### 490 billion nanometers tall

Scales have been on my mind a lot lately—and not just because I have to fit into a wedding dress in 6 weeks.

A few days ago I came across this great line in a story about Louisiana State University’s participation in a NanoDays event,

Will Heitman, a 9-year-old student at Bernard Terrace Elementary, discovered at the event he was 490 billion nanometers tall. [I get the point, but does that number seem a little off to anyone else?!]

And I recently heard this illustration in the context of the national debt,

The height of a stack of 1,000,000,000,000 (one trillion) one dollar bills measures 67,866 miles. This would reach more than one fourth the way from the earth to the moon.

I remember grumbling about losing points for missing units when I was in Physics I. Even more vividly, I remember grumbling about how my Physics I students would leave off their units when I was a TA.

Sure, we all know units are necessary and that you might run into some *minor* resistance if you were to measure out a marathon course in kilometers instead of miles. Some of the runners might not be prepared for an extra 16 miles…

But where do units come from, and who determines them?

This was (partially) the subject of a recent talk by Neil Zimmerman from the National Institute of Standards and Technology (NIST). The talk centered on a NIST experiment to measure whether the charge of an electron (I’m being loose with my language here) inside of a metal is the same as that of a single electron in free space. This, all with the goal of a capacitance standard based on the charge of the electron. There were many subtleties to the talk, for that I will refer you to one of his papers, but I was particularly fascinated by his discussion of the origin of the International System of Units, or more commonly, SI units.

There are seven SI base units: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd). The other SI units are derived from these seven: acceleration is m/s^2, density is kg/m^3, magnetic field strength is A/m, etc.

According to the International Bureau of Weights and Measures (BIPM), the keeper of the units, the SI is "a living system which evolves, and which reflects current best measurement practice."

Here is a quick rundown of the basis for the SI base units, as defined by the governing body, the General Conference on Weights and Measures.

Second--the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. (And, in case you were wondering,it's a cesium atom in its ground state at 0 Kelvin.)

Kilogram--A 1901 platinum-iridium cylinder. Okay, those were my words. But seriously it is.

Ampere--that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.

So we move from a lump of platinum-iridium to infinitely long conductors with no cross section. Such is physics.

Kelvin--the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Mole--the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12.

Candela--the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Meter--the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

Some of these may seem rather obscure, but remember that the system is continually evolving as measurements get more precise. For example, the second was originally defined as 1/86,400 of the mean solar day, but "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom" is more reliable.

So my point (in case you are wondering), is that the aggravating SI units all physics students are forced to learn has a rich history and a potentially rich future. Who knows what Will and his generation will uncover. Maybe in 20 years we will need a whole new standard for something yet undiscovered. But, as for the moment, I'm delighted to know that I am roughly 1,701,800,000 nanometers tall.

Images:
Hundred Dollar Bill Wallet, Amazon.
A replica of the real kg, NIST.

1. The one I wish we could change as an 'SI base unit' is the Ampere. Charge seems to be a much more logical fundamental unit than current.

2. A few too many significant digits for your height, don't you think? Especially since it's exactly 5'7'' :P.
I'm sure some elementary school student out there actually thinks that Europeans grow in exact increments of cm and Americans in exact increments of inches

@Tometheus Candela also confuses me, I guess people had to make a compromise between the physical concepts and the engineering demands.

From a physical point of view, one can argue that meter and second shouldn't be independent, and even the definition of meter implies that.

3. As for meter and second not being independent, there are physicists who work in units such that length, mass, and time are the only fundamentals. Even charge can be expressed in terms of those three. You can reduce it further and use just one (usually energy---I'm about 110 nano-eV tall and weigh 4.5x10^25 TeV). But that's not SI.

4. Sorry, but I can't imagine 9 years old child to be 490 bln nm tall.
1 bln = 10^9, nm = 10^(-9) m
490 x 10^9 nm = 490 x 10^9 x 10^(-9) m = 490 m !
And this is not even problem with the order of magnitude. Children 9 years old are expected to be 1-1.5 m tall, and definitely not 0.49 or 4.9 m tall. Maybe he was 4.9 ft tall?

Conclusion:
I don't really think it will be now possible to make Soyuz-Apollo program successful.

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6. Anonymous 1: You caught me on the sig figs. I bet you did well in chemistry too...

Anonymous 2, I bet you're right about them meaning 4.9 ft. I've been wondering where they went wrong since I saw the number!

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