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On 101st Birthday of Einstein's E=mc2
When light energy is emitted, Mass increases,: Einstein’s Sep.1905
derivation. It is not consistent prediction from Einstein’s Sep 1905 derivation. (written in response to comments) How eq.(13) at page 201 in my paper I incorrect ? Then what is correct equation? In fact Eq.(13) in paper at page 201 is correct absolutely. ””””Eq.(13) is based of Einstein’s Sep 1905 derivation , that THEORETICALLY when body emits Light Energy , the mass of body INCREASE in some cases.””””””” It is explained below in THREE SECTIONS. Section A. (i) Einstein has considered A body of mass 10gm (say), it emits two waves under special conditions (two waves of equal energy L/2 each , emitted in opposite directions w.r.t measuring system) . Obviously mass decreases, which is converted to light energy and Einstein‘s equation is L =dmc2 Energy emitted = decrease in mass .c2 (1) (ii) If we consider the same body , it emits light energy at angle 90 w.r.t to the moving system , then again Einstein’s derivation gives L =mc2 Energy emitted = decrease in mass .c2 (2) Both the cases are correct . Eq.(2) is not derived by Einstein. Einstein’s 27 Sep 1905 paper available at http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ (iii) If we consider the same body , it emits light energy at angle 90 o w.r.t to the moving system , then again Einstein’s derivation gives Ho = H1 + β L( 1 – v/c cos89 o) Ho = H1 + β L (1– 0.017452406 v/c) Now proceeding as in Eq.(5) to Eq.(10) we get Δ m = – 0.03490L/cv + L/c2 (13) at page 201 of paper Thus Einstein’s derivation implies that when body emits light energy at angle 89 o then its MASS must INCREASE. If this angle is 0 then Einstein’s derivation implies that when Light Energy is emitted , mass decreases. Sharma June 2004 paper is available http://www.burningbrain.org/pdf/ajaysharma_einstein.pdf For further elaborated discussion link is https://www.novapublishers.com/catal...oducts_id=4554 Thus Einstein’s derivation is not true in general, it holds good under special conditions only. I have given 2nd and 3rd example purposely that up to which extent Einstein’s derivation depends upon angle. Angle up to 90 o is OK in Einstein’s derivation of Sep 1905. If it slightly decreases (even 89.9 o ) then, then RESULTS ARE CONTRADICTORY to results. Section B It is crystal clear that as Einstein’s derivation as applicable to first example ( two waves of equal energy L/2 each , emitted in opposite directions w.r.t measuring system) and second example ( a single wave of energy L emitted at 89 o or 89.5 o w.r.t measuring system ).Thus Einstein’s derivation is also applicable to third example (a single wave of energy L emitted at 89 o or 89.5 o w.r.t measuring system). As results are inconsistent then it is due to LIMITATIONS of Einstein’s derivation only, as it is equally applicable in all the three cases. It is explained below that law of ‘conservation of momentum’ holds good and ‘conditions of applicability’ of Einstein’s derivation are applicable to ALL THREE CASES. Part I (a) Law of conservation of momentum is obeyed completely. Conservation of momentum is meant for isolated system and mathematically implies that Initial Momentum = Final Momentum (3) mu=mv As mass remains same in classical mechanics. So u=v which is Newton’s First law of motion It is used to calculate the velocity of recoil of body after emission of energy in any way. --It is applicable if body moves or remains at rest after emitting energy. Einstein has done the case when body remain at rest ONLY, I have extended to it even if MOVES. Take example of -----Shot fired from gun, gun moves backward. ------ Light bullet fired from TOY Gun, system remains at rest. Momentum is conserved in ALL THREE CASES and velocity of recoil is more or less can be calculated using Law of conservation of momentum. This is the use of law of conservation of linear momentum in this case. As Einstein did all CALCULATION UNDER CLASSICAL CONDITIONS, hence net REALTIVE velocity of body after recoil must be in classical region. Again as Einstein did calculation under CLASSICAL CONDITIONS then momentum variation has no effect on MASS. Part II Einstein’s derivation is applicable when body remains at REST or MOVES. The basis for this TRUTH lies in Einstein’s derivation. Purposely and Especially eq.(1) shown below which is applicable for one or n waves. (i) The central equation in Einstein‘s equation is l* = l{1 – v/c cos φ } /√[1 – v2 /c2] (1) at page 196 of the paper. This equation is from Einstein’s June 1905 paper AND Einstein used it in derivation of L =mc2. With this equation magnitude of light energy is measured when one there is relative velocity between light emitting body and measuring system. Einstein considered two frames i.e. (x,y,z) at rest (body placed in it) and second frame (X,Y,Z) moving with velocity v ( measuring system) . Let body moves with velocity v’, then relative velocity will be v+v’ and eq.