# So what is the new definition of the kilogram?

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bbbl67
So this article "Quantum leap for mass as science redefines the kilogramme" said that there is a new definition of the kilogram coming. But they neglected to mention what that new definition is exactly. All they said was that it's now based on Planck's Constant. So I worked my way backwards trying to figure out what that is. First I divided the Planck by the kilogram, and came up with this:

h / 1 kg = 6.62607×10^-34 m^2/s

So that unit (m^2/s) looks like I can use the standard constants the speed of light and the metre.

h / (1 kg * 1 m * c) = 6.62607×10^-34 m^2/s / (1 m * c)
= 2.2102191×10^-42

Consequently after rearranging, we get:

1 kg = h / (2.2102191×10^-42 m * c)
~ 4.5244383E+41 h / (c * 1 m)

Is that all there is to it? Just some weird huge number multiplied by the Planck divided by the speed of light and the meter? Do I need to throw some Pi's or Euler's numbers in there too?

Staff Emeritus
Gold Member
The new definition I found is Planck's constant divided by 6.62607015e-37 m-2s

Mentor

Mentor
But they neglected to mention what that new definition is exactly.
The new definition will be:

“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 6.626 070 15 × 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.”

Gold Member
Is the speed of light still defined in SI units as exactly 299,792,458 meters per second?
If so, this would imply that the second would no longer be defined in terms of the cesium clock. It would then instead be defined as the time it takes for light to travel 299,792,458 meters in a vacuum.

Mentor
If so, this would imply that the second would no longer be defined in terms of the cesium clock.
The speed of light is unchanged and the second is still defined in terms of the cesium hyperfine transition. I am not sure what makes you think this is implied.

The new definitions can be seen here:
https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf

You can see that the wording of the definitions of the second and meter have been changed, but not their meaning.

bbbl67 and Buzz Bloom
Staff Emeritus
If so, this would imply that the second would no longer be defined in terms of the cesium clock

Changing the kilogram doesn't change the meter or the second.

Gold Member
The speed of light is unchanged and the second is still defined in terms of the cesium hyperfine transition. I am not sure what makes you think this is implied.
Hi Dale:

I apologize for my senior moment brain lapse and careless reading. I somehow got it into my head that the meter was being redefined.

Regards,
Buzz

Mentor
I somehow got it into my head that the meter was being redefined.
Ah, makes sense.

The excitement is all about getting rid of the international prototype kilogram.

Buzz Bloom
bbbl67
So this video states that not only is kg changing, but they are also now fixing the values of Planck's constant, Avagadro's number, and even the Ampere and the Kelvin!

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Mentor
Yes, there will no longer be any physical prototypes and also they are harmonizing all of the definitions to be of the “defined constant” type. The units will no longer be defined either by a prototype or by a specific experiment. The experiments will serve to realize a unit with a given precision, but will not be the definition.

Homework Helper
Dearly Missed
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bbbl67 and Dale
Mentor
Yay! It was expected, but still it is good to have it official

There was a live stream of some lectures and the final vote at the 26th General Conference on Weights and Measures today. There's a recording on youtube .

Idunno
So, if I have some matter, and I want to know (as best I can) what the mass is, I have to put it in something like a Watt balance. That is, I have to put it in something that allows me to relate it to Planck's constant, the meter and the second. There is no set way to do this, the Watt balance is just one option. Correct?

Mentor
So, if I have some matter, and I want to know (as best I can) what the mass is, I have to put it in something like a Watt balance. That is, I have to put it in something that allows me to relate it to Planck's constant, the meter and the second. There is no set way to do this, the Watt balance is just one option. Correct?
That is correct. There is no special definitive measurement technique.

Gold Member
So, if I have some matter, and I want to know (as best I can) what the mass is, I have to put it in something like a Watt balance.

Many will interpret this statement to mean they will have to do something differently when they weigh something.

That of course is not the case. In fact, even for the government regulators, the process they use to calibrate the standards will not change.

The only thing that will change is the standard itself, and that change is of such a small magnitude as to be totally negligible for the purposes stated above.

