177:
660:, every physicist recognizes immediately what is wrong with the idea of gravitational repulsion: if a ball is thrown high up in the air so that it falls back, then its motion is symmetric under time-reversal; and therefore, the ball falls also down in opposite time-direction. Since a matter particle in opposite time-direction is an antiparticle, this proves according to 't Hooft that antimatter falls down on earth just like "normal" matter. However, Cabbolet replied that 't Hooft's argument is false, and only proves that an anti-ball falls down on an anti-earth – which is not disputed.
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which is incompatible with both quantum mechanics and general relativity. The core idea is that nonzero rest mass particles such as electrons, protons, neutrons and their antimatter counterparts exhibit stepwise motion as they alternate between a particlelike state of rest and a wavelike state of motion. Gravitation then takes place in a wavelike state, and the theory allows, for example, that the wavelike states of protons and antiprotons interact differently with the earth's gravitational field.
22:
124:
728:, and are experimentally indistinguishable. The general idea remains that gravity is the deflection of a continuous particle trajectory due to the curvature of spacetime, but antiparticles 'live' in an inverted spacetime. The equation of motion for antiparticles is then obtained from the equation of motion of ordinary particles by applying the C, P, and T operators (Villata) or by applying
827:; in 2012 ALPHA used such atoms to set the first free-fall loose bounds on the gravitational interaction of antimatter with matter, measured to within ±7500% of ordinary gravity, not enough for a clear scientific statement about the sign of gravity acting on antimatter. Future experiments need to be performed with higher precision, either with beams of antihydrogen (
599:. If matter and antimatter responded oppositely to a gravitational field, then it would take no energy to change the height of a particle–antiparticle pair. However, when moving through a gravitational potential, the frequency and energy of light is shifted. Morrison argued that energy would be created by
749:
The first non-classical, non-quantum physical principles underlying a matter–antimatter gravitational repulsion have been published by
Marcoen Cabbolet. He introduces the Elementary Process Theory, which uses a new language for physics, i.e. a new mathematical formalism and new physical concepts, and
647:
found that it resulted in an amount of kaon regeneration which agrees with observation. He argued that antigravity is a potential explanation for CP violation based on his models on K mesons. His results date to 1992. Since then however, studies on CP violation mechanisms in the B mesons systems have
842:
In 2013, experiments on antihydrogen atoms released from the ALPHA trap set direct, i.e. freefall, coarse limits on antimatter gravity. These limits were coarse, with a relative precision of ±100%, thus, far from a clear statement even for the sign of gravity acting on antimatter. Future experiments
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away, both neutrinos and antineutrinos seem to have been detected virtually simultaneously. If both were actually observed, then any difference in the gravitational interaction would have to be very small. However, neutrino detectors cannot distinguish perfectly between neutrinos and antineutrinos.
501:
When antimatter was first discovered in 1932, physicists wondered how it would react to gravity. Initial analysis focused on whether antimatter should react the same as matter or react oppositely. Several theoretical arguments arose which convinced physicists that antimatter would react the same as
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described by C-inversion. Since this C-inversion does not affect gravitational mass, the CPT theorem predicts that the gravitational mass of antimatter is the same as that of ordinary matter. A repulsive gravity is then excluded, since that would imply a difference in sign between the observable
792:
Some physicists conservatively estimate that there is less than a 10% chance that no regular neutrinos were observed at all. Others estimate even lower probabilities, some as low as 1%. Unfortunately, this accuracy is unlikely to be improved by duplicating the experiment any time soon. The
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spacetime of the true trajectories in the inverted spacetime. However, it has been argued on methodological and ontological grounds that the area of application of
Villata's theory cannot be extended to include the microcosmos. These objections were subsequently dismissed by Villata.
682:, but instead is a hole in the sea of electrons-with-negative-energy-and-positive-gravitational-mass: this yields a modified C-inversion, by which the positron has positive energy but negative gravitational mass. Repulsive gravity is then described by adding extra terms (
619:. However, the renormalization technique used in Schiff's analysis is heavily criticized, and his work is seen as inconclusive. In 2014 the argument was redone by Marcoen Cabbolet, who concluded however that it merely demonstrates the incompatibility of the
176:
708:) to the wave equation. The idea is that the wave function of a positron moving in the gravitational field of a matter particle evolves such that in time it becomes more probable to find the positron further away from the matter particle.
