Explaining Gravity on Earth Through the Lenses of General Relativity

In the framework of Albert Einstein's General Theory of Relativity, gravity is not perceived as a force in the traditional Newtonian sense. Instead, it is understood as a distortion of spacetime caused by the mass of celestial bodies. This explains why objects on Earth stay on the ground. Let's delve into how this concept applies practically on our planet.

Curved Spacetime

Earth's massive presence curves the spacetime around it, creating a distortion that influences the paths of all objects within this curvature. This means that the gravitational force we experience is not a force in the Newtonian sense, but rather a result of moving along the geodesics of this curved spacetime.

Free Fall

Objects in free fall are simply following these geodesics. When you jump, you are not being pushed by an external force; instead, you are moving along a curved path dictated by the spacetime around Earth. This is why gravity and falling seem so natural to us.

Weight and the Normal Force

The sensation of weight is a result of the interaction between your mass and the mass of Earth. You feel this weight because the ground pushes back against you, providing the normal force that counteracts the gravitational pull of the Earth's curved spacetime. In essence, the ground is providing the support necessary to keep you from falling into the deeper well of spacetime created by the Earth's mass.

The Equivalence Principle

The equivalence principle in general relativity suggests that locally in small enough regions, the effects of gravity are indistinguishable from acceleration. When you stand still on Earth, you are not standing in a state of rest relative to the Earth; rather, you are experiencing an accelerated frame of reference due to the curvature of spacetime.

Practical Implications

The fact that we are kept on the ground by the Earth's mass distorting spacetime around it is continually demonstrated. The ground is what prevents us from falling into the deeper well of spacetime. If a cavern or sinkhole suddenly forms beneath our feet, or if we fall into a deep canyon, we are closer to the center of the Earth due to the gravitational pull. This is because the gravitational force draws objects toward the center of the largest mass (in this case, the Earth).

In summary, the explanation for the gravitational force we experience and can measure is rooted in the curved nature of spacetime around massive objects like Earth. The Earth's mass distorts the spacetime around it, causing all objects to move along the geodesics of this curvature. Our perception of weight and the normal force arises from the interaction with this curved spacetime, and the ground provides the necessary force to counteract the Earth's gravitational pull.