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Classical mechanics |
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In physics, gravity (from Latin gravitas 'weight' [1] ) is a fundamental interaction primarily observed as mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. [2] However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.
On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans. The corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another. Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms.
The gravitational attraction between the original gaseous matter in the universe caused it to coalesce and form stars which eventually condensed into galaxies, so gravity is responsible for many of the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away.
Gravity is most accurately described by the general theory of relativity, proposed by Albert Einstein in 1915, which describes gravity not as a force, but as the curvature of spacetime, caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon. [3] However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.
Current models of particle physics imply that the earliest instance of gravity in the universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10−43 seconds after the birth of the universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner. [4] Scientists are currently working to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, [5] which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three fundamental interactions of physics.
Gravitation, also known as gravitational attraction, is the mutual attraction between all masses in the universe. Gravity is the gravitational attraction at the surface of a planet or other celestial body; [6] gravity may also include, in addition to gravitation, the centrifugal force resulting from the planet's rotation . [7]
The nature and mechanism of gravity were explored by a wide range of ancient scholars. In Greece, Aristotle believed that objects fell towards the Earth because the Earth was the center of the Universe and attracted all of the mass in the Universe towards it. He also thought that the speed of a falling object should increase with its weight, a conclusion that was later shown to be false. [8] While Aristotle's view was widely accepted throughout Ancient Greece, there were other thinkers such as Plutarch who correctly predicted that the attraction of gravity was not unique to the Earth. [9]
Although he did not understand gravity as a force, the ancient Greek philosopher Archimedes discovered the center of gravity of a triangle. [10] He postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity. [11] Two centuries later, the Roman engineer and architect Vitruvius contended in his De architectura that gravity is not dependent on a substance's weight but rather on its "nature". [12] In the 6th century CE, the Byzantine Alexandrian scholar John Philoponus proposed the theory of impetus, which modifies Aristotle's theory that "continuation of motion depends on continued action of a force" by incorporating a causative force that diminishes over time. [13]
In 628 CE, the Indian mathematician and astronomer Brahmagupta proposed the idea that gravity is an attractive force that draws objects to the Earth and used the term gurutvākarṣaṇ to describe it. [14] : 105 [15] [16]
In the ancient Middle East, gravity was a topic of fierce debate. The Persian intellectual Al-Biruni believed that the force of gravity was not unique to the Earth, and he correctly assumed that other heavenly bodies should exert a gravitational attraction as well. [17] In contrast, Al-Khazini held the same position as Aristotle that all matter in the Universe is attracted to the center of the Earth. [18]
In the mid-16th century, various European scientists experimentally disproved the Aristotelian notion that heavier objects fall at a faster rate. [19] In particular, the Spanish Dominican priest Domingo de Soto wrote in 1551 that bodies in free fall uniformly accelerate. [19] De Soto may have been influenced by earlier experiments conducted by other Dominican priests in Italy, including those by Benedetto Varchi, Francesco Beato, Luca Ghini, and Giovan Bellaso which contradicted Aristotle's teachings on the fall of bodies. [19]
The mid-16th century Italian physicist Giambattista Benedetti published papers claiming that, due to specific gravity, objects made of the same material but with different masses would fall at the same speed. [20] With the 1586 Delft tower experiment, the Flemish physicist Simon Stevin observed that two cannonballs of differing sizes and weights fell at the same rate when dropped from a tower. [21] In the late 16th century, Galileo Galilei's careful measurements of balls rolling down inclines allowed him to firmly establish that gravitational acceleration is the same for all objects. [22] Galileo postulated that air resistance is the reason that objects with a low density and high surface area fall more slowly in an atmosphere.