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predicts that mass and energy react the same way with gravity, therefore matter and antimatter would be accelerated identically by a gravitational field. From this point of view, matter-antimatter gravitational repulsion is unlikely.
489:, and has been experimentally verified for antihydrogen. However the equivalence of the gravitational acceleration of matter to matter vs antimatter to matter has an error margin of about 20% ( table 3). Difficulties in creating
474:, for reasons still of interest to physicists, complicating efforts to study gravity in systems small enough to be feasibly created in lab, including antimatter systems. Most methods for the creation of antimatter (specifically
677:
The first theory of repulsive gravity was a quantum theory published by Mark Kowitt. In this modified Dirac theory, Kowitt postulated that the positron is not a hole in the sea of electrons-with-negative-energy as in usual
668:
Since repulsive gravity has not been refuted experimentally, it is possible to speculate about physical principles that would bring about such a repulsion. Thus far, three radically different theories have been published.
1064:
Cabbolet, M. J. T. F. (2010). "Elementary
Process Theory: a formal axiomatic system with a potential application as a foundational framework for physics supporting gravitational repulsion of matter and antimatter".
643:. At the time, CP violation had not yet been observed. However, Good's argument is criticized for being expressed in terms of absolute potentials. By rephrasing the argument in terms of relative potentials,
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at CERN with beams of antihydrogen, such as AEgIS, or with trapped antihydrogen, such as ALPHA and GBAR, have to improve the sensitivity to make a clear, scientific statement about gravity on antimatter.
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Further authors have used a matter–antimatter gravitational repulsion to explain cosmological observations, but these publications do not address the physical principles of gravitational repulsion.
603:
matter and antimatter at one height and then annihilating it higher up, since the photons used in production would have less energy than the photons yielded from annihilation.
816:. Antihydrogen, which is electrically neutral, should make it possible to directly measure the gravitational attraction of antimatter particles to the matter of Earth.
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732:(Santilli), which amounts to the same thing: the equation of motion for antiparticles then predicts a repulsion of matter and antimatter. It has to be taken that the
39:
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Antimatter is gravitationally attracted to matter. The magnitude of the gravitational force is also the same. This is predicted by theoretical arguments like the
86:
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Andresen, G. B.; Ashkezari, M. D.; Baquero-Ruiz, M.; Bertsche, W.; Bowe, P. D.; et al. (2011). "Confinement of antihydrogen for 1,000 seconds".
721:
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58:
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1944:
Reynolds, S. P.; Borkowski, K. J.; Green, D. A.; Hwang, U.; Harrus, I.; Petre, R. (2008). "The
Youngest Galactic Supernova Remnant: G1.9+0.3".
65:
1178:
Cabbolet, M. J. T. F. (2014). "Incompatibility of QED/QCD and repulsive gravity, and implications for some recent approaches to dark energy".
2101:
Gabrielse, G.; Kalra, R.; Kolthammer, W. S.; McConnell, R.; Richerme, P.; et al. (2012). "Trapped
Antihydrogen in Its Ground State".
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when brought into contact with matter makes its study a technically demanding task. Furthermore, gravity is much weaker than the other
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Andresen, G. B.; Ashkezari, M. D.; Baquero-Ruiz, M.; Bertsche, W.; Bowe, P. D.; et al. (2010). "Trapped antihydrogen".
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normal matter. They inferred that gravitational repulsion between matter and antimatter was implausible as it would violate
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434:
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Hajdukovic, D. S. (2011). "Is dark matter an illusion created by the gravitational polarization of the quantum vacuum?".
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has been observed by physicists. As was the consensus among physicists previously, it was experimentally confirmed that
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779:. In 1987, three neutrino detectors around the world simultaneously observed a cascade of neutrinos emanating from a
562:, for example) been observed to interact with the gravitational field of ordinary matter exactly as predicted by the
105:
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Pakvasa, S.; Simmons, W. A.; Weiler, T. J. (1989). "Test of equivalence principle for neutrinos and antineutrinos".
