Pascual Jordan: from matrix multiplication to interference law

Pascual Jordan was the first to propose the law of interference of probability amplitudes as a principle of quantum mechanics. We analyze the role of probabilistic ideas played in this proposal from a historical perspective. In particular, we point out the relation between the usual theory of probability that Jordan called elementary and quantum mechanics. Jordan was the first to stress the analogy between the law of total probability and the law of interference. In this regard, we speculate about the intellectual path Jordan might have followed in order to arrive at the interference law. We do not oppose the usual probability to quantum probability. Instead, we are convinced, as Jordan was, that the rules of quantum mechanics are the rules of a probability theory that has ceased to be elementary.