In 1604, Galileo correctly hypothesized that the distance of a falling object is proportional to the square of the time elapsed. [23] This was later confirmed by Italian scientists Jesuits Grimaldi and Riccioli between 1640 and 1650. They also calculated the magnitude of the Earth's gravity by measuring the oscillations of a pendulum. [24]
In 1657, Robert Hooke published his Micrographia , in which he hypothesized that the Moon must have its own gravity. [25] In 1666, he added two further principles: that all bodies move in straight lines until deflected by some force and that the attractive force is stronger for closer bodies. In a communication to the Royal Society in 1666, Hooke wrote [26]
I will explain a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having a simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it....
Hooke's 1674 Gresham lecture, An Attempt to prove the Annual Motion of the Earth, explained that gravitation applied to "all celestial bodies" [27]
In 1684, Newton sent a manuscript to Edmond Halley titled De motu corporum in gyrum ('On the motion of bodies in an orbit'), which provided a physical justification for Kepler's laws of planetary motion. [28] Halley was impressed by the manuscript and urged Newton to expand on it, and a few years later Newton published a groundbreaking book called Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). In this book, Newton described gravitation as a universal force, and claimed that "the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve." This statement was later condensed into the following inverse-square law:
where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant 6.674×10−11 m3⋅kg−1⋅s−2. [29]
Newton's Principia was well received by the scientific community, and his law of gravitation quickly spread across the European world. [30] More than a century later, in 1821, his theory of gravitation rose to even greater prominence when it was used to predict the existence of Neptune. In that year, the French astronomer Alexis Bouvard used this theory to create a table modeling the orbit of Uranus, which was shown to differ significantly from the planet's actual trajectory. In order to explain this discrepancy, many astronomers speculated that there might be a large object beyond the orbit of Uranus which was disrupting its orbit. In 1846, the astronomers John Couch Adams and Urbain Le Verrier independently used Newton's law to predict Neptune's location in the night sky, and the planet was discovered there within a day. [31]
General relativity |
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Eventually, astronomers noticed an eccentricity in the orbit of the planet Mercury which could not be explained by Newton's theory: the perihelion of the orbit was increasing by about 42.98 arcseconds per century. The most obvious explanation for this discrepancy was an as-yet-undiscovered celestial body, such as a planet orbiting the Sun even closer than Mercury, but all efforts to find such a body turned out to be fruitless. In 1915, Albert Einstein developed a theory of general relativity which was able to accurately model Mercury's orbit. [32]
In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. Einstein began to toy with this idea in the form of the equivalence principle, a discovery which he later described as "the happiest thought of my life." [33] In this theory, free fall is considered to be equivalent to inertial motion, meaning that free-falling inertial objects are accelerated relative to non-inertial observers on the ground. [34] [35] In contrast to Newtonian physics, Einstein believed that it was possible for this acceleration to occur without any force being applied to the object.
Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics. As in Newton's first law of motion, Einstein believed that a force applied to an object would cause it to deviate from a geodesic. For instance, people standing on the surface of the Earth are prevented from following a geodesic path because the mechanical resistance of the Earth exerts an upward force on them. This explains why moving along the geodesics in spacetime is considered inertial.