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implies that the difference between the properties of a matter particle and those of its antimatter counterpart is
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Blanchet, L.; Le Tiec, A. (2008). "Model of dark matter and dark energy based on gravitational polarization".
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2167:"Description and first application of a new technique to measure the gravitational mass of antihydrogen"
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Santilli, R. M. (1999). "A classical isodual theory of antimatter and its prediction of antigravity".
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used quantum field theory to argue that antigravity would be inconsistent with the results of the
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Amole, C.; Ashkezari, M. D.; Baquero-Ruiz, M.; Bertsche, W.; Butler, E.; et al. (2013).
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argued that antigravity would result in the observation of an unacceptably high amount of
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One source of experimental evidence in favor of normal gravity was the observation of
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Villata, M. (2011). "Reply to 'Comment to a paper of M. Villata on antigravity'".
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Cabbolet, M. J. T. F. (2011). "Comment to a paper of M. Villata on antigravity".
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Villata, M. (2011). "CPT symmetry and antimatter gravity in general relativity".
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Andersson, E. K.; Baker, C. J.; Bertsche, W.; Bhatt, N. M. (September 27, 2023).
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478:) result in particles and atoms of high kinetic energy, which are unsuitable for
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attracts both matter and antimatter at the same rate within experimental error.
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Villata, M. (2015). "The matter–antimatter interpretation of Kerr spacetime".
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518:. It was also theorized that it would be inconsistent with the results of the
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Benoit-LĂ©vy, A.; Chardin, G. (2012). "Introducing the Dirac-Milne universe".
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Cabbolet, M. J. T. F. (2011). "Addendum to the
Elementary Process Theory".
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Villata, M. (2013). "On the nature of dark energy: the lattice
Universe".
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to occur at such a close range prior to
Supernova 1987A was around 1867.
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1333:"'t Hooft slaat plank mis in blog spookrijders in de wetenschap | DUB"
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Schiff, L. I. (1958). "Sign of the
Gravitational Mass of a Positron".
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526:. Many of these early theoretical objections were later overturned.
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Kowitt, M. (1996). "Gravitational repulsion and Dirac antimatter".
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Morrison, P. (1958). "Approximate Nature of
Physical Symmetries".
886:"Observation of the effect of gravity on the motion of antimatter"
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Classical theories of repulsive gravity have been published by
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550:, which are their own antiparticles in the framework of the
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Journal of Physics B: Atomic, Molecular and Optical Physics
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Nieto, M. M.; Hughes, R. J.; Goldman, T. (March 1988).
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46:. Unsourced material may be challenged and removed.
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991:
989:
736:trajectories of antiparticles are projections on
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787:. Although the supernova happened about 164,000
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554:, have in a large number of astronomical tests (
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2564:Degenerate Higher-Order Scalar-Tensor theories
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648:fundamentally invalidated these explanations.
487:gravitational equivalence of energy and matter
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583:gravitational mass of matter and antimatter.
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2224:"Antimatter atoms are corralled even longer"
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1358:International Journal of Theoretical Physics
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106:Learn how and when to remove this message
55:"Gravitational interaction of antimatter"
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1270:violation. A matter of (anti)gravity?".
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595:argued that antigravity would violate
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143:may be able to help recruit an expert.
2873:Physics in the medieval Islamic world
2796:(2+1)-dimensional topological gravity
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800:Cold neutral antihydrogen experiments
2618:Asymptotic safety in quantum gravity
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497:Theories of gravitational attraction
466:Antimatter's rarity and tendency to
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2370:Gibbons–Hawking–York boundary term
1021:Nieto, M. M.; Goldman, T. (1991).
804:Since 2010 the production of cold
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724:. Both theories are extensions of
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2485:Modified Newtonian dynamics, MOND
2401:Classical theories of gravitation
1266:Chardin, G.; Rax, J.-M. (1992). "
639:in the anomalous regeneration of
137:needs cruft removal and updating.
1231:and the Equivalence Principle".
941:Bertsche, W E (6 October 2015).
831:) or with trapped antihydrogen (
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160:Theory of gravity on antimatter
31:needs additional citations for
2613:Causal dynamical triangulation
2302:Poisson's equation for gravity
2133:10.1103/PhysRevLett.108.113002
1797:Astrophysics and Space Science
1648:Astrophysics and Space Science
1595:Astrophysics and Space Science
1489:Astrophysics and Space Science
1180:Astrophysics and Space Science
968:10.1088/0953-4075/48/23/232001
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712:Santilli and Villata's theory
623:and gravitational repulsion.
