Equation 4 · The Last Artefact: Redefining the Kilogram
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol K_mathrm J
athrm J is part of the quantity the equation computes from the expression on the right.
Symbol e
e is an input to the expression that computes the quantity on the left.
Symbol R_mathrm K
athrm K is an input to the expression that computes the quantity on the left.
Symbol K_mathrm J^2
athrm is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
The remaining question is what the electrical quantities are referred to. The current is obtained from a voltage drop across a stable resistor; both voltages are measured against the Josephson constant, taken as KJ = 2e/h, and the resistance against the von Klitzing constant, taken as RK = h/e², so that KJ²RK = 4/h and the mass reduces to h multiplied by an experimental frequency term and divided by the product of local gravity and coil velocity [ 4 ] : . This is where the quantum electrical standards earn their place. Since 1990 the practical realization of the volt and the ohm had rested on the Josephson and quantum Hall effects, but with conventional values assigned to…
Read the full surrounding passage
The remaining question is what the electrical quantities are referred to. The current is obtained from a voltage drop across a stable resistor; both voltages are measured against the Josephson constant, taken as KJ = 2e/h, and the resistance against the von Klitzing constant, taken as RK = h/e², so that KJ²RK = 4/h and the mass reduces to h multiplied by an experimental frequency term and divided by the product of local gravity and coil velocity [ 4 ] : . This is where the quantum electrical standards earn their place. Since 1990 the practical realization of the volt and the ohm had rested on the Josephson and quantum Hall effects, but with conventional values assigned to the two constants — a decision Taylor and Witt set out when the new reference standards took effect on 1 January 1990, intended to “improve significantly the international uniformity of electrical measurements and their consistency with the SI” [ 9 ] . The consequence was a parallel electrical unit system, close to the SI but not identical to it [ 3 ] . Fixing h and e together dissolved the parallel system: KJ and RK are now calculated exactly from the defining constants, and the conventional values were retired [ 3 ] . A Kibble balance is therefore not merely an accurate balance. It is a mechanical quantity expressed entirely in quantum-referenced electrical terms, which is why the electrical metrology community wanted the kilogram and the ampere redefined in the same act.
Sources cited in the surrounding passage
- [4] Mise en pratique for the definition of the kilogram in the SI ↗
- [9] New international electrical reference standards based on the Josephson and quantum Hall effects ↗
- [3] The revision of the SI—the result of three decades of progress in metrology ↗
These citations give research context. Read each source to check which claims it supports.
Return to The Last Artefact: Redefining the Kilogram