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Hartnett extended Carmeli's model and discarded several assumptions that Carmeli initially had thought were safe. This included the assumption that the matter density of the universe is at the critical level for a "coasting" universe.
 
Hartnett extended Carmeli's model and discarded several assumptions that Carmeli initially had thought were safe. This included the assumption that the matter density of the universe is at the critical level for a "coasting" universe.
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The full derivation of Hartnett's field equation that describes the motion of far-off objects is included in Appendix 2 of his book. Briefly, Hartnett begins with [[Moshe Carmeli]]'s [[Cosmological Relativity]], which adds a dimension of the radial velocity of a far-off object to the Einsteinian dimensions of space and time. This radial velocity is related to the distance of the object by this equation:
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The full derivation of Hartnett's field equation that describes the motion of far-off objects is included in Appendix 2 of his book. Briefly, Hartnett begins with [[Moshe Carmeli]]'s Cosmological Relativity, which adds a dimension of the radial velocity of a far-off object to the Einsteinian dimensions of space and time. This radial velocity is related to the distance of the object by this equation:
    
<math>v = \bigg( \frac{1}{\tau} \bigg) r</math>
 
<math>v = \bigg( \frac{1}{\tau} \bigg) r</math>
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