Einstein s Derivation of E= mc 2 also Predicts E mc 2

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1 Journal of Vetorial Relativity JVR 4 (009) 1-8 Einstein s Derivation of E= m also Predits m A Sharma 1 ABSTRACT. effet on Web has reported variations in fine struture onstant (hene in speed of light) and have diret. Depending upon reent WMAP data, Erikek has suggested that time ould exist before big bang and universe may have reated from empty spae. These aspet is also investigated in view of Einstein s Sep paper whih is origin of light energy-mass inter onversion equation and interesting results are obtained. Now it follows that s only true under speial onditions (from, is speulated) i.e. in general ases ( ) also follows. Thus an alternate equation has been suggested, whih implies that energy emitted on annihilation of mass (or vie versa) an be equal, less and more than predited by. However, E = m L = m E = m E = m L = m L m L = m is yet unonfirmed in the most abundant hemial reations. The total kineti energy U 35 Pu 39 of fission fragments of or is found experimentally 0-60 MeV less than Q-value predited by m, it is explainable with with value of A less than one. Energy emitted by Gamma E m E = m Ray Bursts (most energeti event after Big Bang) in duration s, is J, an be explained with help of. The mass of partile Ds (317) disovered at SLAC, have mass lower than urrent estimates; it an be explained with value of A more than one., is apable of explaining the 55 formation of primitive atom (10 kg ) in state of singularity from dwindling amount of energy (10-50 J or less) i.e. expeptionally- small and A is J or less. This pereption implies gravitational energy is another form of mass (like other energies) and has been originated simultaneously with mass. E = m KEYWORDS: Mass, Energy Inter-onversion,,, m I. INTRODUCTION The word energy derives from energeia whih was oined by Aristotle for first time [1]. Leibniz [ ] put forth idea of vis viva (from the latin living fore) as mv (m as mass and v veloity of body) and stated that it is onserved [-3]. In 1807, Thomas Young [ ] was first to use term 1 Member of the Fundamental Physis Soiety. His Mery Enlave Post Box 107 GPO Shimla India. June, ajay.sharmaa@rediffmail.om

2 A Sharma: Einstein s derivation of E= m, also predits m June, 009 energy instead of vis viva [4-5]. Gustave Coriolis [ ] was first to define work as produt of fore and distane; in 189 he desribed kineti energy as M rest v [4-5]. Further mass is quantity of matter ontained in the body, the real understanding of mass started when Newton defined seond law of motion in the Prinipia. [6]. Newton also stated inter onversion of light energy to mass [7], thus initiated important debate on this issue. Mass energy inter-onversion proesses are the oldest in nature and onstitute the basis of various phenomena. Further the energies have various forms (e.g. sound energy, heat energy, hemial energy, energy emitted volani reations nulear energy, magneti energy, eletrial energy, energy emitted in form of invisible radiations, energy emitted in osmologial and astrophysial phenomena energies o-existing in various forms et.) whih are onverted into mass. At different times various sientists have studied this signifiant topi in different ways and study is ontinuous proess. Aristotle [384-3 BC] believed that all matter on earth onsisted of four pure substanes or elements, whih were earth, air, fire, and water [1]. Here fire may be regarded as energy. Antoine Lavoisier ( ) Frenh Chemist was the first to formulate a law of onservation of matter in hemial reations i.e. matter an neither be reated nor be destroyed but an be transformed from one to other form [8]. Newton [7] has quoted in his book Optiks in 1704 that "Gross bodies and light are onvertible into one another...", It implies that energy is other form of mass. Neither Lavoisier nor Newton gave any mathematial equation relating to mass and energy, hene the dedution is qualitative only. S. Tolver Preston [9] proposed that a vast amount of energy an be produed from matter in his book (now rare book) Physis of the Ether in Preston determined that one grain (one grain = grams) ould lift a 100,000-ton objet up to a height of 1.9 miles. This dedution yields E m. Jules Henri Poinaré [10,11] in 1900 applied the alulations in a reoil proess and reahed at the E E onlusion in the form, mv = From the viewpoint of dimensional analysis, takes on the role of a mass assoiated with radiation, whih yields E = m. Olinto De Pretto [1] speulated E = m viva) beomes E = m, in implying that when v =, then E = mv. (Leibniz s vis JVR 4 (009) 1-8 Journal of Vetorial Relativity

3 A Sharma: Einstein s derivation of E= m, also predits m June, 009 Fritz Hasenohrl [13, 14] in 1904, onluded to the mehanial mass of our system must be added 8E an apparent mass whih is given by, m = 3 where E is the energy of the radiation. In a later 4E paper he further improved result that mass exhanged is, m = Thus in this ase also 3 Ebenezer Cunningham [15] has further improved Hasenohrl s equation as E = m. E m Frederik Soddi [16] and M. Henri Bequerel both have predited that in radioative emissions the mass of body dereases i.e. energy of radiations is at the ost of mass. Thus higher the derease in mass more would be energy of radiation and no onversion fator was given, this inferene is like above one. It also orresponds to E m or E m. Einstein [17] derived under ertain onditions the onversion fator for mass and light energy is preisely equal to. This pereption of light energy mass inter onversion was given by Newton. Then Einstein generalized onversion fator for every energy in speulative way. Einstein [17] pereived that let there be a luminous body at rest in o-ordinate system (x, y, z). The system (ξ, η, ζ ) is in uniform parallel translation w.r.t. system (x, y, z); and origin of system (ξ, η, ζ ) moves along x-axis with relative veloity v. Let a system of plane light waves have energy l relative to system (x, y, z), the ray diretion makes angle φ with x-axis of the system (ξ, η, ζ ). The quantity of light measured in system [ξ, η, ζ] has the energy [17-18]. l v 1 osφ = l v 1 (1) Einstein has given eq. (1) in his paper known as Speial Theory of Relativity [18] and alled eq. (1) as Doppler priniple for any veloities whatever. Let and H are energies in oordinate system (x, y, z) and system (ξ, η, ζ ) before emission of E 0 0 light energy, further and H are the energies of body in the both systems after it emits light E1 1 energy. Thus Einstein wrote various equations as Energy of body in system (x, y, z) E 0 = E L +.5L = 0 1 Energy of body in system (ξ, η, ζ ) E + L () JVR 4 (009) 1-8 Journal of Vetorial Relativity 3

