The ultimate physicist gang war! Those matrices represent the metric signatures used in relativity theory - one favored by particle physicists (−,+,+,+) and the other by relativists (+,−,−,−). It's literally the academic equivalent of Bloods vs Crips, but instead of territory, they're fighting over which sign convention to use when describing spacetime. Both approaches give identical physics results, just with different signs scattered throughout your equations. Smart physicists play both sides of this mathematical turf war, switching conventions depending on which conference they're attending!