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For other uses, see Gravity (disambiguation).

"Gravitation" and "Law of Gravity" redirect here. For other uses, see Gravitation (disambiguation) and Law of Gravity (disambiguation).

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{displaystyle {vec {F}}=m{vec {a}}}{vec {F}}=m{vec {a}}

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File:Apollo 15 feather and hammer drop.ogv

Hammer and feather drop: astronaut David Scott (from mission Apollo 15) on the Moon enacting the legend of Galileo's gravity experiment. (1.38 MB, ogg/Theora format).

Gravity (from Latin gravitas, meaning 'weight'[1]), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light[2]—are brought toward (or gravitate toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing, forming stars—and for the stars to group together 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 increasingly weaker as objects get further 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 a consequence of the curvature of spacetime caused by the uneven distribution of mass. 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 which causes any two bodies to be attracted to each other, with the force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravity is the weakest of the four fundamental interactions of physics, 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 consequence, it has no significant influence at the level of subatomic particles.[4] In contrast, it is the dominant interaction at the macroscopic scale, and is the cause of the formation, shape and trajectory (orbit) of astronomical bodies.

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.[5] Attempts to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three fundamental interactions of physics, are a current area of research.

Contents

1 History of gravitational theory

1.1 Ancient world

1.2 Scientific revolution

1.3 Newton's theory of gravitation

1.4 Equivalence principle

1.5 General relativity

1.5.1 Solutions

1.5.2 Tests

1.6 Gravity and quantum mechanics

2 Specifics

2.1 Earth's gravity

2.2 Equations for a falling body near the surface of the Earth

2.3 Gravity and astronomy

2.4 Gravitational radiation

2.5 Speed of gravity

3 Anomalies and discrepancies

4 Alternative theories

4.1 Historical alternative theories

4.2 Modern alternative theories

5 See also

6 Footnotes

7 References

8 Further reading

9 External links

History of gravitational theory

Main article: History of gravitational theory

Ancient world

The ancient Greek philosopher Archimedes discovered the center of gravity of a triangle.[6] He also 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.[7]

The Roman architect and engineer Vitruvius in De Architectura postulated that gravity of an object did not depend on weight but its "nature".[8]

Main article: List of Indian inventions and discoveries § Sciences

In ancient India, Aryabhata first identified the force to explain why objects are not thrown outward as the earth rotates. Brahmagupta described gravity as an attractive force and used the term "gurutvaakarshan" for gravity.[9][10]

Scientific revolution

Main article: Scientific revolution

Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal[11]) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitational acceleration is the same for all objects. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration.[12] Galileo postulated air resistance as the reason that objects with less mass fall more slowly in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity.[13]

Newton's theory of gravitation

Main article: Newton's law of universal gravitation

English physicist and mathematician, Sir Isaac Newton (1642–1727)

In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, "I deduced 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: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly."[14] The equation is the following:

{displaystyle F=G{frac {m_{1}m_{2}}{r^{2}}} }F=G{frac {m_{1}m_{2}}{r^{2}}}

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.

Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune.

A discrepancy in Mercury's orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton's theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury's orbit. This discrepancy was the advance in the perihelion of Mercury of 42.98 arcseconds per century.[15]

Although Newton's theory has been superseded by Einstein's general relativity, most modern non-relativistic gravitational calculations are still made using Newton's theory because it is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

Equivalence principle

The equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same way, and that the effects of gravity are indistinguishable from certain aspects of acceleration and deceleration. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the same rate when other forces (such as air resistance and electromagnetic effects) are negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example STEP, are planned for more accurate experiments in space.[16]

Formulations of the equivalence principle include:

The weak equivalence principle: The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition.[17]

The Einsteinian equivalence principle: The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.[18]

The strong equivalence principle requiring both of the above.

General relativity

See also: Introduction to general relativity

Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.

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General relativity

Spacetime curvature schematic

{displaystyle G_{mu nu }+Lambda g_{mu nu }={8pi G over c^{4}}T_{mu nu }}G_{mu nu }+Lambda g_{mu nu }={8pi G over c^{4}}T_{mu nu }

IntroductionHistory

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In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground.[19][20] In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force.

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. Like Newton's first law of motion, Einstein's theory states that if a force is applied on an object, it would deviate from a geodesic. For instance, we are no longer following geodesics while standing because the mechanical resistance of the Earth exerts an upward force on us, and we are non-inertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial.

Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor.

Solutions

Notable solutions of the Einstein field equations include:

The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotating uncharged massive object. For compact enough objects, this solution generated a black hole with a central singularity. For radial distances from the center which are much greater than the Schwarzschild radius, the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity.

The Reissner-Nordström solution, in which the central object has an electrical charge. For charges with a geometrized length which are less than the geometrized length of the mass of the object, this solution produces black holes with double event horizons.

The Kerr solution for rotating massive objects. This solution also produces black holes with multiple event horizons.

The Kerr-Newman solution for charged, rotating massive objects. This solution also produces black holes with multiple event horizons.

The cosmological Friedmann-Lemaître-Robertson-Walker solution, which predicts the expansion of the Universe.

Tests

The tests of general relativity included the following:[21]

General relativity accounts for the anomalous perihelion precession of Mercury.[22]

The prediction that time runs slower at lower potentials (gravitational time dilation) has been confirmed by the Pound–Rebka experiment (1959), the Hafele–Keating experiment, and the GPS.

The prediction of the deflection of light was first confirmed by Arthur Stanley Eddington from his observations during the Solar eclipse of 29 May 1919.[23][24] Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. However, his interpretation of the results was later disputed.[25] More recent tests using radio interferometric measurements of quasars passing behind the Sun have more accurately and consistently confirmed the deflection of light to the degree predicted by general relativity.[26] See also gravitational lens.

The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro in 1964 in interplanetary spacecraft signals.

Gravitational radiation has been indirectly confirmed through studies of binary pulsars. On 11 February 2016, the LIGO and Virgo collaborations announced the first observation of a gravitational wave.

Alexander Friedmann in 1922 found that Einstein equations have non-stationary solutions (even in the presence of the cosmological constant). In 1927 Georges Lemaître showed that static solutions of the Einstein equations, which are possible in the presence of the cosmological constant, are unstable, and therefore the static Universe envisioned by Einstein could not exist. Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître. Thus general relativity predicted that the Universe had to be non-static—it had to either expand or contract. The expansion of the Universe discovered by Edwin Hubble in 1929 confirmed this prediction.[27]

The theory's prediction of frame dragging was consistent with the recent Gravity Probe B results.[28]

General relativity predicts that light should lose its energy when traveling away from massive bodies through gravitational redshift. This was verified on earth and in the solar system around 1960.

Gravity and quantum mechanics

Main articles: Graviton and Quantum gravity

In the decades after the publication of the theory of general relativity, it was realized that general relativity is incompatible with quantum mechanics.[29] It is possible to describe gravity in the framework of quantum field theory like the other fundamental interactions, such that the "attractive force" of gravity arises due to exchange of virtual gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons.[30][31] This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,[29] where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required.

Specifics

Earth's gravity

An initially-stationary object that is allowed to fall freely under gravity drops a distance that is proportional to the square of the elapsed time. This image spans half a second and was captured at 20 flashes per second.

Main article: Earth's gravity

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.

If an object with comparable mass to that of the Earth were to fall towards it, then the corresponding acceleration of the Earth would be observable.

The strength of the gravitational field is numerically equal to the acceleration of objects under its influence.[32] 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.[33] 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).

That value, denoted g, is g = 9.80665 m/s2 (32.1740 ft/s2).[34][35]

The standard value of 9.80665 m/s2 is the one originally adopted by the International Committee on Weights and Measures in 1901 for 45° latitude, even though it has been shown to be too high by about five parts in ten thousand.[36] This value has persisted in meteorology and in some standard atmospheres as the value for 45° latitude even though it applies more precisely to latitude of 45°32'33".[37]

Assuming the standardized value for g and ignoring air resistance, this means that an object falling freely near the Earth's surface increases its velocity by 9.80665 m/s (32.1740 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.80665 m/s (32.1740 ft/s) after one second, approximately 19.62 m/s (64.4 ft/s) after two seconds, and so on, adding 9.80665 m/s (32.1740 ft/s) to each resulting velocity. Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time.

According to Newton's 3rd Law, the Earth itself experiences a force equal in magnitude and opposite in direction to that which it exerts on a falling object. This means that the Earth also accelerates towards the object until they collide. Because the mass of the Earth is huge, however, the acceleration imparted to the Earth by this opposite force is negligible in comparison to the object's. If the object does not bounce after it has collided with the Earth, each of them then exerts a repulsive contact force on the other which effectively balances the attractive force of gravity and prevents further acceleration.

The force of gravity on Earth is the resultant (vector sum) of two forces:[38] (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 the 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.

Equations for a falling body near the surface of the Earth

Main article: Equations for a falling body

Under an assumption of constant gravitational attraction, Newton's law of universal gravitation simplifies to F = mg, where m is the mass of the body and g is a constant vector with an average magnitude of 9.81 m/s2 on Earth. This resulting force is the object's weight. The acceleration due to gravity is equal to this g. An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first ?1?20 of a second the ball drops one unit of distance (here, a unit is about 12 mm); by ?2?20 it has dropped at total of 4 units; by ?3?20, 9 units and so on.