4 A Sharma: Einstein s derivation of E= m, also predits m June, 009 v v H 0 = H β L 1 osφ + 1+ osφ where 0 β = 1 v 1 H = H + β L (4) 1 Or, ( H 0 E 0 ) ( E ) = L [ β 1] (5) H 1 1 Einstein alulated, kineti energy of body before emission of light energy, K 0 ( M v energy of body after emission of light energy, K ( a ) as (3) M b v ) and kineti 1 K 0 K = L 1 v 1 Einstein onsidered the veloity in lassial region thus applying binomial theorem, K 0 K = L 4 v v Further Einstein quoted [18] (6) (7) Negleting magnitudes of fourth and higher orders, we may plae. v K 0 K = L 8) M b v M v a v = L (9) or L = ( M ) = m (10) a M b L or Mass of body after emission ( M a ) = Mass of body before emission ( M b ). Now replaing L (light energy) by E (total energy or every energy) Einstein wrote: or E = ( M ) = m (11) a M b E or Mass of body after emission ( M a ) = Mass of body before emission ( M b ) JVR 4 (009) 1-8 Journal of Vetorial Relativity 4

5 A Sharma: Einstein s derivation of E= m, also predits m June, 009 Thus Einstein derived that onversion fator between mass and light energy is preisely equal to, this aspet is elaborated by Fadner [19]. But Einstein s this derivation has been ritially disussed by many suh a Plank [0], Stark [1 ], Ives [], Stanhel [3], Okun [4] and N. Hamdan [5] et. At the same time in some referenes [6-7] it is expressed that Einstein has taken hints to derive equation E = m and from existing literature without aknowledging the work of preeding sientists in some of his papers [9-30]. Max Born [8] has expressed that Einstein should have given referenes of existing literature like other sientists as Plank [0, 9-30] mentioned Einstein s work. Max Plank [9-30] in 1907 made an in-depth investigation of the energy "onfined" within a body, E but he did not use Einstein s approah at all. Plank derived an expression m M =, for heat energy and mass and interpreted that The inertia mass of body is altered by absorption or emission of heat energy. The inrements of mass of body are equal to heat energy divided by square of speed of light. Plank aknowledged Einstein s previous derivation but did not agree with orretness of Einstein s derivation. Ezzat Bakhoum [31-3] has proposed that a total energy equation that satisfies the Compton-de Broglie wave mehanis as well as theory of speial relativity is H = mv (1) where H is total energy of partile, H = mv (or widely regarded as is its mass and v is veloity. Bakhoum has put forth that ) annot do so simultaneously. The pereption is applied to explain various phenomena. Thus again the onversion fator between mass and energy is other than E m is suggested. Hene, m E = m The similar ideas have also expressed by Hamdan [5] and Olinto De Pretto [1] has also suggested: E = m from E = mv. II. THE CONVERSION FACTOR BETWEEN MASS-ENERGY OTHER THAN C IS ALSO SUPPORTED BY SPECIAL CONDITIONS USED IN EINSTEIN S DERIVATION. As already mentioned Einstein s Sep derivation of L = m is true under speial onditions only, this aspet is studied ritially with details by the author [33-45] disussing those aspets whih JVR 4 (009) 1-8 Journal of Vetorial Relativity 5

6 A Sharma: Einstein s derivation of E= m, also predits m June, 009 have not been raised earlier. It automatially implies that onversion fator between mass and energy is under those onditions only. Thus the onversion fator other than is possible, under those onditions whih are not taken in aount in Einstein s Sep derivation. Thus the value of onversion fator other than is also supported from Einstein s derivation. Einstein s derivation [17-18] is only for light energy mass inter-onversion, as Einstein has onsidered only light energy in the derivation. In the derivation of (a) Number of waves emitted, (b) l magnitude of light energy, L = m () Angle φ at whih light energy is emitted and (d) Uniform veloity, v there are FOUR variables e.g.: Einstein has taken speial values of parameters and in general for omplete analysis the derivation an be repeated with all possible values of parameters taking in aount the momentum onservation (whih is disussed in next sub-setion). (A) The body an emit large number of light waves but Einstein has taken only TWO light waves emitted by luminous body. (B) The light waves emitted may have different magnitudes but Einstein has taken EQUAL magnitudes. (C) Body may emit large number of light waves of different magnitudes of energy making DIFFERENT ANGLES (other than 0º and 180º ) assumed by Einstein. (D) Einstein has taken veloity in lassial region ( v << and applied binomial theorem) has not at all used veloity in relativisti region. If veloity is regarded as in relativisti region (v is omparable with ), then equation for relativisti variation of mass with veloity i.e. M rel = M rest v 1 is taken in aount. It must be noted that before Einstein s work this equation was given by Lorentz [46-47] and firstly onfirmed by Kaufman [48] and afterwards more onviningly by Buherer [49]. Einstein on June 19, 1948 wrote a letter to Linoln Barnett [50] and advoated abandoning relativisti mass and suggested that is better to use the expression for the momentum and energy of a body in motion, instead of relativisti mass. JVR 4 (009) 1-8 Journal of Vetorial Relativity 6