(1) becomes l* = l{1 – (v+v’) /c cos φ } /√[1 – (v+v’)2 /c2] (4) So after emission of light energy, body remains at REST or MOVES, eq.(1) [ at page 196 of paper ] is applicable. When ever under any condition, body emits light energy, EINSTEIN’S Sep. 1905 must give that MASS MUST DECREASE. Thus out of three cases first one (two waves) , second one (for one wave) interpretation for Einstein derivation is correct. How it becomes incorrect for third case (one wave, with angle difference of 1 or less) becomes incorrect. It is limitation of Einstein’s derivation. Thus Einstein’s Sep 1905 derivation is correct UNDER SPECIAL CONDITIONS not in GENERAL. Explanation for eq.(16) in paper at page 202. Consider two waves of energy 0.5001L and 0.4999L , then apply law of conservation of momentum the velocity of RECOIL can be calculated as Vr = 1/10000000000000000000000000000000 = 10-^32 m/s. Now v+v’ = v +10-^32 So eq.(1) is valid whether body is at REST or MOVES after emission of light energy. Einstein’s derivation of L =mc2, the body may remain at REST or MOVE, is applicable there is no rule of science which stops it. Section 3 Part I Thus it is concluded that Einstein’s derivation has four variables (i) Number of light waves (ii) Magnitude of energy of light waves (iii) Angle at which light energy is emitted (iv) Relative velocity v ( must be in classical region). All these variables in Einstein’s Sep 1905 derivation have numerous values. Energy may be emitted in any way, the mass of BODY DECREASES experimentally ALWAYS. But THEORETICALLY according to Einstein’s 29 Sep. 1905 derivation, in every time, result is not eq.(1) . L =mc2 Energy emitted = decrease in mass .c2 (1) Einstein’s Sep. 1905 derivation also predicts MATHEMATICALLY that when body emits Light Energy its mass must also INCREASE. It is not true. Hence Einstein’s derivation is true under special conditions only. Part II In addition after deriving L= dmc2 (1) Einstein simply replaced L and SPECULATED ( not derived) E=dmc2 where E is EVERY FORM OF ENERGY ( light energy, heat energy, sound energy, chemical energy in form invisible radiation etc.). However basis for derivation of eq.(1) is only for light energy eq.(1) at page 196 of my paper. Thus we need to derive mass energy equation by other method and generalized equation is dE =Ac2 dm where A is coefficient of proportionality, like others in the existing physics and its value depend upon experimental conditions. For details https://www.novapublishers.com/catal...oducts_id=4554 References of Einstein’s work .. A.Einstein, Annalen der Physik 18 (1905) 639-641. .. DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT? Weblink is Einstein’s 27 Sep 1905 paper available at http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ PartII References of Ajay Sharma’s work My work is available at A. Sharma, Physics Essays, 17 (2004) 195-222. ”The Origin of Generalized Mass-Energy Equation E = Ac2 M; and its applications in General physics and Cosmology”. http://www.burningbrain.org/pdf/ajaysharma_einstein.pdf For details https://www.novapublishers.com/catal...oducts_id=4554 International Conferences It has been accepted for presentation over 55 conferences all over the world --------------------------------------few of them 1. Sharma, A. presented in 19th International Conference on the Applications of Accelerators in Research and Industry , 20-25 August , 2006 Fort Worth Texas, USA 2. A. Sharma, Abstract Book 38th European Group of Atomic Systems ( Euro physics Conference) Isachia (Naples) Italy (2006) 53. 3. A. Sharma , Abstract Book , A Century After Einstein Physics 2005 , 10-14 April 2005 ( Organizer Institute of Physics , Bristol ) University of Warwick , ENGLAND 4. A. Sharma presented in 5th British gravity Conference , OXFORD ENGLAND 5. A. Sharma,. Proc. Int. Conf. on Computational Methods in Sciences and Engineering 2003 World Scientific Co. USA , (2003) 585. 6. A. Sharma, Proc. Int. Conf. on Number, Time, Relativity United Physical Society of Russian Federation, Moscow , (2004) 81 plus more -------------------------------------- Journals This paper ”The Origin of Generalized Mass-Energy Equation E = Ac2 M; and its applications in General physics and Cosmology”. is published in journal Physics Essays , CANADA www.physicsessays.com The paper The past ,present and future of E=mc2 will be published in 2007 Galilean Electrodynamics, Massachusetts, USA. In parts it is published in various others journals. ---------------------- Book 100 Years of E=mc2 For details https://www.novapublishers.com/catal...oducts_id=4554 |
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