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. Lett. 81(14), 2858 (1998). gr-qc/0104064 . doi: 10.1103/PhysRevLett.81.2858Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. D 65(8), 082004 (2002). gr-qc/0104064 . doi: 10.1103/PhysRevD.65.082004Anderson, J.D., Campbell, J.K., Ekelund, J.E., Ellis, J., Jordan, J.F.: Phys. Rev. Lett. 100(9), 091102 (2008). doi: 10.1103/PhysRevLett.100.091102Atchison, J.A., Peck, M.A.: J. Guid. Control Dyn. 33, 1115 (2010). doi: 10.2514/1.47413Bertolami, O., Francisco, F., Gil, P.J.S.: Class. Quantum Gravity 33(12), 125021 (2016). 1507.08457 . doi: 10.1088/0264-9381/33/12/125021Bolton, S.J., Adriani, A., Adumitroaie, V., Allison, M., Anderson, J., Atreya, S., Bloxham, J., Brown, S., Connerney, J.E.P., DeJong, E., Folkner, W., Gautier, D., Grassi, D., Gulkis, S., Guillot, T., Hansen, C., Hubbard, W.B., Iess, L., Ingersoll, A., Janssen, M., Jorgensen, J., Kaspi, Y., Levin, S.M., Li, C., Lunine, J., Miguel, Y., Mura, A., Orton, G., Owen, T., Ravine, M., Smith, E., Steffes, P., Stone, E., Stevenson, D., Thorne, R., Waite, J., Durante, D., Ebert, R.W., Greathouse, T.K., Hue, V., Parisi, M., Szalay, J.R., Wilson, R.: Science 356, 821 (2017). doi: 10.1126/science.aal2108Cahill, R.T.: ArXiv e-prints (2008). 0804.0039Chamberlin, A., Yeomans, D., Giorgini, J., Chodas, P.: Horizons Ephemeris System (2016). http://ssd.jpl.nasa.gov/horizons.cgi . Accessed: 2016-10-27Chao, B.F.: C. R. Géosci. 338, 1123 (2006). doi: 10.1016/j.crte.2006.09.014Coddington, E., Levinson, N.: McGraw-Hill, New York (1955)Debono, I., Smoot, G.F.: Universe 2(4), 23 (2016). doi: 10.3390/universe2040023Desai, S.D.: J. Geophys. Res., Oceans 107(C11), 7 (2002). 3186. doi: 10.1029/2001JC001224Dickey, J.O., Bender, P.L., Faller, J.E., Newhall, X.X., Ricklefs, R.L., Ries, J.G., Shelus, P.J., Veillet, C., Whipple, A.L., Wiant, J.R., Williams, J.G., Yoder, C.F.: Science 265, 482 (1994). doi: 10.1126/science.265.5171.482Dyson, F.W., Eddington, A.S., Davidson, C.: Philos. Trans. R. Soc. Lond., Ser. A 220, 291 (1920). doi: 10.1098/rsta.1920.0009Everitt, C.W.F., et al.: Phys. Rev. Lett. 221101(106) (2011)Feng, J.L., Fornal, B., Galon, I., Gardner, S., Smolinsky, J., Tait, T.M.P., Tanedo, P.: Phys. Rev. Lett. 117, 071803 (2016). 1604.07411 . doi: 10.1103/PhysRevLett.117.071803Folkner, W.M., Williams, J.G., Boggs, D.H., Park, R.S., Kuchynka, P.: IPN Prog. Rep. 42(196) (2014)Fornberg, B.: Math. Comput. 51(184), 699 (1988). doi: 10.1090/S0025-5718-1988-0935077-0Franklin, A., Fischback, E.: The Rise and Fall of the Fifth Force. Discovery, Pursuit, and Justification in Modern Physics, second edition. Springer, New York (2016)Giorgini, J.D.: Personal communication (2015)Hackmann, E., Laemmerzahl, C.: In: 38th COSPAR Scientific Assembly. COSPAR Meeting, vol. 38, p. 3 (2010)Hafele, J.C.: ArXiv e-prints (2009). 