[email protected] , You have made comments that Momentum is not Conserved in my PAPER. It is not

Discussion in 'General Math' started by AJAY SHARMA, Oct 4, 2006.



    , You have made comments that Momentum is not
    Conserved in my PAPER. It is not CORRECT. It is explained in 100 Years
    of E=mc2

    Robert Pasken

    Department of Earth and AtmosphericSciences
    Saint Louis University
    3507 Laclede Avenue
    St.Louis, MO 63103

    See how Momentum is conserved in my paper. All references are given in
    the end.
    Part I
    General meaning , explained in 11th class Physics.
    The law of momentum conservation,
    * In an isolated system, the momentum of system must be

    Mathematically implies that
    Initial Momentum = Final Momentum
    mu=mv (1)
    As mass remains same in classical mechanics.
    So u=v
    which is Newton’s First law of motion.

    Application of momentum conservation.
    When body emits energy ( in this cases light energy)
    then it recoils .Thus it is used to calculate the velocity of recoil.
    It can be applied to following two cases.

    ------ Light bullet fired from TOY Gun, system remains at rest.
    ( body does not recoil with noticeable velocity, it tends to
    The velocity cam be calculated but may be of the order of
    1/100000000000000000000000000000000000 m/s or 10-^40m/s
    This case resembles with Einstein’s two waves of equal energy emitted
    in opposite directions.

    -----Shot fired from gun, gun moves backward.
    the velocity can be calculated from conservation of momentum i.e.

    initial momentum =final momentum
    Vrecoil = mv/M ~ 5m/s (say)
    Thus after emission of energy BODY MAY REMAIN AT REST OR MOVE, the
    Momentum is Conserved. It is basic physics of 11th standard.
    If some one does not want to understand this then it his problem.
    Einstein did all calculation under Classical conditions of velocity (v
    <<c, her v is relative velocity between two systems i.e. system in
    which body emits light and second system in which energy is measured.

    Part II
    The law of conservation of momentum is obeyed in my paper.


    When two waves are emitted. The body recoils with velocity v , with
    magnitude of the order of 10^-32 m/s i.e.
    V (recoil)=1/10000000000000000000000000000000000000000000000000
    It can be easily calculated.

    When two waves of different energies are emitted. If body emits two
    light waves of slightly different energies i.e. 0.5001L and 0.4999L
    (Einstein has used light waves of energy 0.5L and 0.5L) in opposite
    directions. Now using the law of conservation of momentum, it can be
    easily justified that in this case body remains at rest.
    Let the body of mass 10kg
    emits light energy in two waves in visible region equal to
    7.9512×10^-19 J, this energy corresponds to TWO light waves in
    visible region having wavelength 5000ºA or energy, 2hc/λ or
    7.9512×10^-19 J.
    Let towards the observer the body emits light energy 0.5001L i.e.
    3.97639512×10^-19 J i.e. will have momentum ( p1 = E/c)
    1.32546504×10^-27 m/s.
    Secondly, the body emits light wave of energy 0.4999L i.e.
    3.97480488×10^-19 J, away from the observer (φ= 180º) i.e. will
    have momentum ( p2 = E/c) 1.32493496×10^-27 m/s. Let us assume that
    when the body emits light waves of energy and moves (if it actually
    does) with velocity Vb , then according to law of conservation of
    momentum we get
    0 = p1 +p2 +MbVb or Vb = -(p1 +p2) /Mb =
    –5.3×10^-32 m/s (2)
    0 = p1 +p2 +MbVb or Vb = -(p1 +p2) /Mb =
    –5.3×10^-32 m/s (3)
    Thus conservation of momentum requires that body should move with
    velocity –5.3×10^-32 m/s opposite to observer. Thus body will
    tend to move with velocity 5.3×10^-32 m/s ( away from the observer)
    which is immeasurably small by all means, hence the body remains at
    rest. Due to this uniform relative velocity v of the system (ξ, η, ζ
    ) will not change, if body moves then v will vary accordingly.
    =========Einstein’s Sep 1905 paper===========
    The first and basic equation in Einstein’s paper is
    l* = l{1 – v/c cos φ } /√[1 – v2 /c2] (1)
    In eq.(1) v is the relative velocity between light emitting body and
    the measuring system i.e. system (ξ, η, ζ ). If body movesafter
    emission with velocity v’ away from the observer, then relative
    velocity will be v+v’ (say V). Thus in this case eq.(1) becomes
    ℓ* = ℓ{1 – (v+v’) cos φ/c } /√[1 – (v+v’)2 /c2]
    The rest of the calculations remain the same. Thus Einstein’s
    derivation is also valid if the body moves, Einstein has considered the
    simplest case when velocity v’ is zero (V= v+v’ =v), which is
    special case. Also experimentally the law of inter conversion of mass
    energy holds good in all possible cases.

    It is your MISPERCEPTION.

    AJAY SHARMA 2ND Oct 2006

    References of Einstein’s work
    A.Einstein, Annalen der Physik 18 (1905) 639-641.
    Weblink is
    Einstein’s 27 Sep 1905 paper available at

    References of Ajay Sharma’s work

    My work is available at
    A. Sharma, Physics Essays, 17 (2004) 195-222.
    â€The Origin of Generalized Mass-Energy Equation ï„E = Ac2 ï„M; and
    its applications in General physics and Cosmologyâ€.
    For details

    International Conferences
    It has been accepted for presentation over 55 conferences all over the
    --------------------------------------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

    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
    This paper
    â€The Origin of Generalized Mass-Energy Equation ï„E = Ac2 ï„M; and
    its applications in General physics and Cosmologyâ€.
    is published in journal
    Physics Essays , CANADA
    The paper
    The past ,present and future of E=mc2
    will be published in 2007 Galilean Electrodynamics, Massachusetts,
    In parts it is published in various others journals.
    AJAY SHARMA, Oct 4, 2006
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