# The SI Logo

*Intermediate Physics for Medicine and Biology* uses the metric system. On page 1, Russ Hobbie and I write

“The metric system is officially called theSI system(systeme internationale). It used to be called theMKS(meter kilogram second) system.”

In 2018, the International Bureau of Weights and Measures changed how the seven SI base units are defined. They are now based on seven defining constants. This change is summarized in the SI logo.

First let’s see where the seven base units appear in *IPMB*. Then we’ll examine the seven defining constants.

## kilogram

The most basic units of the SI system are so familiar that Russ and I don’t bother defining them. Thekilogram(mass, kg) appears throughoutIPMB, but especially in Chapter 1, where density plays a major role in our analysis of fluid dynamics.

## meter

We define themeter(distance, m) in Chapter 1 when discussing distances and scales: “The basic unit of length in the metric system is the meter (m): about the height of a 3-year-old child.” Both the meter and the kilogram are critical when discussing scaling in Chapter 2.

## second

Thesecond(time, s) is another unit that’s so basic Russ and I take it for granted. It plays a particularly large role in Chapter 10 when discussingnonlinear dynamics.

## ampere

The SI system becomes more complicated when you add electrical units.IPMBdefines theampere(electrical current, A) in Section 6.8 about current andOhm’s law: “The units of the current are C s−1[C is the unit of charge, acoulomb] or amperes (A) (sometimes called amps).”

## kelvin

The unit for absolute temperature-thekelvin(temperature, K)-plays a central role in Chapter 3 ofIPMB, when describingthermodynamics.

## mole

Themole(number of molecules, mol) appears in Chapter 3 when relating microscopic quantities (Boltzmann’s constant, elementary charge) to macroscopic quantities (thegas constant, theFaraday).John Wikswoand I have introduced a name for a mole of differential equations (theleibniz), but the International Bureau of Weights and Measures inexplicably did not add it to their logo.

## candela

Russ and I introduce thecandela(luminous intensity, cd) in Section 14.12 ofIPMB, when comparingradiometrytophotometry: “The number oflumenspersteradianis theluminous intensity, in lm sr−1. The lumen per steradian is also called the candela.” The steradian (the unit ofsolid angle) used to play a more central role in the SI system, but appears to have been demoted.

Now we examine the seven constants that define these units.

## Planck’s constant

InIPMB, the main role ofPlanck’s constant(h, 6.626 × 10−34J s) is to relate the frequency and energy of aphoton.Quantum mechanicsdoesn’t play a major role inIPMB, so Planck’s constant appears less often than you might expect.

## speed of light

Like quantum mechanics,relativitydoes not take center stage inIPMB, so thespeed of light(c, 2.998 × 108m s−1) appears rarely. We use it in Chapter 14 when relating the frequency of light to its wavelength, and in Chapter 17 whenrelating the mass of an elementary particle to its energy.

## cesium hyperfine frequency

Thecesium hyperfine frequency(Δν, 9.192 × 109Hz) defines the second. It never appears inIPMB. Whycesium? Why this particular atomic transition? I don’t know.

## elementary charge

Theelementary charge(e, 1.602 × 10−19C) is used throughoutIPMB, but is particularly important in Chapter 6 aboutbioelectricity.

## Boltzmann’s constant

Boltzmann’s constant(, 1.381 × 10−23J K−1) appears primarily in Chapter 3 ofIPMB, but also anytime Russ and I mention theBoltzmann factor.

## Avogadro’s number

Like Boltzmann’s constant,Avogadro’s number(, 6.022 × 1023mol−1) shows up first in Chapter 3.

## luminous efficacy

Theluminous efficacy(, 683 lm W−1) appears in Chapter 14 ofIPMB: “The ratio /Pat 555 nm is the luminous efficacy forphotopic vision, = 683 lm W−1.” I find this constant to be different from all the others. It’s aprime numberspecified to only three digits. Suppose a society of intelligent beings evolved on another planet. Their physicists would probably measure a set of constants similar to ours, and once we figured out how to convert units we would get the same values for six of the constants. The luminous efficacy, however, would depend on the physiology of their eyes (assuming they even have eyes). Perhaps I make too much about this. Perhaps the luminous efficacy merely defines the candela, just as Avogardo’s number defines the mole and Boltzmann’s constant defines the kelvin. Still, to me it has a different feel.

You can learn more about the SI units and constants in the International Bureau of Weights and Measures’ SI brochure. I’m fond of the SI logo, which reminds me of the circle of fifths. If you’re new to the metric systems, you might want to paste the logo into your copy of *Intermediate Physics for Medicine and Biology*; I suggest placing it in the white space on page 1, just above Table 1.1.

*Originally published at **http://hobbieroth.blogspot.com**.*