Okay, I'm seeing where I misconstrued what "proper time" means (thanks to a surprisingly not particularly good explanation at the Wolfram site). Even with getting that notion squared away, I still see implications that don't square with the notion that there is a contraction that is actual in an absolute sense - which is notion I have been trying to explore. But I don't think there is much value any more in trying to hash it out - at least it doesn't feel that way to me now and there probably hasn't been any value to you in the effort since several posts back. :)

Depends what you mean by "absolute". More importantly, are these effects real? We know that the half-life of cosmic muons is longer than a lab muon's half-life, with the correction exactly as predicted by SR. We know that E = Mc[sup:2rdtathu]2[/sup:2rdtathu]. I have a blog in which I derived that formula exactly how Einstein did it. ( See http://soi.blogspot.ca/2013/06/einstein ... ation.html). You see the factor (1 - v[sup:2rdtathu]2[/sup:2rdtathu]/c[sup:2rdtathu]2[/sup:2rdtathu]) [sup:2rdtathu]1/2[/sup:2rdtathu] appearing in the calculation, so it seems that these effects are real.

Yes, it does depend on what is meant by "absolute" - and what is meant by "real" and what is meant by "apparent" and "actual". The intuition that I tried to follow to see if it was right is that the fundamental disagreement that occurred earlier in this thread is essentially one of semantics - the meaning intended when people use those words in this context.

I'll use the Doppler experiment analogy (as I did in an earlier post to Solitary) to see if it correctly correlates to the point I'm wondering about with respect to contraction in the direction of movement. In Doppler's experiment (as I'm sure you are aware), if I understand it correctly, the observer standing on the side of the tracks with a train whistle blowing as the train approaches the observer at "high" speed will hear the sound that is produced as a higher pitch than an observer traveling on the train. Is the higher pitch real? Yes it is, but the lower pitch heard by the observer on the train is real, too. Some people might be disturbed by this because they want to think of it in terms of ontological absolutes - if the sound is a higher pitch then it can't also be a lower pitch. A response someone could make is that the sound "appears" to be a higher pitch to the observer outside the train and "appears" to be a lower pitch to observer on the train. What they would intend by that semantic formulation is that both are real but that they are experienced (appear) differently to the two different observers. But someone hearing "appears" used in this context might assume that that isn't the intent; instead that the intent of using "appears" is to express the opposite of "real" - as in an optical illusion can fool you because one line appears longer than another but they are "really" the same length. If that is right, then I wonder if something much like that is the heart of the the disagreement earlier in the thread.

Unless there is something crucial that is intrinsically different about the relativity of what the observers of the train whistle hear compared to the relativity of length in Special Relativity, then I still suspect that this semantic ambiguity is likely to be why the disagreement arose early in this thread. The issue I was trying to track down through most of the discussion with you was whether or not there is something intrinsically different about the relativity of Special Relativity theory and the relativity of the pitch of a sound due to the Doppler effect. I still can't tell about that, so I'm not sure if my initial intuition was right or not.