Can the Accuracy of Planck’s Constant Be Increased?

Whether Planck’s constant can become more accurate depends on what you mean by “accuracy.” Before 2019, scientists measured its value in SI units and reported an uncertainty. Today, the SI defines its numerical value exactly. Experiments still matter, but they now test or realize the unit system rather than refine that defined number.

The value is exact in the SI

Since the 2019 revision of the SI, Planck’s constant, denoted by $h$, has the exact value

$$h = 6.62607015 \times 10^{-34}\ \text{J s}.$$

There is no uncertainty attached to this number in SI units. This is part of how the kilogram is defined: the fixed value of $h$, together with the definitions of the metre and second, establishes the kilogram. The joule is a derived unit, with $1\ \text{J} = 1\ \text{kg m}^2\text{s}^{-2}$.

“Exact” here is a statement about the definition of the unit, not a claim that laboratory equipment can measure anything without error. A practical realization of the kilogram can still have uncertainty. For example, a Kibble balance uses electrical and mechanical measurements to relate a mass to the fixed value of $h$. Improving the apparatus or measurement procedure can reduce uncertainty in the realized mass.

What experiments can improve

Before the SI change, researchers combined experimental results to estimate $h$ in SI units. As measurements improved, the estimated value and its uncertainty could change. The CODATA 2017 recommended value, for example, was $6.62607015(69)\times10^{-34}\ \text{J s}$, with a relative standard uncertainty of about $1.0\times10^{-8}$. That was a recommended value based on experimental data, with uncertainty.

Now, experiments can still:

• improve the accuracy and precision of practical mass measurements;
• check whether different methods of realizing the kilogram agree;
• test the consistency of quantum electrical standards and other physical relations;
• reveal experimental errors or unexpected disagreement with accepted theory.

A consistency test can yield a result that, under its stated assumptions, corresponds to a value slightly different from the defined value. That does not make the defined SI value uncertain; it gives scientists evidence to assess the experiment, its uncertainty, and the physical model used to interpret it. If persistent, well-supported discrepancies arose, they could prompt scientific investigation and perhaps a future change to the SI definition. They would not automatically change the present definition.

Worked example: reading an experimental result

Suppose, for illustration, a hypothetical consistency test yields the equivalent inferred result

$$h_{\text{exp}} = 6.62607020(15)\times10^{-34}\ \text{J s}.$$

The parenthetical digits mean an uncertainty of $0.00000015\times10^{-34}\ \text{J s}$ (often written as a standard uncertainty). The experimental central value differs from the defined value by

$$(6.62607020 - 6.62607015)\times10^{-34} = 0.00000005\times10^{-34}\ \text{J s}.$$

That difference is about one-third of the stated uncertainty, since $0.00000005/0.00000015\approx0.33$. The result is therefore consistent with the exact SI value at the scale of this uncertainty. Such an inferred result is a consistency test, not an independent measurement that assigns uncertainty to $h$ in SI units.

Accuracy, precision, and exact definitions

Accuracy describes closeness to a reference value, while precision concerns the spread or repeatability of measurements. In practice, measurement uncertainty is used to express how well a measured result is known. An exact definition removes uncertainty from the defined numerical value, but it does not remove uncertainty from measurements made in a laboratory.

The numerical value also depends on the units. The statement that $h$ is exact refers specifically to joule-seconds in the SI. In another system of units, its numerical value may differ, and converting between systems may involve quantities with their own uncertainties.

Common mistakes

• Saying experiments can no longer measure anything related to $h$. They can test relations involving $h$ or produce inferred estimates in consistency tests, but the SI value itself is fixed and is not independently measured within the SI.
• Treating exactness as perfect laboratory measurement. Realizations of units involve instruments, procedures, and uncertainty.
• Confusing precision with accuracy. Repeated measurements can be very consistent yet share a systematic error.
• Assuming a fixed value means a physical law cannot be tested. Experiments can still test the relationships and procedures that connect measurements to the defined units.