We investigate two-party cryptographic protocols that are secure under assumptions motivated by physics, namely relativistic assumptions (no-signalling) and quantum mechanics. In particular, we discuss split models, i.e. models in which certain parties are not allowed to communicate during certain phases of the protocol, for the purpose of bit commitment. We find the minimal splits that are necessary to evade the Mayers-Lo-Chau no-go argument and present protocols that achieve security in these split models. Furthermore, we introduce the notion of local versus global commands, a subtle issue that arises when the split committer is required to delegate agents to perform the open phase separately, without communication. We argue that classical protocols are insecure in the global command model, even when the committer is split. On the other hand, we provide a rigorous security proof in the global command model for a quantum protocol proposed by Kent. The proof employs two fundamental principles of modern physics, the no-signalling property of relativity and the uncertainty principle of quantum mechanics.