Thermodynamic temperature, measured directly.
Since 2019 the kelvin has been defined by a fixed Boltzmann constant. A thermometer that reads the Nyquist relation is measuring against that definition, and the traceability runs through electrical standards.
The problem here is different
Everywhere else on this site the argument is about drift. In a national measurement institute or a scientific laboratory the argument is about what the number means. ITS-90 is a practical scale: a set of fixed points and defined interpolating instruments that approximates thermodynamic temperature closely, with known and documented deviations from it. Realising and holding that scale is a chain of comparisons, and every link in the chain carries uncertainty and has to be maintained.
In 2019 the kelvin was redefined in terms of the Boltzmann constant, fixed by international agreement at 1.380649 × 10⁻²³ J K⁻¹. The kelvin had been defined through the triple point of water, a property of a material; it is now defined by fixing the numerical value of that constant, which changed what a primary thermometer is for.
What a noise measurement offers
The Nyquist relation ties noise power to temperature, resistance and bandwidth, and the Boltzmann constant. With that constant fixed by definition it contributes no uncertainty, so the three quantities we have left to determine are the noise, the resistance and the bandwidth. All three are electrical.
Our thermometer is traceable to electrical standards instead of to a chain of temperature comparisons, and it gives thermodynamic temperature directly instead of an approximation to it. It does so with no calibrated sensor characteristic anywhere in our measurement, because we take the resistance out of the same block of data as the noise.
- The Boltzmann constant is fixed by international agreement at 1.380649 × 10⁻²³ J K⁻¹, so the Nyquist relation carries no calibrated temperature term
- 1.380649 × 10⁻²³ J K⁻¹
- Sensor resistance and Johnson noise are measured from the same block of data, so the resistance is measured rather than assumed
- 6.5536 s
- The measurement uses a bandwidth of 1.2 MHz
- 1.2 MHz
Does it give the right answer
The first thing a metrologist asks us is whether the physics holds across a range. We measure noise power at several bath temperatures, fit a line, and see where it crosses zero power. The answer should be absolute zero.
On our second-generation prototype that intercept is −273.415 °C, against a true absolute zero of −273.15 °C, with a residual standard deviation about the least-squares fit of 0.017652 K. It is a long projection back to 0 K from a working range near ambient, which is why the residual matters as much as the intercept. It is also more than five times closer than our proof-of-principle system managed, and the authors note the improvement is statistically significant.
- Extrapolating measured noise power to zero gives a temperature-axis intercept of −273.415 °C, against a true absolute zero of −273.15 °C
- −273.415 °C
- The intercept is more than five times closer to absolute zero than the proof-of-principle prototype managed under similar measurement parameters
- −271.79 °C → −273.415 °C
- Weighting the cross-correlation frequency bins by the inverse of their squared uncertainty reduced measurement uncertainty by 28 per cent
- 28 %
Where this has got to
Practical primary thermometry is the phrase we use, and the qualifier is deliberate. Our instrument measures the sensor resistance and the relevant system response during every measurement, which is what makes it usable outside a laboratory, and it is fully primary without being absolute.
Our work is being compared against other primary approaches in the open. ThermoSI work package 2 runs our instrument alongside three others, from the University of Ljubljana, the Czech Metrology Institute and PTB. Paul presented the method with a live demonstration of the prototype at the European summer school on primary thermometry in Santander in May 2026.
- Developed with the National Physical Laboratory
- Presented at the European summer school on primary thermometry
- 13–15 May 2026
If this is your measurement
The thermometer is a working second-generation prototype. Where it goes next will be shaped by real applications. If calibration drift is limiting a measurement you are responsible for, we would like to hear from you.