The Mathematical Proof that got a Physicist out of a Traffic Ticket

Dmitri Krioukov, a UC San Diego physicist, was recently given a ticket for running a stop sign. He went to court to argue the ticket, armed with a scientific paper that mathematically demonstrated that he really had stopped. He won.

Krioukov has since posted the entire paper, rather immodestly called "The Proof of Innocence", on the arXiv server. It's probably debatable how much his ironclad mathematical reasoning really helped determine his innocence - it's just as likely the judge threw out the ticket when it was demonstrated another car had obstructed the ticketing police officer's view. Still, let's take a look at one of science's most audacious papers, albeit a fairly mundane sort of audacity:

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 satised: (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.

So then, according to Krioukov, this triple coincidence created the illusion that the car had never stopped. He goes into some further detail into his introduction about just why the difference between linear and angular velocity is so crucial here:

It is widely known that an observer measuring the speed of an object passing by, measures not its actual linear velocity by the angular one. For example, if we stay not far away from a railroad, watching a train approaching us from far away at a constant speed, we first perceive the train not moving at all, when it is really far, but when the train comes closer, it appears to us moving faster and faster, and when it actually passes us, its visual speed is maximized.

This observation is the first building block of our proof of innocence. To make this proof rigorous, we first consider the relationship between the linear and angular speeds of an object in the toy example where the object moves at a constant linear speed. We then proceed to analyzing a picture reflecting what really happened in the considered case, that is, the case where the linear speed of an object is not constant, but what is constant instead is the deceleration and subsequent acceleration of the object coming to a complete stop at a point located closest to the observer on the object's linear trajectory. Finally, in the last section, we consider what happens if at that critical moment the observer's view is briefly obstructed by another external object.

Krioukov then uses a bunch of graphs and mathematical calculations to reach the now legally inescapable conclusion that "police officer O made a mistake", one that was "fully justified" because, "as a result of this unfortunate coincidence, the O's perception of reality did not properly reflect reality." Feel free to read in as much or as little disdain into that conclusion as you want.

Of course, all this could most likely have been avoided if Krioukov had actually stopped for more than a split-second, which really would have been the safe thing to do in the first place. Minor road safety scolding aside, though, I say kudos to the physicist. Also, I have the sneaking suspicion Dr. Krioukov should start working on his Ig Nobel acceptance speech...

Check out the full paper at arXiv. Via Physics Central. Image by thecrazyfilmgirl on Flickr.