Gravitational interaction of antimatter#The equivalence principle

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 normal matter. They inferred that gravitational repulsion between matter and antimatter was implausible as it would violate CPT invariance, conservation of energy, result in vacuum instability, and result in CP violation.{{cn|date=January 2023}} It was also theorized that it would be inconsistent with the results of the Eötvös test of the weak equivalence principle. Many of these early theoretical objections were later overturned.{{cite journal|last1=Nieto|first1=M. M.|last2=Goldman|first2=T.|title=The arguments against 'antigravity' and the gravitational acceleration of antimatter|journal=Physics Reports|date=1991|volume=205|issue=5|pages=221–281|doi=10.1016/0370-1573(91)90138-C|bibcode = 1991PhR...205..221N |url=https://zenodo.org/record/1258483}} Note: errata issued in 1992 in volume 216.

The equivalence principle 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.

Photons, which are their own antiparticles in the framework of the Standard Model, have in a large number of astronomical tests (gravitational redshift and gravitational lensing, for example) been observed to interact with the gravitational field of ordinary matter exactly as predicted by the general theory of relativity. This is a feature that any theory that predicts that matter and antimatter repel must explain.{{cn|date=January 2023}}

The CPT theorem implies that the difference between the properties of a matter particle and those of its antimatter counterpart is completely 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.{{cite journal|last1=Cabbolet|first1=M. J. T. F.|title=Elementary Process Theory: a formal axiomatic system with a potential application as a foundational framework for physics supporting gravitational repulsion of matter and antimatter|journal=Annalen der Physik|date=2010|volume=522|issue=10|pages=699–738|doi=10.1002/andp.201000063|bibcode = 2010AnP...522..699C |s2cid=123136646}} A repulsive gravity is then excluded, since that would imply a difference in sign between the observable gravitational mass of matter and antimatter.{{cn|date=January 2023}}

In 1958, Philip Morrison argued that antigravity would violate conservation of energy. 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 producing 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.{{cite journal|last1=Morrison|first1=P.|title=Approximate Nature of Physical Symmetries|journal=American Journal of Physics|date=1958|volume=26|issue=6|pages=358–368|doi=10.1119/1.1996159|bibcode = 1958AmJPh..26..358M }}

Later in 1958, L. Schiff used quantum field theory to argue that antigravity would be inconsistent with the results of the Eötvös experiment.{{cite journal|last1=Schiff|first1=L. I.|title=Sign of the Gravitational Mass of a Positron|journal=Physical Review Letters|date=1958|volume=1|issue=7|pages=254–255|doi=10.1103/PhysRevLett.1.254|bibcode=1958PhRvL...1..254S}} 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 Standard Model and gravitational repulsion.{{cite journal|last1=Cabbolet|first1=M. J. T. F.|title=Incompatibility of QED/QCD and repulsive gravity, and implications for some recent approaches to dark energy|journal=Astrophysics and Space Science|date=2014|volume=350|issue=2|pages=777–780|doi=10.1007/s10509-014-1791-4|bibcode = 2014Ap&SS.350..777C |s2cid=120917960}}

In 1961, Myron L. Good argued that antigravity would result in the observation of an unacceptably high amount of CP violation in the anomalous regeneration of kaons.{{cite journal|last1=Good|first1=M. L.|author-link1=Myron L. Good|title=K₂⁰ and the Equivalence Principle|journal=Physical Review|date=1961|volume=121|issue=1|pages=311–313|doi=10.1103/PhysRev.121.311|bibcode = 1961PhRv..121..311G }} 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, Gabriel Chardin found that it resulted in an amount of kaon regeneration which agrees with observation.{{cite journal|last1=Chardin|first1=G.|last2=Rax|first2=J.-M.|title=CP violation. A matter of (anti)gravity?|journal=Physics Letters B|date=1992|volume=282|issue=1–2|pages=256–262|doi=10.1016/0370-2693(92)90510-B|bibcode = 1992PhLB..282..256C }} 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 fundamentally invalidated these explanations.{{cn|date=January 2023}}

According to Gerard 't Hooft, 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.{{Cite web |last='t Hooft |first=Gerard |title=Spookrijders in de Wetenschap |url=https://webspace.science.uu.nl/~hooft101/spookrijders.html |access-date=2023-09-28 |website=webspace.science.uu.nl |language=dutch}} 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.{{Cite web |last=Cabbolet |first=M. J. T. F. |title='t Hooft slaat plank mis in blog spookrijders in de wetenschap {{!}} DUB |url=https://dub.uu.nl/nl/opinie/t-hooft-slaat-plank-mis-blog-spookrijders-de-wetenschap |access-date=2023-09-28 |website=dub.uu.nl}}

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.

