the velocity of luminous body is in relativistic region then two effects take place simultaneously: (i) Mass increases according to eq. (1.24 ) (ii) When light energy is emitted, mass decreases i.e. mass decreases at the expenses of light

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energy. The two opposite effects are simultaneously in the same body, each has to be measured separately. If the results to be interpreted in classical region, then better start with classical equation not with relativistic eq.(1.14). If the derivation is initiated with eq.(1.14) then c comes in picture, even when Binomial Theorem is applied. Or other method of derivation of ∆E= mc2 . So it would be better if derivation of mass energy inter-conversion is independent of velocity. If we start from classical form of equation then c2 does not come in picture. Equation of mass energy inter-conversion for all velocities. Einstein has applied classical conditions (v<

2L M  M = [ – 1] (1.28) b a v 2

v 2 or L = [ ] / [ – 1] 2

Thus if the classical conditions are not applied then light energy emitted will also depend the velocity, v of the observer system (ξ, η, ζ ). Also under relativistic conditions the mass increases considerably. Einstein has eliminated the issue by just choosing the classical conditions of the velocity, which is not complete analysis at all. The equation must be such that it takes in account both classical and relativistic velocities. This aspect will be discussed

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at some other stage with details. Further eq.(1.28) is not defined when observing system (ξ, η, ζ ) when at rest, 2L 1 2L M b  M a = 2 [ – 1] = 0 =  (1.29) v v 2 0 1 c 2 Some heavenly bodies (quasars or galaxies etc.) move with speed equal to that of light or even exceeds c. About objects Faster Than Light ,here is a quote from wikepedia [33] "There are many galaxies visible in telescopes with red shift numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.” Source http://en.wikipedia.org/wiki/Faster-than-light#Universal_expansion When velocity (v) of the system (ξ, η, ζ ) is zero then the derivation is not valid. Einstein intended his perception for radioactive source is always remains at rest. It is not applicable when velocity is in relativistic region. Also the derivation is invalid when v=0 or very-2 small i.e. tends to zero. The mass energy inter-conversion equation holds good all conditions ( body may be at rest, or moving or having relativistic velocity), but Einstein’s derivation is only valid when velocity is in classical region. Thus the such significant derivation of mass energy inter-conversion equation must be independent of velocity.

(a) How Einstein obtained ∆L= mc2 from eq.(1.23) ? Einstein obtained ∆L= under two conditions

(i) When velocity of the system (ξ, η, ζ ) is in classical region v<

If these conditions are not satisfied then ∆L= is not obtained. It is justified as below. Applying Binomial Theorem to eq.(1.23) under condition when v<

 v2 v4 5 v6 35 v8 63 v10  K – K = L 1  3   .  . . ...... 1 0  2 4 6 8 10  (1.23)  2c 8c 16 c 128 c 256 c  Now Einstein has proceeded in the following way. Einstein wrote

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Neglecting magnitudes of fourth and higher orders we may place 1 v 2 Thus only term was retained. Only then we got L= mc2 . Hence eq.(1.23) can be 2 c 2 written as v 2 K – K1= L (1.27) 0 2c 2 In view of eqs.(1.21-1.22), then eq.(1.27) becomes M v 2 M v 2 b – a = (1.30) 2 2

2 or = ( M b  M a ) c = (1.31)

L Mass of body after emission ( M ) = Mass of body before emission ( M ) – (1.32) a b c 2 Thus mass of body decreases when light energy is emitted, the decrease in mass depends upon amount of energy emitted. If body does not emit light energy i.e. L = 0 then

Ma= Mb (1.33) Then Einstein generalized ( or in practical sense got the result which he wanted to get i.e. ∆E= which was existing at that time) the result for every energy and called mass of body is measure of energy content (every energy that is included in a collection). Einstein further wrote in September. 1905 paper

If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference. But Einstein did not clear that (i) What type of energy is possessed by body ? The energy has various types. (ii) How energy is withdrawn from body (iii) How it becomes energy of radiations? (iv) How equation for light energy mathematically and conceptually represent all energies? so that we are led to the more general conclusion that

The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.

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However Einstein never wrote a character ‘E’ or equation ∆E=∆mc2 in his September 1905 derivation [20]. It is concluded that Einstein’s statement means ∆E= mc2 . It is independently concluded by Fadner [31] in American Journal of Physics. It can be obtained by replacing L (light energy) by E (energy-content or every energy). Einstein wrote:

2 ∆ = ( M b  M a ) c = (1.34) E Mass of body after emission ( M ) = Mass of body before emission ( M ) – (1.35) a b c 2 When energy is emitted the mass decreases. Thus Einstein did not differentiate between Light Energy and other energies in the derivation (both conceptually and mathematically), and consequently replaced L (light energy) by E (every energy) to get eq.(1.34). The characteristic equations for describing various energies are different, then it was not taken in account. The equation for light energy does not represent equations for other energies e.g.  v  1 cos  c       does not represent heat energy v 2 1 c 2

does not represent sound energy

does not represent nuclear binding energy.

