Hi, Burt.

Thank you for this.

We are talking about two maxims that you proposed, and that I found baffling.

Let me speak of the local observer (the one who is inertial and present at both events) and the distant observer (the one who is inertial and present at neither event).

The first maxim is about comparing the time intervals between the two events, estimated respectively by the local observer and the distant observer.

Your new post translates your first maxim into the customary mathematical formulation in terms of inertial reference frames. That of course clarifies things, but is not necessarily what I was looking for. I was more directed towards the ordinary language mode of expression as it stood.

I think my bafflement is with the heavy burden carried by the word "observe".

I find it obvious that the local observer will have a simple task to report his findings: just log the two event readings on his own clock. No bafflement there, I think.

But for the distant observer, I am left wondering does observing mean his assembling the data supplied by his own remotely stationed research assistants with their synchronised clocks, that is to say reporting the time assessed in the reference frame of the distant observer; or, as in your post Twin paradox images (edited again), does it mean his using data from the local observer's remotely stationed synchronized clocks, that is to say reporting the time assessed in the reference frame of the local observer; or using calculations based on his own telescopic sightings and perhaps radar soundings to measure the speed of motion of the inertial observer's clock, and if so, whether his calculation will estimate times in terms of the reference system of the local or of the distant observer? Your comment "'Observe' obviously means compensating for light travel times" as I read it clarifies things to the extent that it excludes just measuring the time according to the the non-inertial observer's own clock between his telescopic sightings, and perhaps radar reflections, of the inertial observer's clock.

If the distant observer is merely distant from, but stationary with respect to, the local observer, he will measure the same times as the local observer, not less, I think, but this is a physical inference, not a logical identity; as a physical inference it might be questioned. Anyhow, this is a marginal case.

Your new post tells me about the first maxim; it tells me, I think, that you mean that the distant observer is estimating the time between the two events in his own reference frame, by one of the several methods available to him to get that quantity. That makes sense of it. Is that in fact what you mean? Only you know for certain what you mean.

What really had me puzzled was your second maxim "In the twin's case, the traveling twin is the only one present at the turn-around event and hence will observe a smaller outbound time." It seems to me that you somehow saw that as just obvious. But how? Your maxim uses the word "hence" as if to mean that knowing that the traveling twin is the only one present at the turn-around event makes it obvious that he will observe a shorter time interval.

Now I see what you had in mind here. You were using the first maxim. You reasoned that since the away-twin is inertial in the outbound leg, the set-out event and the turn-around event for him are two events such that he is present at both, and such that he is inertial in the interval between them, so that he qualifies as a local observer for the first maxim. Moreover, the home-twin is inertial but not present at both events, and so he qualifies as a distant observer for the first maxim. It follows from the first maxim that the away-twin's measurement of the time interval between the twp events is less than the interval that the home-twin will estimate in his reference frame. The logic here is that since the travelling twin is the only one present at the turn-around event, it follows that the home-twin is not present at both events; meanwhile, of course, the travelling twin is present at both; now it follows therefore that the first maxim applies. This is the hidden logic that I was asking for; no great mystery, but with my mind clouded by the puzzles of the meaning of the word observe, I did not notice it. I was wondering why being the only observer present at an event was so important in this situation; that wasn't exactly what was important, it turns out.

It seems I have tried to turn your neat aphorisms into a long-winded and tedious text. That isn't quite my aim! I am just looking for ways of making such neat aphorisms as clear as practicable to the newcomer. It takes a long-winded discussion to set out the problems of doing it neatly.

The purpose of my neutral observer demonstration is to show that there is some intuitive comon sense content to the longer time recorded by the home-clock: that intuitive content is that the neutral observer sees the home-clock continuing to travel and tick on its first leg long after the away-clock has finished its leg. This is not related to difference in clock rate, nor to difference in speed of movement; the neutral observer was constructed to ensure that. It is due to a longer leg to be run by the home-clock. This strikes me as intuitively reasonable according to common sense, while stories of clocks changing rates do not. Stories of changing clock rates and more especially of time-dilation require to some extent a suspension of common sense: that is why people find these things puzzling. I aimed to reduce that puzzlement.

Regards,

Christopher