New definition of the international system of units will

take effect on May 20, 2019.

The international system of units, the SI, is the system of units in which:

* the unperturbed ground state hyperfine splitting frequency of the caesium 133 atom Δ𝑣(133Cs)hfs is exactly 9 192 631 770 hertz,

* the speed of light in vacuum 𝑐 is exactly 299 792 458 meter per second,

* the Planck constant ℎ is exactly 6.626 069 57×10−34 joule second,

* the elementary charge 𝑒 is exactly 1.602 176 565×10−19 coulomb,

* the Boltzmann constant 𝑘 is exactly 1.380 648 8×10−23 joule per kelvin,

* the Avogadro constant 𝑁A is exactly 6.022 141 29×1023 reciprocal mole,

* the luminous efficacy 𝐾cd of monochromatic radiation of frequency 540×1012 hertz is exactly 683 lumen per watt,

where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W, respectively, are related to the units second, meter, kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg, A, K,K$\text{K}$, mol, and cd, respectively, according to the relations Hz=s–1(for periodic phenomena), J=kg m2 s–2, C=A s, lm=cd sr, and W=kg m2 s–3. The steradian, symbol sr, is the SI unit of solid angle and is a special name and symbol for the number 1, s so that

sr=m2 m−2=1.

**Deriving Basic Units**

The means by which these constants should be operationalized is also spelled out in the fine print. Specifically:

The choice of physical constants was made on the basis of minimal uncertainty associated with measuring the constant and the degree of independence of the constant in respect of other constants that were being used. Although the BIPM has developed a standard *mise en pratique* (practical technique) for each type of measurement, the *mise en pratique* used to make the measurement is not part of the measurement's definition – it is merely an assurance that the measurement can be done without exceeding the specified maximum uncertainty.

Caesium 133 is used to define the second. The Planck constant is used to define the joule given the second. Boltzmann constant is used to define the degree Kelvin given the joule. The speed of light is used to define the meter given the second. The kilogram, meter and second are used to define the watt. The second and the watt and the properties of a laser of a certain color are used to define the lumen and candela. The elementary charge is used to define the coulomb which is used with the second to define the ampere. The steradian is mathematically defined.

Casesium 133, Planck's constant and the speed of light could also be used to determine the kilogram and the kilogram's mass can also be determined directly from the definition of the mole (I would think that the former is as a practical matter easier to get precise about than the latter). So, the mole is just an alternative (potentially not quite exactly the same at the part per billion level) way to define the kilogram and could have been omitted, even though as a practical matter it is probably easier to operationalize that the method using casesium 133, Planck's constant and the speed of light. A presume that the fine print favors one method over the other, or at least resolves the conflict, if there is a discrepancy between two ways of defining the kilogram.

**The History Of The Metric System**

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In some ways, the reform represents a return to the metric system's

historic roots in physical constants after the Enlightenment motivated post-French Revolution thought that spawned it.

The original definition of the meter adopted in March of 1791 was one ten millionth of the distance between the North Pole and the Equator through Paris. From 1889 until 1960, the meter was defined in terms of reference objects.

From 1889 until May 20, 2019, the kilogram has been defined in terms of reference objects. But, the gram was calibrated originally to be equal to the mass of one cubic centimeter of water.

The size of the degree in Celsius and Kelvin temperatures is designed to be 1% of the difference in temperature between the freezing point of water and the boiling point of water.

The calorie was originally the amount of heat required to raise the temperature of 1 kg of water from 0 to 1 °C at 1 atmosphere of pressure.

The original definition of the second was based on Earth's average rotation during 1750–1892, which takes, on average, about 31,556,736 seconds (60 seconds a minute, 60 minutes an hour, 24 hours a day, 365 days a year except in leap years divisible by four and not divisible by 100 when there are 366 days a year).

An erg is the amount of work done by a force of one

dyne exerted for a distance of one

centimeter. In the CGS

base units, it is equal to one

gram centimeter-squared per

second-squared (g⋅cm2/s2). It is thus equal to 10^−7

joules or 100 nanojoules (

nJ) in

SI units.

The joule is an energy unit that flows naturally from thinking in terms of kilograms, meters and seconds (it is one kg*meter squared per second squared a.k.a. one Newton meter a.k.a. one Pascal times cubic meters). It can also be defined as:

* The work required to move an

electric charge of one coulomb through an

electrical potential difference of one volt, or one coulomb-volt (C⋅V). This relationship can be used to define the volt.