Idunno
Well, suppose I want to explain this to a bunch of high school students. I think that what I'd say is something like "to find the mass of an object precisely as possible, one has to place the object in a device that allows you to relate it as best you can to Planck's constant, the second, and the meter, such as a Watt balance. The Watt balance, if it uses the quantum hall effect, Josephson junctions, etc. will give you an equation where m = hp(n^2)(f^2)/(4gv) where h is Planck's constant, p and n are whatever the hell they are, f is the frequency from the JJunctions, g is local gravitational filed strength, and v is the speed that the mass went at in the Watt balance. But a different device will relate the mass to Planck's constant, the meter, and the second differently."

That's not great, but I think it gives a student a better idea of what is going on than “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 6.626 070 15 × 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.”

diogenesNY
There seems to be a rather significant underlying issue here, notable in that it has been touched on but not really explored in the coverage of this redefinition.

I understand that there has been some observed drift in the mass of the Reference Kilogram, and this addresses that rather directly, BUT---

One thing that is going on here is the shift from an empirically based definition to one that exists as a defined term. This strikes me as pretty major (I know it isn't the first quantity to be so redefined in the last century). Any thoughts on the implications or simply the evolution (pro? con? indifferent?) of moving from empirical to defined standards for metrological quantities?

diogenesNY

Mentor
Defined standards based on (presumably constant) universal constants would seem to be a win. Constants don't ablate, rust, wear, dent, absorb or outgas material or do other sneaky things as physical objects tend to do over time.

Any thoughts on the implications or simply the evolution (pro? con? indifferent?) of moving from empirical to defined standards for metrological quantities?
I appreciate the new SI very much. At first, it is harder to understand than a prototype-based system but basing all units on physical constants is conceptually very clean. It emphasizes that the numerical values of such (dimensionful) constants don't reflect properties of Nature but our desire for having convenient units to describe everyday situations. The new SI is also more similar to important different unit systems like Planck units and atomic units which are also based on the freedom to define physical constants.

Dale
Gold Member
Well, suppose I want to explain this to a bunch of high school students.

I would tell them that Avagadro's Number is a known integer, by definition. And if you have that many atoms of Carbon-12 you have 12 grams of carbon, exactly, by definition. The precision we concerned ourselves with when we measured the mass of that 12-gram sample has been replaced with a concern over our ability to count Avagadro's Number of things precisely.

Homework Helper
Gold Member
Currently there is some traceability in the system in that you can compare your "bag of sugar" to a reference that has itself been compared with the international reference. Will some official body continue to provide the final step in the traceability tree?

I would tell them that Avagadro's Number is a known integer, by definition. And if you have that many atoms of Carbon-12 you have 12 grams of carbon, exactly, by definition.
I don't think that the second sentence is true in the new SI. There isn't a definition which relates the mole and the kg anymore. The mass of one mole of Carbon-12 needs to be determined experimentally.

Dale and PeroK
Mentor
Well, suppose I want to explain this to a bunch of high school students. I think that what I'd say is something like "to find the mass of an object precisely as possible, one has to place the object in a device that allows you to relate it as best you can to Planck's constant, the second, and the meter, such as a Watt balance. The Watt balance, if it uses the quantum hall effect, Josephson junctions, etc. will give you an equation where m = hp(n^2)(f^2)/(4gv) where h is Planck's constant, p and n are whatever the hell they are, f is the frequency from the JJunctions, g is local gravitational filed strength, and v is the speed that the mass went at in the Watt balance. But a different device will relate the mass to Planck's constant, the meter, and the second differently."
For a bunch of high school students, I think the answer is even easier: "Weigh it using the most accurate scale you can find, just like before". he needle and the tick marks on its dial aren't infinitely thin so there will be some uncertainty in the value you read out.

All the new definition of the kilogram does is tell us where the tick marks would be on a mythical perfect dial with an infinitely thin needle and infinitely thin tick marks. The new definition was carefully chosen so that the tick marks on the dials of all currently working scales are correct, just too wide; this allows to build ever more accurate scales in the future.

Mentor
It emphasizes that the numerical values of such (dimensionful) constants don't reflect properties of Nature but our desire for having convenient units to describe everyday situations.
Well said.

Palash_85
This is only good for theory, having a constant number but in real world it makes zero sense and gives a total of zero essence about mass. The previous definition gave us an idea what actually a kilo is and that it is measured for mass, and is measured against a standard physical weight. And if science doesn't explain physical things and is good only on paper, it defeats the very purpose of teaching science to common people. Keep it restricted to exclusive science club where scientists will drool over such impossible to comprehend definitions.

