Newtonian gravity, as described by Isaac Newton's laws of motion and his law of universal gravitation, is incompatible with special relativity due to its assumptions about the nature of space and time.
In Newtonian physics, space and time are treated as separate and absolute entities. Time is assumed to flow uniformly for all observers, and distances and durations are considered to be independent of the relative motion between observers. This framework is known as Galilean relativity.
However, special relativity, formulated by Albert Einstein, introduced a new understanding of space and time. According to special relativity, space and time are unified into a single entity called spacetime, and their measurements depend on the relative motion of observers.
One of the fundamental principles of special relativity is the constancy of the speed of light in a vacuum. This means that the speed of light is the same for all observers, regardless of their relative motion. It also implies that the laws of physics should be the same in all inertial reference frames.
In the context of gravity, special relativity introduces the concept of gravitational time dilation and the curvature of spacetime. According to general relativity, which extends special relativity to include gravity, massive objects such as planets and stars can curve spacetime around them, causing nearby objects to follow curved paths.
In Newtonian gravity, the force of gravity acts instantaneously across distances, which implies an action-at-a-distance mechanism. However, in special relativity, information and causal influences cannot propagate faster than the speed of light. Therefore, the concept of instantaneous action at a distance conflicts with the finite speed of information propagation in special relativity.
Furthermore, special relativity predicts that the passage of time is affected by the gravitational field. Clocks closer to massive objects tick slower compared to clocks in regions of weaker gravitational fields. This phenomenon, known as gravitational time dilation, has been experimentally confirmed.
Therefore, due to the differences in the understanding of space, time, and the behavior of gravity, Newtonian gravity is considered incompatible with special relativity. General relativity, which incorporates special relativity and provides a more comprehensive theory of gravity, is required to explain gravitational phenomena accurately in the context of spacetime curvature.