### Physics Friday – Blackbody Radiation

Friday, November 27th, 2009

Please forgive the bitter tone that follows in this post, but recently I came across an “audiophile” device that I feel may damage the already precarious position of the audiophile industry. First however a little necessary physics background…

A “Blackbody” is an object that does not reflect electromagnetic energy incident upon it, or allow any to pass through it. Any emission from it is entirely thermal in nature with no characteristic emission/absorption lines from any element. This is referred to as “Blackbody Radiation”. Classical theory describes this spectrum with the Rayleigh-Jeans Law:

$$I(\lambda ,T)=\frac{2\pi ckT}{\lambda ^{4}}$$

$$I(\lambda ,T)$$ is the power per unit area

$$c$$ is the speed of light

$$k$$ is Boltzmann’s constant

$$T$$ is the temperature in Kelvin

$$\lambda$$ is the wavelength

This is in agreement with observation at lower frequencies, however the problem with this result is that at higher frequencies (i.e. as $$\lambda \to 0$$) the power approaches infinity! This is certainly not in agreement with observation and has been referred to as the “ultraviolet catastrophe”.

A physicist by the name of Max Plank made an amazing assumption that was to prove instrumental not only for resolving the paradox of the Rayleigh-Jeans law, but for all of quantum mechanics. The assumption is that radiation can only only assume *discrete* energy values:

$$E_{n}=nhf$$

$$n$$ is the energy level

$$h$$ is Planck’s constant

$$f$$ is the frequency.

Therefore the energy between two adjacent energy states is given by:

$$E=hf$$

The power per unit area spectrum that results from this important assumption agrees with observation and is given by the following expression:

$$I(\lambda ,T)=\frac{2\pi hc^{2}}{\lambda ^{5}(exp(\frac{hc}{\lambda kT})-1)}$$

Now I return to the bitter part of my post. As I make clear in my Engineering Perspective article, I am not a big fan of overpriced audio interconnects. I am not saying there isn’t a subjective improvement, but that it may not provide the greatest benefit to cost ratio for the audiophile.

However, at least these overpriced interconnects are *functional.* At worst, they get the signal from point A to point B. Even something as esoteric as a special wooden volume knob that improves your sound at least allows you to turn up the volume! **But a product that claims to dramatically improve your system by acting as an electromagnetic blackbody for your equipment is a complete waste.**

There are people in this world with incredible perception that can detect “impossible” subtleties. The purpose of the audiophile industry is to cater to these individuals – those for whom minute differences matter. Please try to give these gifted individuals the audio experience they deserve and not just another piece of junk backed up with horrible pseudoscience.