Under the same constant gravity assumptions, the potential energy, Ep, of a body at height h is given by Ep = mgh (or Ep = Wh, with W meaning weight). This expression is valid only over small distances h from the surface of the Earth. Similarly, the expression {displaystyle h={tfrac {v^{2}}{2g}}}h={tfrac {v^{2}}{2g}} for the maximum height reached by a vertically projected body with initial velocity v is useful for small heights and small initial velocities only.

Gravity and astronomy

Gravity acts on stars that form the Milky Way.[39]

The application of Newton's law of gravity has enabled the acquisition of much of the detailed information we have about the planets in the Solar System, the mass of the Sun, and details of quasars; even the existence of dark matter is inferred using Newton's law of gravity. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity exerted on one object by another is directly proportional to the product of those objects' masses and inversely proportional to the square of the distance between them.

The earliest gravity (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.[5]

Gravitational radiation

LIGO Hanford Observatory

The LIGO Hanford Observatory located in Washington, US where gravitational waves were first observed in September 2015.

Main article: Gravitational wave

General relativity predicts that energy can be transported out of a system through gravitational radiation. Any accelerating matter can create curvatures in the space-time metric, which is how the gravitational radiation is transported away from the system. Co-orbiting objects can generate curvatures in space-time such as the Earth-Sun system, pairs of neutron stars, and pairs of black holes. Another astrophysical system predicted to lose energy in the form of gravitational radiation are exploding supernovae.

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.

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.[40][41] 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.[42] Neutron star and black hole formation also create detectable amounts of gravitational radiation.[43]. This research was awarded the Nobel Prize in physics in 2017. [44]

As of 2020, the gravitational radiation emitted by the Solar System is far too small to measure with current technology.

Speed of gravity

Main article: Speed of gravity

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.[45] This means that if the Sun suddenly disappeared, the Earth would keep orbiting it normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in the Chinese Science Bulletin in February 2013.[46]

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.[47]

Anomalies and discrepancies

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.

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). The discrepancy between the curves is attributed to dark matter.

Extra-fast stars: Stars in galaxies follow a distribution of velocities where stars on the outskirts are moving faster than they should according to the observed distributions of normal matter. Galaxies within galaxy clusters show a similar pattern. Dark matter, which would interact through gravitation but not electromagnetically, would account for the discrepancy. Various modifications to Newtonian dynamics have also been proposed.

Flyby anomaly: Various spacecraft have experienced greater acceleration than expected during gravity assist maneuvers.

Accelerating expansion: The metric expansion of space seems to be speeding up. Dark energy has been proposed to explain this. A recent alternative explanation is that the geometry of space is not homogeneous (due to clusters of galaxies) and that when the data are reinterpreted to take this into account, the expansion is not speeding up after all,[48] however this conclusion is disputed.[49]

Anomalous increase of the astronomical unit: Recent measurements indicate that planetary orbits are widening faster than if this were solely through the Sun losing mass by radiating energy.

Extra energetic photons: Photons travelling through galaxy clusters should gain energy and then lose it again on the way out. The accelerating expansion of the Universe should stop the photons returning all the energy, but even taking this into account photons from the cosmic microwave background radiation gain twice as much energy as expected. This may indicate that gravity falls off faster than inverse-squared at certain distance scales.[50]

Extra massive hydrogen clouds: The spectral lines of the Lyman-alpha forest suggest that hydrogen clouds are more clumped together at certain scales than expected and, like dark flow, may indicate that gravity falls off slower than inverse-squared at certain distance scales.[50]

Alternative theories

Main article: Alternatives to general relativity

Historical alternative theories

Aristotelian theory of gravity

Le Sage's theory of gravitation (1784) also called LeSage gravity, proposed by Georges-Louis Le Sage, based on a fluid-based explanation where a light gas fills the entire Universe.

Ritz's theory of gravitation, Ann. Chem. Phys. 13, 145, (1908) pp. 267–271, Weber-Gauss electrodynamics applied to gravitation. Classical advancement of perihelia.

Nordström's theory of gravitation (1912, 1913), an early competitor of general relativity.

Kaluza Klein theory (1921)

Whitehead's theory of gravitation (1922), another early competitor of general relativity.

Modern alternative theories

Brans–Dicke theory of gravity (1961)[51]

Induced gravity (1967), a proposal by Andrei Sakharov according to which general relativity might arise from quantum field theories of matter

String theory (late 1960s)

ƒ(R) gravity (1970)

Horndeski theory (1974)[52]

Supergravity (1976)

In the modified Newtonian dynamics (MOND) (1981), Mordehai Milgrom proposes a modification of Newton's second law of motion for small accelerations[53]

The self-creation cosmology theory of gravity (1982) by G.A. Barber in which the Brans-Dicke theory is modified to allow mass creation

Loop quantum gravity (1988) by Carlo Rovelli, Lee Smolin, and Abhay Ashtekar

Nonsymmetric gravitational theory (NGT) (1994) by John Moffat

Tensor–vector–scalar gravity (TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein

Chameleon theory (2004) by Justin Khoury and Amanda Weltman.

Pressuron theory (2013) by Olivier Minazzoli and Aurélien Hees.

Conformal gravity[54]

Gravity as an entropic force, gravity arising as an emergent phenomenon from the thermodynamic concept of entropy.

In the superfluid vacuum theory the gravity and curved space-time arise as a collective excitation mode of non-relativistic background superfluid.

See also

Astronomy portal

icon Physics portal

Space portal

Anti-gravity, the idea of neutralizing or repelling gravity

Artificial gravity

Gauss's law for gravity

Gravitational potential

Gravitational wave

Kepler's third law of planetary motion

Micro-g environment, also called microgravity

Newton's laws of motion

Standard gravitational parameter

Weightlessness

Footnotes

dict.cc dictionary :: gravitas :: English-Latin translation

Comins, Neil F.; Kaufmann, William J. (2008). Discovering the Universe: From the Stars to the Planets. MacMillan. p. 347. Bibcode:2009dufs.book.....C. ISBN 978-1429230421.

"HubbleSite: Black Holes: Gravity's Relentless Pull". hubblesite.org. Retrieved 7 October 2016.

Krebs, Robert E. (1999). Scientific Development and Misconceptions Through the Ages: A Reference Guide (illustrated ed.). Greenwood Publishing Group. p. 133. ISBN 978-0-313-30226-8.

Staff. "Birth of the Universe". University of Oregon. Retrieved 24 September 2016. – discusses "Planck time" and "Planck era" at the very beginning of the Universe

Reviel Neitz; William Noel (13 October 2011). The Archimedes Codex: Revealing The Secrets of the World's Greatest Palimpsest. Hachette UK. p. 125. ISBN 978-1-78022-198-4.

CJ Tuplin, Lewis Wolpert (2002). Science and Mathematics in Ancient Greek Culture. Hachette UK. p. xi. ISBN 978-0-19-815248-4.

Vitruvius, Marcus Pollio (1914). "7". In Alfred A. Howard (ed.). De Architectura libri decem [Ten Books on Architecture]. VII. Herbert Langford Warren, Nelson Robinson (illus), Morris Hicky Morgan. Harvard University, Cambridge: Harvard University Press. p. 215.

Pickover, Clifford (16 April 2008). Archimedes to Hawking: Laws of Science and the Great Minds Behind Them. Oxford University Press. ISBN 9780199792689.

*Sen, Amartya (2005). The Argumentative Indian. Allen Lane. p. 29. ISBN 978-0-7139-9687-6.

Ball, Phil (June 2005). "Tall Tales". Nature News. doi:10.1038/news050613-10.

Galileo (1638), Two New Sciences, First Day Salviati speaks: "If this were what Aristotle meant you would burden him with another error which would amount to a falsehood; because, since there is no such sheer height available on earth, it is clear that Aristotle could not have made the experiment; yet he wishes to give us the impression of his having performed it when he speaks of such an effect as one which we see."

Bongaarts, Peter (2014). Quantum Theory: A Mathematical Approach (illustrated ed.). Springer. p. 11. ISBN 978-3-319-09561-5.

*Chandrasekhar, Subrahmanyan (2003). Newton's Principia for the common reader. Oxford: Oxford University Press. (pp. 1–2). The quotation comes from a memorandum thought to have been written about 1714. As early as 1645 Ismaël Bullialdus had argued that any force exerted by the Sun on distant objects would have to follow an inverse-square law. However, he also dismissed the idea that any such force did exist. See, for example, Linton, Christopher M. (2004). From Eudoxus to Einstein – A History of Mathematical Astronomy. Cambridge: Cambridge University Press. p. 225. ISBN 978-0-521-82750-8.

Nobil, Anna M. (March 1986). "The real value of Mercury's perihelion advance". Nature. 320 (6057): 39–41. Bibcode:1986Natur.320...39N. doi:10.1038/320039a0.

M.C.W.Sandford (2008). "STEP: Satellite Test of the Equivalence Principle". Rutherford Appleton Laboratory. Archived from the original on 28 September 2011. Retrieved 14 October 2011.

Paul S Wesson (2006). Five-dimensional Physics. World Scientific. p. 82. ISBN 978-981-256-661-4.

