Antimatter Free-Fall Experiments and Charge Asymmetry

We propose a method by which one could use modified antimatter gravity experiments in order to perform a high-precision test of antimatter charge neutrality. The proposal is based on the application of a strong, external, vertically oriented electric field during an antimatter free-fall gravity experiment in the gravitational field of the Earth. The proposed experimental setup has the potential to drastically improve the limits on the charge-asymmetry parameter ϵ¯q of antimatter. On the theoretical side, we analyze possibilities to describe a putative charge-asymmetry of matter and antimatter, proportional to the parameters ϵq and ϵ¯q, by Lagrangian methods. We found that such an asymmetry could be described by four-dimensional Lorentz-invariant operators that break CPT without destroying the locality of the field theory. The mechanism involves an interaction Lagrangian with field operators decomposed into particle or antiparticle field contributions. Our Lagrangian is otherwise Lorentz, as well as PT invariant. Constraints to be derived on the parameter ϵ¯q do not depend on the assumed theoretical model.

Antimatter Gravity: Second Quantization and Lagrangian Formalism

The application of the CPT (charge-conjugation, parity, and time reversal) theorem to an apple falling on Earth leads to the description of an anti-apple falling on anti–Earth (not on Earth). On the microscopic level, the Dirac equation in curved space-time simultaneously describes spin-1/2 particles and their antiparticles coupled to the same curved space-time metric (e.g., the metric describing the gravitational field of the Earth). On the macroscopic level, the electromagnetically and gravitationally coupled Dirac equation therefore describes apples and anti-apples, falling on Earth, simultaneously. A particle-to-antiparticle transformation of the gravitationally coupled Dirac equation therefore yields information on the behavior of “anti-apples on Earth”. However, the problem is exacerbated by the fact that the operation of charge conjugation is much more complicated in curved, as opposed to flat, space-time. Our treatment is based on second-quantized field operators and uses the Lagrangian formalism. As an additional helpful result, prerequisite to our calculations, we establish the general form of the Dirac adjoint in curved space-time. On the basis of a theorem, we refute the existence of tiny, but potentially important, particle-antiparticle symmetry breaking terms in which possible existence has been investigated in the literature. Consequences for antimatter gravity experiments are discussed.

Antimatter gravity and the Universe

The aim of this brief review is twofold. First, we give an overview of the unprecedented experimental efforts to measure the gravitational acceleration of antimatter; with antihydrogen, in three competing experiments at CERN (AEGIS, ALPHA and GBAR), and with muonium and positronium in other laboratories in the world. Second, we present the 21st Century’s attempts to develop a new model of the Universe with the assumed gravitational repulsion between matter and antimatter; so far, three radically different and incompatible theoretical paradigms have been proposed. Two of these three models, Dirac–Milne Cosmology (that incorporates CPT violation) and the Lattice Universe (based on CPT symmetry), assume a symmetric Universe composed of equal amounts of matter and antimatter, with antimatter somehow “hidden” in cosmic voids; this hypothesis produced encouraging preliminary results. The heart of the third model is the hypothesis that quantum vacuum fluctuations are virtual gravitational dipoles; for the first time, this hypothesis makes possible and inevitable to include the quantum vacuum as a source of gravity. Standard Model matter is considered as the only content of the Universe, while phenomena usually attributed to dark matter and dark energy are explained as the local and global effects of the gravitational polarization of the quantum vacuum by the immersed baryonic matter. An additional feature is that we might live in a cyclic Universe alternatively dominated by matter and antimatter. In about three years, we will know if there is gravitational repulsion between matter and antimatter; a discovery that can forever change our understanding of the Universe.

The Muonium Antimatter Gravity Experiment

A direct measurement of the gravitational acceleration of antimatter has the potential to show that we live in a “Dirac-Milne” Universe, which could explain cosmological observations without the need for dark matter, dark energy, inflation, or missing antimatter. Such a measurement would also be sensitive to the possible existence of a fifth force. Cooling antimatter to temperatures where gravitational energies are comparable to thermal energies is challenging for most forms of antimatter, which annihilate upon contact with matter. The exception is the antimuon (μ+), which is easily cooled by stopping in cold matter, but the short muon lifetime poses challenges. Positive muons that stop in material will combine with free electrons to form muonium, a neutral leptonic atom with most of its mass derived from the 2nd-generation antimuon. We are developing the Muonium Antimatter Gravity Experiment (MAGE) to measure the gravitational force on muonium using a novel, monoenergetic, low-velocity, horizontal muonium beam directed at an ultra-precise atom interferometer. If successful, MAGE will measure for the first time the gravitational coupling to a 2nd-generation particle in a system whose antimatter-dominated mass is not predominantly strong-interaction binding energy. The novel MAGE beam production approach could also have important applications to other muonium experiments as well as to the measurement ofg– 2.