Monthly Archives: March 2014
Some days ago, the proclamation of a “major discovery” in physics was announced and will be unveiled on Monday during a conference at the Harvard-Smithsonian Center for Astrophysics. Naturally, the physicists gossip factory is working overtime and it is spectulated that this major discovery could be somehow related to a proof of gravitational waves. This would be great and exciting news, of course!
But here and today I don’t want to make speculations and guesses, but take the opportunity to write about a particular aspect of the special theory of relativity. (All the recent estimates of the “major discovery” probably were decisive for me having the idea to answer the question of…
…how to actually see around a corner.
Presumably, everyone knows that the light’s speed isn’t infinitely big, but only finite. Light always travels at 300 000 kilometers per second (186 300 miles per second). This also means, technically speaking, that the picture we get from our environment is somewhat time-delayed since the light has to find its way into our eyes first, which inevitably takes some time.
For the sake of simplicity, let’s replace our eyes with a simple pinhole camera from now on. So for our purposes, the optical device is just a plain box with a little hole in one of its sides through which light can reach the rear wall. (There, in the case of a real pinhole camera, would be a photosensitive plate or something similar to caputure a picture of the environment.)
“Seeing” in our pinhole camera model works in a simple manner: Light falls through the small opening and travels along a straight path until it hits the rear wall (which corresponds to the retina in a real human eye). Then we can determine the light’s point of impact and only after that are we able to reconstruct the original direction of the light beam: We do this by (notionally) drawing a line which goes through both the point of impact and the hole. Hence, it suffices to know the point of impact on the backmost wall in order to find out the original path of the light.
I tried to visualize this process as well as possible in the following animation. Also, this might be a good moment to point out that the angle of the incoming light and the angle of the notional, reconstructed line are exactly the same here.
However, the situation changes if the camera stops standing still and starts moving towards the incoming light. What happens then can be seen in the following animation: The camera “runs to meet the light”, which results in the light travelling for a smaller amount of time and sooner reaching the wall. The crucial point here is that the point of impact moves towards the center of the rear wall due to the light being headed off from its straight path early and, compared to the case of the unmoving camera, having less time to make its downward way. If we subsequently reconstruct the original direction of the light (again, in drawing a line through the impact point and the hole), the resulting line differs from the line of the initial path. In the animation, this is emphasized by the crayoned angle between the initial and the reconstruced beam direction. From our point of view – the one of the camera – it appears that the light arrives from a shallower angle than it actually does.
Now imagine that the shift towards the wall center due to the camera’s motion goes for all impact points. This, strangely enough, results in the perceived picture being warped towards a single point which lies in direction of motion.
The faster the camera moves the more dramatic this effect becomes, of course. If it moves fantastically faster – with a speed near the light speed -, it’s even possible for the camera to capture photons which aren’t initially moving towards it. This might look like this:
The contraction of the picture towards a point in direction of motion in this case is even more drastical: Even light with velocity components parallel to the camera’s direction of movement (i.e., light that partly comes “from the back”) can reach the camera and can be caputured.
This is the reason why one can see around corners if she/he moves with speeds comparable to the speed of light: While dashing along, you just catch and capture light that was reflected on the facing-away side of the corner.
We cannot see this effect in our daily lives, just because the light speed is enormously big compared to our normal motion speeds. It only becomes apparent at high speeds.
As a last point, I really like to recommend some short animations which impressively visualize the above-explained effect. In these videos, the numerical value of the light speed was defined as a much lower number than 300 000 km/s, which enables us to see relativistic effects at even slow speeds. Let me tell you one thing: The world seems bizarre to fast travellers!
(It’s impossible, alas, to embed the videos here, so I’ll directly link to them. You probably have to allow your browser the execution of a player plugin. All animations are made by Ute Kraus and can be found on http://www.tempolimit-lichtgeschwindigkeit.de/)
- Approaching the Brandenburg Gate of Berlin, Germany, with speeds so low that we are actually used to them.
- Approaching it with 90 per cent of the light speed (0.9c): Although you are always moving towards the gate, it looks like the gate would move away from you initially. Indeed, this is due to the contracting effect which I have described today.
- It goes on: Flying through the Brandenburg Gate with 0.9c: Especially concentrate on the picture margins shortly after passing through the gate – you can indeed see some parts of the backside of the building. So you can literally look around the corner.
- Finally, here’s a fast (!) city tour with 99 % of the light speed. Fasten your seatbelts!