The connection between Newton's laws of motion and Einstein's theory of relativity was established through the work of several physicists and mathematicians. However, it is important to note that Einstein's theory of relativity does not simply emerge as a direct consequence of Newton's laws, but rather as an advancement and refinement of them that applies in specific situations.
One of the key figures who played a significant role in bridging the gap between Newtonian physics and relativity was the French mathematician and physicist Henri Poincaré. Poincaré made important contributions to the understanding of the principles of relativity and the mathematics behind it. He investigated the behavior of physical laws under coordinate transformations and demonstrated that Newtonian mechanics could be reformulated to account for the principles of relativity.
Another influential figure was the Dutch physicist Hendrik Lorentz. He developed a set of equations, known as the Lorentz transformations, that described the behavior of space and time coordinates under relativistic effects. These transformations allowed for the reconciliation of Newtonian mechanics with the principles of special relativity, including the constancy of the speed of light.
The final piece of the puzzle came from Albert Einstein himself. In his 1905 paper "On the Electrodynamics of Moving Bodies," Einstein presented his theory of special relativity, which built upon the work of Poincaré and Lorentz. Einstein demonstrated that by incorporating the constancy of the speed of light and the principles of relativity into Newton's laws of motion, a more comprehensive and accurate description of physical phenomena could be achieved.
Einstein's theory of general relativity, which extended his special theory to include gravity and the curvature of spacetime, was further developed by Einstein and other physicists in the following years. The mathematical formulation of general relativity involves a set of highly complex equations known as the Einstein field equations, which describe how matter and energy affect the curvature of spacetime.
In summary, while no single individual "proved" that Newton's laws imply Einstein's laws, a combination of contributions from various scientists, including Poincaré, Lorentz, and Einstein himself, led to the development of the theory of relativity as a more comprehensive and accurate description of the laws of physics in certain regimes, surpassing the limitations of Newtonian mechanics.