Mother Nature’s Units & The Metric System

It is generally underappreciated in the history of science that many new scientific discoveries and theories have been realized from the study of engineering problems. Lord Kelvin (1824-1907) famously understood this when he stated:

The steam engine has done much more for science than science has done for the steam engine.

In the early 1900s, the light bulb was of great importance, but as Sven has said to me: “a light bulb is a heater that produces light as a byproduct.” German industry and the German government wanted a light bulb that would more efficiently produce light from the amount of electricity it dissipated. Max Planck (1858-1947), a physicist, was tasked with looking into black-body radiation. Classical physics expected that higher frequencies would be produced by black-bodies, and an infinite amount of energy could be generated. This was known as the Ultraviolet Catastrophe. Clearly it didn’t happen, but why?

Planck made an assumption that electromagnetic radiation (light) could only be absorbed or emitted in discreet packets of energy, called quanta. The energy of these quanta were directly proportional to the wavelength of the electromagnetic radiation. He introduced a proportionality constant h to related the energy E in each quanta, and its frequency v. E(quanta) = hv. The constant h is now appropriately known as Planck’s constant.

Planck noted in his 1899 paper that:

… it is possible to set up units for length, mass, time and temperature, which are independent of special bodies or substances, necessarily retaining their meaning for all times and for all civilizations, including extraterrestrial and non-human ones, which can be called “natural units of measure”.

Wikipedia gives the original values put forward by Planck as:

NameDimensionExpressionValue (SI units)
Planck lengthlength (L)l_{\text{P}}={\sqrt {\frac {\hbar G}{c^{3}}}}1.616255(18)×10−35 m[7]
Planck massmass (M) m_{\text{P}}={\sqrt {\frac {\hbar c}{G}}}2.176434(24)×10−8 kg[8]
Planck timetime (T) {\displaystyle t_{\text{P}}={\sqrt {\frac {\hbar G}{c^{5}}}}}5.391247(60)×10−44 s[9]
Planck temperaturetemperature (Θ) {\displaystyle T_{\text{P}}={\sqrt {\frac {\hbar c^{5}}{Gk_{\text{B}}^{2}}}}}1.416784(16)×1032 K[10]

The value for Planck length is very small, outside of even the recently expanded prefixes for the metric system. The new prefix quecto is 10-30 so the best we can do with metric prefixes for the Planck Length is 0.000 016 162 quectometers. Wow, that’s really small.

The value for mass can be written in a more familiar manner as 21.764 micrograms. This seems downright large and relatable compared with the Planck length.

It is the definition of the Kilogram that has been of great interest in recent years. The Kilogram has been defined in terms of fundamental constants as:

Kg = (299792458)2/(6.62607015×10−34)(9192631770)hΔνCs/c2

The Kilogram is defined in terms of these three fundamental physical constants:

  • a specific atomic transition frequency ΔνCs, which defines the duration of the second,
  • the speed of light c, which when combined with the second, defines the length of the metre,
  • and the Planck constant h. which when combined with the metre and second, defines the mass of the kilogram.

One can see that a value other than those originally used by Planck is introduced. If one goes through and cancels the different dimensions they will find they all cancel, with only a Kilogram left as the final unit. What we are doing is multiplying to get unity in terms of Mother Nature’s units:

Kg = c2/(h ΔνCs)hΔνCs/c2 = 1 Kilogram

The value hΔνCs/c2 is Planck’s constant, which is (Kg m2/s) multiplied by ΔνCs which is (1/s) all divided by the speed of light squared which is (m/s)2. So we have:

((Kg m2/s)(1/s))/(m/s)2 = Kg (m2/s2) (s2/m2) = 1 Kg

The meters cancel, the seconds cancel and we are solely left with a Kilogram. Sorry for throwing a small amount of math in, but I thought is might make how the Kilogram appears from the constants as they are defined in SI a bit more clear. We normalize it back to obtain the Kilogram in terms of Planck Units.

The table of Planck Units given above also contains a unit of time. Physicists often are asked what happened before the Big Bang. The value they give is the Planck time:

5.391247(60)×10−44 s

Our current models of the universe only allow us to compute backwards to this time following the Big Bang. At this point, Mother Nature does not allow us to peer behind this minimum amount of time. The good news is, She does allow us to define a Kilogram without the use of barleycorns, or other grain. Using grain may seem natural to humans, but it’s not using the very basic values that mother nature has offered us, so we should use them, because it’s not nice to fool with Mother Nature.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.

The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.

The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.