Haugen, Mark P.; C. Lämmerzahl (2001), "Principles of Equivalence: Their Role in Gravitation Physics and Experiments that Test Them", Gyros, Lecture Notes in Physics, 562 (562, Gyros, Clocks, and Interferometers...: Testing Relativistic Gravity in Space): 195–212, arXiv:gr-qc/0103067, Bibcode:2001LNP...562..195H, doi:10.1007/3-540-40988-2_10

"Gravity and Warped Spacetime". black-holes.org. Archived from the original on 21 June 2011. Retrieved 16 October 2010.

Dmitri Pogosyan. "Lecture 20: Black Holes – The Einstein Equivalence Principle". University of Alberta. Retrieved 14 October 2011.

Pauli, Wolfgang Ernst (1958). "Part IV. General Theory of Relativity". Theory of Relativity. Courier Dover Publications. ISBN 978-0-486-64152-2.

Max Born (1924), Einstein's Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)

Dyson, F.W.; Eddington, A.S.; Davidson, C.R. (1920). "A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919". Phil. Trans. Roy. Soc. A. 220 (571–581): 291–333. Bibcode:1920RSPTA.220..291D. doi:10.1098/rsta.1920.0009.. Quote, p. 332: "Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein's generalised theory of relativity, as attributable to the sun's gravitational field."

Weinberg, Steven (1972). Gravitation and cosmology. John Wiley & Sons.. Quote, p. 192: "About a dozen stars in all were studied, and yielded values 1.98 ± 0.11" and 1.61 ± 0.31", in substantial agreement with Einstein's prediction ?? = 1.75"."

Earman, John; Glymour, Clark (1980). "Relativity and Eclipses: The British eclipse expeditions of 1919 and their predecessors". Historical Studies in the Physical Sciences. 11 (1): 49–85. doi:10.2307/27757471. JSTOR 27757471.

Weinberg, Steven (1972). Gravitation and cosmology. John Wiley & Sons. p. 194.

See W.Pauli, 1958, pp. 219–220

"NASA's Gravity Probe B Confirms Two Einstein Space-Time Theories". Nasa.gov. Retrieved 23 July 2013.

Randall, Lisa (2005). Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN 978-0-06-053108-9.

Feynman, R.P.; Morinigo, F.B.; Wagner, W.G.; Hatfield, B. (1995). Feynman lectures on gravitation. Addison-Wesley. ISBN 978-0-201-62734-3.

Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN 978-0-691-01019-9.

Cantor, G.N.; Christie, J.R.R.; Hodge, M.J.S.; Olby, R.C. (2006). Companion to the History of Modern Science. Routledge. p. 448. ISBN 978-1-134-97751-2.

Nemiroff, R.; Bonnell, J., eds. (15 December 2014). "The Potsdam Gravity Potato". Astronomy Picture of the Day. NASA.

Bureau International des Poids et Mesures (2006). "The International System of Units (SI)" (PDF) (8th ed.): 131. Unit names are normally printed in Roman (upright) type ... Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets.

"SI Unit rules and style conventions". National Institute For Standards and Technology (USA). September 2004. Variables and quantity symbols are in italic type. Unit symbols are in Roman type.

List, R.J. editor, 1968, Acceleration of Gravity, Smithsonian Meteorological Tables, Sixth Ed. Smithsonian Institution, Washington, DC, p. 68.

U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is very large.)

Hofmann-Wellenhof, B.; Moritz, H. (2006). Physical Geodesy (2nd ed.). Springer. ISBN 978-3-211-33544-4. § 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".

"Milky Way Emerges as Sun Sets over Paranal". www.eso.org. European Southern Obseevatory. Retrieved 29 April 2015.

Clark, Stuart (11 February 2016). "Gravitational waves: scientists announce 'we did it!' – live". the Guardian. Retrieved 11 February 2016.

Castelvecchi, Davide; Witze, Witze (11 February 2016). "Einstein's gravitational waves found at last". Nature News. doi:10.1038/nature.2016.19361. Retrieved 11 February 2016.

"WHAT ARE GRAVITATIONAL WAVES AND WHY DO THEY MATTER?". popsci.com. Retrieved 12 February 2016.

Abbott, B. P.; et al. (LIGO Scientific Collaboration & Virgo Collaboration) (October 2017). "GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral" (PDF). Physical Review Letters. 119 (16): 161101. arXiv:1710.05832. Bibcode:2017PhRvL.119p1101A. doi:10.1103/PhysRevLett.119.161101. PMID 29099225.

Devlin, Hanna (3 October 2017). "Nobel prize in physics awarded for discovery of gravitational waves". the Guardian. Retrieved 3 October 2017.

Chinese scientists find evidence for speed of gravity, astrowatch.com, 12/28/12.

TANG, Ke Yun; HUA ChangCai; WEN Wu; CHI ShunLiang; YOU QingYu; YU Dan (February 2013). "Observational evidences for the speed of the gravity based on the Earth tide". Chinese Science Bulletin. 58 (4–5): 474–477. Bibcode:2013ChSBu..58..474T. doi:10.1007/s11434-012-5603-3.

"GW170817 Press Release". LIGO Lab – Caltech.

Dark energy may just be a cosmic illusion, New Scientist, issue 2646, 7 March 2008.

Swiss-cheese model of the cosmos is full of holes, New Scientist, issue 2678, 18 October 2008.

Chown, Marcus (16 March 2009). "Gravity may venture where matter fears to tread". New Scientist. Retrieved 4 August 2013.

Brans, C.H. (March 2014). "Jordan-Brans-Dicke Theory". Scholarpedia. 9 (4): 31358. arXiv:gr-qc/0207039. Bibcode:2014Schpj...931358B. doi:10.4249/scholarpedia.31358.

Horndeski, G.W. (September 1974). "Second-Order Scalar-Tensor Field Equations in a Four-Dimensional Space". International Journal of Theoretical Physics. 88 (10): 363–384. Bibcode:1974IJTP...10..363H. doi:10.1007/BF01807638.

Milgrom, M. (June 2014). "The MOND paradigm of modified dynamics". Scholarpedia. 9 (6): 31410. Bibcode:2014SchpJ...931410M. doi:10.4249/scholarpedia.31410.

Haugan, Mark P; Lämmerzahl, C (2011). "Einstein gravity from conformal gravity". arXiv:1105.5632 [hep-th].

References

Halliday, David; Robert Resnick; Kenneth S. Krane (2001). Physics v. 1. New York: John Wiley & Sons. ISBN 978-0-471-32057-9.

Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 978-0-534-40842-8.

Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). W.H. Freeman. ISBN 978-0-7167-0809-4.

Further reading

Thorne, Kip S.; Misner, Charles W.; Wheeler, John Archibald (1973). Gravitation. W.H. Freeman. ISBN 978-0-7167-0344-0.

Panek, Richard (2 August 2019). "Everything you thought you knew about gravity is wrong". Washington Post. Part 2. Einstein's static universe, also known as the Einstein universe or the Einstein world, is a relativistic model of the universe proposed by Albert Einstein in 1917.[1][2] Shortly after completing the general theory of relativity, Einstein applied his new theory of gravity to the universe as a whole. Assuming a universe that was static in time, and possessed of a uniform distribution of matter on the largest scales, Einstein was led to a finite, static universe of spherical spatial curvature.

In order to achieve a consistent solution to the Einstein field equations for the case of a static universe with a non-zero density of matter, Einstein found it necessary to introduce a new term to the field equations, the cosmological constant. In the resulting model, the radius R and density of matter ? of the universe were related to the cosmological constant ? according to ? = 1/R2 = ??/2 where ? is the Einstein constant.[3]

Following the discovery by Edwin Hubble of a linear relation between the redshifts of the galaxies and their distance in 1929,[4] Einstein abandoned his static model of the universe and proposed expanding models such as the Friedmann-Einstein universe and the Einstein-de Sitter universe. In both cases, he set the cosmological constant to zero, declaring it "no longer necessary ... and theoretically unsatisfactory".[5][6][7][8][9]

References

Einstein, Albert (1917). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie". Sitzungs. König. Preuss. Akad.: Sitzungsb. König. Preuss. Akad. 142–152.

Lorentz H.A.; Einstein A.; Minkowski H.; H. Weyl (1923). The Principle of Relativity. New York: Metheun & Co. pp. 175–188.

O'Raifeartaigh; et al. (2017). "Einstein's 1917 static model of the universe: a centennial review". Eur. Phys. J. H. 42 (3): 431–474. arXiv:1701.07261. Bibcode:2017EPJH...42..431O. doi:10.1140/epjh/e2017-80002-5.

Hubble, Edwin (1929). "A relation between distance and radial velocity among extra-galactic nebulae". Proceedings of the National Academy of Sciences. 15 (3): 168–173. Bibcode:1929PNAS...15..168H. doi:10.1073/pnas.15.3.168. PMC 522427. PMID 16577160.

Einstein, Albert (1931). "Zum kosmologischen Problem der allgemeinen Relativitätstheorie". Sitzungsb. König. Preuss. Akad.: 235–237.

Einstein, Albert (1946). Relativity: The Special and General Theories (16th ed.). New York: Metheun. p. 137.

