I have a continuous martingale $X_t$ starting from zero, with quadratic variation
$$[X_t,X_t]=ct$$.
I want to show that $$W_t=c^{-1/2}X_t$$ is a brownian motion.
How can we get from the quadratic variation to the independence of increments and $E(W_{t_1}-W_{t_0})=t_1-t_0$?