Re: [boost] Re: Physical quantities

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.

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