O'Raifeartaigh and McCann (2014). "Einstein's cosmic model of 1931 revisited: an analysis and translation of a forgotten model of the universe". Eur. Phys. J. H. 39 (1): 63–85. arXiv:1312.2192. Bibcode:2014EPJH...39...63O. doi:10.1140/epjh/e2013-40038-x.

Nussbaumer and Bieri (2009). Discovering the Expanding Universe. Cambridge: Cambridge University Press. p. 147.

A. S. Eddington (9 May 1930). "On the Instability of Einstein's Spherical World". Monthly Notices of the Royal Astronomical Society. 90 (7): 668–678. doi:10.1093/mnras/90.7.668. Part 3. Theory of relativity

From Wikipedia, the free encyclopedia

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This article is about the scientific concept. For philosophical or ontological theories about relativity, see Relativism. For the silent film, see The Einstein Theory of Relativity.

Part of a series of articles about

General relativity

Spacetime curvature schematic

{displaystyle G_{mu nu }+Lambda g_{mu nu }={8pi G over c^{4}}T_{mu nu }}G_{mu nu }+Lambda g_{mu nu }={8pi G over c^{4}}T_{mu nu }

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Two-dimensional projection of a three-dimensional analogy of spacetime curvature described in general relativity

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity.[1] Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to other forces of nature.[2] It applies to the cosmological and astrophysical realm, including astronomy.[3]

The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton.[3][4][5] It introduced concepts including spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves.[3][4][5]

Contents

1 Development and acceptance

2 Special relativity

3 General relativity

4 Experimental evidence

4.1 Tests of special relativity

4.2 Tests of general relativity

5 Modern applications

6 See also

7 References

8 Further reading

9 External links

Development and acceptance

Main articles: History of special relativity and History of general relativity

Albert Einstein published the theory of special relativity in 1905, building on many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did subsequent work.

Einstein developed general relativity between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916.[3]

The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the same paper, Alfred Bucherer used for the first time the expression "theory of relativity" (German: Relativitätstheorie).[6][7]

By the 1920s, the physics community understood and accepted special relativity.[8] It rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of atomic physics, nuclear physics, and quantum mechanics.

By comparison, general relativity did not appear to be as useful, beyond making minor corrections to predictions of Newtonian gravitation theory.[3] It seemed to offer little potential for experimental test, as most of its assertions were on an astronomical scale. Its mathematics seemed difficult and fully understandable only by a small number of people. Around 1960, general relativity became central to physics and astronomy. New mathematical techniques to apply to general relativity streamlined calculations and made its concepts more easily visualized. As astronomical phenomena were discovered, such as quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the first black hole candidates (1981),[3] the theory explained their attributes, and measurement of them further confirmed the theory.

Special relativity

Main article: Special relativity

Special relativity is a theory of the structure of spacetime. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists see History of special relativity). Special relativity is based on two postulates which are contradictory in classical mechanics:

The laws of physics are the same for all observers in any inertial frame of reference relative to one another (principle of relativity).

The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source.

The resultant theory copes with experiment better than classical mechanics. For instance, postulate 2 explains the results of the Michelson–Morley experiment. Moreover, the theory has many surprising and counterintuitive consequences. Some of these are:

Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.

Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.

Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.

Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.

The effect of Gravity can only travel through space at the speed of light, not faster or instantaneously.

Mass–energy equivalence: E = mc2, energy and mass are equivalent and transmutable.

Relativistic mass, idea used by some researchers.[9]

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism).

General relativity

Main articles: General relativity and Introduction to general relativity

General relativity is a theory of gravitation developed by Einstein in the years 1907–1915. The development of general relativity began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field (for example, when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall is inertial motion: an object in free fall is falling because that is how objects move when there is no force being exerted on them, instead of this being due to the force of gravity as is the case in classical mechanics. This is incompatible with classical mechanics and special relativity because in those theories inertially moving objects cannot accelerate with respect to each other, but objects in free fall do so. To resolve this difficulty Einstein first proposed that spacetime is curved. In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and any momentum within it.

Some of the consequences of general relativity are:

Gravitational time dilation: Clocks run slower in deeper gravitational wells.[10]

Precession: Orbits precess in a way unexpected in Newton's theory of gravity. (This has been observed in the orbit of Mercury and in binary pulsars).

Light deflection: Rays of light bend in the presence of a gravitational field

Frame-dragging: Rotating masses "drag along" the spacetime around them.

Metric expansion of space: the universe is expanding, and the far parts of it are moving away from us faster than the speed of light.

Technically, general relativity is a theory of gravitation whose defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology of the spacetime and how objects move inertially.

Experimental evidence

Einstein stated that the theory of relativity belongs to a class of "principle-theories". As such, it employs an analytic method, which means that the elements of this theory are not based on hypothesis but on empirical discovery. By observing natural processes, we understand their general characteristics, devise mathematical models to describe what we observed, and by analytical means we deduce the necessary conditions that have to be satisfied. Measurement of separate events must satisfy these conditions and match the theory's conclusions.[2]

Tests of special relativity

Main article: Tests of special relativity

A diagram of the Michelson–Morley experiment

Relativity is a falsifiable theory: It makes predictions that can be tested by experiment. In the case of special relativity, these include the principle of relativity, the constancy of the speed of light, and time dilation.[11] The predictions of special relativity have been confirmed in numerous tests since Einstein published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical to its validation. These are the Michelson–Morley experiment, the Kennedy–Thorndike experiment, and the Ives–Stilwell experiment. Einstein derived the Lorentz transformations from first principles in 1905, but these three experiments allow the transformations to be induced from experimental evidence.

Maxwell's equations—the foundation of classical electromagnetism—describe light as a wave that moves with a characteristic velocity. The modern view is that light needs no medium of transmission, but Maxwell and his contemporaries were convinced that light waves were propagated in a medium, analogous to sound propagating in air, and ripples propagating on the surface of a pond. This hypothetical medium was called the luminiferous aether, at rest relative to the "fixed stars" and through which the Earth moves. Fresnel's partial ether dragging hypothesis ruled out the measurement of first-order (v/c) effects, and although observations of second-order effects (v2/c2) were possible in principle, Maxwell thought they were too small to be detected with then-current technology.[12][13]

The Michelson–Morley experiment was designed to detect second-order effects of the "aether wind"—the motion of the aether relative to the earth. Michelson designed an instrument called the Michelson interferometer to accomplish this. The apparatus was more than accurate enough to detect the expected effects, but he obtained a null result when the first experiment was conducted in 1881,[14] and again in 1887.[15] Although the failure to detect an aether wind was a disappointment, the results were accepted by the scientific community.[13] In an attempt to salvage the aether paradigm, FitzGerald and Lorentz independently created an ad hoc hypothesis in which the length of material bodies changes according to their motion through the aether.[16] This was the origin of FitzGerald–Lorentz contraction, and their hypothesis had no theoretical basis. The interpretation of the null result of the Michelson–Morley experiment is that the round-trip travel time for light is isotropic (independent of direction), but the result alone is not enough to discount the theory of the aether or validate the predictions of special relativity.[17][18]

The Kennedy–Thorndike experiment shown with interference fringes.

While the Michelson–Morley experiment showed that the velocity of light is isotropic, it said nothing about how the magnitude of the velocity changed (if at all) in different inertial frames. The Kennedy–Thorndike experiment was designed to do that, and was first performed in 1932 by Roy Kennedy and Edward Thorndike.[19] They obtained a null result, and concluded that "there is no effect ... unless the velocity of the solar system in space is no more than about half that of the earth in its orbit".[18][20] That possibility was thought to be too coincidental to provide an acceptable explanation, so from the null result of their experiment it was concluded that the round-trip time for light is the same in all inertial reference frames.[17][18]

The Ives–Stilwell experiment was carried out by Herbert Ives and G.R. Stilwell first in 1938[21] and with better accuracy in 1941.[22] It was designed to test the transverse Doppler effect – the redshift of light from a moving source in a direction perpendicular to its velocity—which had been predicted by Einstein in 1905. The strategy was to compare observed Doppler shifts with what was predicted by classical theory, and look for a Lorentz factor correction. Such a correction was observed, from which was concluded that the frequency of a moving atomic clock is altered according to special relativity.[17][18]

Those classic experiments have been repeated many times with increased precision. Other experiments include, for instance, relativistic energy and momentum increase at high velocities, experimental testing of time dilation, and modern searches for Lorentz violations.

Tests of general relativity

Main article: Tests of general relativity

General relativity has also been confirmed many times, the classic experiments being the perihelion precession of Mercury's orbit, the deflection of light by the Sun, and the gravitational redshift of light. Other tests confirmed the equivalence principle and frame dragging.

Modern applications

Far from being simply of theoretical interest, relativistic effects are important practical engineering concerns. Satellite-based measurement needs to take into account relativistic effects, as each satellite is in motion relative to an Earth-bound user and is thus in a different frame of reference under the theory of relativity. Global positioning systems such as GPS, GLONASS, and Galileo, must account for all of the relativistic effects, such as the consequences of Earth's gravitational field, in order to work with precision.[23] This is also the case in the high-precision measurement of time.[24] Instruments ranging from electron microscopes to particle accelerators would not work if relativistic considerations were omitted.

See also

icon Physics portal

icon Science portal

Doubly special relativity

Galilean invariance

General relativity references

Scale relativity

Special relativity references

References

Einstein A. (1916), Relativity: The Special and General Theory (Translation 1920), New York: H. Holt and Company

Einstein, Albert (November 28, 1919). "Time, Space, and Gravitation" . The Times.

