From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>
Date: Mon, 16 Sep 1996 13:43:55 -0500 (CDT)
Hi all-
For the reasons that follow, I agree with Mark, who says:
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Well, I'm not convinced. I know the Parable of the Surveyors: the story line
first deals with using different units for the different axes, along with
coordinate systems rotated wrt each other. There are no dimensional issues
here. Then Taylor & Wheeler introduce the idea of Spacetime. Since we are
doing Relativity and now understand that Space and Time are wondrously fused
into Spacetime, we can swallow (maybe uncomfortably) the business of
measuring distances in seconds. The point is that here we have a theoretical
basis for saying that what we thought were two different physical quantities
are aspects of the same one.
Now nobody is saying that torque and work are really the same: it's just a
banal matter of radial vs circumferential distances. The other similar case
that I know of, i.e. angular momentum vs energy x time, as in dimensions of
the Planck constant, has the same origin. Otherwise, there seems to be a
clear relationship between dimensionality and physical quantity. So why
don't we just legislate away this inconsistency, as John Mallinckrodt
suggests, so that I can sleep peacefully?
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What does dimensionality tell us? When we say that torque and
work have the same "dimensionality", what information are we conveying?
In my view, the dimensionality carries information about the
scaling of value. When we say that torque and work have the same
dimensionality (M*L^2/T^2), we mean that the values of torque and work
scale in the same way when we change the units. So if I change from
grams-cm-s to kg-m-hr, then my values of torque and work will each
be multiplied by a factor of .1296.
Regards,
Jack