Like this many other energies can be interpreted. The eq.(1.14) only represents light energy not other energies. So why general conclusions (equation for every energy) can be drawn from it? 1 v 2 The term (5.55×10-26, v=0.01cm/s) is also neglected. 2 c 2

If the term is neglected compared to unity then eq.(1.12) becomes

 v2 v4 5 v6 35 v8 63 v10  K – K = L 1  3   .  . . ...... 1 0 1  2 4 6 8 10   2c 8c 16 c 128 c 256 c 

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or K 0 – K1 = 0 1 1 M v2 – M v2 = 0 2 b 2 a or M b  M a = 0

M b  M a (1.33)

Mass of body before emission (Mb) = Mass of body after emission (Ma) The same result also follows if the System(ξ, η, ζ ) is at rest i.e. v=0 or v→0. Thus L = ( ) c 2 = mc2 is not obtained in this case. However light waves are emitted with speed of light c, and mass of body decreases. Hence, ∆L = , is obtained under arbitrary conditions. As mass energy inter-conversion takes place in all cases so general equation i.e. meant for both classical and higher velocity must be considered. There is no preferred reason that in equation of mass energy inter-conversion equation is considered in the classical region of velocity not for 1 v 2 higher velocities. Also there is no special reason that why term (5.55×10-26, 2 c 2 v=0.01cm/s) should not be neglected compared to unity. However practically equation is applied for all cases. Just mathematical simplicity must not be the criterion. The mass energy inter-conversion takes place in all cases. The mass energy inter-conversion equation holds good all conditions ( body may be at rest, or moving or having relativistic velocity), but Einstein’s derivation is only valid when velocity is in classical region. Thus the such significant derivation of mass energy inter-conversion equation must be independent of velocity. Fadner [31] has rightly pointed out that in the paper Einstein neither wrote ∆E= nor E in the paper. Thus Einstein was not confident while replacing L by E (however may be pre- motivated.) There is no scope for such arbitrary replacements in science. It is also reflected by the fact that title of the paper is Does the Inertia of a Body Depend upon Its Energy-Content? Hetch [32] maintained that we briefly examine all of Einstein’s conceptual demonstrations of mass energy equation, focusing on their limitations and his awareness of their shortcomings. Although he repeatedly confirmed the efficacy of equation, he never constructed a general proof. Leaving aside that it continues to be affirmed experimentally, a rigorous proof of the

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mass-energy equivalence is probably beyond the purview of the special theory. Hetch’s deduction is verified here. Justifying this conclusion ΔE =Ac2Δm is derived by non- relativistic method in Chapter 3. Thus there are existing deductions by scientists about limitations of derivation ∆E=∆mc2.

2.1 Typical Comments Regarding Classical Region Of Velocity (Not Given By Einstein). Einstein’s derivation also offers the most mysterious and puzzling situation in science. It is explained below, with help of equation,

M rest Mmotion = (1.24) v 2 1 c 2

Let the velocity is in classical region i.e. 10m/s (36 km/hr, ordinary speed of vehicle), then there is no increase in mass of object, it moves with this velocity. The speed of aeroplane is over 500km/hr (138.88m/s), and no increase in mass is observed. For proper understanding the conceptual basis of Einstein’s derivation, consider the followings. Now expanding eq.(1.24) by applying Binomial Theorem we get,

 v2 v4 5 v6 35 v8 63 v10  M = M 1  3   .  . .  ......  (1.25) motion rest  2 4 6 8 10   2c 8c 16 c 128 c 256 c  (i) If the body is emitting light energy in the system(x,y,z) and the observing system i.e. system(ξ, η, ζ ) is at rest i.e. v = 0

Mmotion = Mrest

(ii) If velocity v = 0.01cm/s in typical classical region

-26 -51 Mmotion = Mrest [ 1+ 5.55×10 +4.629×10 + ……………..] (1.36) Here even term 5.55×10-26 is regarded as negligible compared to unity and 4.629×10-51 is further negligible thus

Mmotion = Mrest (1.26)

Thus term 5.55×10-26 has to be neglected only then both masses are equal. Thus Binomial Theorem over estimates mass of body 1gm by 5.55×10-26 gm. v (iii) Similarly the orbital velocity of the earth is 30km/s or 3,0000m/s i.e. =10-4 c

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v 2 3v 4 Mmotion = Mrest [1+ + +……………] 2c 2 8c 4 -9 -17 Mmotion = Mrest [ 1+ 5×10 + 3.75×10 + ……………..] (1.37)

-9 -17 Mmotion = Mrest + Mrest 5×10 + Mrest 3.75×10

The mass of earth remains same 5.98×1024 kg always. Thus here also the term (5×10-9) is neglected compared to unity.