Will, Clifford M (2010). "Relativity". Grolier Multimedia Encyclopedia. Retrieved 2010-08-01.

Will, Clifford M (2010). "Space-Time Continuum". Grolier Multimedia Encyclopedia. Retrieved 2010-08-01.

Will, Clifford M (2010). "Fitzgerald–Lorentz contraction". Grolier Multimedia Encyclopedia. Retrieved 2010-08-01.

Planck, Max (1906), "Die Kaufmannschen Messungen der Ablenkbarkeit der ?-Strahlen in ihrer Bedeutung für die Dynamik der Elektronen (The Measurements of Kaufmann on the Deflectability of ?-Rays in their Importance for the Dynamics of the Electrons)" , Physikalische Zeitschrift, 7: 753–761

Miller, Arthur I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 978-0-201-04679-3

Hey, Anthony J.G.; Walters, Patrick (2003). The New Quantum Universe (illustrated, revised ed.). Cambridge University Press. p. 227. Bibcode:2003nqu..book.....H. ISBN 978-0-521-56457-1.

Greene, Brian. "The Theory of Relativity, Then and Now". Retrieved 2015-09-26.

Feynman, Richard Phillips; Morínigo, Fernando B.; Wagner, William; Pines, David; Hatfield, Brian (2002). Feynman Lectures on Gravitation. West view Press. p. 68. ISBN 978-0-8133-4038-8., Lecture 5

Roberts, T; Schleif, S; Dlugosz, JM (ed.) (2007). "What is the experimental basis of Special Relativity?". Usenet Physics FAQ. University of California, Riverside. Retrieved 2010-10-31.

Maxwell, James Clerk (1880), "On a Possible Mode of Detecting a Motion of the Solar System through the Luminiferous Ether" , Nature, 21 (535): 314–315, Bibcode:1880Natur..21S.314., doi:10.1038/021314c0

Pais, Abraham (1982). "Subtle is the Lord ...": The Science and the Life of Albert Einstein (1st ed.). Oxford: Oxford Univ. Press. pp. 111–113. ISBN 978-0-19-280672-7.

Michelson, Albert A. (1881). "The Relative Motion of the Earth and the Luminiferous Ether" . American Journal of Science. 22 (128): 120–129. Bibcode:1881AmJS...22..120M. doi:10.2475/ajs.s3-22.128.120.

Michelson, Albert A. & Morley, Edward W. (1887). "On the Relative Motion of the Earth and the Luminiferous Ether" . American Journal of Science. 34 (203): 333–345. Bibcode:1887AmJS...34..333M. doi:10.2475/ajs.s3-34.203.333.

Pais, Abraham (1982). "Subtle is the Lord ...": The Science and the Life of Albert Einstein (1st ed.). Oxford: Oxford Univ. Press. p. 122. ISBN 978-0-19-280672-7.

Robertson, H.P. (July 1949). "Postulate versus Observation in the Special Theory of Relativity" (PDF). Reviews of Modern Physics. 21 (3): 378–382. Bibcode:1949RvMP...21..378R. doi:10.1103/RevModPhys.21.378.

Taylor, Edwin F.; John Archibald Wheeler (1992). Spacetime physics: Introduction to Special Relativity (2nd ed.). New York: W.H. Freeman. pp. 84–88. ISBN 978-0-7167-2327-1.

Kennedy, R.J.; Thorndike, E.M. (1932). "Experimental Establishment of the Relativity of Time". Physical Review. 42 (3): 400–418. Bibcode:1932PhRv...42..400K. doi:10.1103/PhysRev.42.400.

Robertson, H.P. (July 1949). "Postulate versus Observation in the Special Theory of Relativity" (PDF). Reviews of Modern Physics. 21 (3): 381. Bibcode:1949RvMP...21..378R. doi:10.1103/revmodphys.21.378.

Ives, H.E.; Stilwell, G.R. (1938). "An experimental study of the rate of a moving atomic clock". Journal of the Optical Society of America. 28 (7): 215. Bibcode:1938JOSA...28..215I. doi:10.1364/JOSA.28.000215.

Ives, H.E.; Stilwell, G.R. (1941). "An experimental study of the rate of a moving atomic clock. II". Journal of the Optical Society of America. 31 (5): 369. Bibcode:1941JOSA...31..369I. doi:10.1364/JOSA.31.000369.

"Archived copy" (PDF). Archived from the original (PDF) on 2015-11-05. Retrieved 2015-12-09.

Francis, S.; B. Ramsey; S. Stein; Leitner, J.; Moreau, J.M.; Burns, R.; Nelson, R.A.; Bartholomew, T.R.; Gifford, A. (2002). "Timekeeping and Time Dissemination in a Distributed Space-Based Clock Ensemble" (PDF). Proceedings 34th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting: 201–214. Archived from the original (PDF) on 17 February 2013. Retrieved 14 April 2013.

Further reading

Einstein, Albert (2005). Relativity: The Special and General Theory. Translated by Robert W. Lawson (The masterpiece science ed.). New York: Pi Press. ISBN 978-0-13-186261-6.

Einstein, Albert (1920). Relativity: The Special and General Theory (PDF). Henry Holt and Company.

Einstein, Albert; trans. Schilpp; Paul Arthur (1979). Albert Einstein, Autobiographical Notes (A Centennial ed.). La Salle, IL: Open Court Publishing Co. ISBN 978-0-87548-352-8.

Einstein, Albert (2009). Einstein's Essays in Science. Translated by Alan Harris (Dover ed.). Mineola, NY: Dover Publications. ISBN 978-0-486-47011-5.

Einstein, Albert (1956) [1922]. The Meaning of Relativity (5 ed.). Princeton University Press.

The Meaning of Relativity Albert Einstein: Four lectures delivered at Princeton University, May 1921

How I created the theory of relativity Albert Einstein, December 14, 1922; Physics Today August 1982

Relativity Sidney Perkowitz Encyclopædia Britannica

External links

Wikiquote has quotations related to: Theory of relativity

Wikisource has original works on the topic: Relativity

Wikisource has original text related to this article:

Relativity: The Special and General Theory

Wikibooks has a book on the topic of: Category:Relativity

Wikiversity has learning resources about General relativity

Theory of relativity at Curlie

Relativity Milestones: Timeline of Notable Relativity Scientists and Contributions

The dictionary definition of theory of relativity at Wiktionary

Media related to Theory of relativity at Wikimedia Commons

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Beyond the Standard Model

CMS Higgs-event.jpg

Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons

Standard Model

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Theories[hide]

Theory of everythingMathematical universe hypothesisGrand Unified TheoryTechnicolorKaluza–Klein theoryQuantum field theoryQuantum field theory in curved spacetimeThermal quantum field theoryTopological quantum field theoryConformal field theoryTwo-dimensional conformal field theoryLiouville field theory6D (2,0) superconformal field theoryQuantum mechanicsQuantum cosmologyBrane cosmologyString theorySuperstring theoryM-theoryRandall–Sundrum modelde Broglie–Bohm theoryStochastic electrodynamicsEigenstate thermalization hypothesisYang–Mills theoryN = 4 supersymmetric Yang–Mills theoryTwistor string theoryDark fluidSuperfluid vacuum theoryDoubly special relativityde Sitter invariant special relativityCausal fermion systemsQuantum thermodynamicsBlack hole thermodynamicsDigital physicsUnparticle physicsGauge theoryGauge gravitation theoryGauge theory gravityHidden-variable theoryPilot wave theoryCPT symmetry

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A theory of everything (TOE[1] or ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe.[2]:6 Finding a TOE is one of the major unsolved problems in physics. Over the past few centuries, two theoretical frameworks have been developed that, together, most closely resemble a TOE. These two theories upon which all modern physics rests are general relativity (GR) and quantum field theory (QFT). GR is a theoretical framework that only focuses on gravity for understanding the universe in regions of both large scale and high mass: stars, galaxies, clusters of galaxies, etc. On the other hand, QFT is a theoretical framework that only focuses on three non-gravitational forces for understanding the universe in regions of both small scale and low mass: sub-atomic particles, atoms, molecules, etc. QFT successfully implemented the Standard Model that describes the three non-gravitational forces -- strong, weak, and electromagnetic force -- as well as all observed elementary particles.[3]:122

Physicists have experimentally confirmed virtually every prediction made by GR and QFT when in their appropriate domains of applicability. Nevertheless, GR and QFT are mutually incompatible – they cannot both be right. Since the usual domains of applicability of GR and QFT are so different, most situations require that only one of the two theories be used.[4][5]:842–844 As it turns out, this incompatibility between GR and QFT is only an issue in regions of extremely small scale - the Planck scale - such as those that exist within a black hole or during the beginning stages of the universe (i.e., the moment immediately following the Big Bang). To resolve the incompatibility, a theoretical framework revealing a deeper underlying reality, unifying gravity with the other three interactions, must be discovered to harmoniously integrate the realms of GR and QFT into a seamless whole: the TOE is a single theory that, in principle, is capable of describing all phenomena in the universe.

