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Visualizing Relativistic Squirrels

Over the years, I've noticed that squirrels living on the campuses of universities and colleges are somewhat "troubled". Imagine you come across a deranged squirrel and you see it suddenly racing towards you at 10 kilometers per hour (based on a true story…). For some reason, you decide to run towards it at 10 kilometers per hour (in reality, I ran faster and in the opposite direction). How fast will you see the squirrel attack you? Well, 10 plus 10, that's 20 kilometers per hour. This is the good old velocity addition rule that we all instinctively relate to. Let's change things a bit. The deranged squirrel now runs towards you at three quarters the speed of light… you run towards it at three quarters the speed of light. How fast will you now see the squirrel attack you? Three quarters plus three quarters, that's 1.5 times the speed of light, right? Wrong! 

The velocity addition rule we are all used to is only approximately correct and works well for speeds much much less than the speed of light (which is 300,000 kilometers per hour). When the speeds involved get more than 10% that of light, the usual velocity addition rule will give you the wrong answer appreciably. The correct answer is obtained using the Special Theory of Relativity. Developed in 1905 by Einstein, Relativity proposes that the speed of light is a law of Nature; and that laws of Nature should appear the same to all observers moving with constants velocities. These are the two postulates of Relativity. They were inspired by the development of Electromagnetism a few decades before - light is after all an electromagnetic disturbance. If the speed of light is to appear the same to different observers that are moving around, you can't then just add velocities… a carefully revised thought process can then tell you that there must be an upper limit on speeds in Nature - a speed limit given by the speed of light. In short, no information can travel faster than the speed of light. 

As a result of the existence of a bound on speed, there is always a time lag in the relay of information. When you are imaging the world with your eyes, light is reaching your eyes from all directions to give you a picture of the world. If you start moving around at speeds comparable to that of light, different objects around you - located at different distances - may start projecting their images in an appreciably asynchronous manner - with a time lag related to how far away they are from you at different points in time. Basically, the light from the objects is playing catch-up with your fast changing position. This creates elaborate distortions of the world as you perceive it. For example, if a squirrel whizzes by you at half the speed of light, you'll see the squirrel 87% thinner… So, how would then the world look like if you were able to travel at speeds near that of light?

The accompanying video was developed as part of a PhD thesis by a graduate student in physics. It is an actual genuine simulation of how things would look like if you were to travel at high speeds. The video has a voice over (a really really bad one), but it would still help if I give a brief guide of what you are about to watch. On the top right corner of the video, you will sometimes see numbers like 0.280 c; this simply means 28% of the speed of light - it's an odometer readout. On the lower left corner, you will see the greek letter gamma (looks like a V) next to a number; this is called the gamma factor and tells you how abnormal things are getting compared to the usual perspective you're familiar with at slow speeds: the closer is gamma to one, the more "normal" are things. For example, the waistline of the squirrel mentioned earlier is given by its original size divided by gamma; for gamma equal to one, there is no distortion. There are three visual effects in Relativity that one needs to consider when trying to picture how things look like at high speeds: geometric aberrations, the doppler effect, and the intensity effect. The video turns these effects on one by one to demonstrate things in a more manageable manner. Geometric aberrations distort the shape of things, like the thinning of the squirrel's waistline. The doppler effect shifts the color of light that you see according to the speed you are moving with. And finally, the intensity effects concentrate the light around you to a point in front of you - along the direction you are heading. Now, time to play the video. Prepare yourself for a real freaky show. Remember, this is absolutely realistic, it is a simulation not just a random animation. I think you'll agree that the first astronaut who will experience these effects will need to change underwear soon afterwards.

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