Seminar: Does quantum theory need complex numbers?

The great theories in the history of physics regularly use complex numbers for convenience but do not fundamentally rely on them. However, since the 1920s it has been asked whether quantum theory might be different in that regard. I discuss the solution to this problem based on [Nature 600 625 (2021)] where we prove that quantum theory without complex numbers gives rise to different physical predictions. I then discuss the experimental tests of real versus complex quantum theory and what all this actually teaches us about quantum theory.