Mmotion [mass of earth in motion] = Mrest [mass of earth at rest] (1.38)

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v 2 If the term (5×10-9) is not neglected then mass of earth will increase per second by 2c 2 significant amount i.e. 5×10-7 %. The mass of earth will increase significantly with time. Thus we find that 5×10-9 is neglected compared to unity in the existing literature. So that mass of the earth remains the same. (iii) Similarly the term 1.272×10-8 neglected compared to unity in mass of Mercury, as mass of the mercury remains same while it orbits around the sun neglected. It can be easily v justified below. The orbital velocity of the mercury 47.8728 km/s or 47.8728×103 m/s or c = 2.544×10-8. 3v 4 Mmotion = Mrest [1+ + +……………] (1.25) 8c 4 -8 -17 Mmotion = Mrest [ 1+ 1.272×10 + 9.54×10 + ……………..] -8 -17 Mmotion = Mrest + Mrest 1.272×10 + Mrest 9.54×10 +………. Thus the %age increase in mass of mercury per second is 1.272×10-8 which is neglected and mass of mercury is regarded as equal to 3.3022×1023 kg. There is no increase in mass of mercury at all since ages. When the term 1.272×10-8 is neglected only then,

Mmotion [mass of mercury in motion] = Mrest [mass of mercury at rest] Thus if terms having magnitudes 5×10-9 and 1.272×10-8 are neglected (to keep masses of earth and mercury same) compared to unity then term, 5.55×10-26 can also be neglected. There is no logic which permits retention of 5.55×10-26 and omission of 1.272×10-8 and 5×10-9 . The various terms neglected compared to unity are shown in Table II

Table II: Terms neglected in calculations and their effects.

Sr. velocity Neglected Result Mrel = Mrest[ 1+ + + …. ] No. term

1 0 Mrel = Mrest none Mrel = Mrest

-8 -8 2 Mercury’s Mmotion = Mrest [ 1+ 1.272×10 + 1.272×10 Mrel = Mrest orbital

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-17 velocity 9.54×10 + ……………..] Mrel = Mrest

47.872km/s or 4.78×104m/s

-9 -9 3 Earth’s orbital Mrel =Mrest [ 1+ 5×10 + 5×10 Mrel =Mrest velocity 3.75×10-17 + ………] 30km/s or 3×104m/s or 1,08,000km/hr

4 v=0.01cm/s Kb –Ka Mb =Ma = L [ 1+ 5.55×10-26 +4.629×10-51 5.55×10-26 or Mass before + ………-1] 0.036km/hr emission or Mb =Ma = Mass after

emission

If terms 1.272×10-8 and 5×10-9 are neglected compared to unity in relativistic mass of the mercury and earth to keep the mass same i.e. equal to rest mass then 5.55×10-26 can also be neglected compared to unity in Einstein’s derivation in similar calculations.

2.2 Appearance of c2 in ∆L= Δmc2 is apparently arbitrary.

If Einstein’s derivation is carefully analyzed, then it becomes clear that c2 is brought in picture i.e. in equation L= Δmc2 using classical conditions. We have eq.(1.23) as

 v2 v4 5 v6 35 v8 63 v10  K – K = L 1  3   .  . . ...... 1 0  2 4 6 8 10  (1.23)  2c 8c 16 c 128 c 256 c  Now consider the same case when velocity is 0.01cm/s or 0.036km/hr, under this conditions eq.(1.23) becomes 1 1 M v2 – M v2 = L [ 1+ 5.55×10-26 +4.629×10-51+ ………..-1] (1.39) 2 b 2 a

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3v 4 1 v 2 (i) Einstein has neglected term retained the term as , and obtained equation 8c 4 2 c 2 1 1 v 2 M v2 – M v2 = L (1.30) 2 b 2 a 2c 2

2 2 or L = ( M b  M a ) c = mc (1.31)

(ii) If the velocity is very-2 small then can be neglected compared to unity. If velocity is 0.01cm/s (typical classical region), then is 5.55×10-26. Depending upon the orbital velocity of the earth (30km/s or 3,0000m/s i.e. v/c =10-4 ) the term (5×10-9 ) can be neglected compared to unity, only then the equation i.e

Mmotion [mass of earth in motion] = Mrest [mass of earth at rest] (1.32) is justified. If 5×10-9 is neglected compared to unity in typical classical region ( v

=0.01cm/s ) = 5.55×10-26 is neglected compared to unity. There is no rule which forbids it. Thus

Mb (mass before emission) = Ma (mass after emission) (1.33)

(iii) Then Einstein neglected higher terms and retained only , thus ∆L= Δmc2 is obtained.

(iv) Now the term (5.55×10-26, v=0.01cm/s) can also be neglected compared to unity as much bigger term 5×10-9 is neglected compared to unity, in eq.(1.39) then we get

Mb = Ma 2 Thus both ∆L= Δmc and Mb = Ma are equally probable and but have entirely different nature. Thus Einstein has brought c2 arbitrarily in equation ∆L= Δmc2, hence in ∆E= Δmc2. There is no scientifically preferred reason that from Einstein’s derivation result ∆L= Δmc2 (1.31) must be taken in account and

Mb (mass before emission) = Ma (mass after emission) (1.33)