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1047:10.1016/0370-1573(91)90138-C
564:general theory of relativity
364:Positron emission tomography
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2475:Infinite derivative gravity
1880:10.1051/0004-6361/201016103
1110:American Journal of Physics
943:"Physics With Antihydrogen"
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808:has become possible at the
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135:. The specific problem is:
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2663:Unified-field-theoric and
1850:Astronomy and Astrophysics
1774:10.1103/PhysRevD.78.024031
1466:10.1209/0295-5075/94/20001
910:10.1038/s41586-023-06527-1
652:Gerard 't Hooft's argument
524:weak equivalence principle
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2585:Canonical quantum gravity
2580:Euclidean quantum gravity
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1946:The Astrophysical Journal
1827:10.1007/s10509-011-0744-4
1678:10.1007/s10509-011-0940-2
1625:10.1007/s10509-011-0939-8
1519:10.1007/s10509-013-1388-3
1421:10.1142/S0217751X99001111
1200:10.1007/s10509-014-1791-4
1165:10.1103/PhysRevLett.1.254
530:The equivalence principle
301:Gravitational interaction
2682:Superfluid vacuum theory
2506:Nonsymmetric gravitation
2355:Post-Newtonian formalism
1923:10.1103/PhysRevD.39.1761
993:"Gravity and Antimatter"
2847:Mechanical explanations
2716:Heterotic string theory
2672:Noncommutative geometry
2591:Wheeler–DeWitt equation
2317:General relativity (GR)
2297:Gauss's law for gravity
2271:Theories of gravitation
2222:Amos, J. (2011-06-06).
2103:Physical Review Letters
1872:2012A&A...537A..78B
1819:2011Ap&SS.334..215H
1670:2012Ap&SS.337...15V
1617:2012Ap&SS.337....5C
1511:2013Ap&SS.345....1V
1253:10.1103/PhysRev.121.311
1192:2014Ap&SS.350..777C
1145:Physical Review Letters
823:, first ALPHA and then
2688:Logarithmic BEC vacuum
2633:Rainbow gravity theory
2511:Scalar–tensor theories
2285:Newtonian gravity (NG)
1721:10.1002/andp.201100194
1572:10.1002/andp.201500154
1331:Cabbolet, M. J. T. F.
1311:webspace.science.uu.nl
1087:10.1002/andp.201000063
810:Antiproton Decelerator
785:Large Magellanic Cloud
597:conservation of energy
556:gravitational redshift
508:conservation of energy
334:Antiproton decelerator
270:Concepts and phenomena
2765:Twistor string theory
2744:Type II string theory
2737:Bosonic string theory
2677:Semiclassical gravity
2642:Unified-field-theoric
2427:Poincaré gauge theory
2171:Nature Communications
560:gravitational lensing
536:equivalence principle
228:Antiprotonic hydrogen
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2801:Gauss–Bonnet gravity
2751:Little string theory
2730:Type 0 string theory
2723:Type I string theory
2598:Loop quantum gravity
2525:Scalar–tensor–vector
2498:Tensor–vector–scalar
2453:Gauge theory gravity
2411:Theory of everything
794:last known supernova
329:Particle accelerator
40:improve this article
2649:Kaluza–Klein theory
2183:2013NatCo...4.1785A
2125:2012PhRvL.108k3002G
2072:2011NatPh...7..558A
2019:10.1038/nature09610
2011:2010Natur.468..673A
1968:2008ApJ...680L..41R
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1766:2008PhRvD..78b4031B
1713:2011AnP...523..990C
1564:2015AnP...527..507V
1458:2011EL.....9420001V
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1370:1996IJTP...35..605K
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1157:1958PhRvL...1..254S
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1039:1991PhR...205..221N
998:Scientific American
959:2015JPhB...48w2001B
902:2023Natur.621..716A
587:Morrison's argument
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233:Antiprotonic helium
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2191:10.1038/ncomms2787
1701:Annalen der Physik
1542:Annalen der Physik
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1305:'t Hooft, Gerard.
