Suppose I am an observer in Minkowski space, observing a particle traveling with a constant velocity $v$. If I want to calculate the particle's Lorentz factor, given that the particle is traveling at a constant velocity, I can say $\gamma = \frac{\Delta (c\cdot t)}{\Delta \tau}$. My question is, to get a value for $\Delta t$, do I look at my clock, or do I look at the particle's clock?