7 A Sharma: Einstein s derivation of E= m, also predits m June, 009 It is strange suggestion as Einstein has used relativisti mass in his work inluding in the expression of relativisti kineti energy [18] from whih rest mass energy is derived [51-53]. (E) In addition Einstein has assumed that body remains at rest before and after emission of light energy. But the body may be at rest i.e. v = 0, veloity may be in lassial region and veloity may be in relativisti region ( v = ), the law of inter-onversion of mass and energy holds good under all onditions. In eletron-positron annihilation, the material partiles are in motion before and after annihilation. In materialization of energy, a gamma ray photon is onverted to eletron positron pair, whih moves in opposite diretions to onserve momentum. Whereas in annihilation of mass, eletron-positron pair ombine to form a gamma ray. In nulear fission and fusion partiles remain in motion in the proess of mass energy inter onversion. The thermal neutron whih auses fission has veloity 185m/s. The law or phenomena of inter-onversion of mass and energy holds good in all ases for all bodies and energies under all onditions. But Einstein has taken speial values of parameters under speial onditions to derive equation L = m i.e. to onfirm that onversion fator between mass and energy is. II.1 L m GENERAL CONDITIONS. IS MATHEMATICALLY CONSISTENT IN EINSTEIN S DERIVATION, UNDER In Einstein s derivation onversion fator between mass and energy is preisely equal to and the derivation utilizes only speial values of the involved variables. It itself implies that onversion fator is preisely equal under speial onditions otherwise its value will vary. The value of onversion fator other than an be easily justified mathematially in Einstein s derivation [33-45]. This aspet is not touhed by the preeding authors [19-3]. (a) In Einstein s derivation if one wave is regarded as to form angle 0.5º rather than 0º then: v v H 0 = H βl 1 os os180 or v H 0 = H 1 + βl or v v K0 K = L + L (13) JVR 4 (009) 1-8 Journal of Vetorial Relativity 7

8 A Sharma: Einstein s derivation of E= m, also predits m June, 009 m = ( M b M a ) = If v is 10m/s, then L L + v (14) m L = 1141 = m (15) L m Further, applying (14) M a ( mass after emission of light energy) = L L + v Aording to Einstein if body emits two light waves of energy 0.5 L eah in opposite diretions then derease in mass is given by eq. (10) i.e. L m = M b and in this ase derease in mass is L L ( v ) thus there is no definite value of derease in mass in Einstein s derivation. In this ase derease in mass is more than as predited by Einstein, hene again the onversion fator other than is onfirmed i.e. L m. Like this there are many examples of this type. (b) The entral equation in Einstein s derivation is eq. (1) and binomial theorem is equally appliable to it at any stage i.e. in the beginning or end. Einstein applied binomial theorem in the end and obtained L = m, but the same equation is not obtained if binomial theorem is applied in the beginning. The binomial theorem is simply a mathematial tool and its appliation at any stage should not affet results i.e. make or mar equation L = m The reason is that typial nature of derivation and eq. (1) is different from other relativisti equations. The energy is salar quantity and independent of diretion but eq. (1) diretional in nature due to angle φ. In ontrast if binomial theorem is applied to Relativisti Kineti Energy in the beginning or at the end then result is same i.e. M v lassial form of kineti energy rest. So there is inonsisteny in appliations. Applying binomial theorem to eq. (1) and repeating the alulations as Einstein did, altogether different results are obtained. v v l = l 1 osφ (1+ 3v ) (16) JVR 4 (009) 1-8 Journal of Vetorial Relativity 8

9 A Sharma: Einstein s derivation of E= m, also predits m June, 009 v v Here <<1, hene l v = l 1 osφ Or, ( H 0 E 0 ) ( H 1 E1 ) = 0 Or K K = 0 a M b v M a v = 0 a and higher terms an be negleted. Thus, Or Mass of body before emission ( M ) = Mass of body after emission ( M ) (17) b a Thus light energy is being emitted, but under this ondition Einstein s this derivation does not provide any relationship (equality or proportionality) between mass annihilated and energy reated. Similar is the situation if veloity v = 0. Hene Einstein s derivation gives derease in mass of body equal to L only under ertain onditions. Thus in all onditions this derivation is not valid. () Let the body emits two light waves of slightly different energies i.e L and L in opposite diretions and other parameters remain the same as assumed by Einstein. In this ase H = H βl 0 1 v v 1 os β L 1 os180 Now proeeding in the same way as Einstein did v v K 0 K = L + L L L Or, = Mass before emission ( M b ) Mass after emission ( M a ) = v or M a = or m L = v L L v + M b L = m [ ] (1) L m (18) (19) (0) JVR 4 (009) 1-8 Journal of Vetorial Relativity 9

10 A Sharma: Einstein s derivation of E= m, also predits m June, 009 Thus eq. (1) means that emitted light energy is proportional to m. It must be noted that neither Newton nor Lavoisier has given any onversion fator between mass and energy. Similar is the approah of Frederik Soddi [16] and M. Henri Bequerel. S. Tolver Preston [9] and Fritz Hasenohrl [13, 14] have given the mass energy inter onversion equation in form of m. (d) Energy emitted in various reations. In Sep paper Einstein derived eq. (10) i.e. L = m and then replaed L by E (total energy) and speulated = m. In eq. (11), = m, E stands for all possible energies of the universe e.g (i) sound energy, (ii) heat energy, (iii) hemial energy, (iv) nulear energy, (v) magneti energy, (vi) eletrial energy, (vii) energy emitted in form of invisible radiations, (viii) energy emitted in osmologial and astrophysial phenomena (xi) energy emitted volani reations (x) energies o-existing in various forms et. et. Now eq. (1) i.e.: l v 1 osφ = l v 1 is put forth for light energy by Einstein in June 1905 paper (as L is light energy, L is light energy in moving frame), it is not meant for other possible energies as quoted above. Einstein never justified eq. (1) for the energies ited above. The parameters used in Einstein s equation are not defined for all energies. Thus by this derivation onditions for light energy only and replaing L = m is derived under speial L by E in eq. (10) it is not enough for being justified. There are evidenes that Einstein worked hurriedly in other ase also e.g. in theory of stati universe the introdution of osmologial onstant proved to be inorret and Einstein aepted the mistake later as quoted by Gamow [54]. It is also justified from the following examples. The various results are shown in Table I. II. CONSERVATION OF MOMENTUM IN GENERAL CASES. The momentum is onserved irrespetive of the fat that body remains at rest or reoils after emission of light energy [55]. Law of onservation of momentum an be used to alulate the veloity JVR 4 (009) 1-8 Journal of Vetorial Relativity 10