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2005:(7324): 673–676.
1903:Physical Review D
1744:Physical Review D
1407:(14): 2205–2238.
1272:Physics Letters B
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2435:
2391:
2390:
2282:
2281:
2264:
2257:
2250:
2241:
2240:
2235:
2234:
2232:
2231:
2219:
2213:
2212:
2202:
2162:
2153:
2152:
2118:
2098:
2092:
2091:
2065:
2045:
2039:
2038:
1994:
1988:
1987:
1961:
1941:
1935:
1934:
1909:(6): 1761–1763.
1898:
1892:
1891:
1865:
1845:
1839:
1838:
1812:
1792:
1786:
1785:
1759:
1739:
1733:
1732:
1696:
1690:
1689:
1663:
1643:
1637:
1636:
1610:
1590:
1584:
1583:
1557:
1548:(7–8): 507–512.
1537:
1531:
1530:
1504:
1484:
1478:
1477:
1451:
1431:
1425:
1424:
1396:
1390:
1389:
1353:
1347:
1346:
1344:
1343:
1328:
1322:
1321:
1319:
1318:
1302:
1296:
1295:
1278:(1–2): 256–262.
1263:
1257:
1256:
1218:
1212:
1211:
1175:
1169:
1168:
1140:
1134:
1133:
1105:
1099:
1098:
1061:
1052:
1050:
1018:
1009:
1008:
1006:
1004:
995:
987:
981:
980:
970:
938:
932:
931:
921:
881:
718:Ruggero Santilli
514:, and result in
482:-related study.
437:
430:
423:
286:Baryon asymmetry
179:
165:
164:
153:
150:
144:
126:
125:
118:
111:
104:
100:
97:
91:
89:
48:
24:
16:
2945:
2944:
2940:
2939:
2938:
2936:
2935:
2934:
2910:
2909:
2908:
2903:
2882:
2858:
2851:
2822:
2820:
2810:
2791:Lovelock theory
2778:
2772:
2763:
2749:
2742:
2735:
2728:
2721:
2714:
2707:
2700:
2686:
2664:
2658:
2637:
2603:
2596:
2589:
2568:
2559:Induced gravity
2539:
2535:Scalar theories
2515:
2496:
2489:
2480:Massive gravity
2440:Teleparallelism
2438:
2433:Einstein–Cartan
2431:
2415:
2406:Quantum gravity
2385:
2384:Alternatives to
2374:
2340:Exact solutions
2311:
2273:
2268:
2238:
2229:
2227:
2220:
2216:
2163:
2156:
2099:
2095:
2046:
2042:
1995:
1991:
1942:
1938:
1899:
1895:
1846:
1842:
1793:
1789:
1740:
1736:
1707:(12): 990–994.
1697:
1693:
1644:
1640:
1591:
1587:
1538:
1534:
1485:
1481:
1432:
1428:
1397:
1393:
1354:
1350:
1341:
1339:
1329:
1325:
1316:
1314:
1303:
1299:
1264:
1260:
1233:Physical Review
1230:
1219:
1215:
1176:
1172:
1141:
1137:
1106:
1102:
1073:(10): 699–738.
