Gravitational interaction of antimatter
The gravitational interaction of antimatter with matter or antimatter has not been conclusively observed by physicists. While the overwhelming consensus among physicists is that antimatter will attract both matter and antimatter at the same rate that matter attracts matter, there is a strong desire to confirm this experimentally.
Antimatter's rarity and tendency to annihilate when brought into contact with matter makes its study a technically demanding task. Most methods for the creation of antimatter (specifically antihydrogen) result in high-energy particles and atoms of high kinetic energy, which are unsuitable for gravity-related study. In recent years, first ALPHA  and then ATRAP  have trapped antihydrogen atoms at CERN; in 2013 ALPHA used such atoms to set the first free-fall bounds on the gravitational interaction of antimatter with matter. Future experiments on ALPHA, as well as experiments on beams of antihydrogen by AEGIS and GBAR should refine these bounds.
- 1 Three hypotheses
- 2 Experiments
- 3 Arguments against a gravitational repulsion of matter and antimatter
- 4 Theories of gravitational repulsion
- 5 See also
- 6 References
Thus far, there are three hypotheses about how antimatter gravitationally interacts with normal matter:
- Normal gravity: The standard assumption is that gravitational interactions of matter and antimatter are identical.
- Antigravity: Some authors argue that antimatter repels matter with the same magnitude as matter attracts matter (see below). This should not be confused with the many other speculative phenomena that may also be called 'anti-gravity'.
- Gravivector and graviscalar: Later difficulties in creating quantum gravity theories have led to the idea that antimatter may react with a slightly different magnitude.
Many scientists[who?] consider the best experimental evidence in favor of normal gravity to come from the observations of neutrinos from Supernova 1987A. In this landmark event, 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 may 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; in fact, the two may be identical, just as the antiparticle of the photon is another photon. 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 both electrons and positrons. However, their charge-to-mass ratio is so large that electromagnetic effects overwhelmed the experiment.
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.
Cold neutral antihydrogen experiments
Since 2010 the production of cold antihydrogen has become possible at the ATHENA, ATRAP and ALPHA experiments at CERN. Antihydrogen, which is electrically neutral, should make it possible to directly measure the gravitational attraction of antimatter particles to the matter Earth. In 2013, experiments on antihydrogen atoms released from the ALPHA trap set direct, i.e. freefall, limits on antimatter gravity. These limits were coarse; future experiments at CERN (ALPHA, AEGIS, GBAR) should refine these limits.
Arguments against a gravitational repulsion of matter and antimatter
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
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.
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 doesn't 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 found 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 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.
Theories of gravitational repulsion
- The first prediction that antimatter is repulsed by the gravitational field of ordinary matter was published by Santilli. He introduces the isodual real numbers, in which the number –1 is the multiplicative identity, so that –1*x = x in the isodual real numbers. On that basis, he constructs isodual versions of conventional Euclidean, Minkowskian and Riemannian geometries. The core principle is then that “antimatter is characterized by the isodual mathematics, that with isodual numbers, fields, spaces, etc., thus having negative–definite units and norm. All characteristics of matter therefore change sign for antimatter represented via isoduality.” When this principle is applied to general relativity, antigravity appears as a prediction. The trajectories of antimatter observed in ‘our’ spacetime are then in principle projections of the actual trajectories in isodual spacetime.
- The first non-classical physical principles underlying a matter-antimatter gravitational repulsion have been published by 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.
- In addition, Villata argued that antigravity of antimatter becomes a prediction of General Relativity when the latter is extended with the CPT theorem. The core of Villata’s theory is that the C, P, and T-operators can be applied to the equation of motion of general relativity for particle in a gravitational field, to yield a new equation for the behavior of antimatter in the gravitational field of ordinary matter. This latter equation then predicts a repulsion of matter and antimatter. 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.
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.
- Dark energy
- Dark matter
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