Lightspeed on Your Desktop
One area of physics that is hard to wrap your head around is relativity. Basically, relativity breaks down into general and special relativity. General relativity deals with large masses and high energies, and it describes how space-time is warped by these. Special relativity deals with what happens during high velocities. Many odd and counter-intuitive effects happen when speeds get close to the speed of light, or c. The problem is that these types of conditions are quite far outside normal experience, so people don't have any frame of reference as to what these effects would look like—enter Lightspeed.
Lightspeed is an OpenGL program that shows what an object would look like as it travels closer and closer to the speed of light. Lightspeed actually models four different effects that occur when you get close to the speed of light. The first effect is called Lorentz contraction. This effect causes objects to appear to shrink in the direction of travel. This is scaled by a factor called gamma. Gamma is calculated by:
1 / sqrt(1 - v2/c2).
So, as you can see, as your velocity (v) gets closer to the speed of light (c), the value gamma increases toward infinity. The length contraction is calculated by
l' = l / gamma.
This means the length of an object in the direction of travel (l) decreases toward zero as the velocity increases toward the speed of light.
The second effect that Lightspeed models is Doppler shifting. You probably have noticed the sound version of Doppler shift when a fire truck drives by with its siren on. You can hear the shift in sound frequency from high to low as it goes by. The same thing happens with light too. As a light source comes toward you, it shifts in color toward blue. As it goes away, the color shifts toward red.
The third effect is something called the Headlight effect. When you have a light source that is moving, the amount of light being emitted isn't the same in all directions if that light source is moving. If the light is coming toward you, it will appear brighter. If it is moving away from you, it will appear darker.
The last effect that Lightspeed models is something called optical aberration. Because light travels at a finite speed, the light from different parts of the object come to you at different times. The end effect is that as an object comes toward you, it looks stretched out. And, when it travels away from you, it looks squashed. This is actually different from Lorentz contraction.
So, how can you see what an object would look like, taking all of these effects into account? This is where Lightspeed comes in. Most distributions should have a package available that you can install using their package management system. If you are interested in building from source, it is hosted at SourceForge. When you first start it up, it opens with a cube set in the middle of a field made up of rods for the edges and balls for the vertices (Figure 1). The beginning velocity is set as 1m/s. Since this is an OpenGL program, you simply can grab the cube with your mouse and spin it around, or up and down, in order to change the view of the object. At the far right, you can set the velocity that the object has relative to you, going from 1m/s all the way up to 299,792,457m/s (the speed of light is 299,792,458m/s).
Figure 1. Initial Scene on Starting Lightspeed
You can change the dimensions of the default cube object by selecting the menu option File→New lattice (Figure 2). You can set how many balls will be drawn in each of the three dimensions. You also can change the smoothness factor when the object is rendered on the display. In this case, it will look like what is shown in Figure 3.
Figure 2. Setting the Number of Vertices in Your Object
Figure 3. Altering the Smoothness of the Rendering
You also have the option of loading your own 3-D object, either in 3D Studio format (*.3DS or *.PRJ) or in LightWave format (*.LWO). This new object is what will be rendered, and the optical effects will be applied to this. You can save a snapshot of a particular object at a particular speed in either PNG or TIFF format. You also can export to an SRS file format (Special Relativity Scene). This is a format used by the program BACKLIGHT, which is a specialized raytracer used to illustrate relativistic effects. This lets you generate much higher resolution images of the affected object.
In the Objects menu item, there are options for drawing supplementary objects. By default, the floating grid is selected. You also can select coordinate axes, identifying the x, y and z axes. You can select the display of a bounding box for your object as well (Figure 4).
Figure 4. Displaying Axes and a Bounding Box around Your Object
Additionally, you can animate the scene by selecting Objects→Animation in the menu. This pops up a dialog box where you can select the starting and ending points on the x axis and the loop time in seconds (Figure 5). The scene then will be animated until you click stop.
Figure 5. Setting Options for an Animation of Your Object
Above, I looked at the four effects Lightspeed can model and apply to your object. By default, all of the effects are selected when you start up. If you want to change which effects are being modeled, you can go to the Warp menu item and select any combination of Lorentz contraction, Doppler red/blue shift, Headlight effect or Optical aberration. So, you can select only the Lorentz contraction and see what it looks like at 90% of the speed of light (Figure 6).
Figure 6. Looking at Just Lorentz Contraction at .9c
You have quite a bit of control over the camera as well in Lightspeed. You can select the focal length of the camera lens, going from 28mm to 200mm. You even can set a custom lens focal length by selecting Camera→Lens→Custom. You can set the position of the camera precisely by clicking Camera→Position. This displays a pop-up dialog, where you can set the exact x, y and z values for its location (Figure 7).
Figure 7. Changing Camera Position for a Better View
You can select what information is displayed on the screen by selecting the menu item Camera→Info display. You can have the velocity, the time, the gamma factor and/or the frame rate displayed on the screen.
The default background color is black, but you can change it to gray, white or very white. This display is an OpenGL display, so you can select the rendering mode. The default is shaded, but you can change it to wireframe rendering.
One of the really cool options is that you can spawn off other cameras by selecting Camera→Spawn camera. This lets you see your object from several different angles at the same time. So, now you can see what it looks like coming and going at the same time (Figure 8).
Figure 8. Setting Up Multiple Cameras for Different Perspectives
Once you have the speed and the relativistic effects set, you probably want to interact with the object a bit to see how it looks from different directions and so on. If you click the left mouse button and drag around, your object will be rotated around. If you click the left mouse button and press Shift at the same time, the camera view will be moved around, pointing in different directions. You can move the camera itself by clicking the middle mouse button and moving it up and down or left and right. You can move the camera in and out from the object by clicking the right mouse button and sliding up and down. If you completely mess up your view, you always can go back to the defaults by clicking the menu item Camera→Reset View.
So, remember this program when you are studying special relativity. Now you finally can see what it would really look like if you were traveling down the tunnel with the protons in the LHC or what the Starship Enterprise would look like as it flew by at sublight speed.