The SI Units, Finalized 2019
On November 16, 2018, in Versailles, France, a group of 60 countries voted unanimously to transform the international system that underpins global science and trade. This action finally established a measurement system based entirely on (presumably) unchanging fundamental properties of nature.
The 2019 redefinition of the SI base units came into force on the 144th anniversary of the Metre Convention, 20 May 2019. In the redefinition, four of the seven SI base units — the kilogram, ampere, kelvin, and mole — were redefined by setting exact numerical values for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (k), and the Avogadro constant (NA), respectively. The other three constants, speed of light (c), luminous efficacy (Kcd), and the transition frequency of cesium 133, (ΔvCs) were already in place.
The goal of the redefinition of the base units is the final elimination of artifacts such as the one kilogram cylinder, as standards of measure, the artifacts having been found to be, in fact, variable. None-the-less, tightly controlled duplicates of the prototype are still produced as the pragmatic realization of a standard kilogram mass. Each of the constants has as suggested protocol for concrete laboratory realization .
One result for early science education of the formal elimination of artifacts is that all of the finalized definitions are meaningless in the primary child’s macro world being defined strictly in terms of the micro, quantum world. See Begin at the Beginning
It is true that in terms of classroom practicalities, the ten rod may still be used as a measure of a meter and a liter of water may still be used as a kilogram of mass. A clock is still a clock. However, it is also true that these new standards are now part of the educational sequence and are the terms in which Tomorrow’s Child will be required to think. As these definitions and the physical constants on which they depend are completely micro in scale, methods must be found to lay a foundation in a child’s primary macro experience. Macro manifestations of the micro constants and the ideas expressed in the base and derived unit definitions will have to be presented.
These constants, and their base and derived units, are not just accounting concepts. They are the aspects of reality that we as a scientific culture choose to recognize. As such, they do not just inform our thinking, they become the form of our thoughts.
In this conceptual structure, the primordial consideration is of Time, which is defined as the constant ground state frequency of Cesium133. Second to Time is the consideration of Length, which is dependent on the time constant and a second constant, the speed of light. The third consideration is Mass, which brings into play a third indirectly physical aspect, Plank’s (proportionality) constant. The forth consideration, Current, adds the constant of the electrical charge of an elemental particle.
The remaining three constants and their base units, the kelvin, the mole and the candela, fill out this thought structure, but it is the first four that truly determine the methods and limitations by which we endeavor to recognize what is fundamentally real.
The Base Units
The first three units, the second, meter and kilogram quantify time, linear space, and mass. These are the measurements traditionally addressed in early education.
The forth unit, the Ampere, quantifies electric current. This consideration is a crucial addition to any primary curriculum in a technological culture.
The fifth unit, the Kelvin, considers thermodynamic temperature, the amount of heat energy present in a system. Temperature in general receives limited treatment but can be readily expanded in a primary curriculum.
The sixth unit, the mole, considers the amount of substance of a material in terms of a fixed number of elementary particles. There is nothing that can make this physically evident on the primary macro level.
The seventh unit, the candela, considers the intensity of light in a given direction. This is seldom considered in a primary environment but easily can be. As a recognition of electromagnetic radiation, it is as necessary to a comprehensive primary curriculum as is the Ampere.
Note: all subsequent quotes are taken from the SI brochure.
1. Time
The first base unit defined is a unit of time, written ‘second or sec” and having the symbol, s, and is defined as
which is,
“the unperturbed ground state hyper-fine transition frequency of a Cesium 133 atom.”
This quantity, ΔvCs, is an event count with a physical constant set at a frequency of 9192631770 Hz and fixed as = 1/sec.
The number is chosen by international agreement.
It is realized in the laboratory through the action of a cesium clock.
