The statement that the curvature of spacetime is "just a mathematical language" and not real is not accurate. In modern physics, the concept of spacetime curvature is a fundamental aspect of our understanding of gravity and is supported by a vast body of experimental evidence.
According to Einstein's general theory of relativity, mass and energy cause spacetime to curve. Objects with mass or energy create a curvature in the fabric of spacetime around them. This curvature then influences the motion of other objects in the vicinity.
When an object, such as the Earth or a satellite, moves through this curved spacetime, it follows a path determined by the curvature. This path appears to us as the force of gravity. Objects with mass-energy are not attracted to the Sun or Earth in the sense of a force pulling them directly. Instead, they move along the natural paths dictated by the curved spacetime geometry.
The concept of spacetime curvature has been extensively tested and confirmed by numerous experiments and observations. For example, the deflection of light by massive objects, such as the Sun, is consistent with the predictions of general relativity. The precise predictions made by the theory, such as the perihelion precession of Mercury and the gravitational redshift of light, have also been experimentally verified.
It's worth noting that while the curvature of spacetime is a mathematical description, it has physical consequences and measurable effects. It provides a comprehensive framework for understanding the nature of gravity and its effects on the motion of objects with mass and energy.