The year 2002 heralded a breakthrough in antimatter research when the first low energy antihydrogen atoms were produced. Antimatter has inspired both science and fiction writers for many years, but detailed studies have until now eluded science. Antimatter is notoriously difficult to study as it does not readily occur in nature, even though our current understanding of the laws of physics have us expecting that it should make up half of the universe. The pursuit of cold antihydrogen is driven

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... a desire to solve this profound mystery. This paper will motivate the current effort to make cold antihydrogen, explain how antihydrogen is currently made, and how and why we are attempting to trap it. It will also discuss what kind of measurements are planned to gain new insights into the unexplained asymmetry between matter and antimatter in the universe. Keywords: antimatter; antihydrogen; antiprotons; positrons; charge, parity and time theorem on July 9, 2017 http://rsta.royalsocietypublishing.org/ Downloaded from 3672 N. Madsen antihydrogen atoms, but again at relativistic speeds (Blanford et al. 1998) . LEAR was discontinued and a new antiproton ring, the antiproton decelerator (AD), was built at CERN. It was at this unique machine that researchers in first the ATHENA and then the ATRAP collaborations succeeded in making low energy antihydrogen in (Amoretti et al. 2002 Gabrielse et al. 2002) . Not only did the new experiments succeed in making the anti-atoms in a low energy trap environment, but the production rate, at least in the case of ATHENA, was many orders of magnitude higher than previous experiments, being several thousands of anti-atoms every few minutes (Amoretti et al. 2004) . The author was part of ATHENA at the time, and of its present successor, ALPHA. Thus, this article will mostly focus on experience gained from these experiments. The quest for antihydrogen is motivated by the current failure of physical theories to completely describe the universe as we see it. There are a number of fundamental problems in modern physics that remain to be addressed, and for which CERN has also built the new Large Hadron Collider. An overarching problem is that the theory of the very small, quantum mechanics, and the theory of the very large, Einstein's general relativity, are not fully compatible. This means, for example, that we cannot achieve a complete, self-consistent, description of black holes (Barceló et al. 2009 ). In fact, we do not really know if they truly exist in the form that Einstein's theory predicts, as the extreme conditions in some black holes require a quantum mechanical version of gravity, which we do not have. But it is not only black holes that pose problems. Even more extreme conditions existed in the early universe, directly after the Big Bang. It is thought that conditions in the early universe provided the origin of the current asymmetry between matter and antimatter. Antimatter is formed when converting energy to matter. Such a conversion follows Einstein's famous equation, which states that E = mc 2 , where E is the energy, m is the mass and c = 300 000 km s −1 is the speed of light in vacuum. When energy (in the form of photons) is converted to matter, equal amounts of antimatter appear. Thus, to make an electron, one needs at least twice the energy of a single electron, as a positron is also necessarily made (in practice, more is needed as momentum needs to be conserved as well as energy). This process, called pair production, has so far never failed when observed. Thus, as the universe started out with no matter, the universe of today should contain equal amounts of matter and antimatter. However, extensive searches for evidence of antimatter in cosmic rays as well as by other means have been unsuccessful. The universe thus seems devoid of antimatter. The mirror-like symmetry between matter and antimatter described above goes further than the expectation of equal production rates. In fact, the charge, parity and time (CPT) theorem which is a fundamental consequence of quantum field theory, states that under the combined symmetries of Charge conjugation (changing the sign of all charges), Parity transformation (exchange of left and right) and Time reversal (letting time go backwards), all physical laws remain the same. If we apply this transformation on a hydrogen atom we end up with antihydrogen, and as all laws remain the same, any experiment on the antihydrogen atom should give the same result as the corresponding one on the hydrogen atom. In other words, the energy levels of antihydrogen should be exactly the same as those of hydrogen. If not, some parts of quantum field theory will have to be reformulated.