In pursuit of this goal, quantum gravity has become one area of active research. One example is string theory, which evolved into a candidate for the TOE, but not without drawbacks (most notably, its lack of currently testable predictions) and controversy. String theory posits that at the beginning of the universe (up to 10?43 seconds after the Big Bang), the four fundamental forces were once a single fundamental force. According to string theory, every particle in the universe, at its most microscopic level (Planck length), consists of varying combinations of vibrating strings (or strands) with preferred patterns of vibration. String theory further claims that it is through these specific oscillatory patterns of strings that a particle of unique mass and force charge is created (that is to say, the electron is a type of string that vibrates one way, while the up quark is a type of string vibrating another way, and so forth).

Contents

1 Name

2 Historical antecedents

2.1 Antiquity to 19th century

2.2 Early 20th century

2.3 Late 20th century and the nuclear interactions

3 Modern physics

3.1 Conventional sequence of theories

3.2 String theory and M-theory

3.3 Loop quantum gravity

3.4 Other attempts

3.5 Present status

4 Arguments against

4.1 Gödel's incompleteness theorem

4.2 Fundamental limits in accuracy

4.3 Lack of fundamental laws

4.4 Impossibility of being "of everything"

4.5 Infinite number of onion layers

4.6 Impossibility of calculation

5 See also

6 References

6.1 Footnotes

6.2 Bibliography

7 External links

Name

Initially, the term theory of everything was used with an ironic reference to various overgeneralized theories. For example, a grandfather of Ijon Tichy – a character from a cycle of Stanis?aw Lem's science fiction stories of the 1960s – was known to work on the "General Theory of Everything". Physicist Harald Fritzsch used the term in his 1977 lectures in Varenna.[6] Physicist John Ellis claims[7] to have introduced the term into the technical literature in an article in Nature in 1986.[8] Over time, the term stuck in popularizations of theoretical physics research.

Historical antecedents

Antiquity to 19th century

Ancient Babylonian astronomers studied the movement pattern of heavenly bodies against a background of the celestial sky, with their interest being to relate celestial movement to human events (astrology), and the goal being to predict events by recording events against a time measure and then look for recurrent patterns. The debate between the universe having either a beginning or eternal cycles can be traced back to ancient Babylonia.[9]

The natural philosophy of atomism appeared in several ancient traditions. In ancient Greek philosophy, the pre-Socratic philosophers speculated that the apparent diversity of observed phenomena was due to a single type of interaction, namely the motions and collisions of atoms. The concept of 'atom' proposed by Democritus was an early philosophical attempt to unify phenomena observed in nature. The concept of 'atom' also appeared in the Nyaya-Vaisheshika school of ancient Indian philosophy, and the Ash?ari school of early Islamic philosophy.

Archimedes was possibly the first philosopher to have described nature with axioms (or principles) and then deduce new results from them. Any "theory of everything" is similarly expected to be based on axioms and to deduce all observable phenomena from them.[10]:340 The scientific method emphasizing precise observation and controlled experimentation was largely developed in the science of the Islamic world, by Arabic alchemists and particularly the Arab physicist Ibn al-Haytham, who proposed that rays of light were streams of tiny particles travelling in straight lines at a finite velocity.[9] Arabic alchemists proposed the theory of corpuscularianism, where unified sulfur and mercury corpuscles (particles), differing in purity, size, and relative proportions, form the basis of a much more complicated process.[11][12]

Following earlier atomistic thought, the mechanical philosophy of the 17th century posited that all forces could be ultimately reduced to contact forces between the atoms, then imagined as tiny solid particles.[13]:184[14]

In the late 17th century, Isaac Newton's description of the long-distance force of gravity implied that not all forces in nature result from things coming into contact. Newton's work in his Mathematical Principles of Natural Philosophy dealt with this in a further example of unification, in this case unifying Galileo's work on terrestrial gravity, Kepler's laws of planetary motion and the phenomenon of tides by explaining these apparent actions at a distance under one single law: the law of universal gravitation.[15]

In 1814, building on these results, Laplace famously suggested that a sufficiently powerful intellect could, if it knew the position and velocity of every particle at a given time, along with the laws of nature, calculate the position of any particle at any other time:[16]:ch 7

An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

—?Essai philosophique sur les probabilités, Introduction. 1814

Laplace thus envisaged a combination of gravitation and mechanics as a theory of everything. Modern quantum mechanics implies that uncertainty is inescapable, and thus that Laplace's vision has to be amended: a theory of everything must include gravitation and quantum mechanics.

In 1820, Hans Christian Ørsted discovered a connection between electricity and magnetism, triggering decades of work that culminated in 1865, in James Clerk Maxwell's theory of electromagnetism. During the 19th and early 20th centuries, it gradually became apparent that many common examples of forces – contact forces, elasticity, viscosity, friction, and pressure – result from electrical interactions between the smallest particles of matter.

In his experiments of 1849–50, Michael Faraday was the first to search for a unification of gravity with electricity and magnetism.[17] However, he found no connection.

In 1900, David Hilbert published a famous list of mathematical problems. In Hilbert's sixth problem, he challenged researchers to find an axiomatic basis to all of physics. In this problem he thus asked for what today would be called a theory of everything.[18]

Early 20th century

In the late 1920s, the new quantum mechanics showed that the chemical bonds between atoms were examples of (quantum) electrical forces, justifying Dirac's boast that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known".[19]

After 1915, when Albert Einstein published the theory of gravity (general relativity), the search for a unified field theory combining gravity with electromagnetism began with a renewed interest. In Einstein's day, the strong and the weak forces had not yet been discovered, yet, he found the potential existence of two other distinct forces -gravity and electromagnetism- far more alluring. This launched his thirty-year voyage in search of the so-called "unified field theory" that he hoped would show that these two forces are really manifestations of one grand underlying principle. During these last few decades of his life, this quixotic quest isolated Einstein from the mainstream of physics. Understandably, the mainstream was instead far more excited about the newly emerging framework of quantum mechanics. Einstein wrote to a friend in the early 1940s, "I have become a lonely old chap who is mainly known because he doesn't wear socks and who is exhibited as a curiosity on special occasions." Prominent contributors were Gunnar Nordström, Hermann Weyl, Arthur Eddington, David Hilbert,[20] Theodor Kaluza, Oskar Klein (see Kaluza–Klein theory), and most notably, Albert Einstein and his collaborators. Einstein intensely searched for, but ultimately failed to find, a unifying theory.[21]:ch 17 (But see:Einstein–Maxwell–Dirac equations.) More than a half a century later, Einstein's dream of discovering a unified theory has become the Holy Grail of modern physics.

Late 20th century and the nuclear interactions

In the twentieth century, the search for a unifying theory was interrupted by the discovery of the strong and weak nuclear forces (or interactions), which differ both from gravity and from electromagnetism. A further hurdle was the acceptance that in a TOE, quantum mechanics had to be incorporated from the start, rather than emerging as a consequence of a deterministic unified theory, as Einstein had hoped.

Gravity and electromagnetism could always peacefully coexist as entries in a list of classical forces, but for many years it seemed that gravity could not even be incorporated into the quantum framework, let alone unified with the other fundamental forces. For this reason, work on unification, for much of the twentieth century, focused on understanding the three "quantum" forces: electromagnetism and the weak and strong forces. The first two were combined in 1967–68 by Sheldon Glashow, Steven Weinberg, and Abdus Salam into the "electroweak" force.[22] Electroweak unification is a broken symmetry: the electromagnetic and weak forces appear distinct at low energies because the particles carrying the weak force, the W and Z bosons, have non-zero masses of 80.4 GeV/c2 and 91.2 GeV/c2, whereas the photon, which carries the electromagnetic force, is massless. At higher energies Ws and Zs can be created easily and the unified nature of the force becomes apparent.

While the strong and electroweak forces peacefully coexist in the Standard Model of particle physics, they remain distinct. So far, the quest for a theory of everything is thus unsuccessful on two points: neither a unification of the strong and electroweak forces – which Laplace would have called 'contact forces' – nor a unification of these forces with gravitation has been achieved.

Modern physics

Conventional sequence of theories

A Theory of Everything would unify all the fundamental interactions of nature: gravitation, strong interaction, weak interaction, and electromagnetism. Because the weak interaction can transform elementary particles from one kind into another, the TOE should also yield a deep understanding of the various different kinds of possible particles. The usual assumed path of theories is given in the following graph, where each unification step leads one level up:

Theory of everything

Quantum gravity

Space Curvature

Electronuclear force (GUT)

Standard model of cosmology

Standard model of particle physics

Strong interaction

SU(3)

Electroweak interaction

SU(2) x U(1)Y

Weak interaction

SU(2)

Electromagnetism

U(1)EM

Electricity

Magnetism

In this graph, electroweak unification occurs at around 100 GeV, grand unification is predicted to occur at 1016 GeV, and unification of the GUT force with gravity is expected at the Planck energy, roughly 1019 GeV.

