Question

How did Einstein's general theory of relativity change our view of gravity? Why do we say that Newton's law of universal gravitation is still a valid approximation to Einstein's theory of gravity?

Short answer

Einstein described gravity as spacetime curvature, differing from Newton's force-based view. Newton's law approximates Einstein's theory in weak gravitational fields and low-speed scenarios.

Step-by-step solution

Understanding Einstein's Theory

Einstein's general theory of relativity proposed that gravity is not simply a force between masses as Newton suggested. Instead, it describes gravity as the curvature of spacetime caused by mass and energy. Massive objects like stars and planets create a depression in the fabric of spacetime, causing other objects to move along these curves, which is perceived as gravity.

Comparison with Newton's View

Newton's law of universal gravitation states that every mass attracts every other mass in the universe with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This view treats gravity as a force acting at a distance and does not incorporate spacetime dynamics.

Approximation to Einstein's Theory

Einstein's equations reduce to Newton's law under certain conditions: when the gravitational field is weak and objects are moving slowly compared to the speed of light. In such cases, the spacetime curvature effects described by Einstein aren't significant, and gravity behaves as a force similar to what Newton predicted.

Key concepts

Einstein's theory of gravity

Unlike the traditional view, Einstein changed how we look at gravity with his general theory of relativity. He introduced the revolutionary idea that gravity is not just a force between two masses. Einstein saw it as the curvature of spacetime itself. Think of spacetime as a flexible sheet. When you place a heavy object like a star or planet on this sheet, it creates a dip or depression. This depression affects how objects move in the "plane" of spacetime.

As objects move through the curved spacetime, they follow paths that are influenced by these curves. This phenomenon is what we interpret as the effect of gravity. In simple terms, rather than being pulled by a mysterious force, objects are simply following the "curved paths" in the fabric of spacetime. This concept was groundbreaking because it united the idea of space and time as a single, dynamic entity affected by mass and energy.

Newton's law of universal gravitation

Before Einstein, Newton gave us a powerful way to understand gravity that worked well for centuries. Newton's law of universal gravitation states that every point mass attracts every other point mass with a force that acts along the line connecting them. This force is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The mathematical expression for this is: \[ F = G \frac{m_1 m_2}{r^2} \]where \( F \) is the gravitational force between two objects, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the objects, and \( r \) is the distance between the centers of the two objects.

Newton's theory assumes gravity is an invisible force acting instantaneously over distance. It works well for everyday situations and celestial mechanics within our solar system, providing an easy-to-use model for understanding how bodies attract each other. However, it doesn't take into account the concepts of spacetime or relativity that Einstein later introduced.

Curvature of spacetime

The notion of spacetime curvature is central to Einstein's theory. Imagine spacetime as a four-dimensional fabric stretched out across the universe. Mass and energy can bend this fabric. Large masses like planets or stars cause spacetime to curve, and this curvature dictates how objects travel through space.

To visualize this, consider how a heavy ball would warp a suspended sheet, causing smaller balls to roll toward the depression. This curved path is what we experience as gravity. This concept helps us understand that gravity is not an invisible pull but rather the interaction of masses with the geometry of spacetime.

• Massive objects create deeper curves.
• Light bended by gravity illustrates curvature.
• Time itself is affected by curvature, affecting clocks' speed.

Einstein's insights clarified many phenomena, such as the bending of light around stars and the time dilation experienced near massive objects. These advances let us further refine our understanding of how the universe operates.