# Color of the Rainbow 1/5/20

A Lesson in Physics by Richard Bleil

Terry Pratchett (a marvelous and extremely witty fantasy author) wrote a book called “The Color of Magic”, which was made into a movie. Well, the way the movie flowed, I get the feeling it may have been made as a television series or mini-series then later crammed together into a two-part movie. In any case, at one point they are discussing the colors of the rainbow. “See that eighth color? That’s the color of magic.”

There is no magic in a rainbow (unfortunately), although prior to quantum mechanics it may have seemed magical. There are seven colors that we, as humans, have defined; Red, Orange, Yellow, Green, Blue, Indigo and Violet (ROY G. BIV if you recall your science classes). Today, these colors tell physicists SO much about the cosmos (and more).

Quantum theory is so named because the energy levels available to a system is “quantized”, meaning “discrete”. We say discrete because we don’t talk about them. So, shhhhhhhhhh…

Quantized is kind of like digital. Before digital processors, electronic circuitry was “analog”, meaning that the voltages can be anything from zero to whatever voltage will blow out the circuit. Today, digital circuitry works in “bits”, meaning zero or one. In a computer, the circuitry uses “transistors” (which I put in quotation marks because these days the transistors are housed in the computer chips) which turn on at about 3.3 volts. So, 3.3 volts or above is “1”, less is “0”. This is “quantized”, it’s either on or its off. There is no in between.

In an atom, the energy of electrons are also quantized, although there are many more levels than simply “on” or “off”. Imagine a car that can travel at 0 miles per hour (which we’ll call it’s “ground state” because it’s the slowest it can go), or 27 mph, or 32 but nothing in between. It would strike us as very strange to suddenly jump from 0 to 27 because we, you and I, are beasts that follow the classical laws of physics. The fact that we can accelerate slowly from 0 to 27 would seem equally bizarre to our quantum friend that follows quantum law.

In reality, we cannot measure the values of these quantum levels directly. However, we can measure changes in acceleration. In other words, we can measure when the car goes from 27 to 0 (a value of 27), 32 to zero (a value of 32) or even from 32 to 27 (a value of 5). We can do this thanks to the law of conservation of energy; as the energy decreases in our quantum car, that energy has to go somewhere (in the cars we actually have most of that energy goes into heat because of friction to slow the car down, although there are other forms of energy that absorb the energy as well such as sound).

In atoms, as the energy of the electrons decreases from a higher to a lower energy level, the energy released is electromagnetic in nature. In other words, the electron gives off light. Because each energy transition has a different energy (like in our example of 32, 27 and 5), each photon of light released has a different energy exactly equal to the energy of the specific quantum transition. Energy in light corresponds to the frequency of the photon, which in turn is related to the wavelength giving the light a specific color. In the electromagnetic spectrum, red is the lowest energy (visible to the human eye), and violet is the highest. So if 32 is violet, and 5 is red, then 27 might be, oh, blue or indigo I suppose.

The energy levels of each type of element is specific to that element, and they can be calculated using standard quantum mechanical calculation approaches. This is spectroscopy; we measure the amount of energy released by elements, and this helps us to identify those elements. For example, drug producing labs use metallic catalysts, but the metal chosen can vary. But these processes all leave behind some off that metal as a contaminant. ICP (Inductively Coupled Plasma) atomic emission spectroscopy on drugs identifies these contaminants which is one way that federal agents can link drugs collected at different locations to one specific lab. In astronomy, measuring the wavelengths of light helps astronomers identify the elemental makeup of stars and other celestial bodies. But it tells us more as well.

Thanks to the Doppler effect, spectroscopy also allows astrophysicists to determine if these celestial bodies are moving toward us, or away from us, and at what speed. The “Doppler effect” is best known to us through sound. If you’ve had a train pass you, you know that the pitch of the train horn drops as it passes. As it is moving towards you, more waves of sound are hitting your ear as it is approaching because the velocity of the train is added to the speed of the sound resulting in a higher frequency and a higher pitch. As the train passes, the speed of the train is subtracted from the speed of the sound, so less waves strike your ear per second, the frequency is lower, and the pitch is lower.

In astrophysics this is called “red shift” and “blue shift”. If the celestial body is moving away from us, this speed is subtracted (kind of) from the speed of the light. Less light strikes us per second, so the frequency is lower and the light appears just ever so slightly more red (shifted “red”) than it should be. If the body is moving towards us, the light will be shifted more blue. The amount of the shift tells us the relative speed of that body compared to us.

And that, my friends, is the color of wizardry. I’d say the color of magic, but I don’t want to infringe on any copyrights. Sorry, Terry. We all miss you.

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