1062:
1055:
1027:Physics Reports
1019:
1012:
1002:
1000:
988:
984:
939:
935:
882:
875:
871:
849:
802:
777:Supernova 1987A
769:
767:Supernova 1987A
764:
756:
747:
722:Massimo Villata
714:
707:
701:
694:
688:
675:
673:Kowitt's theory
666:
658:Gerard 't Hooft
654:
645:Gabriel Chardin
629:
627:Good's argument
611:Later in 1958,
609:
593:Philip Morrison
589:
572:
545:
543:Photon behavior
532:
499:
491:quantum gravity
441:
412:
411:
402:Andrei Sakharov
387:
379:
378:
359:
351:
350:
319:
311:
310:
271:
263:
262:
189:
161:
154:
148:
145:
139:
127:
123:
112:
101:
95:
92:
49:
47:
37:
25:
12:
11:
5:
2943:
2933:
2932:
2927:
2922:
2905:
2904:
2902:
2901:
2896:
2890:
2888:
2887:Related topics
2884:
2883:
2881:
2880:
2875:
2870:
2865:
2864:
2863:
2856:
2844:
2839:
2834:
2828:
2826:
2816:
2815:
2812:
2811:
2809:
2808:
2803:
2798:
2793:
2788:
2782:
2780:
2774:
2773:
2771:
2770:
2769:
2768:
2759:Twistor theory
2756:
2755:
2754:
2747:
2740:
2733:
2726:
2719:
2712:
2705:
2693:
2692:
2691:
2679:
2674:
2668:
2666:
2660:
2659:
2657:
2656:
2651:
2645:
2643:
2639:
2638:
2636:
2635:
2630:
2625:
2620:
2615:
2610:
2609:
2608:
2601:
2594:
2582:
2576:
2574:
2570:
2569:
2567:
2566:
2561:
2556:
2551:
2546:
2545:
2544:
2532:
2527:
2522:
2521:
2520:
2508:
2503:
2502:
2501:
2494:
2482:
2477:
2472:
2460:
2455:
2450:
2445:
2444:
2443:
2436:
2423:
2421:
2417:
2416:
2414:
2413:
2408:
2403:
2397:
2395:
2388:
2380:
2379:
2376:
2375:
2373:
2372:
2367:
2362:
2357:
2352:
2347:
2342:
2337:
2332:
2327:
2321:
2319:
2313:
2312:
2310:
2309:
2304:
2299:
2294:
2288:
2286:
2279:
2275:
2274:
2267:
2266:
2259:
2252:
2244:
2237:
2236:
2214:
2154:
2109:(11): 113002.
2093:
2056:(7): 558–564.
2050:Nature Physics
2040:
1989:
1976:10.1086/589570
1952:(1): L41–L44.
1936:
1893:
1840:
1803:(2): 215–218.
1787:
1734:
1691:
1638:
1585:
1532:
1479:
1426:
1391:
1364:(3): 605–631.
1348:
1323:
1297:
1258:
1239:(1): 311–313.
1228:
1213:
1186:(2): 777–780.
1170:
1151:(7): 254–255.
1135:
1116:(6): 358–368.
1100:
1053:
1033:(5): 221–281.
1010:
982:
933:
872:
870:
867:
866:
865:
860:
855:
848:
845:
801:
798:
768:
765:
763:
760:
755:
752:
746:
743:
713:
710:
705:
699:
692:
686:
674:
671:
665:
662:
653:
650:
628:
625:
621:Standard Model
608:
605:
588:
585:
571:
568:
552:Standard Model
544:
541:
531:
528:
504:CPT invariance
498:
495:
443:
442:
440:
439:
432:
425:
417:
414:
413:
410:
409:
404:
399:
394:
388:
385:
384:
381:
380:
377:
376:
371:
366:
360:
357:
356:
353:
352:
349:
348:
343:
342:
341:
336:
326:
320:
317:
316:
313:
312:
309:
308:
303:
298:
293:
288:
283:
278:
272:
269:
268:
265:
264:
261:
260:
255:
250:
245:
240:
235:
230:
217:
216:
211:
206:
201:
196:
190:
185:
184:
181:
180:
172:
171:
159:
156:
155:
130:
128:
121:
114:
113:
28:
26:
19:
9:
6:
4:
3:
2:
2942:
2931:
2928:
2926:
2923:
2921:
2918:
2917:
2915:
2900:
2897:
2895:
2892:
2891:
2889:
2885:
2879:
2876:
2874:
2871:
2869:
2866:
2861:
2857:
2854:
2853:Fatio–Le Sage
2850:
2849:
2848:
2845:
2843:
2840:
2838:
2835:
2833:
2830:
2829:
2827:
2825:
2819:Pre-Newtonian
2817:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2787:
