Quantum Gravity 169.1: The Intersection in Wormholes From Spheres and Balls Via Probable Causation

From Osher Doctorow

In the intersection of the Universe's spherical front with the
cylindrical Wormhole having axis along the z axis (both sphere and
cylinder being "centered" at (0, 0, 0)), the z coordinate is no longer
arbitrary but was found in 169.0 to be given by:

1) z^2 = rho^2 - r^2

where rho is the radius of the sphere and r is the radius of the
Wormhole cylinder, which are a particular time are fixed although at
different times they grow as time increases. In the Probable
Causation/Influence (PI) analog, we get arguably:

2) 2z = 2rho - 2r

or dividing through by 2:

3) z = rho - r

The length of the Wormhole is 2z, so from (2) we actually have
equation (2) being more informative in a sense than (3). (2) says
that the length of the wormhole at a fixed time t is the radius of the
Universe minus the radius of the wormhole. However, we must be a bit
careful in interpreting this, because this is not what Euclidean
Cartesian/rectangular equation (1) says precisely. It is probably
best to regard (2) and (3) as Probable Causation/Influence Phase
analogs of equation (1) which is the equation that we would ordinarily
use without worrying about Causation.

The actual intersection of the Wormhole cylinder and the Universe's
sphere is, however, a circle, but not just any circular crossection of
the cylinder - it is the circular crossection of the cylinder at the
height or length z_i where the cylinder actually intersections the
sphere, i referring to "intersection". This intersection value of z,
z_i, is what (1) above gives. There is also a circular intersection
at z coordinate -z_i.

Osher Doctorow