Question

On cseligman.com, it is written that

So, we see things falling with an acceleration which we call the acceleration of gravity,and thinking that we live in a straight line , uniformly moving or stationary inertial frame, we attribute that acceleration to a force, the force of gravity. Whereas in reality,objects falling towards the Earth are moving along geodesic paths with no acceleration and according to modified version of law of inertia, have no force acting on them. They fall simply because the curved space-time near the Earth ...
Now, why do the objects falling towards the Earth move along the geodesic paths with no acceleration? That means the objects don't have any force acting on them, but why? A body in a free-fall moves with acceleration g
, so, why is it written like that? Why does the author use Law of inertia on freely falling body?? Law of Inertia can only be applied when no external force acts on the body. So, is the freely-falling body accelerates under force of gravity or moves uniformly while moving through geodesic paths as quoted by the author?

Answer 1

The statement on cseligman.com suggests that objects falling towards the Earth move along geodesic paths with no acceleration, challenging the conventional understanding of gravity as a force. In this context, the author is highlighting the application of the modified version of the law of inertia, indicating that freely falling bodies, despite experiencing an acceleration g, are following geodesic paths in curved space-time and, according to this perspective, are not subject to a force.

Step-by-step explanation:

The key to understanding this concept lies in the framework of Einstein's General Theory of Relativity. According to this theory, gravity is not a force in the traditional Newtonian sense but rather a curvature of space-time caused by the presence of mass.

Objects in free fall, such as those falling towards the Earth, are essentially moving along the curved geodesic paths dictated by the gravitational field. In this context, the acceleration experienced by these objects is not due to a force acting upon them but rather a result of the curvature of space-time itself.

The modified version of the law of inertia referred to by the author acknowledges that the concept of inertia is applicable even in the presence of gravity. While objects in free fall do experience an acceleration (g), this acceleration is not indicative of a force acting on them in the traditional sense.

Instead, it reflects their response to the curvature of space-time. Thus, the use of the law of inertia in this context emphasizes the equivalence between gravitational acceleration and inertial acceleration, revealing the profound connection between gravity and the geometry of space-time.

In conclusion, the author is asserting that objects falling towards the Earth move along geodesic paths with no force acting on them, challenging the traditional interpretation of gravity as a force. The modified version of the law of inertia, within the framework of General Relativity, provides a more accurate description of the relationship between gravity, acceleration, and the motion of freely falling bodies.