There are plenty of ways to get out of a traffic ticket: charm, flattery, fakery, full-on tears, "My uncle is a cop"
all come to mind. Submitting a four-page paper with math equations and graphs proving that your traffic violation was the result of the officer suffering from an optical illusion isn't the strategy most people would employ. It worked, though.
In his paper "The Proof of Innocence" Dmitri Krioukov, a physicist at the University of California in San Diego, outlined for a judge the mathematical reasons why he was not guilty of running a stop sign. It may seem like a lot of effort for one ticket, but Krioukov is no longer on the hook for the $400 he owed.
In making his case, Krioukov wrote that a police officer can perceive a car as not having stopped -- even though it really did stop -- if three different criteria are met:
"(1) the observer measures not the linear but angular speed of the car; (2) the car decelerates and subsequently accelerates relatively fast; and (3) there is a short-time obstruction of the observer's view of the car by an external object, e.g., another car, at the moment when both cars are near the stop sign."
For those who'd like a simpler explanation, the blog Physics Central broke down Krioukov's argument in layman's terms with an illuminating analogy about trains:
When Krioukov drove toward the stop sign the police officer was approximating Krioukov's angular velocity instead of his linear velocity. This happens when we try to estimate the speed of a passing object, and the effect is more pronounced for faster objects.
Trains, for instance, appear to be moving very slowly when they are far away, but they speed past when closer. Despite these two different observations at different distances, the train maintains a roughly constant velocity throughout its trip.
In addition to including colorful diagrams, Krioukov was thorough with his details of the events that transpired: he wrote of having a cold on the day of the supposed violation and expounded on the impact a single sneeze had.
"D.K. was badly sick with cold on that day. In fact, he was sneezing while approaching the stop sign. As a result he involuntary pushed the brakes very hard. Therefore we can assume that the deceleration was close to maximum possible for a car."
Still, in his conclusion, Krioukov was understanding towards the officer in question.
"This mistake is fully justified," he wrote, reiterating the three factors at play that led to the errant ticket. "The O's perception of reality did not properly reflect reality."