Currently we know China possess roughly half of the hash power of the Bitcoin network. We know that China current possesses a "great firewall" that actually causes delays on the bitcoin network.
Hypothetically, if relations deteriorate between US and China and China cut off its internet from the rest of the world. What would happen to the bitcoin network? Would it split into half? Would both sides keep running until they are synchronized (and half the transactions invalidated when it is synchronized?)