Mathematics is actually irrelevent in my opinion, because it can often be misleading. The premise is interesting - however I am at odds with the nature of the source of the energy that generates this space-time field in your Universe. I have a similar theory that gravity occurs as the result of spatial displacement, but there is nothing that I can see which prevents an object from exceeding the rate of
c, because I do not let mathematics tell me so and therefore I am not constrained by its finiteness. To me, space is not nothing, and not dependent on the projection of space-time fields but rather on the displacement of that of which space is comprised by the objects occupying it, probably a type of boson which we may as well call gravitons. The uniformity of space is affected by its continual expansion, and this expansion is in part responsible for the constant creation of virtual particles because the fabric of which space is constructed is not rigid, and neither is the expansion of local space totally uniform given the constantly fluctuating integrity of its structure due to the presence of dynamically interacting gravity fields occurring as the result of the spatial displacement by objects in perpetual motion.
That is not to say that I would disregard the numbers altogether, because the thought experiment is a fascinating one and the mathematical theory might very well have limited application in our limited reality, where many things are possible but which do not involve or are incompatible with the entire realm of cosmic potential.
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The only problem is, any spacecraft passing through the speed of light according to True Relativity, would be entering negative space.
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That is a theory for which you might very well be able to provide the math. In the same way that intuition can't predict the shape of the curve of a complex equation on a two dimensional plane, you might have been surprised by the projections of your own calculation and therefore allowed it to assert its stake in your overall appreciation of the fundamental nature of the reality of your space-time in your Universe. However, I think your statement is psychological in origin, that you still view
c as the holy grail, the way the sound barrier was regarded at the turn of the last century. All of this type of thinking will go the way of the sound barrier once a proper appreciation of the nature of light, and the method by which the characteristic modulations of the excitation energy that give rise to it are atomically propagated through the medium, are understood.
The fact is that corrections in calculating real GPS satellite clock times based on the relative influences of a weaker gravity and high velocity compared to ground based stations have compensated a great deal for what would otherwise have constituted gross innacuracies in determining ground position so Einstein was essentially correct. These calculations are based on what has been established for the sake of global positioning as one, notwithstanding relative, inertial frame of reference, the earth's surface.
The only possibly insurmountable obstacles to achieving perfection in this area are the dynamics of the constantly and very rapidly changing positions of all the satellites involved in determining ground position at any given time, the amount of which are also constantly changing for a given situation, and the time required to make the computations to determine the exact position for a given time and place, which are also not both necessarily static variables. These may very well be the only reason for the lack of absolute perfection that we would like to see in an ideal world.
If it were up to me, I would model your calculations in a simulation to determine whether they might not provide a good alternative or supplement to the existing processes in GPS determinations. You never know...