# Lorentz Factor with V=0

• B

## Main Question or Discussion Point

How do I calculate the Lorentz factor with v=0. Or do I not calculate it since it can be said that the observer is in the same frame of reference?

Related Special and General Relativity News on Phys.org
PeterDonis
Mentor
2019 Award
How do I calculate the Lorentz factor with v=0.
What do you get when you plug $v = 0$ into the formula?

How do I calculate the Lorentz factor with v=0. Or do I not calculate it since it can be said that the observer is in the same frame of reference?
This is one of those situations where just doing the calculations gives some insight. As PeterDonis just said, replace v with zero:

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

Let v = 0:

$\frac{1}{\sqrt{1 - \frac{0^2}{c^2}}}$

$\frac{1}{\sqrt{1 - 0}}$

I'm guessing you can take it from there in terms of arithmetic. So if you saw, say, relativistic momentum

$p = γ(u)mu = \frac{mu}{\sqrt{1 - \frac{u^2}{c^2}}}$

and replaced u with zero, (a) what would the Lorentz factor be and (b) how much momentum would the object have?