Bruce Feist wrote:
> I'm coming into this conversation late; please forgive me if I'm saying
> something that's irrelevant or obvious to everyone. (I did check older
> messages, but only a dozen or so.) Also, I might be being somewhat
> innacurate -- my comment is based on what I remember from learning
> metric in the 1970s.
> The link for a meter, or rather a centimeter, is mathematical rather
> than physical: a cubic centimeter is a milliliter. I don't know how
> this relates to the redefinitions -- do they implicitly redefine a
> liter? What's the dependency -- is a milliliter based on a centimeter,
> and a gram on a milliliter, or is it reversed, or neither?
Dotan Cohen wrote:
> Whoever taught you that is trying to confuse you. A cubic centimeter
> measures volume. A milimeter measures length. So the two are not
> interchangeable. One centimeter is 10 milimeters. Therefore one cubuc
> centimeter is 10^3 = 1000 cubic milimeters.
Bruce never actually mentioned millimetres, just millilitres...
Millilitres, of course, *do* measure volume and *are* effectively
interchangeable with cubic centimetres.
My understanding...
A metre is a fundamental unit, currently defined as the distance light
will travel (in a vacuum) in 1/299 792 458 seconds. A litre is a derived
unit -- it can be expressed in terms of metres (one litre is one cubic
decimetre or 0.001 m³), and this is how a litre is defined. So if the
metre changes slightly, then the litre changes to match.
A kilogram is *not* a derived unit -- the old "one litre of water has a
mass of one kilogram" definition involves physical items (water), and a
laboratory experiment to decide quite how heavy a kilogram is. So a
kilogram is also considered a fundamental unit, currently defined in
terms of a "reference kilogram" held near Paris.
So a litre of water will have the mass of about one kilogram, but this
is not a fundamental relationship.
The old "one litre of water has a mass of one kilogram" definition is no
longer used because the density of water changes with temperature and
pressure. Temperature can be handled, but the unit of pressure (the
Pascal) is defined as 1 kg m⁻¹ s⁻²[1], so you need to know what a
kilogram is to check that you are at standard pressure so you can be
sure that your litre of water is 1 kg.
James.
[1] If you have a *really* good Unicode font, you'll be able to read
that. Otherwise it's 1 kg / m /s^2
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