The concept of the curvature of spacetime is not merely a mathematical language but a fundamental aspect of Einstein's general theory of relativity, which has been extensively supported by experimental evidence. According to general relativity, the presence of mass and energy causes spacetime to curve around them, leading to what we perceive as gravitational attraction.
In this framework, massive objects like the Sun or Earth create a curvature in spacetime. Other objects, such as planets or satellites, move along the curves of this curved spacetime. The motion of these objects is not due to a force pulling them directly towards the massive object, but rather because they follow the curved path dictated by the geometry of spacetime.
To understand this concept more intuitively, imagine placing a heavy ball on a stretched elastic sheet. The ball creates a curvature or depression in the sheet, and if you roll a smaller ball nearby, it will naturally move towards the larger ball due to the curvature of the sheet. Similarly, in general relativity, the curvature of spacetime caused by massive objects results in the motion of other objects along curved paths, appearing as gravitational attraction.
Experimental observations, such as the bending of light around massive objects (gravitational lensing) and the precise predictions of the motion of planets, have confirmed the validity of general relativity and the role of spacetime curvature in explaining gravitational phenomena.
So, to summarize, the curvature of spacetime is not just a mathematical abstraction, but a physical concept that describes the interaction of mass and energy with the fabric of spacetime, leading to the phenomenon of gravitational attraction.