0904.0383ICGEM: International Center for Global Gravity Field Models. http://icgem.gfz-potsdam.de/tom_longtimeIERS: In: Petit, G., Luzum, B. (eds.) IERS Conventions (2010), p. 1. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main (2010)Iess, L., Asmar, S.: Int. J. Mod. Phys. D 16, 2117 (2007). doi: 10.1142/S0218271807011449Iess, L., Asmar, S., Tortora, P.: Acta Astronaut. 65, 666 (2009). doi: 10.1016/j.actaastro.2009.01.049Iess, L., Di Benedetto, M., James, M., Mercolino, M., Simone, L., Tortora, P.: Acta Astronaut. 94, 699 (2014). doi: 10.1016/j.actaastro.2013.06.011Iorio, L.: Sch. Res. Exch. (2009). 0811.3924 . doi: 10.3814/2009/807695Iorio, L.: Astron. J. 142, 68 (2011a). 1102.4572 . doi: 10.1088/0004-6256/142/3/68Iorio, L.: Mon. Not. R. Astron. Soc. 415, 1266 (2011b). 1102.0212Iorio, L.: Europhys. Lett. (2011c). 1105.4145 . doi: 10.1209/0295-5075/96/30001Iorio, L.: Adv. Space Res. 54(11), 2441 (2014a). 1311.4218 . doi: 10.1016/j.asr.2014.06.035Iorio, L.: Galaxies 2, 259 (2014b). 1404.6537 . doi: 10.3390/galaxies2020259Iorio, L.: Universe 1(1), 38 (2015a). doi: 10.3390/universe1010038Iorio, L.: Int. J. Mod. Phys. D 24, 1530015 (2015b). 1412.7673Iorio, L., Giudice, G.: New Astron. 11, 600 (2006). gr-qc/0601055Iorio, L., Lichtenegger, H.I.M., Ruggiero, M.L., Corda, C.: Astrophys. Space Sci. 331, 351 (2011). 1009.3225 . doi: 10.1007/s10509-010-0489-5Jouannic, B., Noomen, R., van den IJSel, J.A.A.: In: Proceedings of the 25th International Symposium on Space Flight Dynamics ISSFD, Munich, Germany (2015)Kennefick, D.: Phys. Today 62, 37 (2009). doi: 10.1063/1.3099578King-Hele, D.: Satellite Orbits in an Atmosphere. Theory and Applications. Blackie and Son Ltd., Glasgow (1987)Lämmerzahl, C., Preuss, O., Dittus, H.: In: Dittus, H., Lammerzahl, C., Turyshev, S.G. (eds.) Lasers, Clocks and Drag-Free Control: Exploration of Relativistic Gravity in Space. Astrophysics and Space Science Library, vol. 349, p. 75 (2008). doi: 10.1007/978-3-540-34377-6_3Le Verrier, U.: C. R. Hebd. Acad. Sci. 49, 379 (1859)Lemoine, F.G.E.A.: NASA/TP-1998-206861 (1998)Lewis, R.A.: In: Robertson, G.A. (ed.) American Institute of Physics Conference Series. American Institute of Physics Conference Series, vol. 1103, p. 226 (2009). doi: 10.1063/1.3115499Longair, M.: Philos. Trans. R. Soc., Math. Phys. Eng. Sci. (2015). doi: 10.1098/rsta.2014.0287McCulloch, M.E.: Mon. Not. R. Astron. Soc. 389, 57 (2008). 0806.4159 . doi: 10.1111/j.1745-3933.2008.00523.xMoe, M.M., Wallace, S.D., Moe, K.: In: Washington DC American Geophysical Union Geophysical Monograph Series, vol. 87, p. 349 (1995). doi: 10.1029/GM087p0349Murphy, E.M.: Phys. Rev. Lett. 83, 1890 (1998). doi: 10.1103/PhysRevLett.83.1890Naval Observatory: Dept. of the Navy, USA (2009)Newcomb, S.: Tables of the Four Inner Planets. Government Printing Office, Washington (1895)Nyambuya, G.G.: ArXiv e-prints (2008). 0803.1370Nyambuya, G.G.: New Astron. 