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Transformation equations presented in a different way

  1. Feb 6, 2007 #1
    Consider a particle that moves with speed u relative to the inertial reference frame I and with speed u' relative to the inertial reference frame I'. Let g(u), g(u') and g(V) be the orresponding gamma factors (V the relative speed of I and I'). m(0) stands for its rest mass, E(0) for its rest energy, p and E for its momentum and enegy measured by observers from I. It is obvious that
    I consider that such a presentation presents some (pedagogical) advantages showing clearly what observers from the I frame measure in the case when u'=0 and when u' and V are both equal to zero.
    Even if I know that the concept of relativistic mass is persona non grata on the Forum I would also suggest for the relativistic mass
    The oppinion of those who teach or learn special relativity theory is highly appreciated of course in the spirit of
    sine ira et studio
  2. jcsd
  3. Feb 7, 2007 #2

    Meir Achuz

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    Never use "it is obvious" in pedagogy. That is like the old mathematics professor joke.
  4. Feb 7, 2007 #3

    Don't you think that [tex]E=\gamma(V)*E(0)[/tex] is much cleaner?
    Last edited: Feb 7, 2007
  5. Feb 7, 2007 #4


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    As an aside, persona non grata means 'an unwelcome person' and is not usually used in reference to a concept. Absit invidia :wink:
  6. Feb 7, 2007 #5
    transformation equation

    Thanks. I think that there is a big difference between posting on the Forum, where the participants can easily transform the usual transformations in those I propose and presenting them in all its steps.
    I know very much joks with teachers of physics and mathematics. Which of them do you mean?
  7. Feb 7, 2007 #6
    transformation equations

    Thanks. Yes it is but I think that the Forum could offer a simple equation editor.
  8. Feb 7, 2007 #7


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    The forum does! LaTex is very easy to learn, and it is easy to use on this forum too; simply put [tex] [ /tex] tags (without the space) around the equations.
  9. Feb 7, 2007 #8
    latina ginta est Regina

    Thanks. My first language is close to Latin. I thought that physicists are able to extrapolate from persona non grata to relativistic mass which is there non grata. I end with
    absit invidia which is shorter and more adequate then sine ira et studio I used so far.
  10. Feb 7, 2007 #9
    [tex]\gamma(u')\gamma(V)(1+Vu'/c^2)=\gamma(u)[/tex] , so the above reduces the the much cleaner, well known :

    Last edited: Feb 7, 2007
  11. Feb 7, 2007 #10


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    The identity (rearranged in a minor way)
    is more recognizable in terms of rapidities:
    \cosh{\theta'}\cosh{\phi}(1+c\tanh{\theta'}\ c\tanh{\phi}/cc)\\
    where u[itex]=c\tanh{\theta}[/itex] is the spatial-velocity obtained by "spatial-velocity-composition of u' and V".

    In addition, in terms of rapidities, one can immediately transcribe the calculation into a spacetime diagram, which provides a hopefully more intuitive interpretation of what is happening physically [and mathematically].

    So, it's not clear to me if anything is gained in the proposed formula, except maybe for a particular type of problem.
    Last edited: Feb 7, 2007
  12. Feb 7, 2007 #11

    Thanks. My intention is to present the transformation equations in such a way that theirs right sides contain only a proper physical quantity and velocities reducing the long discussions related to the concept of relativistic mass. That is the direction in which I hope our discussions will evolve.
    Reading my lines please take into account that English is not my first language.
  13. Feb 18, 2007 #12
    Thank you for having brought the formula to a more transparent shape. Consider the concept of proper mass m(0) and multiply both sides of with it. It leads to[tex]m(0)gamma(u0=m(0)gamma(u')gamma(V)(1+u'V/cc[/tex]An exercised eye will recognise in the left side of the equation the expression of the relativistic mass in I in the left side its expresion as a function of phyhsical quantities measured in I. Do you consider that such a presentation is time saving, transparent and convincing for the fact that conservation laws are not compulsory in the derivation. I do not convinced that the equation will appear correctly in myh message.
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