Observation of the effect of gravity on the motion of antimatter

The weak equivalence principle (WEP), a cornerstone of Einstein's general theory of relativity, posits that all objects, irrespective of their composition, experience the same gravitational acceleration. While extensively tested for matter, direct experimental verification for antimatter has remained elusive due to the significant challenges posed by electromagnetic forces on charged antiparticles. These forces dwarf the gravitational force in Earth's field, making precise measurements extremely difficult. Previous experiments involving confined, oscillating charged antimatter particles have shown behavior consistent with gravitational effects on clocks, but direct ballistic tests remained unfeasible until now. The ALPHA-g collaboration has developed the ability to produce, trap, and manipulate neutral antihydrogen atoms, providing an ideal system for investigating the gravitational behavior of antimatter. This experiment aims to directly observe the direction and magnitude of the gravitational force acting on neutral antihydrogen, providing a crucial test of the WEP and exploring potential deviations from general relativity. The potential for antimatter to exhibit different gravitational behavior compared to matter has significant implications for our understanding of cosmology and fundamental physics. Some theoretical models, albeit controversial, suggest the possibility of repulsive gravity between matter and antimatter. This experiment aims to directly test these unconventional hypotheses, and its outcome will have far-reaching consequences for our current cosmological models.

The theoretical understanding of gravity's effect on antimatter is rooted in the general theory of relativity, with Dirac's theory providing the theoretical foundation for antimatter's existence. However, the lack of a comprehensive quantum theory of gravity leaves room for speculation and opens avenues for investigation in exotic systems. While there is a theoretical consensus that antimatter should be attracted by gravity, some authors have explored the cosmological implications of repulsive matter-antimatter gravity. Previous attempts to measure antimatter's gravitational response faced numerous challenges. Witteborn and Fairbank's experiment attempted to measure the gravitational force on single electrons and positrons but were ultimately inconclusive due to the dominance of electromagnetic forces. Although experiments have examined the behavior of confined, oscillating antimatter particles as clocks within a gravitational field, demonstrating behavior consistent with expectations, these studies did not involve direct ballistic tests of the WEP in Earth's gravitational field. The production and confinement of antihydrogen, a stable and electrically neutral antimatter particle, has opened up a new opportunity for investigating its gravitational behavior in a direct manner. This work builds upon the previous successes of the ALPHA collaboration in creating and trapping antihydrogen, paving the way for high-precision measurements of its gravitational properties.

The ALPHA-g experiment employs a vertically oriented antihydrogen trap designed to observe the effect of gravity on antimatter. The experimental apparatus consists of a complex arrangement of superconducting magnets including an octupole for transverse confinement and two mirror coils for axial confinement, creating a magnetic potential well capable of trapping antihydrogen atoms. Antihydrogen is produced by mixing cold antiprotons from the CERN Antiproton Decelerator and ELENA ring with positrons from a Surko-type accumulator within the trap. Antihydrogen atoms with sufficiently low kinetic energy are trapped due to the interaction between their magnetic moments and the external magnetic field. The experiment involves accumulating antihydrogen atoms over numerous cycles from ELENA, a process referred to as ‘stacking’. After accumulation, the atoms are released by gradually decreasing the current in the mirror coils, allowing them to escape the trap under the influence of gravity and their thermal energy. The escape direction is detected using a radial time projection chamber (rTPC) and a barrel scintillator, allowing for three-dimensional reconstruction of the annihilation events. To minimize the effect of magnetic field gradients which could mimic gravity, the experiment incorporates a sophisticated magnetic bias mechanism. This is achieved by introducing a differential current to one of the mirror coils, allowing for controlled manipulation of the magnetic field difference between the top and bottom of the trap. Electron cyclotron resonance (ECR) measurements are used to precisely determine the magnetic field strength at various points in the trap, both before and after the release. Extensive numerical simulations, using a three-dimensional magnetic field model based on measured fields and the superconducting magnet design, are used to model the antihydrogen atom trajectories and analyze the experimental results. These simulations account for the complex magnetic field geometry, the initial energy distribution of the trapped atoms, and the magnetic bias applied.

The experiment involved numerous trials of antihydrogen accumulation and release at different magnetic bias levels. The results show a clear correlation between the applied bias and the direction of antihydrogen escape. With a positive bias (favoring downward escape), the fraction of anti-atoms escaping from the bottom of the trap increases, while a negative bias increases the upward escape rate. The data exhibit a balance point at a bias close to -1g, which is consistent with the expected gravitational attraction to the Earth in a simplified one-dimensional model. A comparison of the experimental data with numerical simulations, which consider both attractive and repulsive gravity, reveals strong agreement with the attractive gravity model. The best fit to the experimental data indicates that the local gravitational acceleration of antihydrogen is directed towards the Earth and has a magnitude of (0.75 ± 0.13 (statistical + systematic) ± 0.16 (simulation))g, where g is the acceleration due to gravity for matter. The probability of obtaining the observed results assuming gravity does not act on antihydrogen is estimated to be 2.9 × 10⁻¹⁵, effectively ruling out repulsive gravity of 1g between the Earth and antimatter. The results from trials using a 130 s ramp-down time are also consistent with the 20 s data. Additional analysis of events released after the end of the ramp-down indicates their behavior is consistent with the 20 s sample, but further detailed investigations are needed. Detailed error analysis and accounting for various sources of uncertainty, including magnetic field measurements, event detection, and simulations, were incorporated to arrive at the final result.

The findings of this experiment directly address the long-standing question of the gravitational behavior of antimatter. The observed results strongly support the weak equivalence principle and the prediction of general relativity that antimatter, like matter, is attracted by gravity. The high level of agreement between the experimental data and the simulation assuming attractive gravity, coupled with the extremely low probability of obtaining the results under the assumption of no gravity or repulsive gravity, provides compelling evidence for the gravitational attraction of antihydrogen to Earth. The experiment demonstrates the feasibility of precision measurements of the gravitational acceleration of antimatter, which will be crucial for testing the WEP to even greater accuracy in the future. These results have important implications for our understanding of cosmology and fundamental physics, particularly for models relying on repulsive matter-antimatter gravity, which are inconsistent with the findings presented here.

This study presents the first observation of the effect of gravity on neutral antimatter, demonstrating the gravitational attraction of antihydrogen to the Earth and supporting the weak equivalence principle. The measured gravitational acceleration of antihydrogen is consistent with the expected value of 1g. Future research directions include higher precision measurements with colder antihydrogen atoms, utilizing techniques such as laser cooling and adiabatic expansion cooling, to improve the accuracy of the gravitational acceleration measurement. Improvements to magnetic field control and measurement techniques will also be crucial for enhancing the precision of the experiment. Further investigations into the behavior of atoms released after the end of the ramp-down and exploring alternative approaches to measuring antimatter's gravitational properties are warranted. The successful completion of this experiment opens up exciting possibilities for exploring gravity at a fundamental level, allowing for more stringent tests of general relativity.

While the experiment provides strong evidence for the gravitational attraction of antihydrogen, several limitations should be acknowledged. The primary limitation lies in the reliance on numerical simulations for interpreting the results. While efforts were made to precisely model the magnetic field and account for various sources of uncertainty, there remains some degree of uncertainty in the simulation that contributes to the overall uncertainty in the measurement of the gravitational acceleration. The relatively small number of trapped antihydrogen atoms also impacts the statistical precision of the results. Further research to refine the experimental setup and enhance the control and measurement of magnetic fields, along with increasing the number of trapped antihydrogen atoms, will improve the statistical and systematic uncertainty of future measurements.