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must be neglected. This discussion also validates the necessity of categorization of sub ranges of velocity in the classical region. There has to be clear cut guidelines up to which extent the velocity must be taken in classical region, and from which points relativistic results are obtained. In the 1 v 2 observation, term (5.55×10-26, v=0.01cm/s) is retained and higher orders v4/c4, v6/c6, 2 c 2 v8/c8…….. are neglected. Even magnitude more than 5.55×10-26 i.e. 5×10-9 has been neglected. So 5.55×10-26 must be neglected but then result is not ∆L=∆mc2. In brief, if term 5.55×10-26 is only retained then ∆L=∆mc2 is obtained otherwise not. 2.3 Kinetic Energy when all terms are considered

 v2 v4 5 v6 35 v8 63 v10  K – K = L 1  3   .  . . ...... 1 0  2 4 6 8 10  (1.23)  2c 8c 16 c 128 c 256 c 

2 4 6 8 2 3 v 5 v 35 v 63 v or (mb – ma)c = L ( 1+ + + + +……..) 4 c2 8 c 4 32 c6 64 v8 or L = Δmc2 / ( 1+ + + + +……..) (1.41)

Likewise the value for energy can be written as

or E = Δmc2 / ( 1+ + + + +……..) (1.42)

It the value of energy created when mass is annihilated.

2.4 If the measuring system(ξ, η, ζ ) is at rest (v=0), then Einstein’s mathematical derivation of L = ∆mc2 is not applicable. v can also be zero if system (x,y,z) and system (ξ, η, ζ ) move with same velocity. Practically the theoretical derivation of ∆L = ∆mc2, implies that when luminous body emits light energy at rest, then derivation is invalid. It may be regarded as the mass of body does not change under this condition. However in this case (when v =0) experimentally when light energy is emitted mass decreases. It is serious limitation of Einstein’s derivation. When the measuring system (ξ, η, ζ ) is at rest v = 0 then  * = 

Ho = H1 +L/2 +L/2

Eo = E1 + L

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(Ho – Eo) – (H1 –E1) = 0 (1.43)

E0 is energy before emission in system (x,y,z), which is at rest

E1 is energy after emission in system (x,y,z), which is at rest

H0 before emission in system(ξ, η, ζ ), which is assumed to be at rest (v=0)

H1 after emission in system(ξ, η, ζ ), which is assumed to be at rest (v=0)

As body is at rest and measuring system (ξ, η, ζ ) is also at rest, then (Ho – Eo) or (H1 –

E1) cannot be interpreted as kinetic energy. Hence Einstein’s derivation is not further applicable. Practically, there are numerous cases when light energy is emitted by body, mass decreases and measuring system remain at rest (v=0). However under these conditions Einstein’s derivation is not valid, as it states that light energy is emitted but mass of body remains the same. This deduction is contradiction of law of mass energy inter-conversion .

3.0 Einstein took only super special values of variables. In Einstein’s derivation there are four variables which have numerous values e.g. number of light waves, energy of light waves, angles at which waves are emitted and velocity etc. In addition Einstein put another condition in the derivation that body remains at rest. These variables affect the results and their impacts are discussed below. The following arguments can be given that Einstein’s derivation is true under super special or handpicked conditions.

3.1 Einstein’s conditions of derivation, contradict experimental conditions. Einstein [20] has put condition on state of the body: Let there be a stationary body in the system (x, y, z), and let its energy-referred to the system (x, y, z) be E0. Let H0 be the energy of the body relative to the system (ξ, η, ζ ) moving as above with the velocity v. The body also remains stationary in system (x, y, z) after emission of energy. Einstein also assumed that the body also remains stationary after emission of light energy. But practically this condition (luminous body is stationary) is not obeyed in many cases. (i) The nuclear fission is caused by the thermal neutrons which has velocity 2,185m/s. The uranium atom also moves as it is split up in barium and krypton, and emit energy. Thus reactants and products are in motion. Initially projectiles are in motion and also sets the products in motion. (ii) When a gamma ray photon of energy at least 1.02MeV moves near the field of nucleus it is split up in electron and positron pair [34]. The gamma ray photon is in motion (with speed of light) and similar is the state of electron and positron pair. Thus reactants and products are

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in motion. (iii) Similarly the particle and antiparticle moves towards each other for annihilation. The particle and antiparticle collide then annihilation takes place. In nuclear fusion the atoms are set in motion before they fuse. Only then particles will overcome electrostatic forces. (iv) When a paper burns then it is also set in motion and energy in various forms is emitted. Also in volcanic reaction the reactants and products remain in motion. (v) The fast neutrons produced in fission are slowed down and called thermal neutron thus their velocities are not necessarily uniform as can be variable while they cause fission of other nuclei. (vi) When deuterium and titanium fuses, but only after these are set in motion under conditions of high temperature. The velocity of the reactants is not necessarily uniform and gradually they overcome the force of electrostatic repulsion. Thus practically Einstein’s condition that luminous body (reactant) remains at rest, is not obeyed in many cases. It is true in case of heavy radioactive source emitting radiations. Now observing the specially fabricating body of few macrogram exceptionally radioactive sources of radiations, conclusions can be drawn. (vii) Chemical reactions were discovered in Einstein’s time. Einstein never discussed this phenomenon in his works. In chemical reaction it is assumed that energy emitted is too less, thus mass annihilated is incalculable. However there are no evidences that such quantitative tests were ever conducted. So Einstein’s condition that body is stationary, emits light energy and its mass decreases, is not justified in many cases. If 10-9 kg of matter is annihilated then theoretically energy equal to 9×107J will be produced i.e.

