Derivation of relativistic momentum

1. Jul 1, 2014

albertrichardf

Hi all,
Is it possible to derive the equation p = ymv, and hence based on this, kinetic energy formula, without referring to 4-vectors or 2-dimensional collisions, that is derive it in one dimension?
I tried this website/pdf but the mathematics is beyond my understanding. So could some one either explain the pdf, or derive the equation themselves?
Thanks.
Here is the link:
http://arxiv.org/pdf/physics/0402024.pdf

2. Jul 1, 2014

Simon Bridge

... yes - sort of.

You start by showing that p=mv is not conserved in all reference frames.
http://en.wikibooks.org/wiki/Special_Relativity:_Dynamics

Note: in 1D, the 4-vector just has a zero in each of the unused positions.

3. Jul 1, 2014

Staff: Mentor

Since the derivation in the paper you linked to looks valid, I would say yes.

Can you be a bit more specific about what in the pdf you are unable to understand?

4. Jul 2, 2014

albertrichardf

i don't get the mathematical processes from equation 3.6 and 3.7.

5. Jul 2, 2014

PhilDSP

Hi albertrichardf,

In addition to the paper you referred to, Louis De Broglie derived that (and other formulas expressed in 3-vectors) using Hamilton-Jacobi mathematics. It's possible to go still further and derive the relativistic energy equation and all of its variations.

6. Jul 2, 2014

pervect

Staff Emeritus
It's just a taylor series.

Basically the idea is that you can approximate a function near a point by a straight line

If you have f(x) and you want to approximate it near some value "a", the first 2 terms of the series are

f(a) + (df/dx)*(x-a)

see http://en.wikipedia.org/wiki/Taylor_series