897:
Nordström's theory. Moreover, the Brans–Dicke theory is equal to the independently derived theory of Jordan (hence it is often referred to as the Jordan-Brans–Dicke or JBD theory). The Brans–Dicke theory couples a scalar field with the curvature of space-time and is self-consistent and, assuming appropriate values for a tunable constant, this theory has not been ruled out by observation. The Brans–Dicke theory is generally regarded as a leading competitor of general relativity, which is a pure tensor theory. However, the Brans–Dicke theory seems to need too high a parameter, which favours general relativity).
908:(1999) is a recent example of a scalar theory of gravitation. It is not intended as a viable theory of gravitation (since, as Watt and Misner point out, it is not consistent with observation), but as a toy theory which can be useful in testing numerical relativity schemes. It also has pedagogical value.
833:
covariant. This is an important consistency condition, so
Einstein dropped this theory in late 1914. Associating the scalar field with the metric leads to Einstein's later conclusions that the theory of gravitation he sought could not be a scalar theory. Indeed, the theory he finally arrived at in
896:
is a scalar-tensor theory, not a scalar theory, meaning that it represents the gravitational interaction using both a scalar field and a tensor field. We mention it here because one of the field equations of this theory involves only the scalar field and the trace of the stress–energy tensor, as in
900:
Zee combined the idea of the BD theory with the Higgs-Mechanism of
Symmetry Breakdown for mass generation, which led to a scalar-tensor theory with Higgs field as scalar field, in which the scalar field is massive (short-ranged). An example of this theory was proposed by H. Dehnen and H. Frommert
563:
that general covariance was not viable. Inspired by
Nordström's work, he proposed his own scalar theory. This theory employs a massless scalar field coupled to the stress–energy tensor, which is the sum of two terms. The first,
885:
in an attempt to create a five-dimensional unification of gravity and electromagnetism. Its generalization with a 5th variable component of the metric that leads to a variable gravitational constant was first given by
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to the world line of the observer. (Einstein made no attempt, in this theory, to take account of possible gravitational effects of the field energy of the
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Despite these disappointing results, Einstein's critiques of
Nordström's second theory played an important role in his development of general relativity.
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represents the stress–momentum–energy of the scalar field itself. The second represents the stress-momentum-energy of any matter which may be present:
547:, but this disagrees in both sign and magnitude with the observed anomalous precession (the part which cannot be explained using Newtonian gravitation).
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1975:
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1991, parting from the nature of Higgs field interacting gravitational- and Yukawa (long-ranged)-like with the particles that get mass through it.
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Nordström's first idea (1912) was to simply replace the divergence operator in the field equation of
Newtonian gravity with the
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838:, is a tensor theory, not a scalar theory, with a 2-tensor, the metric, as the potential. Unlike his 1913 scalar theory, it is
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The first attempts to present a relativistic (classical) field theory of gravitation were also scalar theories.
1795:
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851:
103:
1823:
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1534:
893:
1740:
1045:
Janssen, Michel (2007). "What did
Einstein know and when did He know it? A Besso Memo Dated August 1913".
248:
48:
1244:
Dehnen, H.; Frommert, H.; Ghaboussi, F. (1992). "Higgs field and a new scalar-tensor theory of gravity".
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The theory fails to predict any deflection of light passing near a massive body (contrary to observation)
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However, several theoretical difficulties with this theory quickly arose, and
Nordström dropped it.
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940:"Einstein, Nordström and the early demise of scalar, Lorentz-covariant theories of gravitation"
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This field theory formulation leads directly to the familiar law of universal gravitation,
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This suggestion signifies that the inertial mass should depend on the scalar field.
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of gravitation. The best known relativistic classical field theory of gravitation,
1761:
1570:
1323:
1209:
Dehnen, H.; Frommert, H. (1991). "Higgs-Field
Gravity within the Standard Model".
55:, is a tensor theory, in which the gravitational interaction is described using a
1129:
Goenner, Hubert (2012). "Some remarks on the genesis of scalar-tensor theories".
1730:
71:. In this theory, the gravitational interaction is completely described by the
31:
1944:
1283:(1999). "Relativistic Scalar Gravity: A Laboratory for Numerical Relativity".
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Dehnen, H.; Frommert, H. (1990). "Scalar gravity and Higgs potential".
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1108:(2005). "The roots of scalar-tensor theory: an approximate history".
1080:
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Lorentzian spacetimes. That is, the metric tensor can be written as
56:
981:"The Hole Argument and Some Physical and Philosophical Implications"
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involves the use of a scalar gravitational field in addition to the
98:(with the mass density acting as the source of the field). To wit:
1307:
Goenner, Hubert F. M., "On the
History of Unified Field Theories";
353:
A year later, Nordström tried again, presenting the field equation
1598:
1143:
1351:
777:{\displaystyle T_{m}^{\mu \nu }=\rho \phi u^{\mu }u^{\nu }}
707:{\displaystyle T_{g}^{\mu \nu }={\frac {1}{4\pi G}}\left}
295:{\displaystyle \square =\partial _{t}^{2}-\nabla ^{2}}
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in which the gravitational field is described using a
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1326:(2004). "Scalar Gravitation and Extra Dimensions".
