The reason why such a complex phase causes CP violation is not immediately obvious, but can be seen as follows. Consider any given particles (or sets of particles) a and b , and their antiparticles a ¯ ¯ and b ¯ ¯ . Now consider the processes a → → b and the corresponding antiparticle process a ¯ ¯ → → b ¯ ¯ , and denote their amplitudes M and M ¯ ¯ respectively. Before CP violation, these terms must be the same complex number. We can separate the magnitude and phase by writing M = | M | e i θ θ . If a phase term is introduced from (e.g.) the CKM matrix, denote it e i ϕ ϕ . Note that M ¯ ¯ contains the conjugate matrix to M , so it picks up a phase term e − − i ϕ ϕ .