ABSTRACT
What does the rapidity β represent? Consider an observer moving at
speed v to the right. This observer’s world line intersects the hyperbola
c2t2 − x2 = ρ2 (ct > 0) (6.1)
at the point A with coordinates (ρ sinhβ, ρ coshβ); this line therefore has
“slope”1
v
c = tanhβ, (6.2)
which is the same as Equation (5.6). Thus, β is nothing more than the
hyperbolic angle between the ct-axis and the worldline of a moving object.
As discussed in Chapter 4, β is precisely the distance from the axis as
measured along the hyperbola (in hyperbola geometry). This relationship
was illustrated in Figures 4.2 and 5.2.
