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The gravitational interaction of antimatter with
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
or
antimatter In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioac ...
has not been observed by physicists. While the consensus among physicists is that
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
is expected to attract both matter and antimatter at the same rate that matter attracts matter, this is not experimentally confirmed. Antimatter's rarity and tendency to annihilate when brought into contact with matter makes its study a technically demanding task. Furthermore, gravity is much weaker than the other
fundamental force In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
s, 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 antihydrogen) result in particles and atoms of high kinetic energy, which are unsuitable for
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
-related study. In addition to uncertainty regarding whether antimatter is gravitationally attracted or repulsed from other matter, it is also unknown whether the magnitude of the gravitational force is the same. Difficulties in creating quantum gravity models have led to the idea that antimatter may react with a slightly different magnitude.


Theories of gravitational attraction

When antimatter was first discovered in 1932, physicists wondered about 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 exactly the same as normal matter. They inferred that a gravitational repulsion between matter and antimatter was implausible as it would violate
CPT invariance Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and ...
, conservation of energy, result in vacuum instability, and result in
CP violation In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be th ...
. 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. Note: errata issued in 1992 in volume 216.


The equivalence principle

The equivalence principle predicts that the gravitational acceleration of antimatter is the same as that of ordinary matter. A matter-antimatter gravitational repulsion is thus excluded from this point of view. Furthermore,
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
s, which are their own antiparticles in the framework of the Standard Model, have in a large number of astronomical tests (
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
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 General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
. This is a feature that has to be explained by any theory predicting that matter and antimatter repel. This is also the prediction
Jean-Pierre Petit Jean-Pierre Petit is a French engineer. Education Jean-Pierre Petit obtained his engineer's degree in 1961 at the Institut supérieur de l'aéronautique et de l'espace (Supaéro). Petit defended his doctoral thesis, ''Applications de la thé ...
made in an article published in 2018: "In addition, the Janus model predicts that the antimatter that will be created in the laboratory in the GBAR experiment will behave like ordinary matter in the Earth's gravitational field." The antigravitation described in the Janus model is produced by antimatter of 'negative' masses (the antimatter produced in laboratories or by cosmic rays has only positive masses), and is fully compliant with general relativity and Newtonian approximations.


CPT theorem

The
CPT theorem Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and ...
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. A repulsive gravity is then excluded, since that would imply a difference in sign between the observable gravitational mass of matter and antimatter.


Morrison's argument

In 1958,
Philip Morrison Philip Morrison (November 7, 1915 – April 22, 2005) was a professor of physics at the Massachusetts Institute of Technology (MIT). He is known for his work on the Manhattan Project during World War II, and for his later work in quantum physi ...
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. However, it was later shown that antigravity would still not violate the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
.


Schiff's argument

Later in 1958, L. Schiff used quantum field theory to argue that antigravity would be inconsistent with the results of the Eötvös experiment. 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.


Good's argument

In 1961, Myron L. Good argued that antigravity would result in the observation of an unacceptably high amount of
CP violation In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be th ...
in the anomalous regeneration of
kaon KAON (Karlsruhe ontology) is an ontology infrastructure developed by the University of Karlsruhe and the Research Center for Information Technologies in Karlsruhe. Its first incarnation was developed in 2002 and supported an enhanced version of ...
s. 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. He argues that antigravity is in fact a potential explanation for CP violation based on his models on K mesons. His results date back to 1992. Since then however, studies on CP violation mechanisms in the B mesons systems have fundamentally invalidated these explanations.


Gerard 't Hooft's argument

According to
Gerard 't Hooft Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating th ...
, 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.G. 't Hooft
Spookrijders in de wetenschap (in Dutch)
DUB (2014)
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.M.J.T.F. Cabbolet
't Hooft slaat plank mis over spookrijders (in Dutch)
DUB (2014)


Theories of gravitational repulsion

As long as repulsive gravity has not been refuted experimentally, one can speculate about physical principles that would bring about such a repulsion. Thus far, three radically different theories have been published.


Kowitt's theory

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
Dirac hole theory Dirac hole theory is a theory in quantum mechanics, named after English theoretical physicist Paul Dirac. The theory poses that the continuum of negative energy states, that are solutions to the Dirac equation, are filled with electrons, and the ...
, 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''g''Φ''g and ''m''g''A''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.


Santilli and Villata's theory

Classical theories of repulsive gravity have been published by
Ruggero Santilli Ruggero Maria Santilli (born September 8, 1935) is an Italo-American nuclear physicist. Mainstream scientists dismiss his theories as fringe science. Biography Ruggero Maria Santilli was born September 8, 1935) in Capracotta. He studied physics ...
and Massimo Villata. Both theories are extensions of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, 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 now '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. These objections were subsequently dismissed by Villata.


Cabbolet's theory

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 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.


Analysis

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.


Experiments


Supernova 1987A

One source of experimental evidence in favor of normal gravity was the observation of
neutrinos A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is ...
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 A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...
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. 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 last known supernova to occur at such a close range prior to Supernova 1987A was around 1867.


Cold neutral antihydrogen experiments

Since 2010 the production of cold antihydrogen has become possible at the
Antiproton Decelerator The Antiproton Decelerator (AD) is a storage ring at the CERN laboratory near Geneva. It was built from the Antiproton Collector (AC) to be a successor to the Low Energy Antiproton Ring (LEAR) and started operation in the year 2000. Antiproto ...
at CERN. Antihydrogen, which is electrically neutral, should make it possible to directly measure the gravitational attraction of antimatter particles to the matter Earth. Antihydrogen atoms have been trapped at CERN, first ALPHA and then ATRAP; 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 (
AEgIS The aegis ( ; grc, αἰγίς ''aigís''), as stated in the ''Iliad'', is a device carried by Athena and Zeus, variously interpreted as an animal skin or a shield and sometimes featuring the head of a Gorgon. There may be a connection with a d ...
) or with trapped antihydrogen ( ALPHA or GBAR). 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.


See also

* Fifth force *
Dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univ ...
*
Dark matter Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not a ...


References

{{Theories of gravitation Antimatter Gravity Anti-gravity