How can I express the force in Special Relativity using four momentum?

[neelakash]

Homework Statement

To write the expression of force in STR

$$\ F=\frac{dp}{dt}=\ m\gamma\ a +\ m\gamma\frac{\ u .\ a}{\ c^2 -\ u^2}\ u$$

Here a is acceleration

Homework Equations

I used the equation $$\ p=\gamma\ m\ u$$

I interpreted F as four force,p as four momentum, a as four-acceleration, u as four velocity etc...

The Attempt at a Solution

Mere differentitation is giving the answer;But I do not know if the method is correct.Because, $$\ p=\gamma\ m\ u$$ for 3 velocity---that's for sure.But is it also true for four velocity and four momentum?

 

[gabbagabbahey]

It occurs to me that you can pretty much answer your own question just by looking up the definitions of "4-momentum", "4-velocity" and "4-force"...surely your text has those definitions?

 

[neelakash]

Seems my instructor did not formulated the problem in the correct way.The expression is for 3velocity;that for 4 velocity is not that simple.

 

[gabbagabbahey]

What exactly is the problem statement?

 

[neelakash]

To show that 4force can be expressed as

$$\ F=\frac{dp}{dt}=\ m\gamma\ a +\ m\gamma\frac{\ u .\ a}{\ c^2 -\ u^2}\ u$$

 

[gabbagabbahey]

But it can't be expressed that way...for starters, if $\textbf{F}$ is the 4-force, $\textbf{P}$ the 4-momentum and $\tau$ the proper time, then

$$\textbf{F}=\frac{d\textbf{P}}{d\tau}\neq\frac{d\textbf{P}}{dt}$$

 

[neelakash]

yea,I also suspect that the expression is not meant for 4 force.