Prove 4 Vectors: Last Hope for Finding an Answer

[M. next]

In books, it is always posted that velocity (dx$^{i}$/dt) is not a 4 vector. While du$^{i}$/ds and momentum are 4 vectors.. But it is never proved.

How to prove this?? I am not finding anyway to it.

You're my last hope!

 

[Simon Bridge]

Do the operation, then see if the result still transforms as a 4-vector.

http://en.wikipedia.org/wiki/4_vector
http://teachers.web.cern.ch/teachers/archiv/hst2002/bubblech/mbitu/velocity_4vector.htm

 

[M. next]

Thank you for the reply, but can you tell me which one to use? I mean which formula from the two links?

 

[Simon Bridge]

Do not apply formulas - test the properties of a 4-vector.
If you do not know how a 4-vector transforms, then learn and revisit the problem of a proof later.

 

[vanhees71]

Have a look at

http://en.wikipedia.org/wiki/4_vector#Derivatives_and_differentials

Then note that $\mathrm{d} \tau$ is a scalar. Then you can easily prove yourself that $u^{\mu}$ is a four-vector!

 

[M. next]

Oh thank you! You mean that if I took the proper time and divided that by ds = cdt $\sqrt{1-(v^2/c^2)}$ I should get the 4 components of U. And I say that yes, these looks like (dA^0, dA^1, dA^2, dA^3) as in your link so it is a 4 vector. Right?

 

[M. next]

sorry I meant if I took Ui and divided that by ..