I once read a short story about some scientist who was convinced that there were aliens/creatures stealing time from the day (so basically there are actually 25 hours in a day but the aliens steal one hour so we only experience 24 hours).
He builds some device based on music/the principle that clocks in different rooms ticks differently (not too sure about this part).
The narrator watches the scientist put on the headphones, slip into the extra hour, and become horrified by what he sees. A short struggle ensues and the narrator (or another one of the scientist's friends there) is forced to break the machine. The narrator notices that there are strangely shaped raised (not sunken) foot prints in the snow outside (apparently it's winter).
The scientist from then on has a split personality disorder, with the normal side pleading to let the creatures "keep their hour" and never come into our time while the alternate side is, well, the complete opposite of his normal personality (rude).
The short story is from a science-fiction collection book (anthology) I'm guessing is published around the mid 1900's. It definitely isn't a "modern" scifi story (so it probably isn't published from 1980's-now).