nice to see we all still geting on in such a civilised manner in this thread (lest lawyers start to appear here - heaven forbid!)
i have to say, i find myself very much in agrement with Tom's description of 'how' the the dilation phenomenon is acounted for.
however, i also find with Johan that the answer is not 'clearly within' SR alone or as Delta V otherwise writes:
DeltaV wrote:"Do Lorentz transforms between inertial frames induce actual, or only apparent, time dilation and length contraction?"
in particular my curent interpretation is:
that the Lorentz tansformation sets the 'magnitude' of any final time dilaltion, during the process of calculation, BUT, does NOT determine to which body/bodies such magnitude is finally 'apportioned': that, 'final' apportionment is decided 'arbitrarily' ONLY when the boundary conditions of the experiment are 'imposedf' on the result.
- and in particular, those boundary conditions include any 'turnarounds' or accelerations or decelerations of one body WITH RESPECT TO the other. (ie. the change of FOR's when one body arbitrarily DECIDES to catch up with/slow down to meet the other).
that is, this problem cannot be 'completely formulated' UNLESS those 'discountinuities' are convolved ( - difficult because there is no easy/compatible algebraic form to mix here - possibly a 'commutator' of some sort - as i believe Einstein/Poincare others have used, or as i have previously sufggested/cited, some form of 'ordered goup/causal set').
thus, as Johan points out (iiuc), the dilation does NOT exist due to the Lorentz transformation alone - that is mearly a calculator - it is just doing its job.
the point, where i suspect Johan's current 'diupute' arises, is i believe, in the 'assumption' that, at the start of the experiment, we can 'synchronise clocks' to a 'single' value when they are moving relative to each other. i believe that we can not. such a value will always be a tuple (0(A(B)),0(B(A))) - represented by two triangles, NOT a line. It is at root the Anrdomeda Paradox (a simpler version of the twins) - (
http://en.wikipedia.org/wiki/Rietdijk%E ... m_argument ).
To be fair Johan did try to address this very point a couple of posts back (
viewtopic.php?t=2137&postdays=0&postord ... start=1275 ), yet, imho, Johan, i can't help thinking you've made the same sort of mistake that you acuse Einstein of making (though i should add, there is indeed historical evidence of Einstein fudging/changing his mind around these exact same points).
i believe this is where the root of the argument lies.
thus, the only 'interpretation' i can place on it is:
'consideration of relative velocity and position alone are INSUFFICIENT to formulate either the probem, or the solution'
thus, when considering bodies in relative motion/at a relitave distance, I 'imagine' that they MUST have ultimately have aquired that 'state' from some historical 'absolute coincidence' in position AND velocity space (ie. the two clocks were in fact the 'same' clock at some point), and/or conversely, that they MUST ultimately re-aquire that same coincident state, in order to be 'finally compared' in a 'physical' AND a 'mathematical' sense. (Lorentz, Minkowski and the bulk of SR take care of what happens (and appears to happen) in-between, but does not adequately formulate this 'action layer' of the description - imho).
- ie. we must (even notionaly) attach some sort of 'impulse vector' or 'comutator actions' to each of the bodies, in order to calculate the 'sense' (or perhaps 'chirality') of the final apportioned dilation magnitide(s).
if such are not taken into consideration, then there is NO WAY of apportioning a result to either body.
finally, for a bit of light relief:: this says it all for me:
http://www.youtube.com/watch?v=8KgQYZCgfnc
Educating Essex: What Is Pi? Where Did It Come From?