Mentor
2022 Award
This is only good for theory, having a constant number but in real world it makes zero sense and gives a total of zero essence about mass.
Which by the way isn't the meaning of units. There is an essential difference between a physical quantity and a scale it is ruled with. The scale does not explain the quantity and has never been meant to do so.
The previous definition gave us an idea what actually a kilo is and that it is measured for mass, and is measured against a standard physical weight.
And now you have lost this idea? You must have an incredible understanding of unbelievable huge numbers, if you can recognize a few atoms more or less. Just saying: the prototype kilogram lost many atoms over the years as well!
And if science doesn't explain physical things and is good only on paper, it defeats the very purpose of teaching science to common people.
Again, don't confuse the object with the ruler! Rulers should not be used for teaching other than by some illustrations. And this didn't change at all. Speaking with "common people" about a meter, nobody has ever asked me about its definition. Not even if we had change from prototype to light speed. They always have been happy with a yardstick.
Keep it restricted to exclusive science club where scientists will drool over such impossible to comprehend definitions.
We will. Good luck when you buy your bread in the future in terms of "handfuls" because someone had redefined the kilogram by an unrecognizable amount.

Mentor
This is only good for theory, having a constant number but in real world it makes zero sense and gives a total of zero essence about mass.
You are misunderstanding what the definition of the kilogram does. Nothing has changed in how we understand mass: it's still resistance to acceleration, we still measure it by comparing the unknown mass that we are weighing with a known mass (balance scale) or observing how it accelerates when subjected to a known force (spring scale), and statements that this object has this much more mass than that object still mean what they always have.

All that's changed is that we have a new and more precise rule for where we put the tick marks on the readout dial of our scales.

Asymptotic
Mentor
This is only good for theory,
On the contrary, this is eminently practical. Instead of an unreliable and privately held nearly inaccessible standard we now have a reliable standard that can be accessed by everyone anywhere. This is the most practical improvement since the abrogation of the prototype meter.

Klystron and fresh_42
lpetrich
BIPM - About the BIPM -- the Bureau International des Poids et Mesures (International Bureau of Weights and Measures) is the custodian of the world's primary measurement standards, the Système Internationale (International System) or SI. It maintains seven primary units: the meter, kilogram, second, ampere, kelvin, mole, and candela.

The candela is a unit of luminous intensity. Standards were originally the luminosities of lamps with various specifications of construction. In 1948, the candela was defined in terms of the blackbody luminosity of melting-point platinum, and in 1979, it was redefined as a certain amount of energy per unit time.

The mole is gram molecular weight, and it's the number of grams that is equal to its component parts' numbers of atomic mass units or daltons. The proportionality constant is Avogadro's number, the number of amu's in a gram. The amu has this history:
• 1803: hydrogen atom -- John Dalton's atomic-weight table
• 1912: 1/16 of an oxygen atom -- led to a split between chemists' natural oxygen and physicists' oxygen-16
• 1961: 1/12 of a carbon-12 atom
• A few days ago: Avogadro's number officially fixed, making the amu a fixed number of grams

The kelvin is temperature, and it has this history:
• 1742: Andreas Celsius makes 100 = freezing point of water, 0 = boiling point of water
• 1743: Independently invented by Jean-Pierre Christin, with 0 = freezing, 100 = boiling
• 1744: Celsius's scale flipped to present form by Carl Linnaeus
• 1802: William Thompson, Lord Kelvin, proposes a scale based on absolute zero with Celsius degrees as its increment. He calculated 0 C = 273 K
• 1948: Triple point of water = 0.01 C
• 1954: Triple point of water = 273.16 K (0 C = 273.15 K)
• A few days ago: Boltzmann's constant officially fixed, defining temperature in terms of energy

lpetrich
Electromagnetic units are a nightmare, with at least four sets of units that have been used: electrostatic, electromagnetic (or more precisely, magnetoelectric), Gaussian, and MKSA (SI). The ampere is electric current, electric charge per unit time. Until a few days ago, its official definition was in terms of the electromagnetic force that two electric currents make on each other. The new definition involves fixing the elementary charge.

