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In this article, educators across schools tell the story of planning, implementing, and reflecting on an elementary antiracist unit focused on mathematizing racial representation in school libraries. Students and teachers engaged in conversations about race, utilized mathematics to visualize erasures of race in literature, and involved parents, administrators and the community in recognizing and taking action to change this injustice. Our team considers tensions and powerful student thinking involved in using mathematics for antiracist learning for second through fifth-grade children. 

Einstein’s general theory of relativity from 1915¹remains the most successful description of gravitation. From the 1919 solar eclipse²to the observation of gravitational waves³, the theory has passed many crucial experimental tests. However, the evolving concepts of dark matter and dark energy illustrate that there is much to be learned about the gravitating content of the universe. Singularities in the general theory of relativity and the lack of a quantum theory of gravity suggest that our picture is incomplete. It is thus prudent to explore gravity in exotic physical systems. Antimatter was unknown to Einstein in 1915. Dirac’s theory⁴appeared in 1928; the positron was observed⁵in 1932. There has since been much speculation about gravity and antimatter. The theoretical consensus is that any laboratory mass must be attracted⁶by the Earth, although some authors have considered the cosmological consequences if antimatter should be repelled by matter^7–10. In the general theory of relativity, the weak equivalence principle (WEP) requires that all masses react identically to gravity, independent of their internal structure. Here we show that antihydrogen atoms, released from magnetic confinement in the ALPHA-g apparatus, behave in a way consistent with gravitational attraction to the Earth. Repulsive ‘antigravity’ is ruled out in this case. This experiment paves the way for precision studies of the magnitude of the gravitational acceleration between anti-atoms and the Earth to test the WEP.

 

Abstract The photon—the quantum excitation of the electromagnetic field—is massless but carries momentum. A photon can therefore exert a force on an object upon collision 1 . Slowing the translational motion of atoms and ions by application of such a force 2,3 , known as laser cooling, was first demonstrated 40 years ago 4,5 . It revolutionized atomic physics over the following decades 6–8 , and it is now a workhorse in many fields, including studies on quantum degenerate gases, quantum information, atomic clocks and tests of fundamental physics. However, this technique has not yet been applied to antimatter. Here we demonstrate laser cooling of antihydrogen 9 , the antimatter atom consisting of an antiproton and a positron. By exciting the 1S–2P transition in antihydrogen with pulsed, narrow-linewidth, Lyman-α laser radiation 10,11 , we Doppler-cool a sample of magnetically trapped antihydrogen. Although we apply laser cooling in only one dimension, the trap couples the longitudinal and transverse motions of the anti-atoms, leading to cooling in all three dimensions. We observe a reduction in the median transverse energy by more than an order of magnitude—with a substantial fraction of the anti-atoms attaining submicroelectronvolt transverse kinetic energies. We also report the observation of the laser-driven 1S–2S transition in samples of laser-cooled antihydrogen atoms. The observed spectral line is approximately four times narrower than that obtained without laser cooling. The demonstration of laser cooling and its immediate application has far-reaching implications for antimatter studies. A more localized, denser and colder sample of antihydrogen will drastically improve spectroscopic 11–13 and gravitational 14 studies of antihydrogen in ongoing experiments. Furthermore, the demonstrated ability to manipulate the motion of antimatter atoms by laser light will potentially provide ground-breaking opportunities for future experiments, such as anti-atomic fountains, anti-atom interferometry and the creation of antimatter molecules.