* The work required to produce one watt of

power for one second, or one watt-second (W⋅s) (compare

kilowatt-hour – 3.6 megajoules). This relationship can be used to define the watt.

Current in ampere's was defined by setting the

magnetic force constant $k_{\mathrm {m} }$ to unity and electric potential is defined in such a way as to ensure the unit of power calculated by the relation

is an erg/second. This was slightly refined to produce the current soon to be replaced definition of the ampere which was that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10^−7 newton per meter of length (i.e. two dynes).

The previous definition of the mole was the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12 (i.e. in 1 gram of a carbon-12 standard based atomic mass unit). The mole was thus derive of the gram which was derivative of the mass of one cubic centimeter of water which was derivative of the meter.

The new physical constant based definitions still bear homage to these motivating concepts for metric system basic units, as the numbers selected aren't natural at all in their own reference frames.

**Other Impacts**

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All measurements in the U.S. customary system of measurements are defined exactly in terms of S.I. units, so they will also change subtly on May 20, 2019.

The

inch in the U.S. customary system is defined to be exactly 0.0254 meters, so all U.S. customary measurements of length, area and volume will change on May 20, 2019. The U.S., the

United Kingdom and other

Commonwealth countries agreed on this definition effective July 1, 1959. (The speed of light in miles per second will now be: 186,282.397 to the nearest part per billion, leaving a rounding error of about 1 part per 20 billion.)

Likewise, the U.S. customary system

pound is defined to be exactly 435.59237 grams by agreement between the U.S., the United Kingdom, and other English-speaking countries in 1959, so all units of weight in the U.S. customary system (or strictly speaking analogs of U.S. customary system measurements of weight converted to measurements of mass).

The degree

Fahrenheit, which is defined as exactly 5/9ths of a degree Kelvin in magnitude, so it will change on May 20, 2019.

A degree Celsius and a degree Kelvin are defined to be equal in magnitude. There is an exact conversion between degrees Celsius and degrees Fahrenheit (since 32 degrees Fahrenheit is exactly 0 degrees Celsius and 212 degrees Fahrenheit is exactly 100 degrees Celsius). But, Celsius is not an S.I. unit.

By international agreement, since 1954 the unit degree Celsius and the Celsius scale are defined by

absolute zero and the

triple point of

Vienna Standard Mean Ocean Water (VSMOW), a specially purified water. This definition also precisely relates the Celsius scale to the

Kelvin scale, which defines the

SI base unit of

thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being exactly 0 K and −273.15 °C. The temperature of the triple point of water is defined as exactly 273.16 K (0.01 °C).

The calorie is also a metric, but non-S.I. unit based upon the properties of water. It is the amount of energy needed to heat on cubic centimeter of liquid water (which has a mass of one gram) by one degree Celsius. It is about 4.1868 J. A dieter's calorie is 1000 calories or one kilocalorie, or about 4186.8 J.

**How to change from U.S. customary units to metric units.**

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I have long recommended that the U.S. make the change over to metric units partially, first converting (1) from Fahrenheit to Celsius and Rankine to Kelvin, (2) from horse power to watts, (3) from BTUs and tons of refrigeration and foot-pounds to joules and

calories, and (4) from

slugs to Newtons, while deferring conversion of more familiar units later. Since few people use Rankine, tons of refrigeration, foot-pounds and slugs, those conversions would be painless. More people use horse power and BTUs, but both are used on a very isolated basis and would require reforms primarily by a few big corporations in a small number of industries. For most people, the first wave would primarily mean converting from Fahrenheit to Celsius.

Conversion from more familiar U.S. customary units of length, area, volume and weight to metric and S.I. units would take place later, to minimize the amount of conversion shock taking place at one time. This is because so many legacy measurements (e.g. land surveys and recipes) are in convenient multiples of U.S. customary units.

This would probably best be broken up into different waves based upon the industry or type of thing measured, continuing current trends which use metric units for some purposes and U.S. customary units for others.

**Commentary**

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One of the subtle issues of the redefinitions is that it obscures, without truly eliminating, issues related to the precision with which we can measure the physical constants that are given exact defined values (most of which were in the parts per billion plus or minus an order of magnitude). The new definitions are generally designed to match existing values to nine significant digits of precision.

I'm disappointed that they didn't decide to define the speed of light in a vacuum to be exactly 300 000 000 meters per second, even though I understand why they did (for back compatibility). The difference would be a reduction of 0.7 millimeters per meter.

Likewise, if we were starting over from scratch, defining the coulomb as as 1 x 10^19 elementary electric charges would have made sense. But, we are victims of our past.