# A question - needing a second opinion on an equation

1. Sep 16, 2012

### Meselwulf

I have been doing independent work on Planck Particles, the general idea's can be found here

http://www.physicsgre.com/viewtopic.php?f=11&t=4765&p=42139#p42139

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

$$\frac{dP}{dt} = e(B \times v)$$

multiplying through by $$dt$$ gives

$$dP = e(B \times vdt)$$

I will take $$vdt = ds$$ which will be a displacement.

The relativistic momentum $$Pc$$ can be written in another form, I believe that form is

$$GM^2 \vec{\sigma} \cdot \nabla_{\chi} = e(B \times ds)$$

Dividing through by $$GM^2$$ gives

$$\vec{\sigma} \cdot \nabla_{\chi} = \frac{(B \times ds)}{\sqrt{G}M}$$

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.

Thanks!

Last edited: Sep 16, 2012
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