Final answer:
Spacetime stretches and curves in the presence of matter, and this curvature is what we perceive as gravity, affecting the motion of objects and light, such as through gravitational lensing.
Step-by-step explanation:
What Causes Spacetime to Stretch and Curve?
The essential concept of Einstein's general theory of relativity is that matter causes the fabric of spacetime to stretch and curve. This phenomenon is essentially what we perceive as gravity. For instance, when a beam of light or an electron moves through this curved spacetime, its path is altered compared to if it were moving through uncurved, or flat, spacetime.
Gravitational lensing is one example of this effect. When light passes near a massive object like the Sun, spacetime is more strongly curved, and the path of the light bends, making distant stars appear in slightly different positions than where they actually are. It's not that the light is directly influenced by gravity, but rather the light is traveling the shortest path through a distorted spacetime - which is curved due to the mass of the object.
The curvature is a result of the mutual influence between space and matter. As John Wheeler succinctly put it, “Matter tells spacetime how to curve; spacetime tells matter how to move.” Thus, massive objects dictate spacetime curvature, and that curvature then determines how other objects and light will move.