Trans-Temporal Field Study

Time travel short story. Assuming that (1) time travel into the past does not alter the present, (2) that people go back in time repeatedly to study the past for the sake of scholarship, what would be the inevitable outcome of of all those forays into the past? Time traveller as history-major graduate student visits medieval England only to encounter ANOTHER time traveller from his far-distant future. His love interest is ignited. They are both in the same occupation, each writing dissertations about the past. What could go wrong?