Winston Smith lives in a world where everyone is watched every second of the day
Is highlighted "the" the synonym of "every"?
Why do we use "the" here instead of "a"?
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It's difficult to explain with fancy grammar terms and the like, but basically what it boils down to is that we use the definite article because on any given day where everyone is watched, we know which specific day it is.
To say "Winston Smith lives in a world where everyone is watched every second of a day." we're not being specific about which day: is it Monday? Three weeks next Wednesday? Yesterday? Non-specificity makes the sentence hard to parse as intended.