40 research outputs found
Division Algebras and Quantum Theory
Quantum theory may be formulated using Hilbert spaces over any of the three
associative normed division algebras: the real numbers, the complex numbers and
the quaternions. Indeed, these three choices appear naturally in a number of
axiomatic approaches. However, there are internal problems with real or
quaternionic quantum theory. Here we argue that these problems can be resolved
if we treat real, complex and quaternionic quantum theory as part of a unified
structure. Dyson called this structure the "three-fold way". It is perhaps
easiest to see it in the study of irreducible unitary representations of groups
on complex Hilbert spaces. These representations come in three kinds: those
that are not isomorphic to their own dual (the truly "complex"
representations), those that are self-dual thanks to a symmetric bilinear
pairing (which are "real", in that they are the complexifications of
representations on real Hilbert spaces), and those that are self-dual thanks to
an antisymmetric bilinear pairing (which are "quaternionic", in that they are
the underlying complex representations of representations on quaternionic
Hilbert spaces). This three-fold classification sheds light on the physics of
time reversal symmetry, and it already plays an important role in particle
physics. More generally, Hilbert spaces of any one of the three kinds - real,
complex and quaternionic - can be seen as Hilbert spaces of the other kinds,
equipped with extra structure.Comment: 30 pages, 3 encapsulated Postscript figure
Gravitational Radiation from Compact Binary Pulsars
An outstanding question in modern Physics is whether general relativity (GR)
is a complete description of gravity among bodies at macroscopic scales.
Currently, the best experiments supporting this hypothesis are based on
high-precision timing of radio pulsars. This chapter reviews recent advances in
the field with a focus on compact binary millisecond pulsars with white-dwarf
(WD) companions. These systems - if modeled properly - provide an unparalleled
test ground for physically motivated alternatives to GR that deviate
significantly in the strong-field regime. Recent improvements in observational
techniques and advances in our understanding of WD interiors have enabled a
series of precise mass measurements in such systems. These masses, combined
with high-precision radio timing of the pulsars, result to stringent
constraints on the radiative properties of gravity, qualitatively very
different from what was available in the past.Comment: Short review chapter to appear in "Gravitational Wave Astrophysics"
by Springer-Verlag, edited by Carlos F. Sopuerta; v3: a few major corrections
and updated references. Comments are welcome
Anomalous accelerations in spacecraft flybys of the Earth
[EN] The flyby anomaly is a persistent riddle in astrodynamics.
Orbital analysis in several flybys of the Earth
since the Galileo spacecraft flyby of the Earth in 1990 have
shown that the asymptotic post-encounter velocity exhibits
a difference with the initial velocity that cannot be attributed
to conventional effects. To elucidate its origin, we have developed
an orbital program for analyzing the trajectory of
the spacecraft in the vicinity of the perigee, including both
the Sun and the Moon¿s tidal perturbations and the geopotential
zonal, tesseral and sectorial harmonics provided by
the EGM96 model. The magnitude and direction of the
anomalous acceleration acting upon the spacecraft can be
estimated from the orbital determination program by comparing
with the trajectories fitted to telemetry data as provided
by the mission teams. This acceleration amounts to a
fraction of a mm/s2 and decays very fast with altitude. The
possibility of some new physics of gravity in the altitude
range for spacecraft flybys is discussed.Acedo Rodríguez, L. (2017). Anomalous accelerations in spacecraft flybys of the Earth. Astrophysics and Space Science. 362(12):1-15. doi:10.1007/s10509-017-3205-xS11536212Acedo, L.: Galaxies 3, 113 (2015)Acedo, L.: Mon. Not. R. Astron. Soc. 463(2), 2119 (2016)Acedo, L.: Adv. Space Res. 59(7), 1715 (2017). 1701.06939Acedo, L., Bel, L.: Astron. Nachr. 338(1), 117 (2017). 1602.03669Adler, S.L.: Int. J. Mod. Phys. A 25, 4577 (2010). 0908.2414 . doi: 10.1142/S0217751X10050706Adler, S.L.: In: Proceedings of the Conference in Honour of Murray Gellimann’s 80th Birthday, p. 352 (2011). doi: 10.1142/9789814335614_0032Anderson, J.D., Nieto, M.M.: In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. IAU Symposium, vol. 261, p. 189 (2010). doi: 10.1017/S1743921309990378Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. 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Networks of cooperation: Water policy in Germany
German water policy-making defies easy categorisation. Policy processes are highly complex, fragmented, and diverse. Concentrating on the areas of drinking water supply and water pollution, the most important feature is the enormous importance of regional government in both the formulation and implementation of policy. The role of local government, and of municipal water utilities, is also crucial. The various forms of horizontal cooperation between individual municipalities and between the Lander are important, the latter having become particularly important as the Lander try to preserve their strong influence in the face of increasing policy activism by the EU. Historically, cooperative solutions have dominated much of policy development since the nineteenth century. In the face of powerful agricultural and industrial interests, the creation of networks of cooperation is still at the heart of policy, but the state relies less on authority or common interest than on exchange, with financial policy instruments coming to dominate. While water policy has been thoroughly reframed as part of environmental policy, environmental groups have played a relatively marginal role, although conflicts conceived in terms of local versus centralised water supply have gained some prominence in particular region