1066:"How Einstein found his field equations: 1912-1915"
559:In 1913, Einstein (erroneously) concluded from his
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67:The prototypical scalar theory of gravitation is
1672:Degenerate Higher-Order Scalar-Tensor theories
477:{\displaystyle g_{\mu \nu }=A\eta _{\mu \nu }}
1363:
525:Nordström's second theory satisfies the weak
8:
1246:International Journal of Theoretical Physics
1211:International Journal of Theoretical Physics
1176:International Journal of Theoretical Physics
518:is a scalar which is a function of position.
1100:
1098:
1073:Historical Studies in the Physical Sciences
1047:Boston Studies in the Philosophy of Science
431:Solutions of Nordström's second theory are
393:{\displaystyle \Phi \square \Phi =-4\pi GT}
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339:{\displaystyle \square \Phi =-4\pi G\rho }
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131:{\displaystyle \Delta \Phi =4\pi G\rho }
1976:Gravitational interaction of antimatter
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235:
1981:Physics in the medieval Islamic world
1904:(2+1)-dimensional topological gravity
1400:Newton's law of universal gravitation
947:Archive for History of Exact Sciences
7:
1726:Asymptotic safety in quantum gravity
236:Nordström's theories of gravitation
225:{\displaystyle F=m_{1}m_{2}G/r^{2}}
94:, which is required to satisfy the
1478:Gibbons–Hawking–York boundary term
1131:General Relativity and Gravitation
829:Unfortunately, this theory is not
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1593:Modified Newtonian dynamics, MOND
1509:Classical theories of gravitation
919:Nordström's theory of gravitation
536:The theory predicts an anomalous
302:. This gives the field equation
145:is the gravitational constant and
1415:History of gravitational theory
1721:Causal dynamical triangulation
1410:Poisson's equation for gravity
28:Scalar theories of gravitation
1:
1344:, Vieweg (Braunschweig) 1955.
554:
1319:. Retrieved August 10, 2005.
985:Living Reviews in Relativity
1583:Infinite derivative gravity
244:created two such theories.
2044:
1771:Unified-field-theoric and
818:vector of an observer, or
1914:Jackiw–Teitelboim gravity
1693:Canonical quantum gravity
1688:Euclidean quantum gravity
1161:10.1007/s10714-012-1378-8
1790:Superfluid vacuum theory
1614:Nonsymmetric gravitation
1463:Post-Newtonian formalism
938:Norton, John D. (1992).
878:{\displaystyle A^{\mu }}
807:{\displaystyle u^{\mu }}
555:Einstein's scalar theory
49:classical field theories
44:This article focuses on
1955:Mechanical explanations
1824:Heterotic string theory
1780:Noncommutative geometry
1699:Wheeler–DeWitt equation
1425:General relativity (GR)
1405:Gauss's law for gravity
1379:Theories of gravitation
1342:Schwerkraft und Weltall
1796:Logarithmic BEC vacuum
1741:Rainbow gravity theory
1619:Scalar–tensor theories
1393:Newtonian gravity (NG)
979:Stachel, John (2014).
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30:are field theories of
1873:Twistor string theory
1852:Type II string theory
1845:Bosonic string theory
1785:Semiclassical gravity
1750:Unified-field-theoric
1535:Poincaré gauge theory
1309:Living Rev. Relativ.
1064:Norton, John (1984).
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846:Additional variations
824:electromagnetic field
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160:{\displaystyle \rho }
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87:{\displaystyle \Phi }
69:Newtonian gravitation
1940:Aristotelian physics
1909:Gauss–Bonnet gravity
1859:Little string theory
1838:Type 0 string theory
1831:Type I string theory
1706:Loop quantum gravity
1633:Scalar–tensor–vector
1606:Tensor–vector–scalar
1561:Gauge theory gravity
1519:Theory of everything
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426:stress–energy tensor
424:is the trace of the
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167:is the mass density.
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2028:Theories of gravity
1757:Kaluza–Klein theory
1258:1992IJTP...31..109D
1223:1991IJTP...30..985D
1188:1990IJTP...29..361D
1153:2012GReGr..44.2077G
1006:10.12942/lrr-2014-1
997:2014LRR....17....1S
852:Kaluza–Klein theory
840:generally covariant
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2002:Gravitational wave
1885:Generalisations /
1773:quantum-mechanical
1681:Quantum-mechanical
1494:general relativity
1468:Linearized gravity
1281:Misner, Charles W.
1279:Watt, Keith &
1266:10.1007/BF00674344
1231:10.1007/bf00673991
1196:10.1007/BF00674437
959:10.1007/bf00375886
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1638:Conformal gravity
1566:Composite gravity
1556:Bimetric theories
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511:{\displaystyle A}
417:{\displaystyle T}
63:Newtonian gravity
16:(Redirected from
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1731:Causal sets
1625:Brans–Dicke
1443:Mathematics
1340:P. Jordan,
1075:: 253–316.
529:. However:
32:gravitation
1945:CGHS model
1932:toy models
1317:lrr-2004-2
1053:: 787–837.
925:References
858:potential
541:precession
538:perihelion
1950:RST model
1736:DGP model
1713:Spin foam
1657:Whitehead
1649:Nordström
1578:) gravity
1528:Classical
1502:Paradigms
1453:Resources
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2007:Graviton
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1438:History
1254:Bibcode
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1458:Tests
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1085:JSTOR
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