Special relativity creates its own optical illusion

Special relativity is best known for letting us know that, as a person's velocity increases, their perception of time slows down. It also creates an interesting little optical illusion that can make objects moving in a straight line appear to twist and turn.

Visualization of special relativity by Joseph Choi

Einstein's theory of special relativity is so popularly known is because it's simple enough for laypeople to understand, but strange enough that we never stop puzzling over it. Two people, one at rest by the side of the road and one in motion on a car, compare watches. The person at rest sees that the person in motion's watch is slow. The person in motion thinks their watch is just fine. They are both right.


Relativity and Physical Changes

Time turning into something that can be stretched out, depending on your particular point of view, is odd enough. Just to confuse people even more, there are things like length contraction. The person in the car will see the car as exactly the same length in motion as it was at rest. To a person sitting by the road, on the other hand, the car will be slightly shorter, and will continue shrinking as it moves faster and faster. The two observers see different things. Again, they're both right.

Except for the fact that the person on the ground doesn't quite see those things. Although length contraction is quite real, it's a logically thought-out consequence of relativity, and not something that is actually observed when it comes to big objects like cars. It's not actually observed, in part, because the person "sitting by the road" would be killed the moment a train going at 80 percent the speed of light came by, and in part because there are so many other weird effects going on with that car that no observer would think to mention the length.


We see because of light, and we see reliably because, when it comes to the world we usually look at, not much has changed between the light leaving its surface and the light smacking into our eyes. When the object approaches the speed of light, a lot can change between light leaving its surface and hitting our eyes, and that makes for some very strange illusions.

The Strangeness of Terrell-Penrose Rotation

Terrell-Penrose Rotation is tough to search for by name. James Terrell and Roger Penrose both published papers about the phenomenon in 1959, and the nomenclature of Terrell, Terrell-Penrose, and Penrose-Terrell rotation has been gently disputed ever since. Whatever it's called, it's a hell of an optical illusion.


Imagine sitting by the side of the road and seeing a car slowly roll past you. All the light you are seeing, including the light from the distant mountains you can see through the car windows, makes the trip to your eye so fast that it doesn't matter how far away the objects you're looking at are. The fraction of a second it takes for the light from the far side of the car to travel across the width of the car and then to you doesn't make a difference.

Once the car gets up to, say, 80 percent the speed of light, that trip across the width of the car does make a difference. There's a reason you never see the back bumper of a car that's traveling towards you, or is just in front of you. Any light that gets bounced from the back bumper towards your eye runs smack into the rest of the car. When the car is going fast enough, this is not the case.


Let's say, a photon takes a second to get from one side of that car to the other. (It would be a very wide car, but dealing in 1/186,000 th fo a second is too much of a hassle.) The photon hits the car one second before it pulls even with you. The photon starts making the trip towards you, and, since the car is moving fast enough, nothing is in the way. The car has literally driven out of the way of the photon.


One second later, the car is even with you. Of course, you don't know that because the photons from it haven't hit your eye yet. If the car were still, the photons that set out from the car and hit your eye would show you a perfect side view of it. Since the car is in fast motion, the photons from the side of the car have a companion – that one little photon from the back bumper that has spent the last second traveling the width of the car. So, when the entire group gets to you, you are not just seeing that perfect side few of the car, you are seeing the perfect side view of that car and all the photons from the back bumper. You are seeing the side and the back at once.

As this is very like the view you would get if the car had rotated slightly away from you, it would probably look as if the car had turned suddenly, and slightly, away from you. That's Terrell-Penrose rotation. Obviously, it wouldn't look perfect. The overall picture, if you snapped a photo, would look off – a perfect side view with a little bit of back view as well. It would have a weird cubist look to it. Overall, it will look like a rotation, even though the car is moving only in a straight line. It's an optical illusion that you could only see if you could see objects moving at relativistic speeds close up.


[Via Inside Relativity, UBC.]


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