The constant in the hyperbola is the same as the time measured by the
one who sees the meson's creation and decay events occur at the same
location. There is only one way that an observer can see this --
the observer would have to be traveling at the same velocity as the meson.
Anybody not traveling with the same velocity as the meson (Remember!
velocity includes direction!) would see the creation and decay at two
different locations; to these folks the meson seems to move.
This is the heart of relativity. Observers with different frames of
reference will observe the same event differently.
A correction factor scales the time. The physics community calls this
correction factor gamma (g). The
scaling equation is: (my time) ÷ g = (meson's
time). The larger the velocity, the larger the disagreement
in the measurements.
g = (1 - relative
Remember, you derived the formula for g
Examining a plot of the lifetimes vs. the decay length of the mesons.