The main difference between Albert Einstein's theory of gravity, known as the theory of general relativity, and Isaac Newton's theory of gravity, often referred to as classical or Newtonian gravity, lies in their conceptual frameworks and mathematical formulations.
Newton's theory of gravity, formulated in the 17th century, proposed that gravitational forces act instantaneously across space. According to Newton, gravity is a force of attraction that exists between any two objects with mass. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Newton's theory successfully explained the motion of celestial bodies and other everyday phenomena, and it is still used as an excellent approximation in many situations.
Einstein's theory of general relativity, developed in the early 20th century, presented a profound revision of our understanding of gravity. Instead of considering gravity as a force acting at a distance, Einstein proposed that gravity arises due to the curvature of spacetime caused by the presence of mass and energy. In other words, massive objects like planets or stars warp the fabric of spacetime around them, and this curvature influences the motion of other objects in the vicinity.
To reach his conclusions, Einstein employed a combination of mathematical reasoning and thought experiments. He developed a set of equations known as the Einstein field equations, which describe the relationship between the distribution of matter-energy and the geometry of spacetime. These equations are complex and involve tensors, a mathematical tool for describing the curvature of spacetime.
Einstein's theory of general relativity made several successful predictions that were later confirmed through observations and experiments. For instance, it accurately explained the anomalous precession of Mercury's orbit, the bending of light around massive objects (gravitational lensing), and the redshift of light in a gravitational field.
In summary, the key distinction between Newton's theory of gravity and Einstein's theory of general relativity lies in their conceptual foundations and mathematical formulations. Newton described gravity as an instantaneous force of attraction, while Einstein proposed that gravity arises due to the curvature of spacetime caused by mass and energy. Einstein's theory provided a more comprehensive and accurate description of gravity, particularly in extreme conditions or when considering the behavior of light near massive objects.