i guess the timeline of the door into summer is similar to time turner in harry potter 3rd movie. the prof in the door into summer said theres no such paralel timeline, so do with those in HP3. theres 2 suichiro(s) and 2 harry(s) + 2 hermione(s) at the same time. but when they back theres only one of them cos the other one (the old ver) is going back to the past. and yes theres would be a looping of repetead action (the old ver going back to the past and the new ver continue living in the current time). coz time is a dimension.