# Gravitational Time Dilation and Equivalence Principle

My question relates to page 118 of these notes, which is reproduced below for your convenience. Specifically, I have difficulty understanding the line "This shows that time slows in a region of stronger gravity (smaller $$\Phi$$)". On the contrary, if we define $$\Phi_A = g(h_0+h)$$ and $$\Phi_B = gh_0$$, then equation (A.1.9) seems to show that the time interval measured by Bob (at the bottom of the rocket) between signals is smaller than that measured by Alice. This is because in this scenario $$\Phi_B - \Phi_A < 0$$. Surely this isn't right. What is going wrong here?