Reflections on the four facets of symmetry: how physics exemplifies rational thinking

In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While their interrelations are examined closely, these four facets of symmetry are scrutinised one after the other in great detail. This decomposition allows us to examine closely the multiple different roles symmetry plays in many places in physics. Furthermore, some connections with others disciplines like neurobiology, epistemology, cognitive sciences and, not least, philosophy are proposed in an attempt to show that symmetry can be an organising principle also in these fields

Two earth years of Mössbauer studies of the surface of Mars with MIMOS II

The element iron plays a crucial role in the study of the evolution of matter from an interstellar cloud to the formation and evolution of the planets. In the Solar System iron is the most abundant metallic element. It occurs in at least three different oxidation states: Fe(0) (metallic iron), Fe(II) and Fe(III). Fe(IV) and Fe(VI) compounds are well known on Earth, and there is a possibility for their occurrence on Mars. In January 2004 the USA space agency NASA landed two rovers on the surface of Mars, both carrying the Mainz Mössbauer spectrometer MIMOS II. They performed for the first time in-situ measurements of the mineralogy of the Martian surface, at two different places on Mars, Meridiani Planum and Gusev crater, respectively, the landing sites of the Mars-Exploration-Rovers (MER) Opportunity and Spirit. After about two Earth years or one Martian year of operation the Mössbauer (MB) spectrometers on both rovers have acquired data from more than 150 targets (and more than thousand MB spectra) at each landing site. The scientific measurement objectives of the Mössbauer investigation are to obtain for rock, soil, and dust (1) the mineralogical identification of iron-bearing phases (e.g., oxides, silicates, sulfides, sulfates, and carbonates), (2) the quantitative measurement of the distribution of iron among these ironbearing phases (e.g., the relative proportions of iron in olivine, pyroxenes, ilmenite and magnetite in a basalt), (3) the quantitative measurement of the distribution of iron among its oxidation states (e.g., Fe2+, Fe3+, and Fe6+), and (4) the characterization of the size distribution of magnetic particles. Special geologic targets of the Mössbauer investigation are dust collected by the Athena magnets and interior rock and soil surfaces exposed by the Athena Rock Abrasion Tool and by trenching with rover wheels. The Mössbauer spectrometer on Opportunity at Meridiani Planum, identified eight Fe-bearing phases: jarosite (K,Na,H3O)(Fe,Al)(OH)6(SO4)2, hematite, olivine, pyroxene, magnetite, nanophase ferric oxides (npOx), an unassigned ferric phase, and a metallic Fe–Ni alloy (kamacite) in a Fe–Ni-meteorite. Outcrop rocks consist of hematite-rich spherules dispersed throughout S-rich rock that has nearly constant proportions of Fe3+ from jarosite, hematite, and npOx (28%, 35%, and 19% of total Fe). Jarosite is mineralogical evidence for aqueous processes under acid– sulfate conditions because it has structural hydroxide and sulfate and it forms at low pH. Hematite-rich spherules, eroded from the outcrop, and their fragments are concentrated as hematite-rich soils (lag deposits) on ripple crests (up to 68% of total Fe from hematite). Olivine, pyroxene, and magnetite are primarily associated with basaltic soils and are present as thin and locally discontinuous cover over outcrop rocks, commonly forming aeolian bedforms. Basaltic soils are more reduced (Fe3+/Fetotal ∼0.2−0.4), with the fine-grained and bright aeolian deposits being the most oxidized. Basaltic soil at Meridiani Planum and Gusev crater have similar Fe-mineralogical compositions. At Gusev crater, the Mössbauer spectrometer on the MER Spirit rover has identified 8 Fe-bearing phases. Two are Fe2+ silicates (olivine and pyroxene), one is a Fe2+ oxide (ilmenite), one is a mixed Fe2+ and Fe3+ oxide (magnetite), two are Fe3+ oxides (hematite and goethite), one is a Fe3+ sulfate (mineralogically not constrained), and one is a Fe3+ alteration product (npOx). The surface material in the plains have a olivine basaltic signature (Morris, et al., Science, 305: 833, 2004; Morris, et al., J. Geophys. Res., 111, 2006, Ming, et al., J. Geophys. Res., 111, 2006) suggesting physical rather than chemical weathering processes present in the plains. The Mössbauer signature for the Columbia Hills surface material is very different ranging from nearly unaltered material to highly altered material. Some of the rocks, in particular a rock named Clovis, contain a significant amount of the Fe oxyhydroxide goethite, α-FeOOH, which is mineralogical evidence for aqueous processes because it is formed only under aqueous conditions