MSimon wrote:So what you are saying is that all that changes is space and time is invariant?
No. Space and time, together, form an invariant quantity called the
interval, which is the spacetime analogy of spatial
distance. The
interval is invariant with respect to Lorentz transformations. But the transformed time is not age.
MSimon wrote:The fact that things appear to live longer in my frame the faster they are going is only appearance.
The appearance is a direct result of the Lorentz transform, which defines how things
appear between inertial frames, so, yeah. Pure kinematics. No calculus, just spacetime geometry. The Lorentz transform has no magical "power" over those things, to change how they age.
MSimon wrote:So the lifetime of fast moving muons is only a function of space and not time?
The average lifetime of a muon, in its own inertial frame, is a function of "muon stuff" (let's call it internal muon dynamics; dynamics needs calculus). It's constant for any inertial frame attached to a muon. For a fast moving muon, the Lorentz transform warps the average, muon-frame lifetime into an apparent lifetime and the muon end-of-life position into an apparent position. Both space and time are involved.
MSimon wrote:My understanding is poor and my math not so good (my calculus is very rusty) so could you put up the appropriate math and explain it?
Why do you need calculus for the pure kinematics of the Lorentz transform?
Here's the math you're after,
http://en.wikipedia.org/wiki/Lorentz_transformation , but you may need to modify that with the Sachs/Prins insights, where necessary.