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Obeying the law is a relative thing

Not all is as it seems when it comes to obeying the law. Dr Karl looks at a case where physics helped a scientist get out of hot water with the authorities.

If you get a traffic fine, in the vast majority of cases it's a fair cop. You fought the law, and the law won. But every now and then, you are genuinely innocent. So take heart from the story of Dmitri Krioukov, a physicist from University of California, who was given a ticket for not stopping at a stop sign.

In court, Dr Krioukov did not merely speak and wave his arms a lot. No, he brought with him a scientific paper that he had written based on his specific situation.

His paper, with the rather leading title of The Proof Of Innocence, claimed that he did stop, and that the police officer's view of the actual act of stopping was blocked by a passing car.

He based his case on three separate circumstances.

The first circumstance is that (using our eyes and brain) we humans do not measure the linear velocity of moving objects - we measure their angular velocity.

For example, suppose that you are standing next to a train line, and that a train is approaching from the distance at a constant speed. Well, at first the train in the far distance seems to be moving very slowly. It has a very low angular velocity - maybe a few degrees every minute.

But as it flashes past right in front of you, it seems to be moving very quickly indeed. It now has an angular velocity of maybe 120° in just a few seconds. It seems that the train sped up as it came past you - but this is an illusion. In reality, the train was always travelling at a fixed linear velocity.

In the case of the alleged offence, the police officer was standing down a side street which was at right angles to the direction of travel of Dr Krioukov. As Dr Krioukov approached the stop sign, his angular velocity was increasing. So the police officer would have thought that Dr Krioukov's car would have been travelling quickly.

The second circumstance is that Dr Krioukov did not drive straight through the red stop sign, without stopping.

Instead, he actually decelerated quickly, reached zero velocity at the stop sign, and then accelerated quickly back to his previous speed. Dr Krioukov maintained in his scientific paper that there was a medical reason for this.

"DK was badly sick with cold on that day. In fact, he was sneezing while approaching the stop sign. As a result, he involuntary (sic) pushed the brakes very hard. Therefore we can assume that the deceleration was close to the maximum possible for the car," he writes.

As a result, according to Dr Krioukov's calculations, the time taken to drop down from his cruising speed to zero at the stop sign, and then back up again was a rather short 1.07 seconds.

The third circumstance involves a bit of a coincidence. Dr Krioukov maintains that during the entire length of the 1.07 second window, the police officer's view was blocked by another car.

Dr Krioukov adds, "the author/defendant (DK) was driving a Toyota Yaris, which is one of the shortest cars available on the market. The exact model of the other car is unknown, but it was similar in length to a Subaru Outback" which is about a metre longer.

If the other car had been travelling at about 19 kilometres per hour, and had been in the right place at the right time, it would have blocked off the police officer's view entirely.

Dr Krioukov concludes, "the police officer made a mistake confusing the real space time trajectory of (my) car, which moved at approximately constant linear deceleration, came to a complete stop at the stop sign, and then started moving again with the same acceleration, for the trajectory of a hypothetical object moving at approximately constant linear speed without stopping at a stop sign. As a result … the police officer's perception of reality did not properly reflect reality".

As a result of all his hard work in writing the paper, and for actually turning up in court to deliver the argument, Dr Krioukov won the case. Or perhaps he won for an even more fundamental reason - he simply pointed out that a passing car had blocked the police officer's view at the critical moment.

Maybe justice is blind after all.

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