11 A Sharma: Einstein s derivation of E= m, also predits m June, 009 of reoil in this ase also. Let the body of mass 10 kg emits in two waves in visible region of wave length 5000ºA, it orresponds to h λ or J, and the energy is divided in two waves. Let body emits light energy (towards the observer, φ= 0º) L i.e. E 1= J () and momentum p 1 = E 1 = kg m/s (3) Seondly, the body emits light wave of energy (away from the observer, φ= 180º) L i.e.: E = J and momentum p = E = kg m/s. Let us assume that when the body emits light waves of energy and reoils (if it atually does) with veloity V then aording to law of onservation of momentum we get: r r [ p ] p1 M b 0 = p1 + p + M bvr or V = = m/s (4) Thus onservation of momentum requires that body should move with veloity m/s opposite to observer. With this veloity the body will reoil for distane equal to m, in one billion year, whih is undetetable by all means hene oneptually body an be regarded as at rest. Thus equations for reoil momentum and reoil kineti energy will be KE reoil P reoil = kg m/s (5) KE reoil = J (6) Thus body will tend to move with veloity m/s ( away from the observer) whih is immeasurably small by all means, hene the body remains at rest. Due to this uniform relative veloity v of the system (ξ, η, ζ ) will not hange, however effet of V an be onsidered for ompleteness. If body reoils after emission with veloity away from the observer, then relative veloity will be v +V r. Einstein s alulations are based upon lassial onditions of veloity, as binomial theorem is applied i.e. v <<. Thus in this ase eq. (1) beomes V r r JVR 4 (009) 1-8 Journal of Vetorial Relativity 11

12 A Sharma: Einstein s derivation of E= m, also predits m June, 009 l [ v V ] + 1 = l 1 r [ v + V ] osφ The rest of the alulations remain the same, as in ase of Einstein derivation. Thus Einstein s derivation is also valid if the body moves, but Einstein has onsidered the speial ase when veloity Vr is zero ( v + V = v ). Also experimentally the law of inter onversion of mass energy holds good in r all possible ases hene this ase is investigated. Thus the eq. (19) beome: 0.000[ v + Vr ] K 0 K = m Or L = L v + + [ ] 1 V r [ v + V ] r + L Thus whether we take in aount the reoil veloity or not the result is the same, the reason is that magnitude of V r is too small i.e m/s. (7) (8) (9) III. EXPERIMENTAL FEASIBILITY WITH CONVERSION FACTORS OTHER THAN (a) Dira [56] was one of the first physiists to suggest that, in onnetion with his theory of large numbers, fundamental dimensional onstants may vary in time during the expansion of the universe. The idea of variation of speed of light is suggested in various osmologial models [57-58] and has been the subjet of attention by physiists in investigations of extra dimensions, strings and branes [59]. Web [60] has reported variations in fine struture onstant over osmologial time sales and hene variations in. This suggestion implies that m. (b) Einstein has derived to L = m (onversion fator between mass and energy is preisely equal ) under the extremely speial or ideal onditions, whih are even diffiult to attain pratially. But the law of inter-onversion of mass and energy holds good under all onditions, not only for the onditions Einstein has derived eq. (10). Obviously if the onditions are not satisfied (i.e. under JVR 4 (009) 1-8 Journal of Vetorial Relativity 1

13 A Sharma: Einstein s derivation of E= m, also predits m June, 009 general onditions) then onversion fators may differ from. is only justified as in eq. (10) under speial onditions. Theoretially onversion fator has been studied for those ases whih are elusive to Einstein s derivation [33-45] in this setion, in all ases it is not. Like wise there are numerous elusive experimental ases whih need to be disussed in light of above findings, as researh is ontinuous proess. The work of sientists before Einstein also justifies m. This disussion does not onfront with existing experimental situation but addresses those theoretial and experimental issues for whih = m is not analyzed yet. The mass energy inter- onversion equation, with onversion fator equal to i.e. = m has been onfirmed in nulear physis and is also basis of nulear physis. Even elementary units of atomi mass (1amu) or and energy (ev) are based upon it. Thus it will remain standard in measurements as seven days a week, its validity in this regard is not doubted at all. The aim is to disuss experimentally those phenomena in whih is not applied yet. The mass energy onversion proesses are weird in nature and all have not been at all studied in view of = m. The onversion fator other than is disussed for suh elusive ases, not for those it is already onfirmed. Hene there is no onfrontation with the established experimental situation at all, but aim is to open a mathematial front ( L m phenomena in nature. This development an be disussed as below. = m ) for numerous experimentally unstudied (i) Unonfirmed Chemial Reations. When Einstein derived = m, hemial reations were the most abundant soures of energy in nature. Till date = m is not onfirmed in the hemial reation and the reason ited for this is that equipments are not enough sensitive [5, 61]. Consider burning of 1kg straw or paper or petrol in ontrolled way i.e. in suh a way that masses, ashes, gases and energy produed an be estimated. Even if kg or 1gm of matter is annihilated then energy equal to J (an drive a truk of mass 1000kg to distane of km) will be produed. Until the equation is not onfirmed in suh reations, then sientifially may not be regarded as preisely true in suh ases. It is equally possible that energy emitted may be less than predited by = m i.e. m is feasible, it is an open possibility unless ruled out. (ii) = m Less Effiieny in Nulear Physis Reations: The effiieny of the nulear weapons as well as nulear reators is far less than the theoretial value predited by = m. Robert Serber (member of first Amerian team entered Hiroshima and Nagasaki in September 1945 to assess JVR 4 (009) 1-8 Journal of Vetorial Relativity 13