It is important to note that this definition is necessarily the first because it is the only one complete in and of itself, and incorporated directly into subsequent base unit definitions. It is further important to note that the physical realization of this number is achieved by counting a regular, repeating event observed in one particular element. And that is all. All that exists or is purported to exist is an elemental atom and all that is counted is a change, an event, internal to that atom. There is no second substance that is sampled, measured, compared, purported or proven to exist. There is no tangible physical entity or dimension that is indicated or delineated. There is just an oscillation between states that is counted.
The importance of this at the primary level is that the meaning of “counting time” can be presented at the macro scale by demonstrating a number of different clocks, different regular, repeating, countable events: the swing of a pendulum, a mechanical metronome, a digital metronome. Even rhythmic clapping can even be used and works well on circle. The underlying lesson is that a clock is any agreed upon regularly repeating, countable event which can be compared to or placed in ratio to any other event or series of events. Such comparison is the sole meaning of “measuring” Time. For this reason modeling Time as a visible, linear, directional, homogeneous, infinitely divisible physical object, i. e., a drawn line, is fundamentally misleading to the primary child.
2. Length
The second base unit is a consideration of distance in space, i.e., a single dimension.
“The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum, c, to be
Defining a base unit of length in terms of speed, which is itself is distance divided by time would be circular save that speed as a general concept is not being used but rather one particular speed of one particular entity. That speed is fixed in theory as a universally constant upper limit. We can therefore take a distance traveled by an entity at that speed during a particular clock event and divide it into as many segments as we like, and then use one of those segments as the base unit of length.
So there are, by definition, 299 729 458 total meters in the distance traveled by light in a vacuum coincident with a period defined by ΔvCs, and a single meter would be 1 / 299729458 of that distance.
The logical inversion here is that speed is not determined by length traveled but rather length is determined by an entity traveling at a fixed constant speed coincident with a fixed number of clock events.
The recommended laboratory realization of the meter is currently achieved by counting the number of wave lengths, λHeNe, of light produced by a Helium Neon laser during the event count ΔvCs. This number being generally accepted as 1579800.762042 wavelengths. By counting a number of emitted wavelengths of a known frequency propagating at a fixed rate, the length of the path traveled can be determined and is limited by the defined constant, the speed of light.
Length now is defined with reference to the speed of light, but the motion of light is not observable at the macro level. One consequence of this is that light should be approached on the primary level by presenting comparisons of its behavior with physical entities that clearly do move. Compare, for instance, that both a beam of light and a ping-pong ball will bounce off of a mirror in the same way. As the ball moves visibly, so does light move.
At the macro level, a standard meter stick is still necessary for practical measurement, but in primary lessons, any agreed upon stick can be used because the core idea of an international definition is that everyone uses the same stick. The question becomes, how do we determine the length of that stick in a primary macro environment? We could take a stick chosen at random as a given. We could also easily incorporate the approach used in this new definition. Roll a ball down a ramp, count “one” when it leaves the ramp and begins to roll on the floor, and mark the spot it passes at the end of the count “one”. That path just rolled can then used as the unit of length, the motion of the ball having substituted for the motion of light. That unit can be used until such time as the exercise is repeated. Eventually it can be explained that the ten rod is the meter stick that everyone everywhere agrees on.
Working with different physical length units is analogous to working with different clocks to emphasize that the individual clock is not the point, the counting of events is the point. In this way, clock counts and unit lengths become correlated.
3. Mass
“The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10^−34 when expressed in the unit J s, which is equal to kg m2 s^−1, where the metre and the second are defined in terms of c and ∆νCs.”
In this last expression, mass is seen to be dependent on Plank’s constant h, and through prior definitions, the speed of light c, and ∆νCs.
The SI definition of mass is meaningless at the macro level. Even at a high school level the logical complexity of an explanation would be problematic. In the primary classroom, mass necessarily must remain equivalent to weight.
Planck’s constant expresses the relationship between Energy (in Joules) and electromagnetic frequency.