The first theory of repulsive gravity was a quantum theory published by Mark Kowitt.{{cite journal|last1=Kowitt|first1=M.|title=Gravitational repulsion and Dirac antimatter|journal=International Journal of Theoretical Physics|date=1996|volume=35|issue=3|pages=605–631|doi=10.1007/BF02082828|bibcode = 1996IJTP...35..605K |s2cid=120473463}} 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 Dirac hole theory, 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 (m_gΦ_g and m_gA_g) 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.{{cn|date=January 2023}}

Classical theories of repulsive gravity have been published by Ruggero Santilli and Massimo Villata.{{cite journal |last1=Santilli |first1=R. M. |date=1999 |title=A classical isodual theory of antimatter and its prediction of antigravity |journal=International Journal of Modern Physics A |volume=14 |issue=14 |pages=2205–2238 |bibcode=1999IJMPA..14.2205S |doi=10.1142/S0217751X99001111}}{{cite journal|last1=Villata|first1=M.|title=CPT symmetry and antimatter gravity in general relativity|journal=EPL|date=2011|volume=94|issue=2|pages=20001|doi=10.1209/0295-5075/94/20001|arxiv = 1103.4937 |bibcode = 2011EL.....9420001V |s2cid=36677097}}{{cite journal|last1=Villata|first1=M.|title=On the nature of dark energy: the lattice Universe|journal=Astrophysics and Space Science|date=2013|volume=345|issue=1|pages=1–9|doi=10.1007/s10509-013-1388-3|arxiv = 1302.3515 |bibcode = 2013Ap&SS.345....1V |s2cid=119288465}}{{cite journal|last1=Villata|first1=M.|title=The matter–antimatter interpretation of Kerr spacetime|journal=Annalen der Physik|date=2015|volume=527|issue=7–8|pages=507–512|doi=10.1002/andp.201500154|arxiv = 1403.4820 |bibcode = 2015AnP...527..507V |s2cid=118457890}} Both theories are extensions of general relativity, 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 isodual maps (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 observed trajectories of antiparticles are projections on our 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.{{cite journal|last1=Cabbolet|first1=M. J. T. F.|title=Comment to a paper of M. Villata on antigravity|journal=Astrophysics and Space Science|date=2011|volume=337|issue=1|pages=5–7|doi=10.1007/s10509-011-0939-8|arxiv = 1108.4543 |bibcode = 2012Ap&SS.337....5C |s2cid=119181081}} These objections were subsequently dismissed by Villata.{{cite journal|last1=Villata|first1=M.|title=Reply to 'Comment to a paper of M. Villata on antigravity'|journal=Astrophysics and Space Science|date=2011|volume=337|issue=1|pages=15–17|doi=10.1007/s10509-011-0940-2|arxiv = 1109.1201 |bibcode = 2012Ap&SS.337...15V |s2cid=118540070}}

The first non-classical, non-quantum physical principles underlying a matter–antimatter gravitational repulsion have been published by Marcoen Cabbolet.{{cite journal|last1=Cabbolet|first1=M. J. T. F.|title=Addendum to the Elementary Process Theory|journal=Annalen der Physik|date=2011|volume=523|issue=12|pages=990–994|doi=10.1002/andp.201100194|bibcode = 2011AnP...523..990C |s2cid=121763512}} He introduces the Elementary Process Theory, which uses a new language for physics, i.e. a new mathematical formalism and new physical concepts, and 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.{{cn|date=January 2023}}

Further authors{{cite journal|last1=Blanchet|first1=L.|last2=Le Tiec|first2=A.|title=Model of dark matter and dark energy based on gravitational polarization|journal=Physical Review D|date=2008|volume=78|issue=2|page=024031|doi=10.1103/PhysRevD.78.024031|arxiv = 0804.3518 |bibcode = 2008PhRvD..78b4031B |s2cid=118336207}}{{cite journal|last1=Hajdukovic|first1=D. S.|title=Is dark matter an illusion created by the gravitational polarization of the quantum vacuum?|journal=Astrophysics and Space Science|date=2011|volume=334|issue=2|pages=215–218|doi=10.1007/s10509-011-0744-4|arxiv = 1106.0847 |bibcode = 2011Ap&SS.334..215H |s2cid=12157851}}{{cite journal|last1=Benoit-Lévy|first1=A.|last2=Chardin|first2=G.|title=Introducing the Dirac-Milne universe|journal=Astronomy and Astrophysics|date=2012|volume=537|page=A78|doi=10.1051/0004-6361/201016103|bibcode=2012A&A...537A..78B|arxiv = 1110.3054 |s2cid=119232871}} have used a matter–antimatter gravitational repulsion to explain cosmological observations, but these publications do not address the physical principles of gravitational repulsion.

