Explanation of the project.

The purpose of this project is to render a spaceship and examine how it would appear to five different observers. All five observers are to be in different spatial locations relative to the spaceship. The appearance of the spaceship moving by at high speeds is not exactly as it is when the spaceship is at rest. A number of distortions occur to what we actually see. It is important to remember that to 'observe' something depends on at what time the light reaches your eyes. Due to this we cannot rely on length measurement when the object we wish to measure is in motion.

For all the points of view used in this project, the pictures shown can be imagined as taken by a very wide angle camera. The axis of the camera's lens is perpendicular to the plane of the page. The motion of the spaceship is always in the direction of the nose of the spaceship. In each case, the picture is taken so that the origin is in line with the axis of the lens, and the distance (d) is measured along the z-outward axis which would be sticking out of the page. Figure 1 shows the dimensions of the spaceship on wire-frame for clarity.

There are three main effects that take place to change the appearance of the spaceship. The are pictured and explained below. Each figure is two pictures: one of the ship at rest and the other of the ship in relativistic motion. The yellow colored bars in each figure demonstrate the effects.

THE LORENTZ CONTRACTION OF LINES IN THE DIRECTION OF MOTION: (figure 2) The length of lines appear to be shortened in the direction of motion as they recede. The length of lines appear to be lengthened as they approach. This is due to the fact that it takes more time for the light from the ends of the yellow bar to reach your eye than it does for the light from the center of the yellow bar. It takes more time because the distance to travel is longer from the ends of the bar to your eye then the middle of the bar.

The length contraction is quite visible in figure 2.

THE APPARENT ROTATION: (figure 3) The object moving by appears to rotate (yaw). It can be noted that the effects seen are not exactly the same as a rotation. There is no change in perspective as there would be in a rotation and there is also another difference. If you examine the yellow bar in figure 3, you can see that back edge of the spaceship actually curves as the z-outward plane becomes hyperbolic. The matter that blocks the light rays when the ship is at rest actually is moving so fast that it move out of the way and the once invisible light rays become quite visible. This is the effect that leads to an apparent rotation. You can see in figure 3, the back of the ship that you cannot see when at rest, become visible as the ship moves.

THE CURVING OF LINES PERPENDICULAR TO THE DIRECTION OF MOTION: (figure 4) lines that were once straight and perpendicular to the direction of motion, appear to curve into hyperbolas. This is also due to the time it takes light to travel. The light from the wing tips has a longer path to follow to get to your eyes then the light from the center of the ship does. Therefore, the light takes longer to get to your eyes and the effect is the curving of the lines mentioned earlier. This can be clearly seen in figure 4.

There is also another type of distortion that takes place. This is the distortion of the wavelength of light. The wavelengths of light distort in a way that is similar to the lorentz contraction but not exactly. This type of distortion of light is know as THE RED SHIFT. As light rays propagate towards you, you can measure a certain wavelength. The wavelength of the light is what determines the hue of the light. The measured wavelength of light emitted from a source that is at rest turns out to be different then the measured wavelength of light emitted from a source that is in motion. When the light source is approaching the observer the wavelength of the light contracts in a way, causing the hue of the light to shift towards the red end of the spectrum. When the light source is reacceding from the observer the hue shifts towards the violet end of the spectrum. The Red Shift is actually a result of the DOPPLER EFFECT. Unfortunately, throughout the project the only diagrams that show the red shift are the red and the green diagrams. This is because of problems I had getting the colors to blend properly. My original plan was to add the red shift effects to every diagram in which they apply but I couldn't get it to work without just having hard lines separate the different hues.

Using the formulae in the appendix I translated 407 points to new locations to illustrate just how things would look. Using five observers in different locations I covered a wide range of perspectives. I tried to do as many as I could and actually ended up doing two more then I had planned. This was the red and the green observers; added to illustrate the red shift and broaden the array of observers. In the green observer diagram, the white light shifts to become mostly inferred rays with still subtle hints of red mixed in, all other colors become inferred rays. In the red observer diagram, the white light becomes mostly ultraviolet rays with only a little violet showing. All other colors become ultraviolet rays. The next observer is the blue observer. This picture shows an excellent representation of the lorentz contraction and the curving of lines that are perpendicular to the direction of motion. The rotation effect is not to apparent in this diagram because the distance (d) is too great. I used d=5m for this diagram when the top of the ship is only 1.5m tall. The yellow observer diagram is much more effective in illustrating the rotation effect because the d value was selected to b 7m; only one meter from the actual side of the ship. At closer distances the rotation effect distorts the image more than at a greater distance. There is also more of a rotation effect on the yellow diagram because there is much more depth to 'rotate'. The more depth a object has (along the z-outward axis) the more this effect will be noticeable. There is also a visible lorentz contraction effect on the yellow diagram. The orange observer is an excellent depiction of all three distortion effects put together, creating an excellent three dimensional image of the effects of special relativity on objects in motion.