## (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
c^{2}/R_{H} ~ 8.74 x 10^{-10} m/s^{2}, where c is the speed of light and R_{H} 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

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### Submission history

[v1] 14 Sep 2009

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