# Should luminous intensity be a fundamental unit?

#### swampwiz

It seems to me that luminous intensity should really be put in terms of energy, not a special unit (which itself is based on some arbitrary specification of energy.) The other 5 units and Avogadro's number should be the only fundamental units.

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#### rbj

i would say that if you want to get really fundamental, then it's just time, length, mass, and electric charge. everything else gets derived from those four. including temperature.

but systems of units (like the SI) exist for human convenience, not just as fundamental physical quantity.

#### swampwiz

i would say that if you want to get really fundamental, then it's just time, length, mass, and electric charge. everything else gets derived from those four. including temperature.

but systems of units (like the SI) exist for human convenience, not just as fundamental physical quantity.
I had thought of that, but since there is the abstraction of temperature that is necessary for the 2nd law of thermodynamics - as well as for dealing with the plethora of activity that causes heat flow (i.e., kinetics of molecules, quantum mechanics, etc.) - temperature is an extraordinarily useful abstraction. I just don't see how luminous intensity is all that useful as the abstraction is very simple.

#### Jasso

It is often convenient to make calculations based on intensity instead of temperature. In fact, most non-contact devices which measure temperature first measure intensity and then do a calculation.

And a fundamental unit is one which can only be measured, not derived from another. As rbj said, the only true fundamental units are time, length, mass, and charge; if a unit can be stated in terms of those four, then it is not fundamental.

#### rbj

I had thought of that, but since there is the abstraction of temperature that is necessary for the 2nd law of thermodynamics - as well as for dealing with the plethora of activity that causes heat flow (i.e., kinetics of molecules, quantum mechanics, etc.)
this is about parameters of a bunch of elementary particles and of specific compounds of stuff. what is the fundamental reason to base a unit definition on that?

- temperature is an extraordinarily useful abstraction.
temperature is another way of saying "energy". the only meaning $k_B$ has is to define what your unit of temperature is. $k_B$ can be anything, as long as it's real, positive, and finite.

I just don't see how luminous intensity is all that useful as the abstraction is very simple.
it isn't. it's superfluous. just as $N_A$ and $k_B$ are (or, more fundamentally, the kelvin and the mole).

It is often convenient to make calculations based on intensity instead of temperature. In fact, most non-contact devices which measure temperature first measure intensity and then do a calculation.

And a fundamental unit is one which can only be measured, not derived from another.
well, the mole is measured in a sense. $N_A$ is not known exactly, unless they redefine what a mole is (and they might very well do that within a decade, maybe not). but i am convinced that the mole is a superfluous unit because what it really reflects is a parameter of the 12C atom.

it was defined when it was for SI for the convenience of chemists. it is not a fundamental unit.

As rbj said, the only true fundamental units are time, length, mass, and charge; if a unit can be stated in terms of those four, then it is not fundamental.
i believe that. as dimensions of physical stuff, i think that time and length and mass are different stuff. but the electrostatic cgs system and i disagree about how fundamental electric charge is. i think it is totally different stuff than the other three base dimensions. but a statcoulomb is derived and equivalent to $\sqrt{\frac{L^3 M}{T^2}}$. essentially, it defines the Coulomb constant $\frac{1}{4 \pi \epsilon_0}$ to be the dimensionless 1.

but that can also be done to $G$, $\hbar$, $c$, and $k_B$ and then you would have Planck units. so maybe no fundamental dimensions of physical stuff exist and it's all just pure numbers in physical reality.

but i like to think of time, length, mass, and charge as fundamental and that $4 \pi G$, $\hbar$, $c$, and $\epsilon_0$ (who gives a rat's @ss about $k_B$?) are all 1 (rationalized Planck units). makes it kinda hard to develop a varying-G or VSL cosmology, if you think it's operationally meaningless that they vary (the only parameters that matter are dimensionless).

#### swampwiz

I will add that Avagadro's number is not really a unit, and is really the mass equivalent of the parameter of the electron charge - i.e., it relates a quantum unit of mass or electrical charge to the standard units of kilogram & coulomb. But it is very important for chemistry and gas thermodynamics.

