Physicist Dmitri Krioukov knew he didn’t deserve the traffic ticket he received for disobeying a stop sign. If it came down to his word against the police officer’s, however, he knew he would likely lose his case. Not one to easily give up, Krioukov went to work, using his expertise in his field of study, to prove his case. He not only proved his innocence, but he published his work and received a prize for his efforts.

Krioukov used mathematical proofs to show that the police officer could not have witnessed the alleged traffic violation. His paper, “The Proof of Innocence,” shows three coincidences happened at the same time to make the police officer erroneously believe that he had seen a stop sign violation:

“[In this paper], we show that if a car stops at a stop sign, an observer, e.g., a police officer, located at a certain distance perpendicular to the car trajectory, must have an illusion that the car does not stop, if the following three conditions are satisfied: (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.”

Krioukov maintained that because the police officer was approximately 30 meters from the intersection where the stop sign was situated, “a car approaching the intersection with constant linear velocity will rapidly increase in angular velocity from the police officer’s perspective.”

The paper includes graphs that demonstrate what would have happened to his angular velocity if he had either been driving at a constant linear velocity or, as he maintains happened as a result of a sneeze, had made a quick stop and then accelerated back to speed. Krioukov says it was during the sneezing incident that another vehicle interrupted the line of sight between the police officer and Krioukov’s car.

Krioukov is quick to point out that the police officer did not fabricate events but simply perceived things incorrectly due to an optical illusion.

Krioukov published his findings and received a $400 special prize, representing the amount that he would have had to pay in fines and court costs had he not successfully contested the citation.

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