A question about 4-velocity vector in relativity

[m.medhat]

Homework Statement

Hello ,
I have the book (An introduction to tensor calculus , relativity and cosmology) , this book defined the 4-velocity vector as :-

And this book stated that :-

How could we obtain (17.4) from (15.6) ?
Please I need help .


Thanks ……..

Homework Equations

The Attempt at a Solution

 

[kuruman]

Calculate the magnitude squared of the four-vector on the right side of 15.6. What do you get?

 

[m.medhat]

i do that but i don't obtain the result (-c^2)
i still need help .

 

[kuruman]

i do that but i don't obtain the result (-c^2)
i still need help .

Show exactly what you did. You probably made a mistake somewhere.

 

[m.medhat]

let (1-[v^2]/[c^2])^-1/2 = y
therefore ?:-
V = y (v,ic)
V^2 = (y^2) ([v^2] + [ic]^2)
then V^2 = [y^2] ([v^2]-c^2)
that's all.



i still need help , please .

 

[kuruman]

let (1-[v^2]/[c^2])^-1/2 = y
therefore ?:-
V = y (v,ic)
V^2 = (y^2) ([v^2] + [ic]^2)
then V^2 = [y^2] ([v^2]-c^2)
that's all.
i still need help , please .

You should have left the denominator alone instead of replacing it by 1/γ. All you need to do is simplify

$$\frac{v^2-c^2}{1-\frac{v^2}{c^2}}$$

 

[m.medhat]

i understand the idea , thank you veryyyyyyyy much .