Re: can someone explain the candela a little?

in article d317a4$t36$1@xxxxxxxxxxxxxxx, Ralph Hartley at
hartley@xxxxxxxxxxxxxxxx wrote on 04/06/2005 22:41:

> robert bristow-johnson wrote:
>> for instance the dimension of force is mass x length / time^2 because we
>> don't look at the concept of force as anything other than the
>> time-derivative of momentum.
> ..
>> it isn't like that the concept of force
>> existed independently in nature without time or length or mass, so we could
>> and did define force solely and naturally in terms of time, length, and
>> mass.
>
> Not a good example.

that may very well be the case. i tried to hedge my bets by introducing the
fictional unit of force, the "farg", but i could have said "pound" i guess.

> The concept of force existed for thousands of years independent of time,
> length, and mass. (I don't know what you mean by a *concept* existing
> "in nature")

the concept i meant was the that of [the physical quantity of force existing
independently in nature outside of the quantities of time, length or
distance, and mass]. a problem of parsing sentences i didn't anticipate.

> The relationship is a rather recent discovery.
>
> Archimedes knew quite a bit about force, but I doubt he used units of
> mass*length/time^2 (not "solely" nor "naturally" nor at all). Naturally
> he used the same units as mass, a practice that survives to this day.
>
> The natural relationship between force and mass in normal life is that
> determined by gravity (on earth).
>
> Produce (in the US) is *still* sold by the pound.

this is fine and good. i was more interested in fundamental physical
measure, not so much in human practice which is more of an anthropological
issue. i just didn't understand where the candela came into this.

> The pound originated
> as a unit of mass. It was later converted into a unit of force. At least
> that's what the textbooks say. It is used far more as a unit of mass. No
> one *ever* uses the "slug".

we did when i took a civil engineering class in the seventies. though soon
we learned to express masses (in the English system) as
(whatever lbs)/(32.174 ft/sec^2). that would be the mass in slugs. i guess
when the numerator was a "pound force" (lbf), that would be a mass of one
"pound mass" (lbm).

> The Newton is better known, but it's use requires knowing a (non power
> of ten) constant in a system that otherwise lacks them. That's is one of
> the (few) advantages of the "English" system: a pound of something
> weighs one pound. A Kilo weighs 9.?? Newtons, I'd have to look it up.
>
> Force measuring devices are *still* the dominant means of measuring mass.

i agree. they depend on g and the spring constant or some kind of measure
of tension.

> Of course we are now so aware of the relationship between force, mass,
> length, and time, that it is hard to imagine anyone *not* knowing.

my poorly exampled point was that, in a closed system there is no net force.
inside when we observe that one body is exerting force on another, what is
really happening is that some quantity of momentum is being transferred from
one body to the other. this concept of "force" is just a measure of the
rate in time of that transfer of momentum. we can just call that time rate
of transfer what it is, we need not introduce a different unit for that rate
along with a conversion factor in Newton's 2nd law.

the fact that there may have existed the concept, in the human experience,
of "force" before Newton, is similar to the fact that humans experienced the
concept of heat before connecting it to kinetic energy of the molecules of
matter. just as we can define a natural unit of force to get rid of any
constant in Newton's 2nd law (because a Newton is nothing more than a
kg m/s^2), we can define a natural unit of temperature to get rid of the
Boltzmann constant because a degree of temperature is nothing more than a
measure of energy per particle.

in the CGS system, the do the same thing, define the unit charge naturally
to get rid of the Coulomb force constant, 1/(4 pi epsilon_0), but i still,
frankly, just cannot fathom a quantity of electromagnetic charge being the
*same* as [velocity x (length x mass)^(1/2)]. it is still, in my mind, some
other "stuff" that exists in or is a property of some subatomic particles
that has a physics of its own. i'm not saying that we can't define a
natural unit for it (similarly to how they do it now), but just because we
can, does not mean it is the same thing as [sqrt(length mass) x velocity].
we can also define natural units for length, time, and mass (the Planck
units that gets rid of c, G, and hbar), but i would say as a result that
reciprocal of length is the same as the reciprocal of time which is the same
as energy which is the same as mass, just that there is a proportional
relationship between these quantities and we can make those constants of
proportionality go away with judicious choice of units.

> But we now also know the relationship between length and time as well.
> If you follow your argument to its logical conclusion, you *must*
> advocate the elimination of the meter as well.

i actually do not, but have had debates with those who do. the big
difference between the two is that the speed of propagation of E&M (and
gravity) is a little more universal than the acceleration of gravity on this
particular planet.

> It is, after all,
> proportional to the second, not a "different kind of stuff" at all.

i actually think that time *is* different kind of "stuff" than length. two
things are identical if all of their corresponding properties are identical.
i understand what we mean by this "arrow of time" and it seems to be
everywhere. but outside of the event horizon of a black hole, i don't think
there is an "arrow of space". so there appears to be at least one
qualitative difference between these two kinds of "stuff". but, if energy
and mass can be interchanged at will (with the conversion factor of c^2),
that sorta suggests that they come from the same well and be different
manifestations of the same "stuff". the Einstein Eq of GR deals with not
just mass density, but with mass+energy density as if they are the same
stuff. so maybe, ultimately c *is* merely a conversion factor and length
and time are the same thing. i dunno.



anyway, my main point (and question) about this was that it seems to make
some sense (although its basis is more anthropocentric than physically
"natural") for the SI system to define base units for length, mass, time,
and electric current (which defines charge) because they are all different
kinds of physical "stuff", and i can see why the Kelvin and mole got in
there. if they simply declared Advogadro's number to be a defined constant
of exactly 6.0221415 x 10^23 , then they couldn't continue to define a mole
as whatever it takes to get exactly 12 grams of carbon 12, and i think that
the latter standard makes the chemists more happy. they can define a
quantity of molecules by weight, rather than try to count them. and the
Kelvin is, of course defined as the temperature difference between boiling
and freezing water (and that is rather anthropocentric, but useful to us
humans). but neither the mole nor the Kelvin are defined units of some
physically unique quantity.

but i can see why they're in the SI base units. at least they describe
something that is purely physical. that is not so for the candela. the
candela has a place in the art and practice of photometry (as "gp" has
pointed out) and in the literature and textbooks of photometry or lighting
design and engineering, it has a place for being defined and used, just as
the dB of perceived loudness does in acoustics, but it isn't purely physics
and, once i understood what it was, i concluded that, even more so over the
mole and the Kelvin, it should not be the base unit of any system of
physical units.

most fundamentally, i think there is only 4 different independent dimensions
of physical "stuff" that need to have base units defined in any general
system of units and that is again: length, time, mass, and electromagnetic
charge. everything else can be derived from those *and* if you want purely
natural definitions of those base units, you choose them to get rid of c,
hbar, G (i think normalizing 4*pi*G would be more natural), and epsilon_0 (i
think that is more natural than normalizing the Coulomb constant). that
would get you the Planck units.

--

r b-j rbj@xxxxxxxxxxxxxxxxxxxx

"Imagination is more important than knowledge."


.

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