Einstein's theory of special relativity, published in 1905, revolutionized our understanding of space, time, and the nature of light. The principle that the velocity of light is constant in all inertial frames is one of the fundamental postulates of special relativity. Einstein did not prove it in the traditional sense of a mathematical proof but instead developed a theoretical framework consistent with experimental observations and logical reasoning.
The key concept behind Einstein's formulation is that the laws of physics should appear the same to all observers in uniform motion relative to each other. Based on this principle, he introduced two postulates:
The Principle of Relativity: The laws of physics are the same in all inertial reference frames. An inertial reference frame is one that is either at rest or moving with constant velocity relative to other inertial frames.
The Invariance of the Speed of Light: The speed of light in a vacuum is constant and has the same value in all inertial frames, regardless of the motion of the source or the observer.
To understand how Einstein arrived at this conclusion, let's consider a thought experiment involving two observers, each in a different inertial frame.
Suppose Observer A is stationary, and Observer B is moving at a constant velocity relative to A. Both observers have light sources and are equipped with measuring instruments. According to classical physics, one might expect that if Observer A measures the speed of light emitted by Observer B, it would be different from the speed of light emitted by A.
However, based on Einstein's postulates, he derived the following conclusions:
Time Dilation: Observer B measures time to be dilated compared to Observer A. As B's velocity increases, time appears to slow down for B relative to A. This phenomenon is described by the time dilation equation derived from special relativity.
Length Contraction: Observer A measures the length of B's moving frame to be contracted along its direction of motion compared to B's own measurement. This phenomenon is described by the length contraction equation derived from special relativity.
By combining these observations with the invariance of the speed of light, Einstein showed that for both observers, the measured speed of light is always the same. This conclusion challenges our intuitive understanding of classical physics but has been confirmed by numerous experiments.
Einstein's approach was based on logical consistency, mathematical reasoning, and the need to reconcile experimental evidence with theoretical predictions. His theory of special relativity, which includes the postulate of the constant speed of light, has been supported by extensive experimental verification and forms the foundation of modern physics.