# Relativistic Density Proof

1. Jun 10, 2008

### t.mil

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

Prove that, in general, Dm = Ds / (1 - (v^2/c^2), where Dm is the relativistic density and Ds is the proper density

2. Relevant equations

Dm = Ds / (1 - (v^2/c^2)

3. The attempt at a solution

I really have no idea...

2. Jun 10, 2008

### Mute

Well, I would probably start with the definition of density: $\rho = m/V$, where rho is the density, m is the mass, and V is the volume.

So, to solve the problem, use the rules for how the mass and volume change when going to a relativistic frame.

That should get you started.

3. Jun 10, 2008

### konthelion

We know that $$density = \frac{mass}{volume}$$ *Edit sorry: I meant volume not velocity
Use the relativistic mass formula i.e. $$mass*\frac{1}{\sqrt{(1-(v/c)^2)}}$$ and likewise relativistic volume.