Back in the 80s I read a story in an anthology book, in which unseen aliens "invade" Earth and force everyone to relive the same day over and over. They do this in order to thoroughly study humanity and find out what makes us tick. At the end of 1 million years (!), the experiment will be over and they'll grant everyone immortality.
The main character argues with his wife that morning, so ends up having the same argument every day for years. Eventually he meets a haunted looking woman on his daily commuter train. She tells him she's a "ghost." She dies in an accident on the loop day, and has to relive her death over and over. Worse yet, once the experiment's over, she'll die one last time and won't become immortal.