The following is exceedingly speculative and some of the arguments are anthropomorphic, so read at your own tolerance level. It relates essentially to interpreting physical world in terms of information theory and possibly quantum measurement theory, instead of directly from quantum mechanics. If we consider space or spacetime as a statistical construction, there may indeed be a relationship between the speed of light and a computational limit principle. If the ideas of quantum measurement apply also to spacetime, then we indeed may be left with a system where spacetime (as well as the events we see play upon it) is a construction by the observer from information received over finite time periods and in finite amounts. There would be then statistical uncertainties which should limit speeds in some contexts, since the observer cannot perceive objects traveling faster than the rate at which he/she can calculate the relationships of a background spacetime. Classical special relativistic effects might be re-interpreted as a type of "spatial blur uncertainty" phenomenon in a statistical space construction. This also immediately suggest the Lorentz transformation should also involve y and z coordinates, not just x cooridinate for very high velocities approaching c. Traveling faster than light might be like trying to have your cake and eat it too...you wouldn't be able to observe a faster than light object because you would not have the time to create the space backdrop from information received. Now there might be very interesting loopholes to this idea which could allow FTL in certain circumstances. A recent very interesting paper published a few years back did indeed find a speed limit for propagation of information within networks regardless of the speed of node-to-node transmission. The types of such spaces that can be "created" by the observer statistically might also have deeper connections with gravity and SU(N) groups. The Euclidean space we generally observe has very simple and unique symmetric properties which might be expected to naturally emerge from a statistical construction of all possible spaces much as Bell curve emerges naturally from statistically independent random variables or Feynman many paths merge toward the least action principle. There are also dimensional (and likely topological) limits for the perception of such a statistical space which might provide clues to how this could come about naturally...for example a random walker will return on average only a finite number of times to the same point in a 3d or higher dimensional open lattice, so it would be impossible for completely open 3d and higher lattice spaces to be uniquely determined by a naiive observer statistically without additional assumptions in such a scenario (and this is actually the case as for open spaces... all perception occurs via a 2d interface and we perceive the world as a 3D projection only). This would not be the case at very small or closed scales (SU(N)?!) interestingly and could provide a guiding principle to the Kaluza-Klein type theories. It is perhaps also telling anthropomorphism that we perceive open 2D spaces in two different ways, as a 2D "photon current" screen like projection in front of us, or as a linear horizon-like projection photon current x radial distance upon the surface of our earth. The later is much less direct and the linearity or lack thereof is controlled by gravity, perhaps reaching ideality at a black holes surface. It would be fascinating if there was a continuous/smooth connection between the two which could form a new duality.
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