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KLT of radio signals from relativistic spaceships in arbitrary motion

Part of the Springer Praxis Books book series (PRAXIS)

Abstract

In three papers [1–3] the present author applied the concept of time-rescaled Brownian motion to aspects of relativistic interstellar flight ranging from communication theory to genetics. The content of the present chapter was fully published in paper form in [11]. In particular, the Gaussian noise (Brownian motion) X(t), emitted by a relativistic spaceship traveling at a constant acceleration g in its own reference frame, was shown to be—see Equation (12.10) or [1, eq. (53)]
$$ X\left( t \right) = B\left( {\frac{c} {g}\arcsin h\left( {\frac{g} {c}t} \right)} \right) = B\left( {\frac{c} {g}\ln \left[ {\frac{g} {c}t + \sqrt {1 + \left( {\frac{g} {c}t} \right)^2 } } \right]} \right), $$
(13.1)
where c is the speed of light, B(t) denotes standard Brownian motion with mean zero, variance t, and initial condition B(0) = 0, and time ranges within the finite interval 0 ≤ tT.

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References

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    C. Maccone, “Relativistic Interstellar Flight and Gaussian Noise,” Acta Astronautica, 17(9) (1988), 1019–1027.CrossRefADSGoogle Scholar
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© Praxis Publishing Ltd, Chichester, UK 2009

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