Key Points in Mechanics
- The Key point should be determined by a wise judgment.
In [Hall, p.679], Halliday makes a careful comparison among three cases [(38-22), (38-23) & (38-24)]. However, Halliday
says the lack of the ether concept in relativity is the reason why [Hall, (38-24)]
looks different from [Hall, (38-22) & (38-23)]. In my opinion, the ether concept
is a related factor, but is not the key factor. Factors should be ordered based
on their priority. The main reason why [Hall,
(38-24)] depends solely on the relative velocity is c + v [where v is the velocity of the
light source] = c.
When we quote a theorem to validate a statement, we do not quote
it more than necessary. That is, we must pinpoint the exact part of the theorem
that makes the statement valid. We have to trace the reason all the way instead of half-way back to its root.
Suppose we want to prove the second equality of [Matv, p.136, (17.5)]. We can
prove the equality by [Wangs, p.406, (25-4)] or by [Wangs, p.408, (25-16)]. I
prefer the former method because it is more to the point.
- Too much detail often blurs the key point.
For the proof of [Matv, (2.54), (2.55) and (2.56)], we can
clearly see the key point in [Fur, p.46, l.-2-p.47,
l.14], but not in [Wangs, p.380, l.-15-p.381, l.19] or
[Born, p.23, l.9-l.-3].
Remark. However, Born's proof has its advantage: it applies to the general
(not necessarily harmonic) electromagnetic plane waves.