I think I have it now:

Gong back to the *definition* of second and metre we have-

"The second is the duration of 9 192 631 770 periods of the radiation
corresponding to the transition between the two hyperfine levels of
the ground state of the caesium 133 atom."

and

"The metre is the length of the path travelled by light in vacuum
during a time interval of 1/299 792 458 of a second."

So as far as the mothership is concerned, letting out pulses at the
above time interval corresponds to "one mothership metre".

For a hovering reflector near the EH, the time taken for the
mothership to receive a particular pulse is long, and the mothership
has in the mean time let out loads of pulses. At the time of reception
of a particular pulse, there will be loads and loads of "in transit"
pulses, all "one mothership metre" apart. So as the reflection point
approaches the EH, the measured "mothership distance" approaches
infinity!

Doh!

Also, for an infalling reflection point, the time between pulses
received at the motherhsip increases arbitrarily. This means that the
object apparently approaches infinite velocity (well, relativistically
c acts like an infinite velocity).

So in "mothership units", the radial distance to the EH is infinite,
and an infalling body speeds up to c.

Ho hum.

I still have a few more doubts relating to how the (idealised) winch
line sees all this, but I'll give it a rest for a few weeks.

BR

p.s. thanks to JB and TR for taking this seriously. Sane people do
contribute!

Dr. Photon wrote:
I think I have it now:

Gong back to the *definition* of second and metre we have-

"The second is the duration of 9 192 631 770 periods of the radiation
corresponding to the transition between the two hyperfine levels of
the ground state of the caesium 133 atom."

and

"The metre is the length of the path travelled by light in vacuum
during a time interval of 1/299 792 458 of a second."

So as far as the mothership is concerned, letting out pulses at the
above time interval corresponds to "one mothership metre".

At first, yes. But as the mothership accelerates, it measures the
distance between pulses differently, due to the relativistic Doppler
effect. Pulses going down are a shorter distance apart in its new
frame of reference; pulses coming up get longer.

For a hovering reflector near the EH, the time taken for the
mothership to receive a particular pulse is long, and the mothership
has in the mean time let out loads of pulses. At the time of
reception
of a particular pulse, there will be loads and loads of "in transit"
pulses, all "one mothership metre" apart. So as the reflection point
approaches the EH, the measured "mothership distance" approaches
infinity!

No, the distance in the frame of reference in which the mothership is
currently at rest does not approach infinity. Just the number of
pulses. The pulses near the mirror are at shorter and shorter
distances apart. The sum of this infinite number of distances, with
successive ones getting smaller and smaller, converges to a finite
value.

Doh!

Also, for an infalling reflection point, the time between pulses
received at the motherhsip increases arbitrarily. This means that the
object apparently approaches infinite velocity (well,
relativistically
c acts like an infinite velocity).

So in "mothership units", the radial distance to the EH is infinite,
and an infalling body speeds up to c.

Your latter statement is almost correct, with a little adjustment,
although I don't understand your reasoning. In the frame of reference
in which the mothership is currently at rest, a falling object will be
close to c if it is near the event horizon at that time, using that
frame's definition of simultaneity. The velocity we're talking about
here is a relative velocity between the the infalling object at the
time it's about to be at the horizon and the mothership. If we wait a
bit longer on the mothership and then analyze the situation again, from
the new frame of reference, we're still condisering the velocity of the
infalling object at about the same time as before. It hasn't changed.
But we're comparing it to the velocity of the mothership at a later
time. During this time, the mothership has accelerated, increasing the
relative velocity. This relative velocity increases indefinitely, but
never reaches c.

Ho hum.

I still have a few more doubts relating to how the (idealised) winch
line sees all this, but I'll give it a rest for a few weeks.

BR

p.s. thanks to JB and TR for taking this seriously. Sane people do
contribute!