Dear Edwin,
I think you raise a number of important issues in your essay, which are often glossed over in the teaching of special relativity. First of all, you point out that time dilation---and, in fact, other relativistic phenomena---can be derived within a framework of absolute space and time. This is true, even if it's often not well appreciated---the best analysis is, I think, due to John Bell (him of the theorem), in his essay 'How to Teach Special Relativity'. There, he shows that, for instance, length contraction can be explained by noting that the shape of the electromagnetic frame of a moving charge will no longer be spherically symmetric, but rather, flattened in the direction of movement; and thus, a rod, made from 'atoms' whose spherical symmetry is no longer given, will contract in length. Similar remarks apply to electrons circulating around these atoms---their period will change in accordance with time dilation.
This is today sometimes glossed as the 'Neo-Lorentzian' interpretation of special relativity; as is proper for any interpretation, there is no experimental means to adjudicate between it and the 'Minkowskian' interpretation in terms of four-dimensional spacetime; hence, it indeed requires a decision to opt for one or the other. (Things do, however, get more difficult once one moves to full-fledged general relativity.)
Another point is that in teaching special relativity, one generally assumes a sort of 'view from nowhere'---imagining one could 'observe' what happens in, say, moving train cars as it happens. But the events within a train car moving past us would look nothing like the naive predictions made by applying the Lorentz transformations---indeed, there are many intriguing optical phenomena attached. For one, flying past a planet at a high fraction of the speed of light, that planet would not look like a flattened pancake at all, as the Lorentz contraction would naively lead us to expect---indeed, it would remain looking perfectly spherical, but, curiously, rotated as compared to the orientation we would see flying past it at lower speed!
This is due to the so-called 'Penrose-Terrell rotation'. The reason for this is that, essentially, an object moving past an observer at a high enough speed gets 'out of the way' of light emitted from its (relative to the observer) backside, so that such light can reach the observer after all. Thus, what we would see when peeking through the walls of a moving train would be very much more complicated than what the simple Lorentz transformation might lead us to expect.
In the relationship between a theory and the world, there are then two sources of potential failures of fit, if one is not sufficiently careful---one, in the observational consequences; and two, in the ontological consequences. Naively, having just learned special relativity, one might conclude that one sees a Lorentz-contracted object moving past, which means that reality needs to be described in terms of a four-dimensional geometry; neither of which is right.
However, I am not sure I see the connection with my remarks to Xerxes Arsiwalla in his essay, and the notion of how distributional systems may overcome Gödelian problems. After all, the sort of systems you discuss here are staunchly computational---and thus, subject to the same issues of undecidability, etc., as any other model of computation. Xerxes seemed, in his essay, to be saying that there is a notion of distributional system that outstrips these capacities, but I'm still not sure what exactly is meant by that.
Anyway, I wish your essay good luck in the contest!
Cheers
Jochen
