Albert Einstein's development of the theory of special relativity, which includes the idea of time dilation with increasing velocity, was driven by a combination of theoretical considerations and experimental evidence.
One of the key motivations for Einstein was the desire to reconcile the laws of electromagnetism, as described by James Clerk Maxwell's equations, with the principles of classical mechanics. Maxwell's equations predicted that the speed of light in a vacuum is constant and independent of the motion of the observer or the source of light. However, classical mechanics, based on Newtonian physics, suggested that the laws of physics should behave the same way in all inertial reference frames.
Einstein started by reexamining the foundations of classical mechanics and the assumptions about space and time. He proposed that the laws of physics should be the same in all inertial frames of reference, regardless of their relative motion. This led him to develop the theory of special relativity, published in his groundbreaking paper in 1905, "On the Electrodynamics of Moving Bodies."
In special relativity, Einstein introduced the concept that the speed of light is constant for all observers, regardless of their motion. This principle forced him to revise our understanding of space and time. He proposed that space and time are not absolute and separate entities but rather are combined into a four-dimensional continuum known as spacetime.
Through mathematical analysis and thought experiments, Einstein derived the Lorentz transformations, which describe how measurements of space and time intervals change for observers moving relative to each other. The Lorentz transformations revealed that as an object's velocity approaches the speed of light, time dilation occurs—meaning that time appears to slow down for the moving object as observed from a stationary reference frame.
Einstein's conclusions were later confirmed by experimental evidence, such as the famous Michelson-Morley experiment, which failed to detect the expected motion of Earth through the hypothetical "ether" medium. Subsequent experiments, including particle accelerators and high-precision atomic clocks, have provided further evidence for the reality of time dilation at high velocities.
In summary, Einstein's development of the theory of special relativity and his conclusion about time dilation with increasing velocity stemmed from his desire to reconcile the laws of electromagnetism with classical mechanics and were supported by both theoretical considerations and subsequent experimental observations.