14 A Sharma: Einstein s derivation of E= m, also predits m June, 009 loses), has indiated [6] that the effiieny of Little Boy weapon [ U 35, 49kg ] that was used against Hiroshima was about % only. It is assumed that all the atoms don t undergo fission, thus material is wasted. But no suh waste material is speifially measured quantitatively. Thus the waste material (nulear reator or weapon) must be measured and orresponding energy be alulated, and it must quantitatively explain that why effiieny is less. It may require the measurements of all types of energies (may o-exist in various forms) in the proesses and experimental errors. Until suh experiments are speifially onduted and = m is onfirmed, m is equally feasible. (iii) Less Energy: In laboratory it is onfirmed [63-64, 31] that using thermal neutrons the total kineti energy (TKE) of fission fragments that result from of U and Pu is 0-60MeV less than Q-value (00MeV) of reation predited by. This observation is nearly four deades old. Bakhoum has explained it on the basis of equation H = mv (energy emitted is less than = m (iv) ). Hene here m is justified. = m Less Mass: Palano [65] has onfirmed that mass of partile Ds (317) has been found less than urrent estimates based upon = m. Thus in this ase m is justified. (v) Binding and Mass Defet in Deuteron: There are two inherent observations [33,37-38] about nuleus: firstly, masses of nuleons are fundamental onstants, i.e. they are the same universally (inside and outside the nuleus in all ases); and seondly nulei possess Binding Energy (BE = m ) owing to a mass defet. To explain these observations, in the ase of the deuteron (BE =.44 MeV), the mass defet of nuleons must be amu or about % of the mass of nuleons, i.e., nuleons must be lighter in the nuleus. This is not experimentally justified, as masses of nuleons are universal onstants. Thus observations and preditions based upon not justified, hene (vi) m is equally feasible. Formation of Primeval Atom in Cosmologial Phenomena: The most suessful theory of understanding of formation of universe, the Big Bang theory ( the biggest energy releasing proess universe) assumes that whole mass of universe (10 55 kg ) was in form of primeval atom (in singular state) and then suddenly exploded [66]. Aording to = m = m are this would have been reated from energy J, but how this enormous amount of energy was reated in spae out of nothing. Thus one query leads to another query. Hene reation of mass or energy in formation of primeval atom is not onsistent with = m. Hene proportionality m may be onsidered. JVR 4 (009) 1-8 Journal of Vetorial Relativity 14

15 A Sharma: Einstein s derivation of E= m, also predits m June, 009 The harateristi onditions of eletron-positrons annihilation proess [5] are different from hemial reations (nuleus remains unaffeted e.g. burning of wood), and those of hemial reations are different from astrophysial or osmologial reations. The energy emitted in Gamma Rays Bursts is of the order of J even in a fration of seond; these are different from hemial reations. Thus in all reations (vii) E = m needs to be speifially onfirmed. Annihilation of Antimatter in Hadron Epoh: After time seonds of big bang, in the Universe roughly equal amounts of matter and antimatter were reated. Now the observable mass of universe is regarded as kg. But so far, no antimatter domains have been deteted in spae within 0 megaparses of the Earth [67]. The antimatter has been annihilated at 10-6 s, in the end of hadron epoh ( s, temperature, K) and temperature of the universe in next lepton epoh ( s) redued to temperature K. It leaves a tiklish situation whih has been overlooked, when huge amount of antimatter is instantly annihilated, then huge amount of energy aording to would have been reated further inreasing the temperature. But temperature of universe dereased simultaneously, whih implies no heat has been generated on annihilation of anti-matter pratially. Thus the feasibility of m III.1 Until an be onsidered in this ase. MATHEMATICAL FORM OF EXTENDED EQUATION = m is not preisely onfirmed experimentally in ALL CASES, it is equally feasible to assume that the energy emitted may be less than = m ( or m ). It does not have any effet on those ases where = m = m = m is onfirmed, it simply sientifially stresses onfirmation of in all ases. Also when reatants are in bulk amount and various types of energies are simultaneously emitted and energies may o-exist. Thus both the possibilities are equally probable until one is not speifially ruled out. In view of weirdness in reations emitting energy in universe, some theoretial inonsistenies in the derivation and non-availability of data, one an explore the seond possibility even as a postulate. All the equations in siene are regarded as onfirmed when speifially justified in all experiments time and again. The reations involving inter-onversion of mass and energy are utmost diverse, weird and new phenomena are being added regularly, thus = m needs to be onfirmed in all ases. Thus in general, in view of above proportionality it may be taken in aount as [33-45] deα. dm JVR 4 (009) 1-8 Journal of Vetorial Relativity 15

