Deriving relativistic momentum p = γmv in one dimension

[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

 

[Simon Bridge]

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?

... 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.

 

[PeterDonis]

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?

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

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?

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

 

[albertrichardf]

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

 

[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.

 

[pervect]

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

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