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From: Kevin Lynch (krlynch_at_[hidden])
Date: 2004-01-09 15:54:29

Phil Richards wrote:
> I *know* that I need user-defined units (many of which will be
> dimensionless standard 7 dimension world), but I honestly can't see any
> case where I would need to define a different set of dimensions (assuming
> I've already got the base 7). I can (tentatively) see a possibility for
> extending the 7, but not replacing them.

SI is nearly worthless to me, beginning straightaway with the
declaration that there are seven fundamental dimensions. But then, I'm
a particle physicist, so I'm a bit wierd :-) Way too many...

But even if there are, there is no compelling reason, other than the SI,
to assume that the seven the SI chose are the correct seven....
Particle physics, astrophysics, and cosmology are better served by using
systems of units where not only are there fewer dimensions, but the ones
we keep around are different. And while the SI has too many dimensions
for some fields, there are issues that it chooses to leave out that
other domains need.

Here are three morsels of thought-food on this issue:

1) Seven is just right: Assume for a minute that you do need seven
dimensions for your system of units. For the first three, you choose
mass, length, and time. I choose mass, time, and energy. Entirely
equivalent. Ditto the choice between charge or current or even force.
Doesn't matter which you call fundamental. I may have darn good reasons
to change them in a particular domain.

2) Seven is not enough: I may deal with, say, units of currency for a
living, so I would want to add a currency dimension. It isn't the same
thing as an "amount of substance", as you don't want "price per bushel
of wheat" to be dimensionless.....

3) From a fundamental physics standpoint, length and time are "the same
thing", in a rigorous sense, since special relativity relates them, and
in many applications to particle physics, you would want them to have
the same dimensionality, because they do. Ditto mass and energy ...
energy is no longer a derived unit, but has the same fundamental
dimension as mass. And it happens to have the same units as inverse
length..... so this case also shows that different physical dimensions
can have the same units in certain problem domains.

Kevin Lynch				voice:	(617) 353-6025
Physics Department			Fax: (617) 353-9393
Boston University			office:	 PRB-361
590 Commonwealth Ave.			e-mail:	 krlynch_at_[hidden]
Boston, MA 02215 USA

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