I've been watching this thread from the sidelines, and I must admit I find
it frustrating, as I find threads on several other recurrent subjects,
which I could list:
1. The definition of the radian and its dimensions and units.
2. Centripetal and centrifugal force.
3. The tides.
4. Lift on an airplane wing.
Why frustrating? Because in each of these, there's no "problem" to be
discussed, for the subjects have been thoroughly thrashed into submission
previously, but too many haven't bothered to seek out the primary
literature on the subject, preferring to reinvent the wheel in their own
way. Too often that results in square wheels.
In the case at hand, "dimensions and units", the subject has been
standardized and codified decades ago, and in fact represents a subfield
of physics/engineering which, apparently, few physicists have bothered to
study. Some participants of this thread seem not to have read anything
authoritative on the subject, beyond elementary texts (whose treatments
are shoddy, misleading, and often wrong, indicating that many textbook
writers haven't "read up" on the subject either). I can understand that,
for it is not an interesting subject. Once you grasp it, and realize that
it is a reasonable organizing system, with no problems worth bothering
about, the working physicist proceeds to ignore the literature on the
subject.
There are good textbooks on the subject. But as I have given away much of
my library far and wide prior to retirement, only one book on that subject
remains, purely by accident: A. G. Chertov, _Units of Measurement of
Physical Quantities_, Hayden, 1964. Chapter 1, sections 1 and 2 treat
dimensions, and, if read, would end this thread immediately. I would
convert those sections to e-text and put it here if I had the time, but I
won't get that kind of time till after Jan 1.
I did a web search on this subject and found a few pathetic documents,
mostly contradictory. No help to you there.
A readily available reference I found which you could consult is the long
entry on Dimensional Analysis by John W. Stewart (U. of Virginia) in "The
McGraw-Hill Encyclopedia of Physics," Second edition, 1993. This, or
better, its larger form, "The McGraw-Hill Encyclopedia of Science" ought
to be in any college or university library.
Stewart's References are:
H. A. Becker, _Dimensioness Parameters: Theory and Methodology_, 1976.
P. W. Bridgman, _Dimensional Analysis_, 1931, reprint 1976.
H. I. Langhaar, _Dimensional Analysis and Theory of Models_, 1951, reprint
1980.
C. I. Staicu, _Restricted and General Dimensional Analysis_, 1982.
As you can see, this subject has been around a while. Surely a search of
AJP archives would yield something, but I do not have these journals
readily available.
I would modestly suggest that anyone who has not yet read any of these, or
something equally authoritative, refrain from pontificating on the matter
until they have. I shall take my own advice and refrain until at least Jan
1.
-- Donald
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Dr. Donald E. Simanek
dsimanek@eagle.lhup.edu http://www.lhup.edu/~dsimanek
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