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Register a new userA Brief History of Dark Energy
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C Sivaram
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Gurzadyan-Xue Dark Energy was derived in 1986 (twenty years before the paper of Gurzadyan-Xue). The paper by the present author, titled The Planck Length as a Cosmological Constant, published in Astrophysics Space Science, Vol. 127, p.133-137, 1986 contains the formula claimed to have been derived by Gurzadyan-Xue (in 2003).
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I give a brief review of the search for a proper definition of energy in General Relativity (GR), a far from trivial quest, which was only completed after four and a half decades. The equally (or perhaps more) difficult task of establishing its positivity -- it was to take another fifteen plus years -- will then be summarized. Extension to cosmological GR is included. Mention is made of some recent offshoots.
We reconstruct the chain of events, intuitions and ideas that led to the formulation of the Gorini, Kossakowski, Lindblad and Sudarshan equation.
Understanding the nature of time remains a key unsolved problem in science. Newton in the Principia asserted an absolute universal time that {it `flows equably}. Hamilton then proposed a mathematical unification of space and time within the framework of the quaternions that ultimately lead to the famous Minkowski formulation in 1908 using four-vectors. The Minkowski framework is found to provide a versatile formalism for describing the relationship between space and time in accordance with relativistic principles, but nevertheless fails to provide deeper insights into the physical origin of time and its properties. In this paper we begin with a recognition of the fundamental role played by three-dimensional space in physics that we model using the Clifford algebra multivector. From this geometrical foundation we are then able to identify a plausible origin for our concept of time. This geometrical perspective also allows us to make a key topological distinction between time and space, with time being a point-like quantity. The multivector then allows a generalized unification of time and space within a Minkowski-like description.
The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization. Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics --- that of an intrinsically out-of-equilibrium many-body phase of matter. We include a compendium of necessary background, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. We formalize the notion of a time-crystal as a stable, macroscopic, conservative clock --- explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. We also cover a range of related phenomena, including various types of long-lived prethermal time-crystals, and expose the roles played by symmetries -- exact and (emergent) approximate -- and their breaking. We clarify the distinctions between many-body time-crystals and other ostensibly similar phenomena dating as far back as the works of Faraday and Mathieu. En route, we encounter Wilczeks suggestion that macroscopic systems should exhibit TTSB in their ground states, together with a theorem ruling this out. We also analyze pioneering recent experiments detecting signatures of time crystallinity in a variety of different platforms, and provide a detailed theoretical explanation of the physics in each case. In all existing experiments, the system does not realize a `true time-crystal phase, and we identify necessary ingredients for improvements in future experiments.
In 2015, the New Horizons spacecraft flew past Pluto and its moon Charon, providing the first clear look at the surface of Charon. New Horizons images revealed an ancient surface, a large, intricate canyon system, and many fractures, among other geologic features. Here, we assess whether tidal stresses played a significant role in the formation of tensile fractures on Charon. Although presently in a circular orbit, most scenarios for the orbital evolution of Charon include an eccentric orbit for some period of time and possibly an internal ocean. Past work has shown that these conditions could have generated stresses comparable in magnitude to other tidally fractured moons, such as Europa and Enceladus. However, we find no correlation between observed fracture orientations and those predicted to form due to eccentricity-driven tidal stress. It thus seems more likely that the orbit of Charon circularized before its ocean froze, and that either tidal stresses alone were insufficient to fracture the surface or subsequent resurfacing remove these ancient fractures.
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