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A question - needing a second opinion on an equation

  1. Sep 16, 2012 #1
    I have been doing independent work on Planck Particles, the general idea's can be found here


    Now, I decided to begin with the relativistic (but not manifestly relativistic equation)

    [tex]\frac{dP}{dt} = e(B \times v)[/tex]

    multiplying through by [tex]dt[/tex] gives

    [tex]dP = e(B \times vdt)[/tex]

    I will take [tex]vdt = ds[/tex] which will be a displacement.

    The relativistic momentum [tex]Pc[/tex] can be written in another form, I believe that form is

    [tex]GM^2 \vec{\sigma} \cdot \nabla_{\chi} = e(B \times ds)[/tex]

    Dividing through by [tex]GM^2[/tex] gives

    [tex]\vec{\sigma} \cdot \nabla_{\chi} = \frac{(B \times ds)}{\sqrt{G}M}[/tex]

    Does anything seem wrong with this result, I keep looking at it but something just seems a bit off about it... Was hoping for some suggestions or any mistakes that could be pointed out by someone.

    Last edited: Sep 16, 2012
  2. jcsd
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