1. The problem statement, all variables and given/known data Given: in its own reference frame a proton takes 5 minutes to cross the Milky Way (10^5 meters). (a) What is the approximate energy of the proton? (b) About how long would the proton take to cross the galaxy as measured by an observer in the galaxy's reference frame? 2. Relevant equations All those equations for special relativity I imagine. L = L0 Sqrt[1-(v/c)^2] t = t0 Sqrt[1-(v/c)^2] 3. The attempt at a solution So I keep doing this over and over again, getting a wrong answer. The way I approach it is this: I think L is the distance as measured by the proton when crossing the galaxy, and t is the time the proton measures (5 minutes). Since v is the same in both reference frames (how fast the galaxy thinks the proton is moving and how fast the proton thinks the galaxy is moving) I can say that L/t = v. Using those equations I do it all out and find that v = c. Not very useful when I plug it into my equations for energy and find the proton has infinite energy. Where am I going wrong? Also, I think this should be doable without the Lorentz transformations.