So I guess there should be 5 fundamental units and Avagadro's number for a lot of uses, and the electron charge for particle/quantum physics. It is interesting that the folks who developed the Planck units share my view on this.

#### Andy Resnick

Science Advisor
Education Advisor
It seems to me that luminous intensity should really be put in terms of energy, not a special unit (which itself is based on some arbitrary specification of energy.) The other 5 units and Avogadro's number should be the only fundamental units.
Luminous intensity *is* a 'base unit' (the candela), while energy is a derived unit:

http://physics.nist.gov/cuu/Units/units.html

#### Dickfore

It seems to me that luminous intensity should really be put in terms of energy, not a special unit (which itself is based on some arbitrary specification of energy.) The other 5 units and Avogadro's number should be the only fundamental units.
But, then, you end up with a contradiction, since energy and power are derived units in SI.

EDIT:
Oh, I see. You want to get rid of it from the list of fundamental physical quantities altogether.

If you notice, this quantity enters solely in the field of subjective photometry, and nowhere else, similarly to "quantity of chemical substance" (it really is the same as number of particles) which finds limited application in chemistry.

Indeed, Avogadro's constant plays the role of a conversion factor between the true number of particles and the number of moles.

Similarly, you may derive a conversion factor between a candella and watts per steradian. However, since, unlike quantity of chemical substance, which is defined through mass, luminous intensity is defined through the energy flux. Therefore, this conversion factor is incoropated in the definition.

A similar situation occurs with the kelvin and the ampere, where the conversion factors are Boltzmann's constant, and the permeability of free space.

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#### Rap

Avogadro's number is not fundamental. The atomic mass unit (AMU) could be taken as a fundamental unit of mass. Then you have the kilogram, originally defined as the mass of a thousandth of a cubic meter of water. Water is rather fundamental, but now you have the meter, originally defined as one ten thousandth of the distance from the equator to the north pole of some random planet in the universe called Earth. So Avogadro's number is defined roughly as the number of water molecules in a box that is one one hundred thousandth of the distance from the equator to the north pole of some random planet in the universe called Earth. Not very fundamental. If the metric system had never been invented, and we were using the English system, then Avogadro's number would be the number of AMU's in a pound-mass (slug). The pound was originally defined as the weight of 9600 grains of wheat. So Avogadro's number would be roughly the number of AMU's in an elementary substance that had the same mass as 9600 seeds of some plant growing on some random planet in the universe named Earth. Again, not very fundamental.

Luminous intensity is based on averages of the measured response of the eyes of a bunch of people who served as test subjects. So the candela is based on the response of the photoreceptors of a bunch of homo sapiens living on some random planet in the universe named Earth. Not very fundamental

Temperature is a way of measuring energy, originally by chopping up the temperature scale defined by, I don't know, mercury, or some rarified, practically ideal gas, using freezing and boiling water as the endpoints, into 100 parts (centigrade), or the freezing point of salt water and boiling water into 212 parts (Fahrenheit). That's somewhat fundamental. Boltzmann's constant is the ratio of the energy represented by temperature to the kinetic energy of one kilogram travelling at one meter per second. We already know about the fundamental-ness of the kilogram and the meter. The second was originally defined as one 1/864,400 of the length of the day, which is the average time for some random planet in the universe to make a rotation which brings the star which it is rotating about into the same angular position. So Boltzmann's constant is not very fundamental. Consider the definition of the Boltzmann constant if we were using English units. Consider what a bunch of aliens living on a jupiter-size planet practically covered with liquid methane instead of water would define Boltzmann's constant to be.

Subsequent refinements of the Earth-centric meter, kilogram, and second are for the sake of stability, they do not stray far from their original definition. The mean distance from the equator to the north pole is now measured at 10,001.965 meters - the fact that it is within 0.02 percent of 10,000 is no coincidence. 9600 grains of wheat weigh about a pound - no coincidence. 1 cc of water weighs about a gram - no coincidence.

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