On Special Relativity

Alan Cai

Decemer 15, 2023

Special relativity seems ostensibly intimidating. It is, along with general relativity and mass-energy equivalence, one of Einstein’s most prominent and unifying theories. Yet, despite its revolutionary nature and academic prestige, its core principles are not too difficult for non-scientists to understand. Most special relativity simplifications invoke an elevator or truck analogy. In this article, I will attempt to explain it in the most direct way.

The speed of light is constant in all vacuum reference frames. Maxwell’s equations and various astronomy experiments can provide evidence to support this theory but only varying material types will have the ability to affect the speed of light. For the purposes of this article, we will assume all activities occur in a vacuum.

Light moves at 299,792,458 meters per second exactly. Since the meter is pegged on the speed of light, more accurate measurements of c(the abbreviation for the speed of light) will result in more accurate definitions for the meter rather than a more precise constant.

Consider observing light moving from left to right in front of your eyes, perhaps as any flying insect would. It is moving at exactly 299,792,458 meters per second. Now imagine that you are moving at a significant fraction of the speed of light and have a flashlight pointed forward. An observer watching you move from left to right would observe the light from the flashlight moving at 299,792,458 meters per second while you move right behind it at an appreciable fraction of c. Thus, it should be reasonable to expect that light is leaving you at c-[your speed]. However, it is actually still moving away from you at c because we have previously postulated that light moves at the same speed in all inertial reference frames.

Where does the discrepancy come from? How can light be moving away from you at c, and yet still be moving at c when you are traveling at a considerable fraction of c in the direction of the light? Einstein theorized that in order for both to be true, time must travel slower for you than for the observer. Therefore, light can be moving away from you at 299,792,458 meters per second and still be moving at 299,792,458 meters from the perspective of a spectator observing you and the flashlight.

Special relativity is the dominant modern theory that relates space and time. It, along with Einstein’s other theories, forms the key link between Newtonian physics and modern experimental results.