One source of experimental evidence in favor of normal gravity was the observation of neutrinos from Supernova 1987A. In 1987, three neutrino detectors around the world simultaneously observed a cascade of neutrinos emanating from a supernova in the Large Magellanic Cloud. Although the supernova happened about 164,000 light years away, both neutrinos and antineutrinos seem to have been detected virtually simultaneously.{{clarify|date=December 2013}} 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. 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%.{{cite journal|last1=Pakvasa|first1=S.|last2=Simmons|first2=W. A.|last3=Weiler|first3=T. J.|title=Test of equivalence principle for neutrinos and antineutrinos|journal=Physical Review D|date=1989|volume=39|issue=6|pages=1761–1763|doi=10.1103/PhysRevD.39.1761|pmid=9959839|bibcode = 1989PhRvD..39.1761P }} Unfortunately, this accuracy is unlikely to be improved by duplicating the experiment any time soon. The last known supernova to occur at such a close range prior to Supernova 1987A was around 1867.{{cite journal|last1=Reynolds|first1=S. P.|last2=Borkowski|first2=K. J.|last3=Green|first3=D. A.|last4=Hwang|first4=U.|last5=Harrus|first5=I.|last6=Petre|first6=R.|title=The Youngest Galactic Supernova Remnant: G1.9+0.3|journal=The Astrophysical Journal|date=2008|volume=680|issue=1|pages=L41–L44|doi=10.1086/589570|bibcode=2008ApJ...680L..41R|arxiv = 0803.1487 |s2cid=67766657}}

Since 2010 the production of cold antihydrogen has become possible at the Antiproton Decelerator at CERN. Antihydrogen, which is electrically neutral, should make it possible to directly measure the gravitational attraction of antimatter particles to the matter of Earth.{{cn|date=January 2023}}

