Einstein didn't prove that the velocity of light is constant in all inertial frames through a single experiment or mathematical demonstration. Instead, he developed the theory of special relativity, which incorporated the constancy of the speed of light as one of its foundational postulates. The theory of special relativity provides a consistent and mathematically coherent framework that explains the behavior of objects moving at high speeds.
Einstein's theory was based on two postulates:
The principle of relativity: The laws of physics are the same in all inertial frames of reference. An inertial frame is a reference frame in which an object not influenced by any forces appears to be at rest or moving with a constant velocity.
The constancy of the speed of light: The speed of light in a vacuum is constant and independent of the motion of the source or the observer.
By incorporating these postulates into his theory, Einstein was able to derive a set of mathematical equations that describe the relationships between space and time, known as the Lorentz transformations. These transformations allow for consistent descriptions of phenomena at high speeds and ensure that the speed of light remains constant in all inertial frames of reference.
The constancy of the speed of light was supported by previous experiments and observations, including the Michelson-Morley experiment in 1887, which attempted to measure the motion of Earth through the hypothetical luminiferous ether. The experiment yielded a null result, indicating that the speed of light is constant and independent of the observer's motion.
While Einstein's theory of special relativity provided a conceptual and mathematical framework for understanding the constancy of the speed of light, it is important to note that scientific theories are continually tested and refined through experimentation and observation. The predictions of special relativity have been extensively verified through numerous experiments, further strengthening our confidence in the constancy of the speed of light as a fundamental aspect of the universe.