Unless we wish to begin discuss Lorentz Transformations (something which I admit I have little experience in, and even less experience in english terminology of it), I suggest we leave four-vectors alone. However, since you declaration of Minkowski-space reference for the rulers I will deal with.Vitor Goncalves said:Snip
You set the event spacial vectors close to eachother. Why? To get an impressivly small sounding difference in measurement, that has nothing to do with the fact that there is a difference. And my argument has been that with sufficient difference in the timelike v(0) vectors of two events, an observer that is event 2 would measure the foot-long object that is event 1 as 13 inches long.
To put it simply: you chosen as an example specifically limited four-vectors, precisely because if we unbind the fourvectors, the possibility to measure a 13 inch foot exists.
Precisely why we have Lorentz Transformation: to make sense of and combine the reference grids in the odd cases such as this, as you said. Without it we would be hard-pressed to explain hypothetical observations such as this, or the very real observations we do make of celestial objects.
We seem to be talking of two slightly disconnected things: I argue that it is possible to measure a 13inch long foot (thereby, for the observer, making the foot-long object be 13 inches long), you argue that the foot-long object is always 12 inches long and only our perception of it changes.
Almost as if we are saying the same thing, but from a completely opposite viewpoint.
EDIT: the difference here seems to stem from me saying that there is no absolute frame of reference, whereas you hold the only practical frame (that being our own) as the default basis to compare things to.