16 A Sharma: Einstein s derivation of E= m, also predits m June, 009 The above proportionality deα. dm an be hanged into equation by introduing a onstant of proportionality. The ineption of proportionality onstant is onsistent with enturies old pereption of onstant of proportionality in physis sine days of Aristotle and Newton. In seond law of motion ( F = k. ma ) the value of onstant of proportionality, k is always unity (like universal onstant) i.e. F = ma. When more and more omplex phenomena were studied or values of onstants of proportionality were determined then it showed dependene on the inherent harateristis of the phenomena. In ase onstant of proportionality varies from one situation to other then it is known as o-effiient of proportionality e.g. o-effiient of thermal ondutivity or visosity et. Thus removing the proportionality between de and dm, we get: de = A dm (30) where A is a oeffiient used to remove that sign of proportionality; it depends upon inherent harateristis of the proesses in whih onversion of mass to energy takes plae and it is dimensionless. It has nature preisely like Hubble s onstant {50 and 80 kilometers per seond- Megaparse (Mp)} or oeffiient of visosity ( poise to poise) or o-effiient of thermal ondutivity (0.0Wm -1 K -1 to 400 Wm -1 K -1 ) et. Thus, in fat Hubble s onstant may be regarded Hubble s variable onstant or Hubble s oeffiient, as it varies from one heavenly body to other. If A is equal to one, then we will get de = dm i.e. same as Einstein s equation. In eq. (30) A is regarded as onversion fator as it desribes feasibility and extent of onversion of mass into energy. For example out of bulk mass, the mass annihilated to energy is maximum in matter-antimatter annihilation, apparently least in hemial reations, undetermined in volani reations and osmologial reations. It (the o-effiient A ) depends upon the harateristi onditions of a partiular proess. It may be onstant for a partiular proess and varies for the other depending upon involved parameters or experimental situation. Thus A annot be regarded as universal onstant, just like universal gravitational onstant G and in Newton s Seond Law of Motion. The reason is that mass energy inter-onversion are the bizarre proesses in nature and not ompletely studied. Now onsider the ase that when mass is onverted into energy. Let in some onversion proess mass dereases from M (initial mass) to M (final mass), orrespondingly energy inreases from i f k Ei (initial energy) to E f (final energy). The eq. (30) gives infinitesimally small amount of energy JVR 4 (009) 1-8 Journal of Vetorial Relativity 16

17 A Sharma: Einstein s derivation of E= m, also predits m June, 009 de reated on annihilation of mass dm. To get the net effet the eq. (30) an be integrated similarly Einstein has obtained the relativisti form of kineti energy in June 1905 paper [18] de = A dm Initial limit of mass = M i Initial limit of Energy = Final limit of mass = M Final limit of Energy = f Initially when mass of body is M, then E is the initial energy of the system. When mass (initial i i E i E f mass, M i ) is onverted into energy by any proess under suitable irumstanes the final mass of system redues to M. Consequently, the energy of system inreases to E the final energy. Thus f f M f and E f are the quantities after the onversion. Hene, eq. (30) beomes or E E = A [ M M ] (31) f i f i or (3) Energy evolved = A (derease in mass) (33) If the harateristi onditions of the proess permit then whole mass is onverted into energy i.e. after the reation no mass remains ( M f = 0) E = A (34) M i In this ase energy evolved is negative implies that energy is reated at the ost of annihilation of mass and the proess is exo-energeti in nature (energy is emitted whih may be in any form). Energy is salar quantity having magnitude only, thus no diretion is assoiated with it. Thus the generalized mass-energy equivalene may be stated as: The mass an be onverted into energy or vie-versa under some harateristi onditions of the proess, but onversion fator may or may not always be ( m /s ) or -. IV. APPLICATIONS OF GENERALIZED MASS ENERGY INTER CONVERSION EQUATION (i) It is already mentioned in setion(3.0) that if kg or 1gm of matter is annihilated then energy equal to J (an drive a truk of mass 1000 kg to distane of km) will be JVR 4 (009) 1-8 Journal of Vetorial Relativity 17

18 A Sharma: Einstein s derivation of E= m, also predits m June, 009 produed. Suh or similar preditions are not experimentally onfirmed and energy emitted an be found less than preditions Let the energy observed is J orresponding to mass annihilated 0.001kg, then value of A from A = will be 0.5 i.e. m = 16 3 Thus in this ase mass energy inter-onversion equation beomes = 0.5 m (ii) Let the TKE of fission fragments of U and Pu is 175MeV (as experimentally it is observed less), instead of expeted 00MeV. It an be explained with help of with value of A is equal to i.e. 175 A = = = (37) m 00 Thus energy of fission for fragments of U 35 and Pu 39 is given by = m (38) Thus value of A, less than one, is justified experimentally in this ase. (iii) The anomalous observation of exess mass of Ds(317) an be understood with help of, as mass of the observed partile is found less [65] than preditions of E = m. In this ase value of A will be more than one. For understanding onsider energy equal to 10 6 J is onverted into mass, then orresponding mass must be kg.we are onsidering the ase that mass is found more than this. Let the mass be kg. The value of A this ase is 0.99, as alulated from i.e. (35) (36) 6 10 A = = 0.99 (39) Thus in this mass energy inter onversion equation beomes = 0.99 m or m = 0.99 Thus orresponding to small energy more mass is emitted. (iv) is useful in explaining the binding energy (.44MeV or (40) -13 J), mass defet ( amu or amu) and universal equality of mass of nuleons ( m n = JVR 4 (009) 1-8 Journal of Vetorial Relativity 18