57, 22 (2017). doi: 10.1016/j.newast.2017.06.001Páramos, J., Hechenblaikner, G.: Adv. Space Res. 79–80(7), 76 (2013). 1210.7333v1Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Westview Press, Perseus Books Group, London (1995)Pinheiro, M.J.: Phys. Lett. A 378, 3007 (2014). 1404.1101Pinheiro, M.J.: Mon. Not. R. Astron. Soc. 461(4), 3948 (2016)Renzetti, G.: Cent. Eur. J. Phys. 11, 531 (2013). doi: 10.2478/s11534-013-0189-1Rievers, B., Lämmerzahl, C.: Ann. Phys. 523, 439 (2011). 1104.3985 . doi: 10.1002/andp.201100081Roseveare, N.T.: Mercury’s Perihelion, from Le Verrier to Einstein. Clarendon Press, Wotton-under-Edge (1982)Rubincam, D.P.: Icarus 148, 2 (2000). doi: 10.1006/icar.2000.6485Standish, E.M.: In: Macias, A., Lämmerzahl, C., Camacho, A. (eds.) Recent Developments in Gravitation and Cosmology. American Institute of Physics Conference Series, vol. 977, p. 254 (2008). doi: 10.1063/1.2902789Standish, E.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. 179 (2010). doi: 10.1017/S1743921309990354Thompson, P.F., Abrahamson, M., Ardalan, S., Bordi, J.: In: 24th AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, New Mexico, January 26–30, 2014 (2014). http://hdl.handle.net/2014/45519Turyshev, S.G., Toth, V.T.: Living Rev. Relativ. (2010). 1001.3686 . doi: 10.12942/lrr-2010-4Turyshev, S.G., Toth, V.T., Kinsella, G., Lee, S.-C., Lok, S.M., Ellis, J.: Phys. Rev. Lett. 108(24), 241101 (2012). 1204.2507 . doi: 10.1103/PhysRevLett.108.241101Varieschi, G.U.: Gen. Relativ. Gravit. 46, 1741 (2014). 1401.6503 . doi: 10.1007/s10714-014-1741-zWilhelm, K., Dwivedi, B.N.: Astrophys. Space Sci. 358, 18 (2015). doi: 10.1007/s10509-015-2413-5Will, C.M.: Living Rev. Relativ. 3(9) (2006)Will, C.M.: Class. Quantum Gravity (2015). doi: 10.1098/rsta.2014.0287Will, C.M.: In: Peron, R., Colpi, M., Gorini, V., Moschella, U. (eds.) Gravity: Where Do We Stand? Astrophysics and Space Science Library, vol. 349, p. 9 (2016). doi: 10.1007/978-3-319-20224-2_2Williams, J.G., Boggs, D.H.: Celest. Mech. Dyn. Astron. 126, 89 (2016). doi: 10.1007/s10569-016-9702-3Williams, J.G., Dickey, J.O.: In: Noomen, R., Klosko, S., Noll, C., Pearlman, M. (eds.) Proceedings of 13th International Workshop on Laser Ranging, p. 75 (2003). http://cddisa.gsfc.nasa.gov/lw13/lw_proceedings.htmlWilliams, J.G., Newhall, X.X., Dickey, J.O.: Phys. Rev. D 53, 6730 (1996). doi: 10.1103/PhysRevD.53.6730Williams, J.G., Turyshev, S.G., Boggs, D.H.: Phys. Rev. Lett. 93(26), 261101 (2004). gr-qc/0411113 . doi: 10.1103/PhysRevLett.93.261101Williams, J.G., Turyshev, S.G., Boggs, D.H.: Planet. Sci. 3, 2 (2014). doi: 10.1186/s13535-014-0002-5Williams, J.G., Boggs, D.H., Yoder, C.F., Ratcliff, J.T., Dickey, J.O.: J. Geophys. Res. 106, 27933 (2001). doi: 10.1029/2000JE001396Wolfram, S.: The Mathematica Book, fifth edition. Wolfram Media, Champaign (2003

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