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chronophobia

n. Fear of the passing of time, or more generally of time itself.

Wikipedia
Chronophobia

Chronophobia is described by Pamela Lee as the fear of time. There are three categories of phobia including agoraphobia, social phobia, and specific phobias which includes spiders, snakes, dogs, water, and heights. Rosemary Stolz states that chronophobia falls under the category of specific phobia because time is a specific object that one can fear. Chronophobia is especially common in prison inmates and the elderly, but it can manifest in any person who has an extreme amount of stress and anxiety in their life.