2784:
2783:
2781:
2775:
2766:
2762:
2761:
2760:
2757:
2752:
2748:
2745:
2741:
2738:
2734:
2731:
2727:
2724:
2720:
2717:
2713:
2710:
2706:
2703:
2699:
2698:
2697:
2696:String theory
2694:
2689:
2685:
2684:
2683:
2680:
2678:
2675:
2673:
2670:
2669:
2667:
2661:
2655:
2652:
2650:
2647:
2646:
2644:
2640:
2634:
2631:
2629:
2626:
2624:
2621:
2619:
2616:
2614:
2611:
2606:
2602:
2599:
2595:
2592:
2588:
2587:
2586:
2583:
2581:
2578:
2577:
2575:
2571:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2542:
2538:
2537:
2536:
2533:
2531:
2528:
2526:
2523:
2518:
2514:
2513:
2512:
2509:
2507:
2504:
2499:
2495:
2492:
2488:
2487:
2486:
2483:
2481:
2478:
2476:
2473:
2471:
2469:
2465:
2461:
2459:
2456:
2454:
2451:
2449:
2446:
2441:
2437:
2434:
2430:
2429:
2428:
2425:
2424:
2422:
2418:
2412:
2409:
2407:
2404:
2402:
2399:
2398:
2396:
2392:
2389:
2387:
2381:
2371:
2368:
2366:
2365:ADM formalism
2363:
2361:
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2336:
2333:
2331:
2328:
2326:
2323:
2322:
2320:
2318:
2314:
2308:
2305:
2303:
2300:
2298:
2295:
2293:
2290:
2289:
2287:
2283:
2280:
2276:
2272:
2265:
2260:
2258:
2253:
2251:
2246:
2245:
2242:
2225:
2218:
2210:
2206:
2201:
2196:
2192:
2188:
2184:
2180:
2176:
2172:
2168:
2161:
2159:
2150:
2146:
2142:
2138:
2134:
2130:
2126:
2122:
2117:
2112:
2108:
2104:
2097:
2089:
2085:
2081:
2077:
2073:
2069:
2064:
2059:
2055:
2051:
2044:
2036:
2032:
2028:
2024:
2020:
2016:
2012:
2008:
2004:
2000:
1993:
1985:
1981:
1977:
1973:
1969:
1965:
1960:
1955:
1951:
1947:
1940:
1932:
1928:
1924:
1920:
1916:
1912:
1908:
1904:
1897:
1889:
1885:
1881:
1877:
1873:
1869:
1864:
1859:
1855:
1851:
1844:
1836:
1832:
1828:
1824:
1820:
1816:
1811:
1806:
1802:
1798:
1791:
1783:
1779:
1775:
1771:
1767:
1763:
1758:
1753:
1750:(2): 024031.
1749:
1745:
1738:
1730:
1726:
1722:
1718:
1714:
1710:
1706:
1702:
1695:
1687:
1683:
1679:
1675:
1671:
1667:
1662:
1657:
1653:
1649:
1642:
1634:
1630:
1626:
1622:
1618:
1614:
1609:
1604:
1600:
1596:
1589:
1581:
1577:
1573:
1569:
1565:
1561:
1556:
1551:
1547:
1543:
1536:
1528:
1524:
1520:
1516:
1512:
1508:
1503:
1498:
1494:
1490:
1483:
1475:
1471:
1467:
1463:
1459:
1455:
1450:
1445:
1441:
1437:
1430:
1422:
1418:
1414:
1410:
1406:
1402:
1395:
1387:
1383:
1379:
1375:
1371:
1367:
1363:
1359:
1352:
1338:
1334:
1327:
1312:
1308:
1301:
1293:
1289:
1285:
1281:
1277:
1273:
1269:
1262:
1254:
1250:
1246:
1242:
1238:
1234:
1227:
1223:
1217:
1209:
1205:
1201:
1197:
1193:
1189:
1185:
1181:
1174:
1166:
1162:
1158:
1154:
1150:
1146:
1139:
1131:
1127:
1123:
1119:
1115:
1111:
1104:
1096:
1092:
1088:
1084:
1080:
1076:
1072:
1068:
1060:
1058:
1048:
1044:
1040:
1036:
1032:
1028:
1024:
1017:
1015:
999:
994:
986:
978:
974:
969:
964:
960:
956:
952:
948:
944:
937:
929:
925:
920:
915:
911:
907:
903:
899:
895:
891:
887:
880:
878:
873:
864:
861:
859:
856:
854:
851:
850:
844:
840:
838:
834:
830:
826:
822:
817:
815:
811:
807:
797:
795:
790:
786:
782:
778:
774:
759:
751:
742:
739:
735:
731:
727:
723:
719:
709:
704:
698:
691:
685:
681:
670:
661:
659:
656:According to