E = ∆mc2 = 10-9 ×9×1016 kg m2/s2 = 9×107 J (1.13)

This energy can derive a truck of mass 1,000 kg to distance of 90 km. Such or similar predictions are not experimentally confirmed in specific experimentation. In daily life it appears that this prediction may not be justified, as even huge amount of wood is burnt then energy appears to be emitted too less than that above prediction to be justified [7]. Nearly 2 quintals (200kg) wood is required for burning in a dead body, this observation is seen daily by thousands of people. How much mass is annihilated? How much energy is released? It is not justified to regard ∆E = ∆mc2 true without all relevant experiments, rather it should be clearly mentioned that E = ∆mc2 is not confirmed in such cases. Thus

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results are wide open unless specific experiments are not conducted and ∆E = ∆mc2 is confirmed. If atom bombs are exploded, then it does not mean ∆E = ∆mc2 is experimentally confirmed, it is end of scientific investigations.

3.2 Other Conditions On Einstein’s Derivation.

Einstein’s September 1905 derivation [20] of L = mc2 is true under super special conditions or handpicked conditions only. It is justified below. In the derivation of L = mc2. Einstein has considered a luminous body and measuring system in the mathematical treatment, there are FOUR variables e.g.

(a) Number of waves emitted by luminous body,

(b) l magnitude of light energy emitted by body,

(c) Angle  at which light energy is emitted by body and

(d) Uniform velocity (relative velocity), v of both the systems. Further values of various variables can be different.

3.3 Nature of v According to Einstein: v is the relative velocity between system (x, y, z) and system (ξ, η, ζ ). The system (x,y,z) is at rest and system ( ξ, η, ζ ) moves with velocity v, then v is relative velocity between two systems. If the system (x,y,z) and system (ξ, η, ζ ) both move with same velocity then relative velocity v is zero. Also v is zero if both systems are at rest. Further Einstein strictly took the value of velocity as uniform. These conditions affect the results significantly.

Practically the law of inter-conversion of mass and light energy holds good if (i) Velocity v is in classical region. (ii) Velocity v is in relativistic region. Then mass of body increases with velocity as given by eq.(1.19). (iii) Velocity v is zero (iv) Velocity v is variable or uniform

These variables have numerous values. The law of inter conversion of mass and energy holds good under all conditions of velocity. But Einstein has considered just one condition

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1 v 2 i.e. velocity is constant in classical region and term (5.55×10-26, v=0.01cm/s) is 2 c 2 retained and higher terms are neglected. Thus derivation of is exceptionally arbitrary and in narrow range of parameters. Einstein started from relativistic equation but did calculations under classical conditions with handpicked values of velocity. If calculations are to be done under classical conditions, then Einstein should have started from the classical equation. The classical equations does not involve c, hence L =mc2 has not been obtained.

3.4 Einstein’s Guesswork or Speculation of E =mc2 from L =mc2.

It is obvious that Einstein stated his work for light energy, from eq.(1.14) i.e.  v  1 cos  c       (1.14) v 2 1 c 2 where  is light energy emitted by body in frame (x,y,z) and  * is light energy measured in system (ξ, η, ζ ), and v is velocity with which the frame or system (ξ, η, ζ ) is moving. . This equation was given in Einstein’s June 1905 paper in section 7 and is called Doppler principle for any velocity whatever [30]. But there is no specific derivation to the equation. Then this equation is used in derivation which is basically equation of conservation of energy. Using this equation Einstein obtained equation L =mc2 Light Energy emitted = (Mass annihilated)c2

Thus this derivation is for inter-conversion of light energy to mass or vice-versa, not for inter- conversion of every energy to mass. Here Einstein’s guesswork came in picture when equation was generalized for every energy. There are various of energies in nature e.g. 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,

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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. So Einstein speculated without logic that whatever is true for light energy is true for every energy , E. Perhaps only Einstein can give arguments of conceptual and mathematical similarity or resemblance.

4.0 The derivation of mass energy inter-conversion equation must be independent of velocity. The derivation of L = mc2 Einstein has used equation

 v  1 cos  c       (1.14) v 2 1 c 2 which involves velocity v. Einstein has eliminated the velocity v by applying classical conditions i.e. v<

The general equation for mass energy inter-conversion is 2L 1 M b  M a = 2 [ – 1] ` v v 2 1 c 2 If equation is written for relativistic and classical velocities then results are different from L = mc2. Further for completeness if velocity is considered in relativistc region then If the velocity of luminous body is in relativistic region then two effects take place simultaneously: (i) Mass increases according to eq. (1.24 ) (ii) When light energy is emitted, mass decreases i.e. mass decreases at the expenses of light energy. The two opposite effects are simultaneously in the same body, each has to be measured

