Kuchař and Isham's 'problem of time' literature documents that the canonical approach's chief difficulty is precisely the absence of a classical background time, not its reliance on one.

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Canonical approach(as the method being critiqued): A standard method physicists use to turn Einstein's gravity theory into a quantum theory; 'canonical' just means 'the official or traditional way.'
Kuchař and Isham(as the authors being referenced): Physicists and philosophers who studied how time works in quantum gravity; they wrote influential papers on why time is problematic in certain physics theories.
Problem of time(the core issue being discussed): A major unsolved puzzle in physics: when you combine quantum mechanics with gravity, time doesn't behave the way our equations predict it should, and physicists don't know how to fix this.
classical background time(the assumed framework that the statement says is missing): The ordinary, everyday experience of time that flows in one direction—the kind of time described by physics before quantum mechanics was discovered.

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