Steve
Re our exchange in Ben's blog.
While I would never understand some of the maths, I do not want to comment too much on the underlying logic (spacetime, c, etc) because I might just be pre-empting conclusions which I have in my head but want to confirm by finishing that paper (the first half of which was a response on Ben's blog).
Though the history is irrelevant, my simple understanding is that Voigt and Doppler were using the concept of local time. Understandably though, because they were trying to represent effects which occurred over time. Lorentz uses local time later, with Poincaré in the background with his misconception of time and timing. In very crude terms: it was rather like 'pin the tail on the donkey'. Through all the deliberations over ether, ether movement, light, light speed and direction, earth movement, etc, there was deemed to be variance, and time finally provided a suitable candidate. The problem is that this is just associated with observation. Hence the appearance of c in so many equations. Which raises the rather obvious question as to what has the speed of an effect in photons got to do with it?? It could be that a differential in gravitational force applied, ie a force, because only differences have the effect, could cause dimensional alteration, as well as momentum change. This was their original position, it was never rescinded, and could be correct.
SR is a red herring
γ is really a generic expression for the relationship between a rate of change as is with that rate as is when referred to another reference which is altering. Forget c. It could be any v. Again, c is just a reflection of the fact that the entire model of physical reality has been built with c as the determinant. Light just enables sight!!
Neither is physical reality only three dimensional spatially, this just represents the minimum number conceptually possible. From any given spatial position, the smallest elementary particle could move (ie alter spatial position) by next occupying any other adjacent spatial point, of which there will be a definite number determined by the size (spatial footprint) of that elementary particle. So, the number of possible physical dimensions is half that number of those possible directions, as the concept of dimension relates to a direction, either way.
Physical existence (as it can only be known to us) is an n spatially dimensional state of the substance which comprises it, which exists in one definitive physically existent state at a time. The rate of change, obviously, being determined by the fastest form of change in physical existence. That does not imply that everything has changed in that duration, but if something has, then there is a different physically existent state. This is the tick rate of physical existence.
The big question here is, what can we assume to be the relationship between a unit of spatial relationship and a unit of change.
Paul