649:
646:
642:
638:
634:
633:Myron L. Good
624:
622:
618:
614:
604:
602:
598:
594:
584:
581:
577:
567:
565:
561:
557:
553:
549:
540:
537:
527:
525:
521:
517:
513:
509:
505:
494:
492:
488:
483:
481:
477:
473:
469:
464:
462:
458:
454:
450:
438:
433:
431:
426:
424:
419:
418:
416:
415:
408:
405:
403:
400:
398:
395:
393:
390:
389:
383:
382:
375:
372:
370:
367:
365:
362:
361:
355:
354:
347:
344:
340:
337:
335:
332:
331:
330:
327:
325:
324:Cloud chamber
322:
321:
315:
314:
307:
304:
302:
299:
297:
294:
292:
289:
287:
284:
282:
279:
277:
274:
273:
267:
266:
259:
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
225:
224:
223:
222:
215:
212:
210:
207:
205:
202:
200:
197:
195:
192:
191:
188:
187:Antiparticles
183:
182:
178:
174:
173:
170:
167:
166:
163:
152:
142:
138:
134:
131:This article
129:
120:
119:
110:
107:
99:
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
2930:Anti-gravity
2867:
2821:theories and
2654:Supergravity
2467:
2463:
2325:Introduction
2228:. Retrieved
2217:
2174:
2170:
2106:
2102:
2096:
2053:
2049:
2043:
2002:
1998:
1992:
1949:
1945:
1939:
1906:
1902:
1896:
1853:
1849:
1843:
1800:
1796:
1790:
1747:
1743:
1737:
1704:
1700:
1694:
1654:(1): 15–17.
1651:
1647:
1641:
1598:
1594:
1588:
1545:
1541:
1535:
1492:
1488:
1482:
1442:(2): 20001.
1439:
1435:
1429:
1404:
1400:
1394:
1361:
1357:
1351:
1340:. Retrieved
1336:
1326:
1315:. Retrieved
1310:
1300:
1275:
1271:
1267:
1261:
1236:
1232:
1225:
1216:
1183:
1179:
1173:
1148:
1144:
1138:
1113:
1109:
1103:
1070:
1066:
1030:
1026:
1003:December 21,
1001:. Retrieved
997:
985:
950:
946:
936:
893:
889:
841:
818:
806:antihydrogen
803:
770:
757:
748:
737:
733:
730:isodual maps
729:
715:
702:
696:
689:
683:
676:
667:
655:
637:CP violation
630:
610:
590:
579:
573:
546:
533:
522:test of the
516:CP violation
510:, result in
500:
484:
476:antihydrogen
465:
448:
446:
346:Penning trap
300:
296:CP violation
281:Baryogenesis
276:Annihilation
243:True muonium
219:
218:
209:Antihydrogen
162:
149:January 2023
146:
136:
132:
102:
96:January 2023
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
2623:Causal sets
2517:Brans–Dicke
2335:Mathematics
1222:Good, M. L.
863:Dark matter
858:Dark energy
853:Fifth force
789:light years
762:Experiments
576:CPT theorem
570:CPT theorem
253:Positronium
204:Antineutron
2920:Antimatter
2914:Categories
2837:CGHS model
2824:toy models
2230:2013-09-03
1601:(1): 5–7.
1495:(1): 1–9.
1342:2023-09-28
1317:2023-09-28
1313:(in Dutch)
869:References
580:completely
468:annihilate
457:antimatter
397:Paul Dirac
386:Scientists
258:Quarkonium
214:Antihelium
199:Antiproton
169:Antimatter
66:newspapers
2842:RST model
2628:DGP model
2605:Spin foam
2549:Whitehead
2541:Nordström
2470:) gravity
2420:Classical
2394:Paradigms
2345:Resources
2116:1201.2717
2063:1104.4982
1959:0803.1487
1888:119232871
1863:1110.3054
1810:1106.0847
1782:118336207
1757:0804.3518
1729:121763512
1686:118540070
1661:1109.1201
1633:119181081
1608:1108.4543
1580:118457890
1555:1403.4820
1527:119288465
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