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.

Is it possible to appear that you’re moving when you’ve actually stopped? (Source: Robert Linder/stock.xchng)

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.

Tags: death, psychology

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Published 26 June 2012

2012 Karl S. Kruszelnicki Pty Ltd

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Comments for this story are now closed. If you would like to have your say on this story, please email ABC Science

26 Jun 2012 5:53:25pm

I once had an officer attempt to book my on my motorcycle, stating I did not stop because I did not put my foot down.
I demonstrated to him, that I could stop for several seconds without putting my feet down. I then demonstrated that I could put my foot down at 60km/h.
End of discussion.

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28 Jun 2012 5:10:41pm

Indeed sir. Several times over the years. I once actually contested it, using a second hand GPS tie I bought specially for the theatrical event. That worked much better than the obvious demonstration of physics and common sense that you and I and many others no doubt could recount. Says rather a lot in itself might I suggest. (What’s worse, I went to public schools!)

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01 Jul 2012 11:48:12pm

I got the same fine. My new BMW had such a fat back tyre, and my balance was that good… I told him I had stopped and gave great detail of every vehicle at the intersection. Including the make, model and colour of car I had to stop behind first – before I got to the line.
He was obviously an a-hole because he scrutinized a brand new bike looking for faults (none found) and said I had to put my foot down. Which I’d know this article then, because, how could he see my foot down as a car goes past and I wait to pull away. All happens in a couple of seconds. Lost 3 points and nearly $300 😦

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26 Jun 2012 8:57:40pm

This paper was an April fools joke. Now. It looks like the author is the fool! Ha!

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02 Jul 2012 10:12:56am

I agree.While no doubt playing up his “underdog” status(as he is well entitled) he bamboozled all & sundry w/ a “sci` paper”,large words in phrases that give the interp` of logic.

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27 Jun 2012 12:25:44am

i don’t like this.

a true scientist would never provide evidence for an event he KNOWS didn’t happen…

thats what lawyers do…

but maybe he was fighting fire with fire?

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27 Jun 2012 1:58:05pm

I tried this once with a red light camera arguing that my 0.36 second infraction of the light was caused by my judgment that, given the state of the road traffic at the time, it would have been more risky for me to brake heavily for the light and so I chose to go through, not having seen exactly when the light turned amber. I got the fine waived but got slugged with costs of $95. The fine was $110 so I got $15 for my time in turning up and waiting for the court appearance – about 3 hours! I think next time I will cop the fine and save my precious time…or better yet don’t breach the camera and potentially cause a rear end accident – but at least it will not be my fault as I was merely obeying the law.

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27 Jun 2012 2:15:25pm

A nice arguement, But I would have questioned him further as to where the Yaris would have been had it not stopped, and where it would have been had it done so. 1.7 sec does not look long enough to stop and restart a car from/to traffic speed, especially a gutless Yaris. Something doesn’t add up. Bull baffles brains!

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27 Jun 2012 5:06:17pm


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27 Jun 2012 5:49:38pm

Or the author could have installed an on-board video/GPS recorder in his car to prove that his speed dropped to zero (but the legal validity of on-board recorders might be questioned)

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28 Jun 2012 12:51:47pm

Surely the Subaru Outback-like car had windows through which the police officer could have observed the varying relative position of the Yaris

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28 Jun 2012 3:46:12pm

Hey Timmy.
Looky here.

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02 Jul 2012 1:06:32am

This same thing happen to my dauther with me in the car and we wish we were this smart to fight and win but she payed the ticket 😦

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02 Jul 2012 12:45:38pm

I have three things to say about this:
1/ If people (both DK and those here regaling us with traffic stories) put this much effort into advocating for real issues of civil rights incursion (because traffic fines are NOT) we would have a fairer society, one not preoccupied with individuals getting pinged for things they most probably did trying to justify why they personally should not have to obey laws that everyone else has to.
2/This story proves those that claim the Sheldon Cooper character on Big Bang Theory is a gross parody of physicists are wrong.
3/If it had been an Australian court he would have done himself in, as the requirement is to stop for minimum of three seconds anyway (at least in SA)

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01 Oct 2012 4:43:02pm

A STOP sign or a STOP line means you must give way to all vehicles travelling in,
entering or approaching the intersection, whether vehicles are turning left or right,
or going straight ahead. You must give way to any pedestrians crossing the road
into which you are turning.
Giving way at a STOP sign means the driver must remain stationary until it is safe
for the driver to proceed.

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09 Jul 2012 12:11:48pm

There are flaws in the chain of events in this sneeze induced max g deceleration based defence. The argument seems to be either 1)the sneeze increased the the force of braking, 2) the sneeze delayed braking until the point where near max g deceleration was needed to come to a full stop before the stop sign line at the junction 3) the acceleration needed from zero to the speed previously being driven requires acceleration of the same magnitude as the previous deceleration


if the sneeze increased the force of braking but brought the car to a safe but momentary halt there has to be an argument that the car could only have been brought to a safe stop by the application of the same degree of braking applied at the same moment in order to have carried out the claimed braking and starting manoeuvre. This leads to two issues:why was the car being driven so fast as to need a near maximum deceleration to come to a safe and legal stop, this argues towards the car being driven too fast for a timely normal halt, which leads to speculation that either the manoeuvre was not carried out or the driver was not driving with due care and attention or that the driver noticed the police officer at the last moment carried out the manoeuvre in order to comply with the stop requirement. This argues that driving profile is not consistent with driving with due care and intention.
The second issue arising from the sneeze is that it may have happened before the stop and the driver once recovering from the sneeze felt it necessary to apply the max breaking manoeuvre. This defence however would be self incrimination as the car would by admission have not been under the control of the driver immediately before the braking event, not being fully in control of the car is an offence to which the sneeze may or may not be a mitigation if the stop had been necessitated by a child running into the road rather than a stop sign that should have already been altering the drivers speed then driving while not fully in command of the vehicle could have had very serious consequences.
In order to accelerate to normal town driving speed and therefore allegedly fool the observing police officer that the car had not slowed would require acceleration of the same magnitude as the deceleration which would be equal to maximum performance 0-30 which is not the normal behaviour or regular drivers.

In addition to the acceleration profile it would be necessary after coming to a halt for the driver to safely assess the road in both directions before commencing the acceleration this would add at least a further second to the elapsed time making the acceleration to steady legal limit driving impossible to achieve.

( the defence did not argue that the car was all ready decelerating before the max braking event, therefore there it would be arguable that the car was traveling at full legal speed before braking and accelerated back to t

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