How to Measure Temperature

Measuring temperature accurately is a delicate procedure.

This is a comment to the discussion in recent posts of the proclaimed perfect blackbody spectrum of Cosmic Microwave Background CMB radiation with temperature 2.725 K.  

You can measure your body temperature by body contact with a quicksilver thermometer or at distance by an infrared thermometer. Both work on a principle of thermal equilibrium between source and thermometer sensor as a stable state over time. Your body is assigned the temperature recorded by the thermometer. 

Temperature can be seen as a measure of energy in the form of heat energy or vibrational energy of a vibrating system like an atomic lattice as the generator of radiation as radiative heat transfer.

Computational Blackbody Radiation offers a new analysis of radiative heat transfer using classical wave mechanics as a deterministic form of Planck's analysis based on statistics of quanta. The basic element of the analysis is a radiation spectrum from a vibrating atomic lattice: 

• $E(\nu ,T)=\gamma T\nu^2$ for $\nu \le \frac{T}{h}$        (1a)
• $E(\nu ,T)= 0$ for $\nu >\frac{T}{h}$                               (1b)

where $\nu$ is frequency on an absolute time scale, $T$ is temperature on a lattice specific energy scale, $\gamma$ and $h$ are lattice specific parameters and $\frac{T}{h}$ is a corresponding high-frequency cut-off frequency setting a upper limit to frequencies being radiated. Here a common temperature $T$ for all frequencies expresses thermal equilibrium between frequencies. 

It is natural to define a blackbody BB to have radiation spectrum of the form (1) with maximal $\gamma$ and high-frequency cut-off and to use this as a universal thermometer measuring the temperature of different bodies by thermal equilibrium. 

Consider then a vibrating atomic lattice A with spectrum according (1)-(2) with different parameters $\bar\gamma <\gamma$ and $\bar h >h$ and different temperature scale $\bar T$ to be in equilibrium with the universal thermometer. The radiation law (1) then implies assuming that A is perfectly reflecting for frequencies above its own cut-off:

• $\bar\gamma \bar T = \gamma T$                                         (2)

to serve as the connection between the temperature scales of BB and A. This gives (1) a form of universality with a universal $\gamma$ reflecting the use of a BB as a universal thermometer.

In reality the abrupt cut-off after at radiation maximum is replaced by a gradual decrease to zero over some frequency range as a case-specific post-max part of the spectrum.  A further case-specific element is non-perfect reflectivity above cut-off. Thermal equilibrium according to (2) is thus an ideal case.  

In particular, different bodies at the same distance to the Sun can take on different temperatures in thermal equilibrium with the Sun. Here the high-frequency part of the spectrum comes in as well as the route from non-equilibrium to equilibrium. 

Why CMB can have a perfect blackbody spectrum is hidden in the intricacies of the sensing. It may well reflect man-made universality.