rgill,
Your simple construct to simulate a single point on a unit sphere of either S^3 or R^4, and do so at once, looks very interesting in that it would provide an easily identifiable initial state from which to protract a comparison of the respective points vis-à-vis their own reference frame to the other.
In classical space the spherical full field of gravitational influence subsumes the electro-magnetic, and nuclear forces, of a rest mass; the photon however is a discrete entity as an elongation of that spherical volume to uniformly conform to the longitudinal space inside, say, a soda straw. Its still an inertial reference frame, and if quantum mechanics must borrow the classical gravitational theory in any part, it really can't change the rules. The point of any moment in time which can be chosen as translating an effect across any length of space inside that inertial reference frame is therefore 'center of rest' from which the longitudinal length of the attenuated field extends at 180^o at that arbitrary moment, and that translation of effect operates across any density of the energy within the envelope of the reference frame co-variantly so at any measured position it is at light velocity. Time keeping is local to the reference frame, and global within it. Whether taken as Lorentz invariant or co-variant, the moment of center of rest is thereby associated with mass. My own quibble is; that should mean that only a portion of the quantity of energy en masse ought be prescribed as existant at a density equivalent to the whole energy in the field; ie; mc^2/cm^3. The argument being; what part of 'center of rest' does not prescribe inertia?
Quantum Mechanics, lacking a gravitational rationale (so far) employs R^4, Euclidean space in which at any and every point, time is progressing in step with Newton's heartbeat. Fine. But that leaves us with the dichotomy of QM seeing the photon as a discrete clump moving at light velocity through Euclidean space, and any field associated with it that would be projected as described in classical space, is therefore seen as propagating affects in excess of light velocity, specifically c^2. Where from the discrete classical inertial reference frame, if anything is moving; it's a point in Euclidean space, relative to the point at center of rest, becoming a point in the classical past.
So it is not like a simple comparison of statistical distribution without 'time'. Time can zeroed out of the equation, but to reconcile quantum and classical distributions it can't be zeroed out of existence.
What I 'meant' was to extend a welcome to Judy Nabb, in recognition that we all have personality traits expressed in ways that are simply off-hand or flippant. And there are things in this world which can require the choice of dying on ones feet or living on ones knees, and arguing a theoretical point ain't one of them. Given this website is the type subject to the interest of some not content with what might be offered up as content, and the current stakes, as a statistician by trade if you aren't being facitious about kicking around Vienna, then you've got work. Any new clients of the bread and butter sort since you started offering comments on this particular blog? (Your right, it is the most exciting and relevant, and I can gather you also understand the wisdom of 'always tip the bartender'.) jrc