Antihydrogen atoms have been trapped at CERN, first ALPHA{{Cite journal | last1 = Andresen | first1 = G. B. | last2 = Ashkezari | first2 = M. D. | last3 = Baquero-Ruiz | first3 = M. | last4 = Bertsche | first4 = W. | last5 = Bowe | first5 = P. D. | last6 = Butler | first6 = E. | last7 = Cesar | first7 = C. L. | last8 = Chapman | first8 = S. | last9 = Charlton | first9 = M. | last10 = Deller | first10 = A. | last11 = Eriksson | first11 = S. | last12 = Fajans | first12 = J. | last13 = Friesen | first13 = T. | last14 = Fujiwara | first14 = M. C. | last15 = Gill | first15 = D. R. | last16 = Gutierrez | first16 = A. | last17 = Hangst | first17 = J. S. | last18 = Hardy | first18 = W. N. | last19 = Hayden | first19 = M. E. | last20 = Humphries | first20 = A. J. | last21 = Hydomako | first21 = R. | last22 = Jenkins | first22 = M. J. | last23 = Jonsell | first23 = S. | last24 = Jørgensen | first24 = L. V. | last25 = Kurchaninov | first25 = L. | last26 = Madsen | first26 = N. | last27 = Menary | first27 = S. | last28 = Nolan | first28 = P. | last29 = Olchanski | first29 = K. | last30 = Olin | first30 = A. | display-authors = 5 | title = Trapped antihydrogen | journal = Nature | year = 2010 | pmid = 21085118 | doi = 10.1038/nature09610|bibcode = 2010Natur.468..673A | pages = 673–676 | volume=468 | issue=7324| s2cid = 2209534 }}{{Cite journal | last1 = Andresen | first1 = G. B. | last2 = Ashkezari | first2 = M. D. | last3 = Baquero-Ruiz | first3 = M. | last4 = Bertsche | first4 = W. | last5 = Bowe | first5 = P. D. | last6 = Butler | first6 = E. | last7 = Cesar | first7 = C. L. | last8 = Charlton | first8 = M. | last9 = Deller | first9 = A. | last10 = Eriksson | doi = 10.1038/NPHYS2025 | first10 = S. | last11 = Fajans | first11 = J. | last12 = Friesen | first12 = T. | last13 = Fujiwara | first13 = M. C. | last14 = Gill | first14 = D. R. | last15 = Gutierrez | first15 = A. | last16 = Hangst | first16 = J. S. | last17 = Hardy | first17 = W. N. | last18 = Hayano | first18 = R. S. | last19 = Hayden | first19 = M. E. | last20 = Humphries | first20 = A. J. | last21 = Hydomako | first21 = R. | last22 = Jonsell | first22 = S. | last23 = Kemp | first23 = S. L. | last24 = Kurchaninov | first24 = L. | last25 = Madsen | first25 = N. | last26 = Menary | first26 = S. | last27 = Nolan | first27 = P. | last28 = Olchanski | first28 = K. | last29 = Olin | first29 = A. | last30 = Pusa | first30 = P. | display-authors = 5 | title = Confinement of antihydrogen for 1,000 seconds | journal = Nature Physics | volume = 7 | issue = 7 | pages = 558–564 | year = 2011 |arxiv = 1104.4982 |bibcode = 2011NatPh...7..558A | s2cid = 17151882 }} and then ATRAP;{{Cite journal | last1 = Gabrielse | first1 = G. | last2 = Kalra | first2 = R. | last3 = Kolthammer | first3 = W. S. | last4 = McConnell | first4 = R. | last5 = Richerme | first5 = P. | last6 = Grzonka | first6 = D. | last7 = Oelert | first7 = W. | last8 = Sefzick | first8 = T. | last9 = Zielinski | first9 = M. | last10 = Fitzakerley | first10 = D. W. | last11 = George | first11 = M. C. | last12 = Hessels | first12 = E. A. | last13 = Storry | first13 = C. H. | last14 = Weel | first14 = M. | last15 = Müllers | first15 = A. | last16 = Walz | first16 = J. | display-authors = 5 | title = Trapped Antihydrogen in Its Ground State | doi = 10.1103/PhysRevLett.108.113002 | journal = Physical Review Letters | volume = 108 | issue = 11 | year = 2012 | pmid = 22540471|arxiv = 1201.2717 |bibcode = 2012PhRvL.108k3002G | page=113002| s2cid = 1480649 }} 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,{{cite journal|last1=Amole|first1=C.|last2=Ashkezari|first2=M. D.|last3=Baquero-Ruiz|first3=M.|last4=Bertsche|first4=W.|last5=Butler|first5=E.|last6=Capra|first6=A.|last7=Cesar|first7=C. L.|last8=Charlton|first8=M.|last9=Eriksson|first9=S.|last10=Fajans|first10=J.|last11=Friesen|first11=T.|last12=Fujiwara|first12=M. C.|last13=Gill|first13=D. R.|last14=Gutierrez|first14=A.|last15=Hangst|first15=J. S.|last16=Hardy|first16=W. N.|last17=Hayden|first17=M. E.|last18=Isaac|first18=C. A.|last19=Jonsell|first19=S.|last20=Kurchaninov|first20=L.|last21=Little|first21=A.|last22=Madsen|first22=N.|last23=McKenna|first23=J. T. K.|last24=Menary|first24=S.|last25=Napoli|first25=S. C.|last26=Nolan|first26=P.|last27=Olin|first27=A.|last28=Pusa|first28=P.|last29=Rasmussen|first29=C. Ø|last30=Robicheaux|first30=F.|last31=Sarid|first31=E.|last32=Silveira|first32=D. M.|last33=So|first33=C.|last34=Thompson|first34=R. I.|last35=van der Werf|first35=D. P.|last36=Wurtele|first36=J. S.|last37=Zhmoginov|first37=A. I.|last38=Charman|first38=A. E.|display-authors=5|title=Description and first application of a new technique to measure the gravitational mass of antihydrogen|journal=Nature Communications|date=2013|volume=4|pages=1785|doi=10.1038/ncomms2787| pmid = 23653197| pmc =3644108 |bibcode = 2013NatCo...4.1785A}}{{citation needed|reason=Quantitative statement does not link to evidence|date=July 2015}} 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 (AEgIS) or with trapped antihydrogen (ALPHA or GBAR).{{cn|date=January 2023}}

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 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.{{cite news|last1=Amos |first1=J.|url=https://www.bbc.co.uk/news/science-environment-13666892 |title= Antimatter atoms are corralled even longer |publisher=BBC News Online |date=2011-06-06 |access-date=2013-09-03}}

In 2023 ALPHA achieved the first result that proved that antimatter has the same sign for gravitational free fall acceleration as regular matter.{{cite news|last1=Johnston |first1=H.|url=https://physicsworld.com/a/antimatter-does-not-fall-up-cern-experiment-reveals |title=Antimatter does not fall up, CERN experiment reveals |publisher=Physics world |date=2023-09-27 |access-date=2025-01-16}}

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Category:Antimatter

Category:Anti-gravity