Stephen Hawking (1942-2018), Towards a Complete Understanding of the Universe

Two of the major achievements of Stephen Hawking are described in elementary terms. They are his work on the beginning of the universe and his work on the end of black holes. These are perhaps the scientific achievements for which he is best known. Some of the qualities that enabled his great achievements are also described. The article is a slightly edited version of one solicited by the Proceedings of the (US) National Academy of Sciences for their Retrospectives section and will appear there.Comment: 4 page

The Quantum Mechanical Arrows of Time

The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time --- the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the direction of the thermodynamic arrow of the quasiclassical realm of everyday experience. But in the more general context of cosmology we seek an explanation of all observed arrows, and the relations between them, in terms of the conditions that specify our particular universe. This paper investigates quantum mechanical and thermodynamic arrows in a time-neutral formulation of quantum mechanics for a number of model cosmologies in fixed background spacetimes. We find that a general universe may not have well defined arrows of either kind. When arrows are emergent they need not point in the same direction over the whole of spacetime. Rather they may be local, pointing in different directions in different spacetime regions. Local arrows can therefore be consistent with global time symmetry.Comment: 9 pages, 4 figures, revtex4, typos correcte

Murray Gell-Mann, A Short Appreciation

On September 25, 2014 Murray Gell-Mann was presented with the Helmholz Medal of the Berlin Brandenburg Academy of Sciences and Humanities in a ceremony at the Santa Fe Institute. The author, among others, was asked to speak for fifteen minutes on Murray and his accomplishments. The following is an edited transcription of the author's speaking text.Comment: 6 pages, revtex, picture added, typos fixe