19 A Sharma: Einstein s derivation of E= m, also predits m June, amu, m = amu ). Obviously neutron and protons ontribute equally towards the p mass defet ( amu), then mass of neutron inside nuleus must be amu (mass outside nuleus i.e. in Free State is amu). Similarly orresponding mass of proton in the nuleus must be amu (mass of proton outside nuleus amu). But derease in mass of nuleons inside nuleus is not justified, as masses of nuleons are universally same [ 33, ]. Thus mass defet of deuteron must be infinitesimally small, only then masses of nuleons are same inside nuleus and outside nuleus. Also binding energy must be.44mev as experimentally observed. Both these experimentally onfirmed fats an be explained with help of. Let in this ase the mass defet is negligibly small i.e amu or kg. Then value of A (oeffiient of proportionality or mass energy inter onversion oeffiient) is i.e. for annihilation of infinitesimally small mass exeptionally large amount of energy is liberated. Thus, A = m = 10 (v) = m = (41) Webb [60] has reported results for time variability of the fine struture onstant or Sommerfeld fine struture onstant (α ) using absorption systems in the spetra of distant quasars. The variation in magnitude of alpha has been observed as: α α then α = α α now now = (43) Aording to CODATA urrently aepted value of alpha ( α now (4) ) is Hene from eq. (43), α = (44) then Now orresponding to the redued value of α ( α then = ) the speed of light an be determined from equation α then = e α then εh (45) as m/s ( where all terms have usual meanings ). Currently aepted value of speed of light 8 is m/s. JVR 4 (009) 1-8 Journal of Vetorial Relativity 19

20 A Sharma: Einstein s derivation of E= m, also predits m June, 009 To explain the energy emitted with this value of speed of light is the value A ( ) A = then = (46) Thus in this ase mass energy inter onversion equation beomes = m (47) (vi) The annihilation of antimatter (10 55 kg, as equal amount of matter and antimatter has been produed in the big bang) during hadron epoh ( s) and falling temperature ( K) an be explained with help of. Aording to E = m on annihilation of mass kg, in short time would result in huge amount of energy J i.e. on annihilation of mass kg, in short time would result in huge amount of energy J i.e. E = = J (48) Thus, the temperature of universe would have further risen. It an be explained if we assume that negligibly small amount of energy has been produed during hadron epoh, let this energy be only 1 J. Now the value of A must be i.e. 1 = A (49) Or A = (50) Thus, = m 7 (51) Hene antimatter is not observable as it is annihilated during hadron epoh without raising the temperature, hene no energy should be regarded as emitted during annihilation. Thus this pereption justifies big bang theory. (vii) Creation of Mass Before Big Bang. Erikek and olleagues [69] dedued on the basis of NASA s Wilkinson Mirowave Anisotropy Probe (WMAP) that existene of time is possible before Big Bang and universe may be reated from empty spae. Although mirowave bakground is mostly smooth but Cobe satellite disovered some flutuations. Erikek and olleagues believed that these flutuations ontain hints that out universe bubbled off from previous one. Exatly similar is the foundation of the existing pereption (how primeval atom was formed and exploded?), in view of generalized mass energy equation i.e.. Initially spae was reated and whole the spae was filled with infinitely large number of partiles of zero mass or undetetable by any means, may be termed as Zeroans. The Zeroans are the most JVR 4 (009) 1-8 Journal of Vetorial Relativity 0

21 A Sharma: Einstein s derivation of E= m, also predits m June, 009 primitive onstituents of the universe in spae, may be moving with infinitely large veloities. The numerous numbers of Zeroans moving with infinitely large veloities ated as the smallest possible (but just pereivable or imaginable) units of energy of nearly similar magnitudes. It is the postulatory assumption in this pereption, but now reent researh based upon data from WMAP supports it. These may have mass trillion-trillion times smaller than axioms, hypothetial partiles proposed by Peei [68 ], and are virtually isolated. Suh partiles are onstituents of dark matter. In due ourse of time infinitely large number of Zeroans resulted or ombined together to form pulse of energy, J or less (smallest permissible units of energy) i.e. exeptionally - small. It may be alled the primordial quantum of energy, whih is subdivided in numerous parts or pulses of energy in empty spae. As reation of universe the intriate proess, thus suh a low of amount of energy or mass is pereived. is appliable to all peuliar ases where mass-energy inter-onversion takes plae, as in this ase the onversion fator is not rigidly. Due to its general nature was appliable even in pre big bang era. Thus, the equation speifially predits that in this primordial era, diminishingly small pulse of energy, say J (or less), manifested itself in mass kg, in due ourse of time. Under this ondition the value of A uni an be determined as: A uni = m = = (5) These values are too peuliar, as the situation so and unaddressed. Now if the value of energy is J and value of A is J then mass an be alulated as uni m = m = 1 16 = kg (53) Thus, is the first equation whih at least theoretially predits that universe (10 55 kg) has been reated ( and resulted to primordial or primeval atom ) from minusule or immeasurably small amount of energy (10-50 J or less). However atual proess of reation of mass may be quite tedious and time onsuming proess. As already mentioned this explanation is not possible from (viii) E = m The Origin of Gravitation. The mass may be regarded is primary form of energy in nature, is onverted to other forms of energies whih may o-exist in various forms. In eletri bulb eletrial energy hanges to light energy, in radio eletrial energy is onverted into sound energy, in ell hemial energy is hanged to eletrial energy, in photoell light energy hanges to eletrial energy there are many suh examples. JVR 4 (009) 1-8 Journal of Vetorial Relativity 1