Plank’s constant is a proportionality constant. As such, it is does not indicate a physical entity but rather a relationship between certain aspects of physical entities. Plank’s constant is taken to be a universal physical constant and fixed by definition.
The Joule is a complex derived variable which, in one of its forms, is purely mechanical and, in another, incorporates the base unit of electricity to construct an equation relating kinetic energy and electromagnetic energy.
There are currently two independent primary methods that are capable of physically realizing the mass of the kilogram. The first relies on determining the unknown mass using an electromechanical balance specially designed for the purpose. The second method compares the unknown mass to the mass of a single atom of a specified isotope by established by counting the number of atoms in a crystal, where the mass of the atom is well-known in terms of h, c and∆νCs.
When Plank’s constant is realized through the use of a Kibble (Watt) Balance in which gravity is countered by electromotive force to balance a given mass, the process itself requires the measurement of voltage, current, velocity and the local gravitational constant.
4. Current
“The Ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 ×10^−19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ∆νCs.”
The unit C, Coulomb, is the net electric charge present and in turn dependent on the SI fixed number of elementary charges e in the base unit, the mole.
Like the kilogram, the micro definition of Ampere is meaningless at the primary level. At the same time, the ideas of charge and current are key in primary physics. One recommended method of practical realization of the ampere is,
“by using Ohm’s law, the unit relation A = V/Ω, and using practical realizations of the SI derived units the volt V and the ohm Ω, based on the Josephson and quantum Hall effects, respectively,”
Ohm’s Law can be presented at the primary macro level. Current can be physically observe and manipulated, and can be quantified in simple electrical circuits. Current can described qualitatively through a push-resist model in which current is how much charge gets pushed. It can be expressed in terms of two derived units, the Volt and Ohm, as they are combined in Ohm’s Law. See A Child’s Electricity.
5. Temperature
“The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 ×10−23 when expressed in the unit J K−1, which is equal to kg m2 s−2 K−1, where the kilogram, metre and second are defined in terms of h, c and ∆νCs.”
Again, this definition is entirely micro in scale. However, the SI brochure further states that,
“Primary thermometry is carried out using a thermometer based on a well-understood physical system,”
and
“Defined temperature scales allow to assign temperature values, determined by primary thermometry, to a series of naturally occurring and highly reproducible states (e.g., the freezing and triple points of pure substances).”
So as a liter of water can still stand a liquid kilogram, the triple point of water can still stand as the zero point of the Celsius scale.
Degrees Kelvin are equal in magnitude to degrees Celsius, and so temperature also can be directly quantified and measured on the macro scale through the use of an easily managed infrared thermometer, and also in concert with the direct sensory experience of the Montessori Thermic Bottles.
In addition, while the triple point of water cannot be presented in the absence of a partial vacuum, the idea of three states coexisting can be indicated by ice melting in visibly evaporating liquid water.
6. Amount of Substance
“The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit 1/mol and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.”
“In practice, chemical measurements require the realization, across all types of chemical entities, of derived units involving amount of substance that are relevant to practical chemical measurement, such as the amount of substance concentration (mol/m3), the amount of substance content (mol/kg) or the amount of substance fraction (mol/mol).”
It is not possible to present elementary entities on the macro level. It is possible to make a connection between a unit of weight or mass of an element and a mol of that element in order to a physical establish meaning for the term. One mol of any element has an equivalent weight in grams, the molar mass. One can weigh out the appropriate amount of various elements, 63.5 grams for copper, 27 grams for Aluminum, 65.3 grams for Zinc, etc., and present these as a molar exercise, similar to a density exercise, thus giving physical content to the meaning of the word mol, which will eventually be useful, given the eventual importance of the idea in chemistry.
7. Luminous Intensity
“The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 ×1012 Hz, Kcd, to be 683 when expressed in the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ∆νCs.”
The candela cannot be presented directly. However, the physical reality, luminous intensity, underlying the unit can be easily presented and can also be quantified in derived units using simple devices. Luminous Intensity is easily approximated with a common Lux meter or an available smart phone app.
