24.2 Spacetime and Gravity

Spacetime and Gravity

Einstein's theory of general relativity replaced the old idea of gravity as a force pulling between objects. Instead, gravity is the warping of spacetime by massive bodies. Objects moving through this warped spacetime follow curved paths, which is what we observe as orbits, falling objects, and even the bending of light.

Spacetime Warping by Massive Objects

Spacetime is the four-dimensional fabric of the universe: three dimensions of space combined with one dimension of time. Massive objects like stars and planets cause this fabric to curve around them. The more massive the object, the greater the curvature. A black hole, for instance, creates an extreme warp in spacetime compared to something like Earth.

Objects moving through curved spacetime follow what's called a geodesic, the straightest possible path through that curved geometry. These geodesics look like curved paths to us, and that's what we interpret as the effect of gravity.

• Planets orbit the Sun because they're following geodesics in the Sun's curved spacetime, not because a force is "pulling" them.
• An apple falls from a tree because it follows the geodesic in Earth's curved spacetime toward the ground.
• Tidal forces arise when spacetime curvature differs across the size of an object. The side closer to a massive body experiences stronger curvature than the far side, stretching the object.

Newton's Gravity vs. Einstein's Spacetime

Newton described gravity as a force acting between two masses. His law of universal gravitation says the force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:

$F = G \frac{m_1 m_2}{r^2}$

where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between them.

Einstein's general relativity describes gravity differently: not as a force, but as the geometry of spacetime itself. Objects move along curved paths because spacetime is curved, not because something is pushing or pulling them.

Both theories give nearly identical predictions for everyday situations. You can use Newton's equation to calculate satellite orbits or plan a rocket launch and get perfectly accurate results. Einstein's theory only becomes necessary in extreme environments: near black holes, in very strong gravitational fields, or when you need extreme precision (like GPS satellites, which must account for relativistic time effects).

Light Paths in Curved Spacetime

Light also follows geodesics through curved spacetime. Near a massive object, the path of light bends because spacetime itself is curved. This means a beam of starlight passing close to the Sun will follow a slightly curved trajectory.

Gravitational lensing is the observable result of this bending. When light from a distant galaxy passes near a massive foreground object (like another galaxy or galaxy cluster), the spacetime curvature deflects that light. This can cause the distant source to appear distorted, magnified, or even show up as multiple images in different positions around the foreground object.

The amount of deflection depends on two factors:

• Mass of the lensing object: More massive objects create stronger curvature and bend light more. A supermassive black hole deflects light far more than an ordinary star.
• Distance between the light path and the object: Light passing closer to the massive object gets deflected more than light passing farther away.

Gravitational lensing provided some of the earliest direct evidence for general relativity. In 1919, astronomer Arthur Eddington measured the positions of stars near the Sun during a total solar eclipse. The stars appeared slightly shifted from their expected positions, exactly matching Einstein's predictions for how much the Sun's spacetime curvature should bend their light.

Principles and Effects of General Relativity

Three key effects emerge from general relativity that you should know:

• The equivalence principle states that gravitational acceleration is indistinguishable from acceleration due to any other force, at least locally. If you were in a sealed elevator accelerating upward in deep space, you couldn't tell the difference between that and standing on Earth's surface. This insight was Einstein's starting point for developing general relativity.
• Gravitational time dilation means time passes at different rates depending on the strength of the gravitational field. A clock near a massive object (like on Earth's surface) ticks slightly slower than a clock farther from that mass (like on a GPS satellite in orbit). The difference is tiny for Earth, but near a black hole it becomes dramatic.
• Gravitational redshift occurs when light climbs out of a gravitational field. The light loses energy as it moves away from the massive object, and since a photon's energy is tied to its wavelength, the light shifts toward longer (redder) wavelengths. Light falling into a gravitational field gains energy and blueshifts instead.