Several Grand Unified Theories (GUTs) have been proposed to unify electromagnetism and the weak and strong forces. Grand unification would imply the existence of an electronuclear force; it is expected to set in at energies of the order of 1016 GeV, far greater than could be reached by any possible Earth-based particle accelerator. Although the simplest GUTs have been experimentally ruled out, the general idea, especially when linked with supersymmetry, remains a favorite candidate in the theoretical physics community. Supersymmetric GUTs seem plausible not only for their theoretical "beauty", but because they naturally produce large quantities of dark matter, and because the inflationary force may be related to GUT physics (although it does not seem to form an inevitable part of the theory). Yet GUTs are clearly not the final answer; both the current standard model and all proposed GUTs are quantum field theories which require the problematic technique of renormalization to yield sensible answers. This is usually regarded as a sign that these are only effective field theories, omitting crucial phenomena relevant only at very high energies.[4]

The final step in the graph requires resolving the separation between quantum mechanics and gravitation, often equated with general relativity. Numerous researchers concentrate their efforts on this specific step; nevertheless, no accepted theory of quantum gravity – and thus no accepted theory of everything – has emerged yet. It is usually assumed that the TOE will also solve the remaining problems of GUTs.

In addition to explaining the forces listed in the graph, a TOE may also explain the status of at least two candidate forces suggested by modern cosmology: an inflationary force and dark energy. Furthermore, cosmological experiments also suggest the existence of dark matter, supposedly composed of fundamental particles outside the scheme of the standard model. However, the existence of these forces and particles has not been proven.

String theory and M-theory

Question, Web Fundamentals.svg Unsolved problem in physics:

Is string theory, superstring theory, or M-theory, or some other variant on this theme, a step on the road to a "theory of everything", or just a blind alley?

(more unsolved problems in physics)

Since the 1990s, some physicists such as Edward Witten believe that 11-dimensional M-theory, which is described in some limits by one of the five perturbative superstring theories, and in another by the maximally-supersymmetric 11-dimensional supergravity, is the theory of everything. However, there is no widespread consensus on this issue.

A surprising property of string/M-theory is that extra dimensions are required for the theory's consistency. In this regard, string theory can be seen as building on the insights of the Kaluza–Klein theory, in which it was realized that applying general relativity to a five-dimensional universe (with one of them small and curled up)[clarification needed] looks from the four-dimensional perspective like the usual general relativity together with Maxwell's electrodynamics. This lent credence to the idea of unifying gauge and gravity interactions, and to extra dimensions, but did not address the detailed experimental requirements. Another important property of string theory is its supersymmetry, which together with extra dimensions are the two main proposals for resolving the hierarchy problem of the standard model, which is (roughly) the question of why gravity is so much weaker than any other force. The extra-dimensional solution involves allowing gravity to propagate into the other dimensions while keeping other forces confined to a four-dimensional spacetime, an idea that has been realized with explicit stringy mechanisms.[23]

Research into string theory has been encouraged by a variety of theoretical and experimental factors. On the experimental side, the particle content of the standard model supplemented with neutrino masses fits into a spinor representation of SO(10), a subgroup of E8 that routinely emerges in string theory, such as in heterotic string theory[24] or (sometimes equivalently) in F-theory.[25][26] String theory has mechanisms that may explain why fermions come in three hierarchical generations, and explain the mixing rates between quark generations.[27] On the theoretical side, it has begun to address some of the key questions in quantum gravity, such as resolving the black hole information paradox, counting the correct entropy of black holes[28][29] and allowing for topology-changing processes.[30][31][32] It has also led to many insights in pure mathematics and in ordinary, strongly-coupled gauge theory due to the Gauge/String duality.

In the late 1990s, it was noted that one major hurdle in this endeavor is that the number of possible four-dimensional universes is incredibly large. The small, "curled up" extra dimensions can be compactified in an enormous number of different ways (one estimate is 10500 ) each of which leads to different properties for the low-energy particles and forces. This array of models is known as the string theory landscape.[10]:347

One proposed solution is that many or all of these possibilities are realised in one or another of a huge number of universes, but that only a small number of them are habitable. Hence what we normally conceive as the fundamental constants of the universe are ultimately the result of the anthropic principle rather than dictated by theory. This has led to criticism of string theory,[33] arguing that it cannot make useful (i.e., original, falsifiable, and verifiable) predictions and regarding it as a pseudoscience. Others disagree,[34] and string theory remains an active topic of investigation in theoretical physics.[35]

Loop quantum gravity

Current research on loop quantum gravity may eventually play a fundamental role in a TOE, but that is not its primary aim.[36] Also loop quantum gravity introduces a lower bound on the possible length scales.

There have been recent claims that loop quantum gravity may be able to reproduce features resembling the Standard Model. So far only the first generation of fermions (leptons and quarks) with correct parity properties have been modelled by Sundance Bilson-Thompson using preons constituted of braids of spacetime as the building blocks.[37] However, there is no derivation of the Lagrangian that would describe the interactions of such particles, nor is it possible to show that such particles are fermions, nor that the gauge groups or interactions of the Standard Model are realised. Utilization of quantum computing concepts made it possible to demonstrate that the particles are able to survive quantum fluctuations.[38]

This model leads to an interpretation of electric and colour charge as topological quantities (electric as number and chirality of twists carried on the individual ribbons and colour as variants of such twisting for fixed electric charge).

Bilson-Thompson's original paper suggested that the higher-generation fermions could be represented by more complicated braidings, although explicit constructions of these structures were not given. The electric charge, colour, and parity properties of such fermions would arise in the same way as for the first generation. The model was expressly generalized for an infinite number of generations and for the weak force bosons (but not for photons or gluons) in a 2008 paper by Bilson-Thompson, Hackett, Kauffman and Smolin.[39]

Other attempts

Among other attempts to develop a theory of everything is the theory of causal fermion systems,[40] giving the two current physical theories (general relativity and quantum field theory) as limiting cases.

Another theory is called Causal Sets. As some of the approaches mentioned above, its direct goal isn't necessarily to achieve a TOE but primarily a working theory of quantum gravity, which might eventually include the standard model and become a candidate for a TOE. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between relative past and future distinguishing spacetime events.

Outside the previously mentioned attempts there is Garrett Lisi's E8 proposal. This theory attempts to construct general relativity and the standard model within the Lie group E8. The theory doesn't provide a novel quantization procedure and the author suggests its quantization might follow the Loop Quantum Gravity approach above mentioned.[41]

Causal dynamical triangulation does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.

Christoph Schiller's Strand Model attempts to account for the gauge symmetry of the Standard Model of particle physics, U(1)×SU(2)×SU(3), with the three Reidemeister moves of knot theory by equating each elementary particle to a different tangle of one, two, or three strands (selectively a long prime knot or unknotted curve, a rational tangle, or a braided tangle respectively).[42]

Another attempt may be related to ER=EPR, a conjecture in physics stating that entangled particles are connected by a wormhole (or Einstein–Rosen bridge).[43][44]

Present status

At present, there is no candidate theory of everything that includes the standard model of particle physics and general relativity and that, at the same time, is able to calculate the fine structure constant or the mass of the electron. Most particle physicists expect that the outcome of the ongoing experiments – the search for new particles at the large particle accelerators and for dark matter – are needed in order to provide further input for a TOE.

Arguments against

In parallel to the intense search for a TOE, various scholars have seriously debated the possibility of its discovery.

Gödel's incompleteness theorem

A number of scholars claim that Gödel's incompleteness theorem suggests that any attempt to construct a TOE is bound to fail. Gödel's theorem, informally stated, asserts that any formal theory sufficient to express elementary arithmetical facts and strong enough for them to be proved is either inconsistent (both a statement and its denial can be derived from its axioms) or incomplete, in the sense that there is a true statement that can't be derived in the formal theory.

Stanley Jaki, in his 1966 book The Relevance of Physics, pointed out that, because any "theory of everything" will certainly be a consistent non-trivial mathematical theory, it must be incomplete. He claims that this dooms searches for a deterministic theory of everything.[45]

Freeman Dyson has stated that "Gödel's theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. […] Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them."[46]

Stephen Hawking was originally a believer in the Theory of Everything, but after considering Gödel's Theorem, he concluded that one was not obtainable. "Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind."[47]

Jürgen Schmidhuber (1997) has argued against this view; he points out that Gödel's theorems are irrelevant for computable physics.[48] In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like halting problems is extremely hard to detect but does not at all prevent formal TOEs describable by very few bits of information.[49]

Related critique was offered by Solomon Feferman,[50] among others. Douglas S. Robertson offers Conway's game of life as an example:[51] The underlying rules are simple and complete, but there are formally undecidable questions about the game's behaviors. Analogously, it may (or may not) be possible to completely state the underlying rules of physics with a finite number of well-defined laws, but there is little doubt that there are questions about the behavior of physical systems which are formally undecidable on the basis of those underlying laws.

Since most physicists would consider the statement of the underlying rules to suffice as the definition of a "theory of everything", most physicists argue that Gödel's Theorem does not mean that a TOE cannot exist. On the other hand, the scholars invoking Gödel's Theorem appear, at least in some cases, to be referring not to the underlying rules, but to the understandability of the behavior of all physical systems, as when Hawking mentions arranging blocks into rectangles, turning the computation of prime numbers into a physical question.[52] This definitional discrepancy may explain some of the disagreement among researchers.

Fundamental limits in accuracy

No physical theory to date is believed to be precisely accurate. Instead, physics has proceeded by a series of "successive approximations" allowing more and more accurate predictions over a wider and wider range of phenomena. Some physicists believe that it is therefore a mistake to confuse theoretical models with the true nature of reality, and hold that the series of approximations will never terminate in the "truth". Einstein himself expressed this view on occasions.[53] Following this view, we may reasonably hope for a theory of everything which self-consistently incorporates all currently known forces, but we should not expect it to be the final answer.