The reason for this odd move is because of two effects that permit very high precision of voltage and current measurements: the Josephson effect and the quantum Hall effect. The Josephson effect permits very high-precision measurements of voltage, and the quantum Hall effect very high-precision measurements of resistance. The Josephson constant is h/(2e), and the QHE or von Klitzing constant is h/e2, both in terms of Planck's constant h and the elementary charge e. Both h and e were recently fixed, thus fixing these two constants.

This has the consequence that the magnetic permeability of the vacuum becomes a measured quantity, though the electric permittivity of the vacuum continues to have a fixed relationship with it.

So:
• (Voltage) ~ (h/e) * (frequency)
• (Current) ~ (voltage) / (resistance) ~ (h/e) / (h/e2) * (frequency) ~ e * (frequency)
• (Power) ~ (voltage) * (current) ~ (h/e) * e * (frequency)2 ~ h * (frequency)2

lpetrich
Now for the meter. It has gone through these definitions:
• 1798: 10-7 of the equator-pole distance.
• 1799: Platinum bar
• 1889: Platinum-iridium bar at 0 C
• 1927: Clarified: pressure = 1 atm, the bar is to be on rollers
• 1960: A multiple of the wavelength of an electronic transition of krypton-86
• 1983: The speed of light in a vacuum officially fixed, defining length in terms of time
The speed of light in a vacuum is related to the geometry of space-time.

The second has gone through these definitions:
• Prehistoric: day, month, year from astronomical observations
• Antiquity: division of daytime and nighttime into 12 hours each
• Antiquity: recognition of approximate constancy of total day (daytime+nighttime)
• Antiquity: recognition of variations of total day, leading to definition of mean solar day
• Late medieval Europe: division of total day into 24 equal-length hours
• Late medieval and early modern Europe: division of hour into 60 of pars minuta prima (first small part: the minute), division of minute into 60 of pars minuta secunda (second small part: the second). No continuing to a pars minuta tertia (third small part).
• 1956: a fraction of some year used as a reference
• 1967: from the cesium-133 ground-state hyperfine-transition frequency
Astronomical measurements were more precise than clocks for all of humanity's history until the 1960's.

lpetrich
The (kilo)gram has gone through these conventions:
• 1795: gram = mass of one cubic centimeter of water at 0 C
• 1799: changed to 4 C, where water has maximum density
• 1799: platinum cylinder
• 1889: platinum-iridium cylinder
• A few days ago: Planck's constant is officially fixed, defining mass in terms of length and time
Thus using quantum mechanics.

The current realization of relating mass to electromagnetic and quantum phenomena is the Kibble balance, formerly called the Watt balance. It measures the gravitational force on an object by making an electromagnetic force with an electric current going through a coil in a magnet's magnetic field. That field, in turn, is measured by making the coil oscillate and then finding the coil's induced voltage. Gravitational force is related to mass by measuring the local acceleration of gravity very precisely. Thus,
• (Mass) ~ (force) ~ (current) * (magnetic field)
• (Magnetic field) ~ (voltage)
• (Mass) ~ (voltage) * (current) ~ (power) ~ h
(omitting length and time factors)

An alternate approach involved making very precisely machined spheres of single-crystal silicon-28, the most common isotope. The atoms in them would then be counted by measuring the sizes of the spheres and then measuring the crystal-lattice unit sizes. One may then measure the masses of the individual silicon atoms by making them orbit magnetic field lines and then pushing them up and down in their orbits with radio waves (cyclotron resonance).

diogenesNY
New York Times coverage of the redefinition of the Kilogram - Interesting and contains a good bit of history and background color.

The Kilogram Is Dead. Long Live the Kilogram!
After a vote (and a century of research), the standard measure for mass is redefined, and the long reign of Le Grand K is ended.

By XiaoZhi Lim
Nov. 16, 2018

Since 1889, Le Grand K, a sleek cylinder of platinum-iridium metal, has ruled from its underground vault in Paris. An absolute monarch, it was the very definition of one kilogram of mass. Scientists from around the world made pilgrimages to it, bringing along their national kilogram standards to weigh in comparison.
[Article Continues]: https://www.nytimes.com/2018/11/16/...k&module=Well&pgtype=Homepage&section=Science

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diogenesNY