# Four momentum expression

1. Sep 5, 2009

### neelakash

1. The problem statement, all variables and given/known data

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

2. Relevant 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...

3. 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?

2. Sep 5, 2009

### 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?

3. Sep 5, 2009

### 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.

4. Sep 5, 2009

### gabbagabbahey

What exactly is the problem statement?

5. Sep 5, 2009

### neelakash

To show that 4force can be expressed as

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

6. Sep 5, 2009

### 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

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

7. Sep 5, 2009

### neelakash

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