- #1

- 6

- 0

## Homework Statement

In a particular inertial frame of reference, a particle with 4-velocity V is observed by an

observer moving with 4-velocity U. Derive an expression for the speed of the particle

relative to the observer in terms of the invariant U · V

## Homework Equations

##U.V=U'.V'##[/B]

## The Attempt at a Solution

[/B]

I used the relation the

**##U.V=U'.V'##**because U.V is invariant.

Using the rest frame of the observer I obtained

**##U'.V' = -\gamma(u_R)c^2##**

Then rearranging to find

**##u_R##**I obtained

**##u_R = c*sqrt(1-(c^4/(U.V)^2))##**

I'm just wondering if I used the correct method and got the correct result for

**##u_R##**

Any insight is appreciated