General relativity is a theory that describes how matter, energy, time, and space interact. It treats space and time as a single unified four-dimensional “spacetime.” The equivalence principle states that the forces caused by gravity and acceleration are equivalent. Space cannot be Euclidean for all observers, and objects in general relativity don’t always move in straight lines. Gravitational forces and acceleration forces are completely equivalent, causing objects near gravitational sources to appear to slow time and bend light.
General relativity is a scientific theory that describes how matter, energy, time and space interact. It was first published by Albert Einstein in 1917 as an extension of his special theory of relativity. General relativity treats space and time as a single unified four-dimensional “spacetime”; under general relativity, matter warps the geometry of spacetime, and warps of spacetime cause matter to move, which we see as gravity.
The basic assumption of general relativity is that the forces caused by gravity and the forces caused by acceleration are equivalent. If a closed box is undergoing acceleration, no experiments done inside the box can tell whether the box is at rest within a gravitational field, or being accelerated through space. This principle, that all physical laws are the same for accelerated observers and observers in a gravitational field, is known as the equivalence principle; it has been experimentally tested to an accuracy of over twelve decimal places.
The most important consequence of the equivalence principle is that space cannot be Euclidean for all observers. In curved space, like a warped sheet, the normal laws of geometry don’t always hold. In curved space it is possible to construct a triangle whose angle sum is greater or less than 180 degrees, or to draw two parallel intersecting lines. Special relativity becomes more and more accurate as the curvature of spacetime goes to zero; if spacetime is flat, the two theories become identical. How matter curves space is calculated using Einstein’s field equations, which take the form G = T; G describes the curvature of space, while T describes the distribution of matter.
Because space is curved, objects in general relativity don’t always move in straight lines, just like a ball won’t move in a straight line if you roll it down a funnel. A free-falling object will always take the shortest path from point A to point B, which is not necessarily a straight line; the line it travels is known as a geodesic. We see deviations from straight lines as the influence of “gravity”: the Earth does not move in straight lines because the Sun warps spacetime in the vicinity of the Earth, causing it to move in an elliptical orbit.
Since gravitational forces and acceleration forces are completely equivalent, all effects on a fast-moving object in special relativity also apply to objects deep in gravitational fields. An object near a source of gravity will emit Doppler light, just as if it were speeding away. Objects near gravitational sources will also appear to slow time, and any incoming light will be bent by the field. This can cause a strong source of gravity to bend light like a lens, bringing distant objects into focus; this phenomenon is often found in deep-sky astronomy, where one galaxy will bend the light of another so that more images appear.
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