Albert Einstein's theory of special relativity revolutionized our understanding of space, time, and the nature of light. He did not prove the constancy of the speed of light in all inertial frames through a single experiment, but rather developed the theory based on a series of logical arguments and thought experiments.
One of the key postulates of special relativity is that the laws of physics are the same in all inertial reference frames, which are frames of reference that move at a constant velocity relative to each other. From this postulate, Einstein derived several important conclusions, including the constancy of the speed of light.
To understand how Einstein arrived at this conclusion, we need to explore the thought experiments he used. One of the most famous is the "light clock" thought experiment. Imagine a clock consisting of two mirrors facing each other, with a beam of light bouncing back and forth between them. The time it takes for the light to travel from one mirror to the other and back can be used to measure time.
Now, let's consider two inertial reference frames, one stationary and the other moving relative to the first at a constant velocity. According to classical physics, if the moving frame is traveling in the same direction as the light beam in the light clock, the light would have to travel a longer path in the moving frame because the mirrors are in motion. Consequently, the time measured by the light clock in the moving frame should be longer than the time measured in the stationary frame.
However, Einstein argued that if the laws of physics are the same in all inertial frames, then the measured speed of light should be the same in both frames. To reconcile this with the assumption that the time is longer in the moving frame, he introduced the concept of time dilation. According to time dilation, as an object moves faster relative to an observer, time appears to pass more slowly for that object.
Using this concept, Einstein concluded that the moving frame must experience time dilation to compensate for the longer path the light beam travels. In other words, time slows down for the moving frame so that the measured speed of light remains constant. This conclusion led to the famous equation E=mc², which shows the equivalence of mass and energy.
Einstein's theory of special relativity has been supported by a wealth of experimental evidence gathered over the years, including measurements of the speed of light in different inertial frames. These experiments consistently confirm that the speed of light is constant and independent of the motion of the source or the observer.
While Einstein did not prove the constancy of the speed of light through a single experiment, his logical reasoning and thought experiments laid the foundation for special relativity, providing a profound understanding of the nature of space, time, and light.