Keith Dysart wrote:
Why would anyone refuse to calculate the length of
600 ohm line needed to produce 0 ohms? I think I
was the first to calculate it at 43.4 degrees.

Exactly. Why would anyone refuse?

Nobody has refused so it is a rhetorical question
the meaning of which is obscure.

So the next question is: What is the phase change
at the terminals of the black box?

You list the phase changes at the terminals of the
black boxes. An s-parameter analysis will prove those
are valid values. Have you done that s-parameter
analysis yet?

b1 = s11*a1 + s12*a2

b2 = s21*a1 + s22*a2

The phase shift is the relative phase between b1 and a2.
And also the relative phase between b2 and a1.

1) -93 degrees? (previous answer when it was a capacitor)

I might be wrong about that one. It might instead be
180 - 93, but that would just be a stupid math mistake.
The main thing is that it is different from the other two.

2) 36.6 degrees? (previous answer when it was 10 degrees of 100 ohm
line)
3) 0 degrees? (previous answer when it was 46.6 degrees of 600 ohm
line)

There's nothing wrong with those answers except maybe
a stupid math error. Each condition indeed does have a
different phase shift that can be measured one inch on
the other side of the terminals if one is simply allowed
to make those measurements. If s11 is measured and stamped
on the black boxes, the phase changes can be easily
calculated.

This is an example of how models can get you into trouble.
Not allowing us to look inside the black box doesn't change
the laws of physics and make all the phase shifts the same.
It just means that the phase shifts are unknown and need
to be measured.

Using that same logic, if you were shackled at the bottom
of Carlsbad Caverns, night and day would stop happening
just because you couldn't see it happening.

Do you really expect us to believe that the phase shift
is the same for all the black boxes but changes abruptly
when the reflection coefficients are measured?
--
73, Cecil http://www.w5dxp.com