[paulhodge]

When your game does regain control, it can run the simulation for N steps (however many it usually does for the given dt), then finally render the scene using the latest state. (so the game will appear to pause, then skip ahead). Or it can try to play catch-up, it does 1 tick and render at a time, but with a reduced delay between frames until it's "caught up". (so the game will pause, then appear fast-forwarded for a bit).

Either way Tlark is right, you really don't want the game logic to be affected by framerate.