On the other hand, it is often claimed that, despite the apparently ever-increasing complexity of the mathematics of each new theory, in a deep sense associated with their underlying gauge symmetry and the number of dimensionless physical constants, the theories are becoming simpler. If this is the case, the process of simplification cannot continue indefinitely.

Lack of fundamental laws

There is a philosophical debate within the physics community as to whether a theory of everything deserves to be called the fundamental law of the universe.[54] One view is the hard reductionist position that the TOE is the fundamental law and that all other theories that apply within the universe are a consequence of the TOE. Another view is that emergent laws, which govern the behavior of complex systems, should be seen as equally fundamental. Examples of emergent laws are the second law of thermodynamics and the theory of natural selection. The advocates of emergence argue that emergent laws, especially those describing complex or living systems are independent of the low-level, microscopic laws. In this view, emergent laws are as fundamental as a TOE.

The debates do not make the point at issue clear. Possibly the only issue at stake is the right to apply the high-status term "fundamental" to the respective subjects of research. A well-known debate over this took place between Steven Weinberg and Philip Anderson[citation needed].

Impossibility of being "of everything"

Although the name "theory of everything" suggests the determinism of Laplace's quotation, this gives a very misleading impression. Determinism is frustrated by the probabilistic nature of quantum mechanical predictions, by the extreme sensitivity to initial conditions that leads to mathematical chaos, by the limitations due to event horizons, and by the extreme mathematical difficulty of applying the theory. Thus, although the current standard model of particle physics "in principle" predicts almost all known non-gravitational phenomena, in practice only a few quantitative results have been derived from the full theory (e.g., the masses of some of the simplest hadrons), and these results (especially the particle masses which are most relevant for low-energy physics) are less accurate than existing experimental measurements. The TOE would almost certainly be even harder to apply for the prediction of experimental results, and thus might be of limited use.

A motive for seeking a TOE,[citation needed] apart from the pure intellectual satisfaction of completing a centuries-long quest, is that prior examples of unification have predicted new phenomena, some of which (e.g., electrical generators) have proved of great practical importance. And like in these prior examples of unification, the TOE would probably allow us to confidently define the domain of validity and residual error of low-energy approximations to the full theory.

The theories generally do not account for the apparent phenomenon of consciousness or free will, which are instead often the subject of philosophy and religion.

Infinite number of onion layers

Frank Close regularly argues that the layers of nature may be like the layers of an onion, and that the number of layers might be infinite.[55] This would imply an infinite sequence of physical theories.

Impossibility of calculation

Weinberg[56] points out that calculating the precise motion of an actual projectile in the Earth's atmosphere is impossible. So how can we know we have an adequate theory for describing the motion of projectiles? Weinberg suggests that we know principles (Newton's laws of motion and gravitation) that work "well enough" for simple examples, like the motion of planets in empty space. These principles have worked so well on simple examples that we can be reasonably confident they will work for more complex examples. For example, although general relativity includes equations that do not have exact solutions, it is widely accepted as a valid theory because all of its equations with exact solutions have been experimentally verified. Likewise, a TOE must work for a wide range of simple examples in such a way that we can be reasonably confident it will work for every situation in physics.

See also

icon Physics portal

Absolute (philosophy)

Argument from beauty

Attractor

Beyond black holes

Beyond the standard model

Big Bang

Bit-string physics

cGh physics

Chronology of the universe

Electroweak interaction

ER=EPR

Holographic principle

Mathematical beauty

Mathematical universe hypothesis

Multiverse

Penrose interpretation

Scale relativity

Standard Model (mathematical formulation)

Superfluid vacuum theory (SVT)

The Theory of Everything (2014 film)

Timeline of the Big Bang

Unified Field Theory

Zero-energy universe

References

Footnotes

Fran De Aquino (1999). "Theory of Everything". arXiv:gr-qc/9910036.

Steven Weinberg (2011-04-20). Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature. Knopf Doubleday Publishing Group. ISBN 978-0-307-78786-6.

Stephen W. Hawking (28 February 2006). The Theory of Everything: The Origin and Fate of the Universe. Phoenix Books; Special Anniv. ISBN 978-1-59777-508-3.

Carlip, Steven (2001). "Quantum Gravity: a Progress Report". Reports on Progress in Physics. 64 (8): 885–942. arXiv:gr-qc/0108040. Bibcode:2001RPPh...64..885C. doi:10.1088/0034-4885/64/8/301.

Susanna Hornig Priest (14 July 2010). Encyclopedia of Science and Technology Communication. SAGE Publications. ISBN 978-1-4522-6578-0.

Fritzsch, Harald (1977). "THE WORLD OF FLAVOUR AND COLOUR". CERN Report. Ref.TH.2359-CERN. (download at http://cds.cern.ch/record/875256/files/CM-P00061728.pdf )

Ellis, John (2002). "Physics gets physical (correspondence)". Nature. 415 (6875): 957. Bibcode:2002Natur.415..957E. doi:10.1038/415957b. PMID 11875539.

Ellis, John (1986). "The Superstring: Theory of Everything, or of Nothing?". Nature. 323 (6089): 595–598. Bibcode:1986Natur.323..595E. doi:10.1038/323595a0.

Hodge, John C. (2012). Theory of Everything: Scalar Potential Model of the Big and the Small. pp. 1–13, 99. ISBN 9781469987361.

Chris Impey (26 March 2012). How It Began: A Time-Traveler's Guide to the Universe. W. W. Norton. ISBN 978-0-393-08002-5.

The Mineral Exhalation Theory of Metallogenesis in Pre-Modern Mineral Science JOHN A. NORRIS AMBIX, Vol. 53, No. 1, March 2006, 43–65, Society for the History of Alchemy and Chemistry 2006, doi:10.1179/174582306X93183

Newman, William Royall (2006). Atoms and alchemy: chymistry and the experimental origins of the scientific revolution. University of Chicago Press. p. 13. ISBN 978-0-226-57697-8.

William E. Burns (1 January 2001). The Scientific Revolution: An Encyclopedia. ABC-CLIO. ISBN 978-0-87436-875-8.

Shapin, Steven (1996). The Scientific Revolution. University of Chicago Press. ISBN 978-0-226-75021-7.

Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy. II. p. 255.

Sean Carroll (2010). From Eternity to Here: The Quest for the Ultimate Theory of Time. Penguin Group US. ISBN 978-1-101-15215-7.

Faraday, M. (1850). "Experimental Researches in Electricity. Twenty-Fourth Series. On the Possible Relation of Gravity to Electricity". Abstracts of the Papers Communicated to the Royal Society of London. 5: 994–995. doi:10.1098/rspl.1843.0267.

Gorban, Alexander N.; Karlin, Ilya (2013). "Hilbert's 6th Problem: Exact and approximate hydrodynamic manifolds for kinetic equations". Bulletin of the American Mathematical Society. 51 (2): 187. arXiv:1310.0406. Bibcode:2013arXiv1310.0406G. doi:10.1090/S0273-0979-2013-01439-3.

Dirac, P.A.M. (1929). "Quantum mechanics of many-electron systems". Proceedings of the Royal Society of London A. 123 (792): 714–733. Bibcode:1929RSPSA.123..714D. doi:10.1098/rspa.1929.0094.

Majer, U.; Sauer, T. (2005). Hilbert's "World Equations" and His Vision of a Unified Science. Einstein Studies. 11. pp. 259–276. arXiv:physics/0405110. Bibcode:2005ugr..book..259M. doi:10.1007/0-8176-4454-7_14. ISBN 978-0-8176-4454-3.

Abraham Pais (23 September 1982). Subtle is the Lord : The Science and the Life of Albert Einstein: The Science and the Life of Albert Einstein. Oxford University Press. ISBN 978-0-19-152402-8.

Weinberg (1993), Ch. 5

Holloway, M (2005). "The Beauty of Branes" (PDF). Scientific American. 293 (4): 38–40. Bibcode:2005SciAm.293d..38H. doi:10.1038/scientificamerican1005-38. PMID 16196251. Retrieved August 13, 2012.

Nilles, Hans Peter; Ramos-Sánchez, Saúl; Ratz, Michael; Vaudrevange, Patrick K. S. (2009). "From strings to the MSSM". The European Physical Journal C. 59 (2): 249–267. arXiv:0806.3905. Bibcode:2009EPJC...59..249N. doi:10.1140/epjc/s10052-008-0740-1.

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External links

Wikiquote has quotations related to: Theory of everything

The Elegant Universe, Nova episode about the search for the theory of everything and string theory.

Theory of Everything, freeview video by the Vega Science Trust, BBC and Open University.

The Theory of Everything: Are we getting closer, or is a final theory of matter and the universe impossible? Debate between John Ellis (physicist), Frank Close and Nicholas Maxwell.

Why The World Exists, a discussion between physicist Laura Mersini-Houghton, cosmologist George Francis Rayner Ellis and philosopher David Wallace about dark matter, parallel universes and explaining why these and the present Universe exist.

Theories of Everything, BBC Radio 4 discussion with Brian Greene, John Barrow & Val Gibson (In Our Time, Mar. 25, 2004)

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