The Basics of Special Relativity and Length Contraction

Special Relativity is a theory developed by Albert Einstein in 1905 in order to explain why certain experimental results gathered on the physics of light did not follow the previously accepted laws of classical mechanics. While it was initially heavily questioned by physicists when the theory was first hypothesised by Einstein it is now widely accepted in physics for explaining certain phenomena. Originally, light was believed to have a set speed which many believed could be measured given the correct experimental setup. This led Michelson and Morley to set up an experiment in 1887 which was designed to measure the speed of light as it passed through our world. However, they realised that there was no experimentally detectable difference in the speed of light through any previously hypothesised medium in which light travelled in comparison to what was expected. This led to many people wondering how this could be reconciled, leading to Einstein theorising Special Relativity.

Special Relativity takes a non-intuitive approach to how it sets up its system when compared to classical mechanics. By setting the speed of light in a vacuum to be the upper limit on how fast an object can travel, this lead to many strange results, one such event being that the closer to this speed you get, the slower it seems that time passes for you if others are observing you while they are motionless. This concept leads to the idea of length contraction. Taking two systems, one motionless where we have one observer present, system 1, and another system moving close to the speed of light with an object of a known length moving at the same speed, system 2, we can see that length contraction occurs. As seen in the graph below, if system 2 starts moving at a speed near the speed of light it will appear to squeeze the axes of system 1 to be narrower in comparison to system 1 itself. This needs to happen as time seems to slow down when an object moves close to the speed of light in a different frame as demonstrated by the graph. For an object in system 2 as it moves at this high speed it has a real length, as can be seen by the black dotted line along the changed distance axis, x’. However, a motionless observer in system 1 will see a shorter apparent length as the object continues to move. This can be seen in the graph as the constant length of the object in system 2 is shorter than the constant length in system 1. The measurement of length in neither system is incorrect as the measurement of length is ‘relative’ to each observer. This relative measurement of values depending on the scenario observed is what gives special relativity its name.

Due to its impact on how certain measurements are read for high speed objects, length contraction has a massive impact on physics and needs to be factored in and used frequently when measuring objects moving at very high speeds, which is fundamental in fields of research such as particle physics and astrophysics.

Fig: Space-Time Diagram describing how length contraction occurs at speeds close to the speed of light. x’ = distance axis moving near the speed of light, ct’ = time axis moving near the speed of light