Re: Just what's in a unit...
- From: Darwin123 <drosen0000@xxxxxxxxx>
- Date: Sat, 29 Nov 2008 22:17:11 -0800 (PST)
On Nov 29, 8:15 pm, Edward Green <spamspamsp...@xxxxxxxxxxx> wrote:
Please do not direct me to the Wiki page on "units". I know what aOperationally? It means the energy output in joules divided by
"unit" is.
I merely want to launch a musing which questions whether the clear cut
distinction between "numbers with units" (or "dimensions") and
"dimensionless numbers" is so clear cut.
For example: the ratio of two powers is independent of whether the
power is expressed in watts or horsepower. So this is a
"dimensionless number". Presumably, a particular power when expressed
in watts is not. But what does it mean (no puns, please) to express
power in watts?
the time of output in seconds is equal to that number. There does not
have to be a reference "watt" at all. In fact, the power standard is
has never to my knowledge been kept by any National Bureau of
Standards. The ratios are in terms of different quantities, not a
ratio of something with the power standard.
It means to form the ratio of a given power to aOperationally, one can't do that. This is because two power
fixed reference power called a "watt".
sources running for different periods of time can come up with
different energies, and yet have the same "power." Therefore, one
usually has energy standards and time standards but no power
standards. Power is not considered a fundamental property. How would I
be able to measure "power" anyway?
I can measure current with an ammeter, energy with a bomb
calorimeter (including a thermometer), and charge with a pendulum
coulometer. All these provide direct measurements with what could be a
standard. However, I can't take two engines of known "power" and
directly compare them.
The only clear differenceAs I said, power is a poor example because it is the ratio of
between case #1 and case #2 is that in case #1 we imagine the
denominator of the ratio to be some _arbitrary_ arbitrary quantity,
whereas in case #2 we imagine it to be some _fixed_ arbitrary
quantity.
other quantities that are subject to more direct measurements. You may
say that energy and time are more "fundamental" than power, but there
is some philosophical ambiguity in the term "fundamental." However, in
terms of physical engineering the difference is significant. "Power"
standards are rather poor.
Note: When one is choosing a light bulb supposedly one is
choosing a "power." But it turns out the actual measurements is by
multiplying the current, measured by an ammeter, by the voltage,
measured by a voltmeter. Measuring the actual "power" output is
important but involves less direct measurements.
I would say that the word "watt" is not a fundamental unit. So
So, I claim puckishly, a figure like "10 watts" has just as much claim
to be a dimensionless ratio as any other dimensionless ratios; the
"watts" is just to remind us of the absolute size of the denominator!
in a sense you are correct. What should be stated is the joules per
second. Because that phrase contains all the quantities that are
directly measurable. Or maybe one should call it "volt-amps" or "amp-
volts." Note: when choosing a UPS to protect your computer those are
the units used. Watts means something very specific which turns out to
be irrelevant.
Such thinking makes itself visible in radio conventions. What couldActually, my favorite non-unit is the radian. Followed by the
be more "dimensionless" than a decibel?
neper. Neper is similar to decibel, only in base e.
I am fascinated by units, too. I have thought about it, and I
think there are actually two classes of units. Once class is the
linear units, like joules per second. Watt is really just a
contraction of joules per second.
The other type of unit is logarithmic units. Decibel is a
logarithmic unit. It is the base 10 logarithm of watts (times a
factor). However, believe it or not, radian is also a logarithmic
unit. The radian is the logarithm of a complex number, divided by
i=sqrt(-1). Radians and nepers are merely real and imaginary
components of the same neparian logarithm. One can interchange
logarithmic units in different bases merely by conversion factors.
Watt?
.
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