I quote from exercise R1S.2 in Moore's _Six Ideas_
relativity book:
Imagine that Frames R Us, Inc., is constructing an
economy reference frame whose price will be below
every other frame on the market. Placing a clock at
every point in the frame lattice is too expensive,
so the company decides to place /one/ clock at the
origin. At all other positions, the company simply
places a flag that springs up when an object goes by.
The flag has the lattice location printed on it, so an
observer sitting at the origin can assign spacetime
coordinates to every event by noting /when/ he or she
sees the flag spring up (according to the clock at the
origin). Why /doesn't/ this method yield the same
spacetime coordinates as having a clock at every
location would? Pinpoint the /assumption/ that the
Frames R Us engineers are making that is incorrect.
So ... a student comes to me and objects to the premise
of the question. The engineers are "assuming" that the
observer is not stupid, and will therefore apply the
obvious propagation-time corrections. Are we going to
assume that temperature does not exist, because the
observer is too stupid to apply emergent-stem corrections
when using a thermometer? Are we going to assume that
mass does not exist, because the observer is too stupid
to apply buoyancy corrections when weighing things? Are
we going to assume that pressure does not exist, because
the observer is too stupid to correct for parallax when
reading the needle on the pressure gauge?
Speaking for myself now, I think the student has a point.
Propagation delay is not an issue of principle. It's not
even a relativity issue. Seismologists routinely infer
the time of far-away events by applying corrections for
the speed of /sound/. They don't need a clock sitting
at the event. Correcting for the speed of light is no
different.
My policy is to assume that astronomers are not stupid.
Indeed, Ole Rømer was so confident of his ability to apply
propagation-time corrections that he used the idea in
reverse to obtain a decent estimate of the speed of light
... back in 1676.
Furthermore, even if you bought the "deluxe" frame with
clocks everywhere, you would still need to synchronize
the clocks, which would require applying exactly the same
sort of propagation-time corrections. So if the cheapskate
frame is "wrong" the expensive frame is "wrong" also.
As I see it, propagation delay is not a special relativity
issue. It's a pre-high-school physics issue: Distance
equals rate times time.
===================================
There remains the possibility that there is something /else/
wrong with the cheapskate frame ... but I'm not seeing it.
So, I leave it as a question: Is there chance that R1S.2
makes sense, as it stands? Is there really a relativity
issue here? What am I not seeing?
(I can think of lots of ways of repairing it,
but now we're talking about a different question.)