Question

Why does Einstein's theory of relativity imply that gravity is a nonexistent force?

Short answer

Einstein's theory shows gravity as spacetime curvature, not an actual force.

Step-by-step solution

Understand Newtonian Gravity

In classical physics, gravity is understood as a force that attracts two masses toward each other. According to Newton's law of universal gravitation, this force depends on the masses of the objects and the distance between them. The equation is given by: \[ F = G \frac{m_1 m_2}{r^2} \]where \( F \) is the force of gravity, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between the centers of the two masses.

Introduction to Einstein's Theory of Relativity

Einstein's theory of relativity, specifically General Relativity, provides a different framework for understanding gravity. Instead of viewing gravity as a force, Einstein proposed that gravity is the result of the curvature of spacetime caused by the presence of mass and energy.

Curvature of Spacetime

In Einstein's view, massive objects cause a distortion in the fabric of spacetime, creating a 'curvature'. This curvature dictates the motion of objects, which move along paths called geodesics. The geodesics describe the straightest possible path in curved spacetime, which appears as the gravitational attraction to an observer.

Gravity as Apparent Force

According to General Relativity, what we perceive as the force of gravity is actually the effect of geodesics guiding the motion of objects through curved spacetime. Objects move as if they're experiencing a force, but in reality, they are following the natural curvature created by mass.

Conclusion

Einstein's theory implies that gravity is not a true force in the sense that electromagnetism or other classical forces are. Instead, it is a consequence of spacetime geometry. The apparent 'force' is simply the object responding to the curvature of spacetime.

Key concepts

Einstein's Theory

Einstein's theory of relativity revolutionized our understanding of the universe. Before Einstein, gravity was seen as a force pulling objects together. However, in his theory of General Relativity, Einstein presented a groundbreaking notion: gravity is not a force but a curving of spacetime. This means that mass and energy can influence the shape of the universe itself. As a result, objects move not because they are "pulled" by a force but because they follow natural paths in a warped spacetime.

This conceptual shift was monumental because it offered a more complete explanation of gravitational phenomena. For example, Einstein's theory accounts for the precession of Mercury's orbit in a way Newtonian gravity could not. It also predicted the bending of light around massive objects, a phenomenon observed and confirmed during a solar eclipse in 1919.

Spacetime Curvature

The concept of spacetime curvature is central to Einstein's theory. Imagine spacetime as a fabric stretching across the universe. Mass and energy warp this fabric, creating curves and dips. The larger the mass, the more it bends the spacetime around it. This curvature changes how objects move through space and time.

When we observe planets orbiting the sun, they follow the curves in the spacetime caused by the sun's massive presence. Similarly, light follows these curvatures, which is why light can be "bent" around stars and black holes, resulting in phenomena like gravitational lensing. This bending of spacetime is responsible for what we experience as gravity.

Newtonian Gravity

Newtonian gravity views gravity as a force acting between two masses. According to Newton's law of universal gravitation, every point mass attracts every other point mass by a force along a line intersecting the centers of both masses. The equation describing the force is: \[ F = G \frac{m_1 m_2}{r^2} \] where:

• \( F \) is the gravitational force between two masses,
• \( G \) is the gravitational constant,
• \( m_1 \) and \( m_2 \) are the masses,
• \( r \) is the distance between their centers.

Newtonian gravity provides an excellent approximation for most everyday phenomena but fails to describe certain astronomical observations. General relativity builds on this foundation by explaining these exceptions through spacetime curvature.

Geodesics

Geodesics are the paths that objects naturally follow in curved spacetime. In essence, they represent the straightest possible line in a warped space. Imagine throwing a ball through the air: in flat space, it moves in a straight line. But in curved spacetime, it follows a geodesic path that could look like an arc due to gravity's influence.

Any moving object, from a spaceship to a photon of light, follows these geodesic paths when no other forces act upon it. This is why planets orbit their stars or why galaxies have a spiral shape. They follow the natural flow of spacetime curvature created by the mass and energy of celestial bodies, ensuring that the concept of a gravitational "force" is unnecessary. Instead, the geometry of spacetime itself guides their journey.