22 A Sharma: Einstein s derivation of E= m, also predits m June, 009 Energy in one form = k (energy in the other form) (54) where k is onversion fator just like J ( erg al -1 ) in W = JH. E = m states that mass is onverted into energy or vie versa, whereas aording to eq. (54) energy hanges from one form to other. In unontrolled nulear fission or in nulear reators mass is onverted to light energy, heat energy, sound energy and energy in form of invisible radiations is emitted et or energy may o-exist in various forms. In nuleus the mass is onverted into the binding energy (attrative like gravitational energy). The attrative binding energy exists within nuleus and attrative gravitational energy exists on large sale, but both arise from the annihilation of mass. In view of eq. (54) the analogous relation between mass annihilated and gravitational energy produed (measure of gravitational fore or pull) an be written as Energy emitted in annihilation of mass ( A m ) = k Gravitational energy ( U ) (55) g A m or, Gravitational energy ( U ) = Energy emitted in annihilation of mass ( ). g k Where k is a onversion fator whih determines the extent of onversion of mass to gravitational energy. Thus higher the value of produed. The values of A and A and smaller the value of k more gravitational energy will be k depend upon inherent harateristis of the proess. The inter onversion of energy to mass is ontinuous proess. The fration of mass (so produed) simultaneously hanged into gravitational energy as desribed by eq. (55). This gravitational energy held together the reated mass, if the gravitational energy produed in one partiular ase is onsiderable then that matter remained in ohesive state. So, formation of mass of universe and origin of gravitation are both simultaneous proesses. The gravitational energy is universally prevalent and is inherent property of bodies, it unites the bodies and these are produed. At the same time it is just possible that some partiles whih were reated from primordial energy, may have not developed onsiderable amount of gravitation energy, hene not ondensed to bigger units and may be even as suh now. These may have mass trillion-trillion times smaller than axioms, hypothetial partiles proposed by Peei [68] and are virtually isolated. Suh partiles are onstituents of dark matter. (ix) Formation of Primordial Atom And Its Explosion Or Big Bang. Thus, lighter partiles or bodies stuk together (under extreme onditions of temperature, pressure and gravitational energy) JVR 4 (009) 1-8 Journal of Vetorial Relativity

23 A Sharma: Einstein s derivation of E= m, also predits m June, 009 then their mass inreased. Thus high temperature and high gravitational pull aused onstituents of universe to ontrat to a single point. As the proess of annihilation of mass to energy ontinued so the rise in temperature and inrease in gravitational energy equally ontinued. Thus bodies were quikly attrated and ondensed as being extremely hot they ompressed to small size due to high gravitational energy onsequently radius of the universe dereased. This proess was repeated again and again and whole mass of the universe ondensed to a single point in super dense state in due ourse of time. The nature of gravitational fore so developed, may be regarded as similar to inter-atomi fore. The inter-atomi fore is attrative up to some extent (maximum r = 5Aº) and when distane between the moleules dereases it turns strong repulsive fore. As the gravitational energy inreases (higher A, less k ), so the size of onstituents of universe dereases. As long as the size of ompressed mass of universe is optimum, there is no onsiderable repulsion between onstituents. When the size of the universe is further dereased (due to extreme onditions of heat and gravitational energy) i.e. distane between nulei dereased beyond the optimum distane. At this stage (size of universe dereased beyond optimum size), the primordial atom exploded as universe was in extremely unstable, repulsive and reative state. At this stage, even small mass may have been onverted to mammoth amount of energy as permissible by equation weird reation. It is alled Big Bang and ever sine onstituents of universe are reeding away. Thus this pereption not only justifies the Big Bang Theory of Universe but also explains its origin., in (x) Blak Holes. On the basis of the reason for formation of blak hole ( density of the order of kg/m 3 ) is that due to small annihilation of mass, enormous amounts of heat and gravitational energies are produed. If the gravitational pull of a heavenly body is exeptionally- higher then even visible light does not esape from it and remains invisible. Aording to this pereption the pre-requisite for formation of the blak hole is that it must have unimaginably high value of gravitational energy. Aording to eq. (55) it is only possible if the value of A must be exeptionally high and that of A bh = k must be exeptionally small. Mathematially, ku g (56) m This pereption implies that for annihilation of small mass, huge amount of gravitational energy is gained by body whih even does not allow light to esape ( here k is another fator whih is measure of inter-onversion of one energy to other). If this ondition is satisfied then even bodies of smaller JVR 4 (009) 1-8 Journal of Vetorial Relativity 3

24 A Sharma: Einstein s derivation of E= m, also predits m June, 009 mass may beome blak holes. In view of this the lightest blak holes are also possible, and reside in the youngest galaxies. (xi) Gamma Ray Bursts. Gamma ray bursts (GRBs) are intense and short (approximately seonds long) bursts of gamma-ray radiations and originate at very distant galaxies (several billion light years away). GRBs are the most energeti events after the Big Bang in the universe and emit energy up to J in exeptionally short time. The origin of GRB an be understood on the basis of this pereption also. If for blak hole (formation desribed above) the value of A is higher and value of k is less and remains ative, then it ontrats beyond a optimum limit due extreme onditions of gravitation and temperature. Thus it may further result in a detonation known as blak bang emitting exeptionally high amount of energy in form of GRBs, due high value of A. Thus the explosion like big bang are ontinuing even now but at muh smaller sale emitting energy in form of GRBs and orresponding to annihilation of small mass huge energy is emitted with high value of A. This disussion permits that GRBs may be emitted from blak holes of smaller bodies omparatively. Aording to E = m if energy emitted is J, then mass annihilated will be kg, that too in few seonds. This annihilated mass is omparable with mass of Sun is kg. In GRB, the energy equal to J an be emitted from 10 kg of mass is annihilated in body if value in, is i.e. A grb = = (57) m Likewise explanation for other osmologial phenomena and bodies an be given on the basis of the generalized mass energy inter-onversion equation, = A shown in Table II. m. The various values of A grb A are V. CONCLUSIONS Dira suggests that in onnetion with his theory of large numbers, fundamental dimensional onstants may vary in time during the expansion of the universe. In aordane with this Web has reported variations in fine struture onstant (hene in speed of light) the same is also stated in other osmologial models as well and have diret effet on This aspet is also investigated in view of Einstein s Sep paper whih is origin of light energy -mass inter onversion equation and interesting results are obtained. Now it follows that E = m L = m is only true under speial onditions JVR 4 (009) 1-8 Journal of Vetorial Relativity 4