Monday, 6 June 2011

How to (Legally) Jump a Red Light.

So I went on an extended hiatus from blogging for a while because I was very busy by my AS-Level examinations. Now with only one exam on physics (MCQ) left I shall temporarily re-enter the blogosphere.

With physics buzzing about in my mind I thought I'd do something about physics. So today I am going to tell you how to jump a red traffic light and get away with it (even if you're caught) using the indomitable power of physics.

Imagine yourself in this situation. You're speeding down a long deserted highway, it's an emergency and you're confronted with one of those annoying red lights. You need to get home as quickly as possible but those sneaky cameras are always on the watch for people who want to bend the rules a bit. What do you do?

Use the Doppler Effect.

I wonder how many will get this reference?

Many people are familiar with the Doppler Effect that's observed with sound. They may be able to recall that the sound of a train which is speeding towards them is at a higher pitch that the sound of the same train when it has passed you and is moving away from you. In simple terms this is because the sound waves in front of the train get squeezed together and has a shorter wavelength and consequently a higher frequency that the waves in front which are stretched out.

The amazing thing is that this Doppler Effect will work with light too because light essentially consists of electric and magnetic fields oscillating at right angles to each other. The colour of the light depends on it's frequency and wavelength. In light it is called the Relativistic Doppler Effect because the effect was first brought to light by Albert Einstein.

So to jump the red light, all we have to do travel fast enough for the red traffic light to be blushifted to a green colour. 

So we apply the equation for the Doppler shift of light. $\frac{\lambda_s}{\lambda_0} = \sqrt{\frac{c-\nu_s}{c+\nu_s}}$.

$\lambda_s$ is the wavelength at the source, which is equal to 650 nm (Typical for red light).

$\lambda_0$ is the wavelength observed, which is equal to 520 nm (Typical for green light).

$c$ is the speed of light which is 299792458 m/s .

$\nu_s$ is the speed of the source away from the observer which is what we need to find. 

If the calculation is carried out you will find that the required speed is about $6.6 \times 10^7 m/s$ or about 237 600 000 km/hr.

And there you have it! Travel at 237 600 000 km/h and you can legally jump the red light because at that speed the red light is no longer red. It is green.

By now, the more intellectually keen reader might have spotted a huge gaping hole hole in this grand plan. A big question will be burning in their minds. The will say, if we are travelling at 237 600 000 km/h are we not breaking the speed limit? However, as it turns out my plan is unbelievably foolproof. At 237 600 000 km/h, you're travelling so fast that any speed trap foolish enough challenge you (which by the way utilizes the Doppler Effect to measure the speed of your car) will find that by the time, it's microprocessors are done calculating your speed and ready to snap a photograph of your numberplate, you'll be miles away. Even if there existed a microprocessor that could calculate fast enough, you'd just be an unrecognizable speed blur on the photograph. 

Well now, we have a another problem don't we? Have you seen it yet? You might be thinking, that if the cameras are too slow to photograph you when you travel that fast, why did I go to all that trouble to calculate the blueshift of light? Why didn't I just tell you at the very beginning, without going through all this rigmarole, that all you needed to do was zoom by at 237 600 000 km/h?

I just felt that getting around the problem using Relativistic Doppler Shift Equations were a more elegant way of bending the rules than just "speeding". That's all.

[EDIT: I watched an episode of the famous Mythbusters in which they showed that all you need to do to beat the speed camera is a car that travels at over 300 miles per hour which translates to about 483 km/hr. So that's the minimum speed you need.]


Disclaimer: The author is not responsible for any unpleasant effects the enthusiastic experimenter may suffer from as a result of carrying out this experiment. Any damages suffered by the experimenter such as those due to relativistic time dilation, time paradoxes, getting lost int time, changing the course of human history etc. are the sole responsibility of the experimenter