Re: QUESTION - establishment of units of measurement

In article <1139437188.085922.99490@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
BD <bobby_dread@xxxxxxxxxxx> wrote:
Hey, all.

I've been bothered by this for awhile - it's not so much a physics
question, but I think it's relevant to physics.

Many of the principles and 'truths' in physics have been compressed and
summarized with very succinct mathematical equations - best example I
can think of is e=mc^2.

Each variable in this equation is measured in units that the human race
discovered or invented. A metre is a certain measurement of length, a
joule is a certain measurement of energy, a gram is a measurement of
mass (or is it weight? whatever), etc.

But when these units of measurement were discovered/created/invented,
were they not done so 'arbitrarily'? Did some 'council' not agree at
some point that a metre would be 'this long' and a 'joule' would be
'this much energy?

The units are arbitrary. But they must be used consistently to get a
meaningful result. For instance, if mass is in kilograms and speed in
meters per second, then energy will be in joules, which have the units of
kilograms*meters^2/seconds^2.

As you might suspect, the joule is not defined independently of the
kilogram, the meter, or the second. It's basically defined by the
equation for kinetic energy,

K = 1/2 m v^2

If you have a known m that moves at a given v, then that defines the
energy it has. If something can make it go that fast, then it can impart
that much energy to it.

If mass is in pounds and speed is in feet per second, then energy will
have units of pounds*feet^2/second^2.

If there is an independently defined unit of energy, like the greg, then
the equation must be expressed in a form like

E = kmc^2

where k is a factor that converts from joules to gregs, or from whatever
system you're using.
--
"We need to remember that when we are faced with an unstructured problem
it is we who create the model in the form of a quantitative metaphor;
there is no correct model waiting in the wings for us to call onstage." --
Thomas L. Saaty, "Mathematical Methods of Operations Research" (1988)
.

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