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separately. If the results to be interpreted in classical region, then better start with classical equation not with relativistic eq.(1.14). If the derivation is initiated with eq.(1.14) then c comes in picture, even when Binomial Theorem is applied. Or other method of derivation of ∆E= mc2 . If the body is at rest (v=0) then Einstein derivation is invalid. So it would be better if derivation of mass energy inter-conversion is independent of velocity. Such an equation i.e. ∆E =Ac2 ∆m is derived in Chapter 3 and analyzed. 5.0 Mass energy equation after Einstein’s work Max Planck was compatriot of Einstein. He studied Einstein’s derivation E =mc2 or L =mc2 and pointed out its limitation [35-36]. However Planck did not point out the limitations which are discussed here. Max Planck in 1907 made an in-depth investigation of the energy "confined" within a body, but he did not use Einstein’s approach at all. Planck E derived an expression, m-M= , for heat energy and mass and interpreted that c 2

” The inertia mass of body is altered by absorption or emission of heat energy. The increments of mass of body are equal to heat energy divided by square of speed of light.”

Planck acknowledged Einstein’s previous derivation but did not agree with correctness of Einstein’s derivation. Ezzat Bakhoum [27,28] has proposed that a total energy equation that satisfies the Compton-de Broglie wave mechanics as well as theory of special relativity is H = mv2 (1.26) where H is total energy of particle, m is its mass and v is velocity. The energy emitted is less as v cannot be more than c. Bakhoum has put forth that H=mc2 (or widely regarded as E=mc2) cannot do so simultaneously. The perception is applied to explain various phenomena. Here it is assumed that H=mc2 is the maximum limit of energy. Thus again the conversion factor between mass and energy is other than c2 is suggested. Hence E  mc2

Afterwards many scientists wrote critical papers on Einstein’s derivation but the same were contradicted by other scientists hence not discussed here.

5.1 Generalized form of mass energy equation, ∆E =Ac2 ∆m

The author has pointed out the hidden limitations of Einstein’s September 1905 paper or

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derivation of E =mc2 and hence suggested a generalized mass energy inter-conversion equation ∆E =Ac2 ∆m. In equation ∆E =Ac2 ∆m , A is coefficient of proportionality like numerous others existing in physics and depend upon inherent characteristics of the mass energy inter-conversion processes. The concept of co-efficient of proportionality is existing since days of Aristotle. Speed is proportional to motive force, and inversely proportional to resistance. v  F/R

F v = k R where k is coefficient of proportionality, which is s determined experimentally and depend upon inherent conditions of the process. Newton’s second law of motion as given in the Principicia, we have “The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.” F (v-u) F =K (v-u) where K is coefficient of proportionality and depend upon inherent experimental conditions. Similarly there are many examples of the coefficient of proportionality in the exsinting literature, so nothing new is done in this case. If A is equal to unity then ∆E =Ac2 ∆m becomes equal to E =mc2, otherwise magnitude of energy predicted can be less or more than E =mc2. So the theme of discussion is that energy is emitted on annihilation of mass(m) can be less or more than emitted by E =mc2, as there are vast number of mysterious reactions ( discovered or undiscovered in nature). The biological reactions can be considered in this regard. In many cases E =mc2 is regarded as true but not experimentally confirmed in all cases. Thus ∆E =Ac2 ∆m can be discussed in such cases [37]. All these aspects are discussed in the forthcoming chapters.

6.0 General Discussion Einstein’s mass energy equation is the most celebrated equation in theoretical and experimental physics. Its inception and derivation is critically discussed in unbiased way. However there are many more aspects which are to be discussed complete understanding of the equation. These aspects are different from its conception, derivation and development.

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6.1 Work of predecessors It is pertinent to mention that Einstein did not acknowledge work of his predecessors implying that all work is done by him. But the basics of Special Theory Relativity i.e. postulate of relativity existed before Einstein in one form or other. Similar is situation of relativistic variation of mass, time dilation and length contraction etc. The equation for relativistic variation of mass was given by Lorentz [38-39] in 1889 and 1904. The time dilation was given by Larmor[40] in 1897. The length contraction was given physicist George Francis FitzGerald [41] to explain negative results of Michelson Morely experiment in 1889. The length contraction and time dilation also follows from the Lorentz Transformations. So these phenomena existed before Einstein. So Einstein simply edited all existing laws judiciously in an article but did not discover, invent or theorize them. If someone rewrites Newton’s laws and publishes in journal or book without mentioning name of Newton, then it does not mean author gets credit of the innovation of the legend. Under the perceived condition Newton cannot be deprived of the credit, if so then numerous Newtons will be there. Purposely Einstein did not give any reference in his paper of already existing concepts, indicating that nothing existed before and all is his original contribution. Also these facts were not pointed out by Editor the German journal Annalen der Physik. If the paper was sent by Editor to an expert for review, the same was also neglected by expert. Or other possibility is that paper was published by Editor as Einstein sent it without analysis. It is anyone’s guess , if the 1905 record of the journal exists then mystery will be clear. However at that time in the same journal authors gave references of the existing work. Albert Einstein has given references his own works in his papers, one specific example is of the paper which he published in Annalen der Physik [42]. Einstein has given references of work of J Stark. It is evident that Einstein was aware of existing facts in scientific literature but did not acknowledge the contributing scientists. The main aspects as discussed by Einstein in papers existed already in the literature e.g. (i) Postulate of Relativity ( inventor Italian Galileo Galilee in 1638, in book, Two New Sciences discussion between Simplicio and Salviati ), Galileo postulated his relativity hypothesis:

any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments

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The first postulate of relativity as stated by Einstein in his June paper ( known as theory of Relativity)

The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.

