How to perform a binomial expansion on $m*v^2$? I have been told by a couple of folks in passing, one of whom was a mathematician, that through binomial expansion of $m*v^2$ (where v is used in place of c), that all 5 Major Forces (Strong Force, Electromagnetism, Weak Force, Gravity, and Magnetism) can be shown.
Unfortunately I have been out of the mathematical loop for over a decade and I was hoping that someone might demonstrate how to expand something like this with some basic instructions to the process.
 A: What you have been told is utter nonsense.  I would ignore it.
A: The "$m$" you've been told about is the so-called relativistic mass. Usually, when physicists talk about mass they're actually talking about $m_o$ the rest mass. In contrast, the "$m$" your acquaintances have mentioned is captured by
$$ m(v) = \frac{m_o}{\sqrt{1-v^2/c^2}} $$
where $c$ is the speed of light in vacuo and $v$ is the speed at which the particle in question travels. Often the ratio $\frac{1}{\sqrt{1-v^2/c^2}}$ is called $\gamma$ and sometimes $\beta = v/c$ hence $\gamma = (1-\beta^2)^{-1/2}$. Apply the binomial series to obtain:
$$ \gamma = 1-\frac{1}{2}\beta^2+ \cdots $$
multiply by $m_oc^2$ to obtain: note $c^2\beta^2=v^2$ hence,
$$ mc^2 = m_o\gamma c^2 = m_oc^2+ \frac{1}{2}mv^2 + \cdots $$
The first term is the rest-energy and the second term is the classical kinetic energy. Now, what this has to do with the weak, strong forces and general relativity? Well, not much, except that special relativity (the physical theory which introduced this concept) is presupposed by all other modern physical theories which followed (since 1905) the relativistic mass is naturally included in those theories. However, $m_o$ is more basic in my opinion.
A: For more information about the question, you can look at this interview of Boyd Bushman, former Lockheed Martin Skunk works senior scientist(timemark 16:00): https://www.youtube.com/watch?v=hNPBYtJyfZo