Einstein's description of gravity was quickly accepted by the majority of physicists, as it was able to explain a wide variety of previously baffling experimental results. [36] In the coming years, a wide range of experiments provided additional support for the idea of general relativity. [37] : p.1-9 [38] [39] [40] [41] Today, Einstein's theory of relativity is used for all gravitational calculations where absolute precision is desired, although Newton's inverse-square law is accurate enough for virtually all ordinary calculations. [37] : p.79 [42]
In modern physics, general relativity remains the framework for the understanding of gravity. [43] Physicists continue to work to find solutions to the Einstein field equations that form the basis of general relativity and continue to test the theory, finding excellent agreement in all cases. [44] [45] [37] : p.9
The Einstein field equations are a system of 10 partial differential equations which describe how matter affects the curvature of spacetime. The system is often expressed in the form where Gμν is the Einstein tensor, gμν is the metric tensor, Tμν is the stress–energy tensor, Λ is the cosmological constant, is the Newtonian constant of gravitation and is the speed of light. [46] The constant is referred to as the Einstein gravitational constant. [47]
A major area of research is the discovery of exact solutions to the Einstein field equations. Solving these equations amounts to calculating a precise value for the metric tensor (which defines the curvature and geometry of spacetime) under certain physical conditions. There is no formal definition for what constitutes such solutions, but most scientists agree that they should be expressable using elementary functions or linear differential equations. [48] Some of the most notable solutions of the equations include:
Today, there remain many important situations in which the Einstein field equations have not been solved. Chief among these is the two-body problem, which concerns the geometry of spacetime around two mutually interacting massive objects, such as the Sun and the Earth, or the two stars in a binary star system. The situation gets even more complicated when considering the interactions of three or more massive bodies (the "n-body problem"), and some scientists suspect that the Einstein field equations will never be solved in this context. [57] However, it is still possible to construct an approximate solution to the field equations in the n-body problem by using the technique of post-Newtonian expansion. [58] In general, the extreme nonlinearity of the Einstein field equations makes it difficult to solve them in all but the most specific cases. [59]
Despite its success in predicting the effects of gravity at large scales, general relativity is ultimately incompatible with quantum mechanics. This is because general relativity describes gravity as a smooth, continuous distortion of spacetime, while quantum mechanics holds that all forces arise from the exchange of discrete particles known as quanta. This contradiction is especially vexing to physicists because the other three fundamental forces (strong force, weak force and electromagnetism) were reconciled with a quantum framework decades ago. [60] As a result, modern researchers have begun to search for a theory that could unite both gravity and quantum mechanics under a more general framework. [61]
One path is to describe gravity in the framework of quantum field theory, which has been successful to accurately describe the other fundamental interactions. The electromagnetic force arises from an exchange of virtual photons, where the QFT description of gravity is that there is an exchange of virtual gravitons. [62] [63] This description reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length, [64] where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required.
Testing the predictions of general relativity has historically been difficult, because they are almost identical to the predictions of Newtonian gravity for small energies and masses. [65] Still, since its development, an ongoing series of experimental results have provided support for the theory: [65] In 1919, the British astrophysicist Arthur Eddington was able to confirm the predicted gravitational lensing of light during that year's solar eclipse. [66] [67] Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. Although Eddington's analysis was later disputed, this experiment made Einstein famous almost overnight and caused general relativity to become widely accepted in the scientific community. [68]
In 1959, American physicists Robert Pound and Glen Rebka performed an experiment in which they used gamma rays to confirm the prediction of gravitational time dilation. By sending the rays down a 74-foot tower and measuring their frequency at the bottom, the scientists confirmed that light is redshifted as it moves towards a source of gravity. The observed redshift also supported the idea that time runs more slowly in the presence of a gravitational field. [69] The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro in 1964 in interplanetary spacecraft signals. [70]
In 1971, scientists discovered the first-ever black hole in the galaxy Cygnus. The black hole was detected because it was emitting bursts of x-rays as it consumed a smaller star, and it came to be known as Cygnus X-1. [71] This discovery confirmed yet another prediction of general relativity, because Einstein's equations implied that light could not escape from a sufficiently large and compact object. [72]
General relativity states that gravity acts on light and matter equally, meaning that a sufficiently massive object could warp light around it and create a gravitational lens. This phenomenon was first confirmed by observation in 1979 using the 2.1 meter telescope at Kitt Peak National Observatory in Arizona, which saw two mirror images of the same quasar whose light had been bent around the galaxy YGKOW G1. [73] [74]
Frame dragging, the idea that a rotating massive object should twist spacetime around it, was confirmed by Gravity Probe B results in 2011. [75] [76] In 2015, the LIGO observatory detected faint gravitational waves, the existence of which had been predicted by general relativity. Scientists believe that the waves emanated from a black hole merger that occurred 1.5 billion light-years away. [77]
Every planetary body (including the Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.
