# Quantum = Pink

Need we say more?

What color do you imagine when you close your eyes and think “Quantum”? If you are to buy a case for your quantum computer, have you already picked your favorite color? (Okay, maybe it’s too early for that.)
Below I argue that the collective unconscious has already made the choice for you: it is going to be pink.

Excited?

Fear not. We will easily differentiate ourselves from warm and fluffy pink slippers. Our color is pink on black. Closer to purple, actually. We have good heritage: purple with white was the color of kings. But kings are no more, so let’s admit it: People think that “spooky” quantum phenomena have a purple glow around them. The disaster movie “Quantum Apocalypse” has a mysterious purple vortex approach Earth. Sci-fi now has “quantum cannons” shooting pink aura at the enemies, unleashing the chaos of uncertainty. You can’t fly your battlecruiser if you’re no longer certain you still have a battlecruiser.

Not convinced yet?

Well, you are reading a science blog, not a fashion magazine. The latter would feed its readers a collection of random examples and speculations, while we go looking for underlying principle. Alas, nobody knows how things get into the collective unconscious, nor are there any reliable ways to map it out. (Maybe it had to be two decades since the “Quantum Leap” TV show ended for people to forget the “blue flash”.) Instead, let us consciously find the relationship between pink and quantum.

If you have light with frequency distribution $1/f$, where $f$ is the frequency of the light-wave, it looks pink. The reason is that the color of an object is determined by the distribution of wavelengths of the electromagnetic waves emitted by the object. Since wavelength is inversely proportional to frequency (why?), colors corresponding to lower wavelengths dominate a $1/f$ power spectrum, because the amount of color mixed into this type of frequency distribution is the area under the curve $1/f$, so the higher frequencies end up with a larger representation (that is, the smaller range $40$$60$ Hz contributes the same area as the much larger range $4000$$6000$ Hz, in a $1/f$ power spectrum). And guess which visible color has the lowest wavelength… purple! Pink is what we see when purple is mixed with the rest of the colors according to a $1/f$ frequency distribution. Which is why the color pink seems to dilute purple with softer hues of red!

All my time as an undergraduate I thought that both pink and white (the “flat distribution” color – a mix of all frequencies with equal weight) noise comes from a single formula for fluctuating position of, say, an atom in a trap:

where $f$ is the frequency of a quantum harmonic oscillator, $T$ is the temperature of the environment and $\textrm{coth}(z) = \frac{e^{2z}+1}{e^{2z}-1}$ is the hyperbolic cotangent. Imagine my surprise when I read this: http://en.wikipedia.org/wiki/Quantum_1/f_noise.
They say that quantum origins of the observed $1/f$ power spectrum are not so easy to derive. After careful inspection, the above expression for the average kinetic energy of a quantum oscillator gives $1/f$ for the wrong limit of high $T$ (temperature), where quantum effects are negligible. To see this, note that the hyperbolic cotangent has the following expansion around $0$: $\textrm{coth} (f/T) = T/f + f/(3T) - f^3/(45T^3) +\ldots$, which is dominated by $T/f \sim 1/f$, when the ratio $f/T$ is much smaller than $1$ (i.e. for large temperatures $T$, since the atoms we study have fixed frequency of oscillation $f$).
What it teaches us is that fluctuations (and, hence, kinetic energy!) do not disappear at absolute-zero temperature (since $\textrm{coth(f/T)} \rightarrow 1$ as $T \rightarrow 0$), and that’s the only quantum effect in this system. The fact that the formula gives $1/f$ classically is probably just a coincidence, and the true nature of pink noise lies in many-body physics. Wikipedia quotes papers which prove that $1/f$ has nothing to do with quantum physics! For instance, if you run statistics on scores of classical pieces, you also find $1/f$ distribution of notes, though Mozart and Beethoven were not very quantum and their music was definitely not just noise. [Daniel J. Levitin, This Is Your Brain on Music]

Still, if we believe that human-scale time-travel will one day be possible, we may as well believe that the walls of our time portal will shine pink due to quantum gravity effects. [Michio Kaku, Physics of the Impossible, note color of the cover.]

## 2 thoughts on “Quantum = Pink”

1. Why not a superposition of all the colors…