He's the only kid ever to get into trouble before he was born.
Why it is hard sci-fi
A comedy. The DeLorean does not pretend to be physics. What it does take seriously is causality. The film commits to a single timeline that responds to changes in the past, with the photograph as a visible counter that updates as events drift. That is internally consistent and the rest of the trilogy keeps the rule.
Science inside it
Time travel as fiat. The conserved currency of the script is causality. The flux capacitor delivers 1.21 gigawatts in a single instant, the DeLorean has to reach 88 mph, the past can be rewritten and the present updates. The mathematics is missing but the rules are constant.