Relativity and Cosmology


(Anti) de Sitter Relativity, Modified Newtonian Dynamics, Noncommutative Phase Spaces and the Pioneer Anomaly

Authors: Carlos Castro

It is shown how the de-Sitter Relativistic behaviour of the hyperbolic trajectory of Pioneer, due to the expansion of the Universe (non-vanishing cosmological constant), is the underlying physical reason for the observed anomalous acceleration of the Pioneer spacecraft of the order of c2/RH ~ 8.74 x 10-10 m/s2, where c is the speed of light and RH is the present Hubble scale. We display the explicit isomorphism among Yang's Noncommutative space-time algebra, the 4D Conformal algebra SO(4,2) and the area-bi-vector-coordinates algebra in Clifford spaces. The former Yang's algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = h/R (maximal length R, infrared cutoff ). It is shown how Modified Newtonian dynamics is also a consequence of Yang's algebra resulting from the modified Poisson brackets. To finalize we study the deformed Kepler and free motion resulting from the modified Newtonian dynamics due to the Leznov-Khruschev noncommutative phase space algebra and which stems also from the Conformal algebra SO(4,2) in four dimensions. Numerical examples are found which yield results close to the experimental observations, but only in very extreme special cases and which seem to be consistent with a Machian view of the Universe.

Comments: 24 Pages. This article appeared in Adv. Studies Theor. Phys., Vol. 2, no. 7 (2008) 309 - 332

Download: PDF

Submission history

[v1] 14 Sep 2009

Blog Trackbacks

Einstein vs Teoria Conectada: Las Transformaciones Relacionales [posted October 20, 2009]

Unique-IP document downloads: 116 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus