The gravitational interaction of antimatter with matter or antimatter has not been observed by physicists. While the consensus among physicists is that gravity 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 forces, 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-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.
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, conservation of energy, result in vacuum instability, and result in CP violation. 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.
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, 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 has to be explained by any theory predicting that matter and antimatter repel. This is also the prediction Jean-Pierre Petit 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.
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. A repulsive gravity is then excluded, since that would imply a difference in sign between the observable gravitational mass of matter and antimatter.
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. However, it was later shown that antigravity would still not violate the second law of thermodynamics.
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.
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. 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.
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. 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.
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.
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, 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 (mgΦg and mgAg) 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.
Classical theories of repulsive gravity have been published by Ruggero Santilli and Massimo Villata. 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 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.
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.
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.
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.[clarification needed] 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.
Physicist William Fairbank attempted a laboratory experiment to directly measure the gravitational acceleration of electrons, with hopes of attempting the same method for positrons. However, their charge-to-mass ratio is so large that electromagnetic effects overwhelmed attempts to measure the impact of gravity on electrons. Fairbank was never able to attempt the experiment with positrons.
It is difficult to directly observe gravitational forces at the particle level. For charged particles, the electromagnetic force overwhelms the much weaker gravitational interaction. Even antiparticles in neutral antimatter, such as antihydrogen, must be kept separate from their counterparts in the matter that forms the experimental equipment, which requires strong electromagnetic fields. These fields, e.g. in the form of atomic traps, exert forces on these antiparticles which easily overwhelm the gravitational force of Earth and nearby test masses. Since all production methods for antiparticles result in high-energy antimatter particles, the necessary cooling for observation of gravitational effects in a laboratory environment requires very elaborate experimental techniques and very careful control of the trapping fields.
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 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) 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. Recent experiments with positronium in LHe  could be the first step in this line of research, in this case being able to stabilize antimatter may lead eventually to a way for its properties to be studied, specifically its properties in a gravitational field. It has been suggested that a material capable of holding a proton/antiproton pair in the same way might be more useful as protons are substantially more massive than electrons and any gravitational effects would be magnified by several orders of magnitude up to a point where detection is trivial using a cooled accelerometer or other quantum displacement sensor. Also an antimatter catalyzed fusion reactor would be massively simplified if positronium were produced and stored at a separate location though this would also cause problems with transport as positrons are typically produced "hot" at high relative velocities e.g. by collision of particles with gold foil. The antimatter reactor cited would be a variant of the Farnsworth-Hirsch fusor where positronium is accelerated into the core by potential well and electron diverted along a magnetic field line.