page_title: Introduction to general relativity
section_title: Probing the gravitational field
hierarchical_section_title: Introduction to general relativity / Geometry and gravitation / Probing the gravitational field
caption_attribution_description: Illustration produced for Introduction to general relativity to illustrate how lines of longitude that start out parallel at the equator converge at the pole.
context_page_description: General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational effect between masses results from their warping of spacetime.
  By the beginning of the 20th century, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses. In Newton's model, gravity is the result of an attractive force between massive objects. Although even Newton was troubled by the unknown nature of that force, the basic framework was extremely successful at describing motion.
  Experiments and observations show that Einstein's description of gravitation accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the orbits of Mercury and other planets. General relativity also predicts novel effects of gravity, such as gravitational waves, gravitational lensing and an effect of gravity on time known as gravitational time dilation. Many of these predictions have been confirmed by experiment or observation, most recently gravitational waves.
context_section_description: In order to map a body's gravitational influence, it is useful to think about what physicists call probe or test particles: particles that are influenced by gravity, but are so small and light that we can neglect their own gravitational effect. In the absence of gravity and other external forces, a test particle moves along a straight line at a constant speed. In the language of spacetime, this is equivalent to saying that such test particles move along straight world lines in spacetime. In the presence of gravity, spacetime is non-Euclidean, or curved, and in curved spacetime straight world lines may not exist. Instead, test particles move along lines called geodesics, which are "as straight as possible", that is, they follow the shortest path between starting and ending points, taking the curvature into consideration.
  A simple analogy is the following: In geodesy, the science of measuring Earth's size and shape, a geodesic (from Greek "geo", Earth, and "daiein", to divide) is the shortest route between two points on the Earth's surface. Approximately, such a route is a segment of a great circle, such as a line of longitude or the equator. These paths are certainly not straight, simply because they must follow the curvature of the Earth's surface. But they are as straight as is possible subject to this constraint.
  The properties of geodesics differ from those of straight lines. For example, on a plane, parallel lines never meet, but this is not so for geodesics on the surface of the Earth: for example, lines of longitude are parallel at the equator, but intersect at the poles. Analogously, the world lines of test particles in free fall are spacetime geodesics, the straightest possible lines in spacetime.  But still there are crucial differences between them and the truly straight lines that can be traced out in the gravity-free spacetime of special relativity.  In special relativity, parallel geodesics remain parallel. In a gravitational field with tidal effects, this will not, in general, be the case. If, for example, two bodies are initially at rest relative to each other, but are then dropped in the Earth's gravitational field, they will move towards each other as they fall towards the Earth's center.
  Compared with planets and other astronomical bodies, the objects of everyday life (people, cars, houses, even mountains) have little mass. Where such objects are concerned, the laws governing the behavior of test particles are sufficient to describe what happens. Notably, in order to deflect a test particle from its geodesic path, an external force must be applied. A chair someone is sitting on applies an external upwards force preventing the person from falling freely towards the center of the Earth and thus following a geodesic, which they would otherwise be doing without matter in between them and the center of the Earth. In this way, general relativity explains the daily experience of gravity on the surface of the Earth not as the downwards pull of a gravitational force, but as the upwards push of external forces. These forces deflect all bodies resting on the Earth's surface from the geodesics they would otherwise follow. For matter objects whose own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how to move.
caption: Converging geodesics: two lines of longitude (green) that start out in parallel at the equator (red) but converge to meet at the pole.
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