Re: QUESTION - establishment of units of measurement
- From: "PD" <TheDraperFamily@xxxxxxxxx>
- Date: 9 Feb 2006 10:36:17 -0800
BD 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?
Is it not _extremely_ serendipitous (or even unlikely) that a
mathematical equation such as e=mc^2 could actually 'work', given how
the units of measurement used therein originated? It strikes me as
incredibly lucky that all the units of measurement we use here could
fit together so 'cleanly' unless there was something - dare I say -
unified about their acceptance.
Or maybe 'metres' and 'joules' weren't arbitrary in their origins...
Any comments? Is there something obvious about all this that nullifies
my question? In a way, I hope there is... ;)
There is, but it's not obvious.
When you introduce conventions for the sizes of some units, there are
some constraints and in other cases no constraint was imposed. Where
you don't have constraints, a conversion constant is introduced. A
conversion constant is merely a number that connects two unconstrained
set of units.
As an example of a constrained set, a joule is *defined* so that
1 joule = 1 kilogram * (1 meter)^2 / (1 second)^2.
That is, there was a well-recognized connection between energy on the
left and the quantities on the right, and so the unit was *chosen* so
that the conversion factor was simple (1).
As an example of an unconstrained set, consider length and time. For
ages and ages, we thought the two were not connected and so the units
were not constrained to each other. We know now that this is not the
case. There is therefore a *conversion* factor, c, that converts our
units of time to units of units of distance and vice versa.
1 meter = (c) * 1 second
Another example is the unconstrained units for gravitational force and
mass. We know now (actually, since Newton) that there is a connection
and so there is a conversion factor, G, that stitches those units
together:
1 newton = (G) * (1 kilogram)^2 / (1 meter)^2.
It is perfectly acceptable to choose a different set of units so that
most, if not all, of these conversion factors disappear -- these are
often called "natural units". They are unfamiliar units for the
beginning student but the laws of physics are essentially the same
except for the absence of a lot of those extraneous conversion factors
like c.
PD
.
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