Independence of Brownian Motion with respect to a stopping time

Question

Let $B_t$ be a brownian motion, $B_0=0$, and $\gamma \in \mathbb{R}$. Now, let's build the following stopping time: \begin{equation} T = \inf \{ t \geq 0 : |B_t + \gamma t| = 1 \}. \end{equation} If $\gamma = 0$, how would you argue that $B$ and $T$ are independents?