The strength of the gravitational field is numerically equal to the acceleration of objects under its influence. [78] The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on latitude, surface features such as mountains and ridges, and perhaps unusually high or low sub-surface densities. [79] For purposes of weights and measures, a standard gravity value is defined by the International Bureau of Weights and Measures, under the International System of Units (SI).
The force of gravity experienced by objects on Earth's surface is the vector sum of two forces: [7] (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is weakest at the equator because of the centrifugal force caused by the Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles. [80] [81]
General relativity predicts that energy can be transported out of a system through gravitational radiation. The first indirect evidence for gravitational radiation was through measurements of the Hulse–Taylor binary in 1973. This system consists of a pulsar and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the Nobel Prize in Physics in 1993. [82]
The first direct evidence for gravitational radiation was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion light years from Earth were measured. [83] [84] This observation confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including the Big Bang. [85] Neutron star and black hole formation also create detectable amounts of gravitational radiation. [86] This research was awarded the Nobel Prize in Physics in 2017. [87]
In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light. [88] This means that if the Sun suddenly disappeared, the Earth would keep orbiting the vacant point normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in Science Bulletin in February 2013. [89]
In October 2017, the LIGO and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from the same direction. This confirmed that the speed of gravitational waves was the same as the speed of light. [90]
There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways.
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever present matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations.
In classical physics and special relativity, an inertial frame of reference is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration.
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies.
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang.
The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.
A theory of everything (TOE), final theory, ultimate theory, unified field theory, or master theory is a singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe. Finding a theory of everything is one of the major unsolved problems in physics.
The following is a timeline of gravitational physics and general relativity.
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Albert Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothesis attempted to explain how rotating objects, such as gyroscopes and spinning celestial bodies, maintain a frame of reference.
Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Separated objects attract and are attracted as if all their mass were concentrated at their centers. The publication of the law has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.
General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping of spacetime.
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.
In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times. The first extant sources discussing such theories are found in ancient Greek philosophy. This work was furthered through the Middle Ages by Indian, Islamic, and European scientists, before gaining great strides during the Renaissance and Scientific Revolution—culminating in the formulation of Newton's law of gravity. This was superseded by Albert Einstein's theory of relativity in the early 20th century.
The mathematics of general relativity is complicated. In Newton's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be solved by algebra alone. In relativity, however, an object's length and the rate at which time passes both change appreciably as the object's speed approaches the speed of light, meaning that more variables and more complicated mathematics are required to calculate the object's motion. As a result, relativity requires the use of concepts such as vectors, tensors, pseudotensors and curvilinear coordinates.
This article will use the Einstein summation convention.
The following outline is provided as an overview of and topical guide to black holes:
Jürgen Ehlers was a German physicist who contributed to the understanding of Albert Einstein's theory of general relativity. From graduate and postgraduate work in Pascual Jordan's relativity research group at Hamburg University, he held various posts as a lecturer and, later, as a professor before joining the Max Planck Institute for Astrophysics in Munich as a director. In 1995, he became the founding director of the newly created Max Planck Institute for Gravitational Physics in Potsdam, Germany.
Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.
Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an entropic force—a force with macro-scale homogeneity but which is subject to quantum-level disorder—and not a fundamental interaction. The theory, based on string theory, black hole physics, and quantum information theory, describes gravity as an emergent phenomenon that springs from the quantum entanglement of small bits of spacetime information. As such, entropic gravity is said to abide by the second law of thermodynamics under which the entropy of a physical system tends to increase over time.
In physics, a non-relativistic spacetime is any mathematical model that fuses n–dimensional space and m–dimensional time into a single continuum other than the (3+1) model used in relativity theory.
§ 2.1: "The total force acting on a body at rest on the earth's surface is the resultant of gravitational force and the centrifugal force of the earth's rotation and is called gravity.
for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation