The S-matrix is the quantity that describes how a collection of incoming particles turn into outgoing ones. Heisenberg proposed to study the S-matrix directly, without any assumptions about space-time structure. But when transitions from the far-past to the far-future occur in one step with no intermediate steps, it becomes difficult to calculate anything. In quantum field theory, the intermediate steps are the fluctuations of fields or equivalently the fluctuations of virtual particles. In this proposed S-matrix theory, there are no local quantities at all.