Introduction
The purpose of this project was to demonstrate the effects of Special Relativity when one travels at a velocity close to that of the speed of light (around 995%). Using mathematics such as the Lorentz transformations and vector calculus, an accurate depiction was developed of time dilation and length contraction in a three dimensional star field. An equation was also developed to express the Doppler effect which represents the change in frequency of of lightwaves as seen by the viewer, and also exhibits the specific effects of time dilation and length contraction.
Visualizing the Demonstration
Several sources, such as Einstein's On the Electrodynamics of Moving Bodies, were required in order to retrieve the amount of information required to correctly represent Special Relativity. Though the research was never fully complete, a sufficient basis was developed to being coding the first steps of the project. Beginning with a simple star field, this initial code allowed for a base on which to build the final demonstration.
After coding the first star field, a simple proportionality was developed that proved useful in programming the later demonstrations.
After, a function was developed which coded for the Doppler effect which was used in a manipulate of a sphere situated on an x, y, and z axis, with two sliders for change in y position and change in velocity, and it allowed for the sphere to shift from red to blue by using the equation for the Doppler effect.
With a function for the Doppler shift written, it was adjusted in order to program it to function for multiple points, in this case, multiple stars, and was then applied to an adapted code from the original star field. Though it was not the final product, the change of color, when initially applied, did not follow the initial proportionality developed, and therefore the velocity and time were not relative.
For the final demonstration, the shift of the Doppler effect was modified so that as the stars began blue-shifted, but after passing the viewer (represented by a cuboid), redshifted. The same rule applied for stars traveling laterally. Three buttons were creating representing the front, back, and side, and an example of the result is shown below:
Conclusion
When finished, this demonstration successfully illustrated the effects of Special Relativity when traveling at .995% the speed of light through the Lorentz Transformation, time dilation, and length contraction. Thus, it allows us to view Special Relativity in action if, one day, we could travel through a star field at a velocity close to that of the speed of light. In the future, the "Searchlight Effect", otherwise known as "Relativistic Aberration", would be added to improve accuracy and further explore the realms and impacts of Special Relativity.