(ii) Constancy of speed of light (French Henry Poincare in 1898 ),

The first postulate of relativity as stated by Einstein in his June paper ( known as theory of Relativity)

Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

(iii) Relativistic variation of mass (British J.J Thomson, 1881, German Walter Kauffmann 1903, Max German Abraham 1904), (iv)Time Dilation (Irish Joseph Larmor, 1897, Dutch Henri Antoon Lorentz, 1892 ), (v) Length Contraction ( Irish George FitzGerald, 1889, Dutch Henri Antoon Lorentz, 1892) existed earlier. But in June 1905 paper Einstein quoted these without references, as he is original inventor of the concepts. Also Editor and reviewer of the journal should have corrected the facts, it appears paper was not refereed before publication.

6.2 Einstein and Priority in Science

Einstein [43] 1himself acknowledged Poincaré’s work [10,11] and in other cases refused to acknowledge any other priority. Here by word priority we mean that who is the first scientist to present the scientific concept? Einstein [44] purposely wrote an article titled

“On the Inertia of Energy Required by the Relativity Principle" and justified his approach and claim.

Planck and Stark were convinced that Einstein’s derivation of E = mc2 is inconsistent; Johanne Stark [45] stated that Planck gave first complete and correct derivation. However, Planck’s derivation pertains to conversion of heat energy and mass only, and Einstein’s derivation originally pertains to light energy and mass. Initially Einstein in 1905 derived equation for light energy-mass inter-conversion i.e. L = mc2 then speculated

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from it E = mc2 analogously. Similarly in 1906 Max Planck derived equation for heat energy –mass inter-conversion, can also be generalized as E = mc2.

In Einstein’s time E = mc2 may be regarded as existing as speculated by De Pretto in 1903 and 1904 precisely same form. Similarly when Planck derived equation for heat energy – mass inter-conversion equation, Einstein had earlier derived L = mc2 mathematically. Thus, both Einstein and Planck have nearly similar situation.

Einstein derived E = mc2 in 1905, which was existing at that time earlier suggested by De Pretto in 1903-04. Einstein may or may not be knowing about the existing work, it is anybody’s guess now. As there is similarity, there is also drastic difference between the legends. Planck [46] in 1907 acknowledged the existing work of Einstein but Einstein did not acknowledge work of De Pretto, which was published in 1903-04 (just a year before Einstein’s work), and F. Hasenöhrl [15, 16] in 1904.

When Johanne Stark [45] maintained that credit for first complete and correct derivation must go to Max Planck; then Einstein [47] wrote Stark on 17 Feb 1908.

“I was rather disturbed that you do not acknowledge my priority with regard to the connection between inertial mass and energy.” Max Born (1882-1970) in his book Physics in my Generations, co-originator of Quantum Mechanics stated [48] "The striking point is that it contains not a single reference to the previous literature.” Therefore, Born’s remarks confirm beyond any doubt that Einstein should have given existing references in the papers. Einstein’s unreferenced paper is the main reason that some scientists want the logical discussion of on the topic, which is absolutely right. There is unanimity in the scientific community that genuine innovator must be given credit. It is better late than never.

Similar is the problem with Einstein’s unreferenced June 1905 paper which known as Special theory of Relativity. Some of the concepts discussed (e.g. postulate of relativity and postulate of constancy of light, relativistic variation of mass, length contraction and time dilation etc.) were already existing.

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6.3 Einstein’s Unreferenced Papers It must be noted that Einstein’s June 1905 and September 1905 are unreferenced. i.e. no references are given which books, journals or documents were consulted in preparing the paper. The references are given by scientists normally at the end of paper that these books, journals, reports etc. are consulted during writing the article or paper. Nevertheless, Einstein’s above two papers do not carry any reference, which implies that all work (e.g. postulate of relativity and postulate of constancy of light, relativistic variation of mass, length contraction and time dilation etc.) is originally given by him i.e. the work did not exist at time of writing the article or paper. It is also the responsibility of Editor or referee of the journal or book to check this aspect. If such mandotary steps are not taken then that journal is not international or recognized. The some work, which Einstein quoted in his papers, existed before Einstein, and he did not mention about it in the papers. Editor and referee of article did not point it out apparently that existed earlier. If the paper was sent to referee then he did not appreciate the work of existing scientists. One can only guess the reasons. There are mainly two reasons e.g. either editor published the paper as Einstein sent it or referee was not aware of the recent developments on the topic.

