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A naïve observational viewpoint doesn't automatically try to correct for signal delays. In other words, the time co-ordinate is retarded.

For example:

In popular expositions of relativity you'll find things like "moving observers see each other's clocks as running slow". If you're lucky it's made clear that "see" is not the everyday, well-understood meaning, but is technical jargon that involves correcting for signal delays. Often this point will be buried, sometimes it is not mentioned at all, and sometimes expositors just get confused on this point. (Even competent ones!)

Anyway, even if it makes it clear that this isn't what you actually see, it won't tell you what you do actually see. This is unfortunate because it doesn't seem like a very esoteric fact to me that oncoming clocks run fast. Is there a good low-level exposition that covers this, and other basic phenomena of special relativity, as they naïvely appear?

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Popular-level writings on science leave out so much! This particular confusion troubled me as a kid in the early 1970s - are we talking about how a moving stick appear, or after we calculate light travel times, and what if there's an index of refraction involved? – DarenW Jan 26 '13 at 3:37
Retarded Potential, you are speaking I think of Doppler effects? The broadcast frequency appears higher (faster) as the object approaches, then lower (slower) as it departs? – Terry Bollinger Jan 26 '13 at 4:08
Language is imperfect, and I'd posit that there is surely no way to perfectly describe relativity---in a way which is both 'low-level' and conceptual, and still technically accurate and detailed. 'see' seems like a perfectly legitimate way of indicating perception. You seem to be confusing two entirely unrelated concepts: that of time dilation (isotropic), and the doppler effect (direction dependent). If the object flashes a light every second (in its frame), the moving observer will quite literally see it running slower from relativistic effects. – DilithiumMatrix Jan 26 '13 at 4:13
Also: Domenico Giulini's paperback Special Relativity: A First Encounter is a nice and very solidly based introduction someone who knows SR and its history very well. He refuses to get sloppy, which I really appreciate. He even acknowledges and dissects the curious case of muons traveling through the atmosphere, which most less well-versed authors refuse even to touch (it's what I would call one of those "proximate" problems). Alas, I don't recall if he specifically addresses the (Doppler?) problem you noted. – Terry Bollinger Jan 26 '13 at 4:17
I notice a striking difference between SR and other disciplines. In an SR introduction writing about uncorrected-for-signal-delay observations will confuse the reader. To keep the introduction clear it must describe only corrected-for-signal-delay data. A good introduction to SR will simply not discuss any uncorrected-for-signal-delay observations. While for other disciplines descriptions of direct observation are useful (either real or thought experiments), for introducing SR they aren't. – Cleonis Jan 26 '13 at 23:08

Way back when I wondered about such things, Hermann Bondi's "Relativity and Common Sense" cleared up most of the confusion. At Amazon

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Thanks for this recommendation, it looks promising. – Retarded Potential Feb 4 '13 at 20:37

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