This is a conceptual problem, right out of a book. Say Mavis is moving in a spaceship at 0.6c relative to Stanley on earth. When Mavis just passes earth, both of them start their clocks. When Mavis reads 0.4s, what does Stanley read on his? Now here's the problem. I think 0.4s being proper time, the time interval will seem longer from Stanley's reference frame. So, it should be γτ where τ=0.4s. But the book would have me believe otherwise. What's wrong here?