Some scientists working in the field strongly believe that Einstein should have given references of the existing work, and as Einstein has used the existing concepts (e.g. postulate of relativity and postulate of constancy of light, relativistic variation of mass, length contraction and time dilation etc.). This thought is gaining momentum gradually. In today’s context, we cannot perceive a scientific article without references; Editors and referees cross check the same. Thus in an unbiased manner Einstein alone should not be held completely responsible for publishing the unreferenced papers.

This topic is discussed by many scientists including Bartocci [13] and Bjerknes [14], and has blamed Einstein for plagiarism. Bjerknes even wrote a book , Albert Einstein The Plagiarist of the Century, however Einstein has been called Person of the Century by Time Magazine. Poincaré wrote 30 books and over 500 papers on philosophy, mathematics and physics. Einstein wrote on mathematics, physics and philosophy, but claimed he'd never read Poincaré's contributions to physics. Yet many of Poincaré's ideas - for example, that the speed of light is a limit and that mass increases with speed - wound up in Einstein's paper, "On the Electrodynamics of Moving Bodies" without being credited. Thus, plagiarism in view of Einstein’s work was also discussed

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after publication of September 1905 paper. Nevertheless, this discussion continued only for short time as at that moment the significance of E = mc2 was not transparent. Therefore, it remained confined to Planck, Stark and Einstein only. Einstein’s paper was published in German language but it was discussed only German speaking scientists Max Planck and Johanne Stark. Had it been published in English then it would have caught attention of other scientists as well. The paper was published in English in the book The Principle of Relativity, published in 1923 , it was translated by W. Perrett and G.B. Jeffery. In the discussion, even Einstein [42] accepted that he had used some existing concepts. So by his own admissions Einstein was aware of the existing scientific concepts, so he would have acknowledged the original inventors are sources. As Einstein did not do so, it is duty of every one to give due credit to original inventors. It is also true in Newton’s context. Newton has given three laws of motion in the master piece The Principia. The first and third laws of motion as we teach now are same as given by Newton but the second law of motion is not the same as given by Newton. Who gave second law of motion and gifted it to Newton. Still scientific community is not unanimous about it. Apparently unanimity is on the issue don’t raise this issue. Anyhow by comparison is very interesting results are obtained: Newton was given the credit for second law of motion i.e. F=ma which he did not discover. And on the other hand Einstein took the credit for the phenomena which he did not discover. What is the truth? Both the issues need to be dealt in unbiased way. In his lifetime Newton did not know that credit of discovery of F=ma was given him. But knowingly Einstein proceeded in such a way that credit of other’s work was received by him. Further Einstein defended was right. This is difference between two legends. Science is lighting one lamp from the other.

However, these critics do not suggest in concrete way to whom credit of discovery of E = mc2 be given i.e. to Preston or De Pretto or F. Hasenöhrl. On the basis of this discussion and unbiased interpretation it is undoubtedly true that Einstein was the first who derived light energy mass equation L = mc2 in specific derivation under special conditions. Then Einstein speculated from E = mc2 from L = mc2 on analogous basis. Until all issues are not specifically and quantitatively addressed, the discussion will remain inconclusive. Einstein [49] in 1907 spelled out his views on plagiarism:

"It appears to me that it is the nature of the business that what follows has already been partly solved by other authors. Despite that fact, since the issues of concern are here addressed from a new point of view, I am entitled to leave out a thoroughly pedantic survey of the

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literature..." Thus Einstein admitted that existing concepts were partly solved by others. Thus knowingly he avoided giving references to their work, so deprived others their due credit. By not giving references to the existing facts, Einstein simply pretended the scientific community that all is his work and none of the scientists existed who has given the ideas quoted by him. How and why Einstein neglected the scientific existence of great Galileo’s observation of principle of relativity, and simply changing the words published the same as first postulate of relativity. Einstein can be easily contradicted here. Einstein has commented that

“I am entitled to leave out a thoroughly pedantic survey of the literature..." The work of De Pretto in 1903-1904 and that of F. Hasenöhrl in 1904-1905 cannot be called pedantic (obscure, sophistic, hair-splitting etc). This work is done nearly at the time of Einstein. Therefore, this work cannot be called obscure, as Einstein has pointed out.

The definition of "to plagiarize" from an unimpeachable source, Webster's New International Dictionary of the English Language [50].

"To steal or purloin and pass off as one's own (the ideas, words, artistic productions, etc. of one another); to use without due credit the ideas, expressions or productions of another.” In addition, Einstein quoted that,

‘what follows has already been partly solved by other authors’. Thus Einstein has admitted that this work was partly done by others i.e. idea of mass energy inter-conversion, postulates of theory of relativity, relativistic variation of mass, length contractions and time dilation existed in the scientific literature and he interpreted the same. Now it can be seen that what is Einstein’s new explanation or interpretation about this? In Einstein’s own admissions work was partly solved by others, then why references were not given? That is why Einstein came under the clouds of plagiarism .

In addition, in science, pre-search, search, research and post search are continuous processes.

7.0 Conclusions. 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,

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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.

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