The Doctor takes the Ponds to what he promises will be a stunningly beautiful planet but turns out to be a sort of hospital in a quarantined plague zone. The plague kills within a day so this place has set up an automated facility for visitors to watch their loved ones live out their entire lives in 24 hours. They do this by having multiple timestreams; the visitors sit in the regular stream and the ill live in a vastly accelerated one. Things go almost instantly awry and Amy winds up in the accelerated time stream. The Doctor can’t go in after her because his species is susceptible to the plague. He warns her to avoid the facility’s well-meaning robots, as the medicine they kindly dispense is deadly to humans.
Rory goes off to the rescue, but the Amy he finds has lived 36 years in her timestream. She’s more than a little angry and blames the Doctor for abandoning her there. In her solitude, she’s had to fend off the robots and eke out a meager existence in the facility’s grungy basement. At first, she refuses to help Rory rescue the past version of herself, as it means the current version will cease to exist. She finally agrees on the condition that the Doctor rig up the TARDIS so that both versions can come along. She and Rory fight their way through the robots, but it turns out that not even the TARDIS can handle the paradox and only one Amy can survive. Rory has to decide whether to save his hot young wife or his bitter old wife. To his credit, it really tears him up. In the end, it’s old Amy who makes the decision for him, sacrificing herself so that her younger self can live.