Question

Let's have two objects touching each other, i.e. you standing on the earth. We propel the smaller object directly away from the larger, i.e. you jump. The objects move apart, slow down and then return along the same path. According to Einstein, what's happening here is that the mass of the objects are bending space causing the straight line of my momentum to appear to bend in a 180 degree angle. However, because Einstein also says that this bending of space is happening in the forth dimension we can safely assume that we are not dealing with Euclidian geometry. So according to the math what is that angle if not 180 degrees? Also that bend causes an acceleration of 9.8 m/s/s, correct? Would different angles change that acceleration? More precisely what is the relationship between the angle and the acceleration? Bonus question: What does that bend look like at a black hole?

Answer 1

Einstein's general relativity describes gravity as the curvature of space-time caused by mass. The concept of angles from traditional Euclidean geometry doesn't apply in curved space-time. The 9.8 m/s^2 acceleration due to gravity is a local feature of Earth's space-time curvature and does not vary based on the angle of motion in curved space-time.

Step-by-step explanation:

Understanding Gravity in Einstein's General Relativity

According to Einstein's theory of general relativity, mass warps the fabric of space-time, which results in the gravitational attraction we observe. This is often visualized as a deformation in a two-dimensional plane, but in reality, it is a complex distortion in the four dimensions of space-time. The angle of a trajectory in this context isn't measured in traditional Euclidean geometry, but rather in the geometry of curved space-time. Hence, the notion of a 180-degree angle in a Euclidean sense does not apply when considering the curvature caused by mass in space-time.

The acceleration due to gravity near the surface of the Earth, which is approximately 9.8 m/s2, is the result of this space-time curvature. Different angles of trajectories in curved space-time wouldn't alter this value, because locally, the acceleration doesn't depend on the direction of motion; it's a property of the space-time itself around the Earth. Any object, regardless of the path it takes when released, will experience this same acceleration. When one approaches a black hole, the curvature of space-time becomes extremely steep. The 'bend' near a black hole would be of such magnitude that the space-time provides a barrier called the event horizon, beyond which escape is impossible even for light. This intense curvature means the object—or in Einstein’s thought experiment, a light ray—would curve so sharply that it cannot escape the gravity well of the black hole.