The Derived Units
The derived units considered here are the first that the primary child can meaningfully address. They represent only a handful of the many derived units used in the real world. They will be described in common formulaic terms, equivalent base unit expressions and in terms of qualitative considerations. They are the first three term equations the child encounters. Three term equations require only the four basic arithmetic operations to be used quantitatively. They require no operations at all in order to be understood qualitative and physically.
Derived units are combinations of base units. Derived units important to the primary macro level should be limited to equations that are 1) reducible to three terms, 2) require only the four basic arithmetic operations, and 3) are capable of physical example and qualitative description without the use of arithmetic operations.
Speed
The first derived unit is Speed, symbol S. Speed answers the macro scale question, “how fast?”.
Speed completes the first primary three part equation
S = m / sec
Because the defined base units are micro in definition, Speed is realized in the classroom through the act of moving, or observing motion, from place to place, while a clock counts. “How fast?”, is answered by the comparison, or the combination in ratio, of distance covered and total clock events counted.
Qualitative comparisons of length and duration are within the primary child’s skills. The discussion of the idea that speed combines distance and time forms a concrete basis for the three part equation that can emerge after the arithmetic operations are acquired.
Acceleration
Acceleration, symbol A, is changing Speed. Acceleration is written
which can be qualitatively expressed as,
Acceleration, changing speed, is distance or direction and time changing together.
Time defined as ∆νCs can be physically presented as a clock counting. Time squared can eventually be written and operated on meaningfully, and results in real physical reference, but unlike distance squared, “time squared” has no a real physical referent which can manifest on a macro level. However, despite being defined on a micro scale and containing a non-physical quantity, the derived idea acceleration can be experienced physically on the macro level. Any case of being pushed while in motion, say while walking or swinging back and forth or riding a merry-go-round, provides palpable acceleration and can be used to give the term real physical content.
Force
Force, with a unit name Newton and symbols, N or F, is written
Described qualitatively Force has simple meaning in the same way acceleration does. F = ma means qualitatively that,
Force is how much mass is moved a distance at a changing speed.
Force is palpably presented by imparting motion, literally pushing objects of different weights through differing speeds. Push a wagon faster and faster, then push it faster and faster with someone in it. Force can also be presented through collisions of variably sized balls being variably accelerated by rolling down ramps at varying inclines and colliding with other balls.
Pressure
Pressure is an extended consideration of Force as applied to liquids and gasses, has the unit name pascal, symbol pa, and can be written,
Qualitatively, concerning liquids, pressure can be discussed as how hard it is to push water through tubes of varying sizes. Or how hard water feels or how far it travels when it exits a syringe with variable nozzles. It can be quantified with the use of a simple gauged air pump.
Pressure varies with volume and temperature. This physical phenomenon that underlies the gas laws. It can be realized by inflating various objects and then subjecting them to changing thermal conditions, e.g., putting a balloon in a freezer.
Current
The ampere is an example of a base unit that cannot be expressed in its defining micro constants or in an alternative definition based on complex derived units, but can be present in terms of a primary three part equation involving direct quantification of a simple electrical circuit. The three part equation is Ohm’s Law and the variable are the volt, V, and the ohm, Ω, which is resistance.
As SI derived variables they are,
and clearly of no use at a primary level. However, qualitatively they can be simply described.
As mentioned above in base units, Current can be described as how much charge is pushed. So Ohm’s Law,
can be discussed as,
How much gets pushed, current, is a matter of how hard you push, voltage, and how hard it is to push, resistance. See A Child’s Electricity.
These units can be realized at the primary macro level through simple metered electric circuits.
In a technological culture, the complexities of the finalized SI constants and units are an inevitable part of the child’s educational future. In a scientific culture and economy, they are basic vocabulary. Their foundation can and should be established in Primary education.
