Appendix A

Breaking the Universe to Bits
(Quantum Mechanics Part 1)

“Those who are not shocked when they first come across quantum theory
cannot possibly have understood it.” ~ Niels Bohr

The Universe Is Made Up of Incredibly Tiny
Bits of Matter and Force

I’ve broken quantum mechanics into two appendixes. Appendix A follows how experimental results from the 1800s showed that the real world is made up of unimaginably small particles of matter and force. Those particles only come in specific increments, specific sizes. Specific quantum. Appendix B explores the bizarre behavior of those quantum particles.

What is this “quantum” of which I speak?

When you pay for something at the grocery store (in U.S. currency) the smallest bit of money you can use is a penny. You can think of that as a quantum particle of money. You can use multiple pennies, but the clerk will not accept a fraction of a penny.

The universe turns out to be built on similar rules. Each type of matter and force comes in its own specific-sized particles. Multiple particles are fine, but the universe does not accept fractions of these quantum particles. Period.

It’s even down to the point that the electrons bound up in atoms are bound at specific energy levels. An electron will ignore any bit of force, any quantum particle of energy, that is not exactly the difference between its current energy level and another energy level allowed by its atom.

Since the time of the ancient Greeks and the Vedic scholars, there has been debate about whether the “stuff” of the world is solid and continuous, or whether it is made up of unimaginably small bits. The Greeks called these tiny bits “atomos” from the prefix “a” (not) and the Greek word “temnein” (to cut). In other words, these atomos were the uncuttable, indivisible bits that make up all of the stuff in the world. In modern English, we’ve shortened atomos to atom. Unfortunately IMHO, as the centuries rolled by, the word atom was assigned to bits of matter that we now know are cuttable. But the concept that stuff is made up of a phenomenal number of uncuttable bits still holds. These days we call the truly uncuttable bits of matter and force “elementary particles.” Appendix A follows how the existence of these tiny bits was settled by experiments performed in the 1800s. And those experimental facts (those “observed phenomena”) tumbled scientists down the rabbit hole into the quantum realm.

It’s too much to go into here, but Appendix A also takes you into the granular nature of light and lays out the difference between our various human units of measure and the natural (Planck) units that the universe actually functions on.

The you-can-do-this-at-home activity for Appendix A is the easiest in the book!


The Temperature of Color

To my mind, the watershed experiment that led to quantum mechanics was an experiment performed in 1800 by William Herschel. His experiment revealed that different colors of sunlight have different amounts of energy. Different colors have different temperatures.

Now, it gets a little dicey when discussing color temperature because physicists and artists have opposite definitions of color temperature.

To an artist, the blue end of the rainbow (green, blue) represents the cooler temperatures. Green forests and the blue pools of water, for instance. The red end of the spectrum represents heat. Red fire, the orange-yellow Sun.

To a physicist, the temperature of a color has to do with the amount of energy contained in one quantum of light. One photon. A single photon at the violet end of the rainbow has been shown to have roughly twice the energy of a single photon at the red end of the rainbow.

For an artist, red is warm, and blue is cold. For a physicist, red is low temperature, and blue and violet are high temperature.

These definitions collide beautifully in the packaging of lightbulbs. Or is it that they are resolved beautifully? I can’t decide.

If you have a carton of lightbulbs around, look for a temperature chart on the packaging. Otherwise, search for “lightbulb temperature” online. You will find a chart or graph that illustrates my point. Lightbulb temperature is given in degrees Kelvin. The red (warm) end of the temperature range is in the relatively low Kelvin rating around 2700 or so. The blue (cool) end of the temperature range is in the relatively high Kelvin rating around 5000 or so. A temperature of 5000 Kelvin is almost twice as hot as 2700 Kelvin — but don’t try telling that to an artist, they have good reasons for their classification, which have nothing to do with the energy of the photons of each different color.

Since this little book is about physics rather than art, we will be thinking about the temperature of color in terms of the energy of a single photon of that color. Red low, violet high. And of course, photons exist at lower energy than red and at higher energy than violet. An example of a lower energy photon is a photon in the infrared. An example of a higher energy photon is a photon in the ultraviolet. See the “Electric Light” section of Chapter 8 of this book for what is lower energy than infrared and what is higher energy than ultraviolet.

Anyhoo — here’s a link to a kind of fun interactive graph that you can play with to explore the temperature of color:
https://phet.colorado.edu/sims/html/blackbody-spectrum/latest/blackbody-spectrum_en.html


Here are the links from the text in Appendix A:

108. Biography “William Herschel | Biography, Education, Telescopes, & Facts ….” 11 Nov. 2020,
https://www.britannica.com/biography/William-Herschel

109. Deeper Dive “Herschel’s Experiment | Cool Cosmos.”
https://coolcosmos.ipac.caltech.edu/page/herschel_experiment

110. Deeper Dive “Black-body radiation – Wikipedia.”
https://en.wikipedia.org/wiki/black-body_radiation

111. Biography “Gustav Kirchhoff – Biography, Facts and Pictures.”
https://www.famousscientists.org/gustav-kirchoff/

112. Biography “John William Strutt, 3rd Baron Rayleigh – Wikipedia.”
https://en.wikipedia.org/wiki/John_William_Strutt,_3rd_Baron_Rayleigh

113. Biography “Sir James Jeans | British physicist and mathematician | Britannica.”
https://www.britannica.com/biography/James-Jeans

114. Deeper Dive/Physics-Speak “Rayleigh–Jeans law – Wikipedia.”
https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law

115. Biography “Max Planck – Wikipedia.” 
https://en.wikipedia.org/wiki/Max_Planck

116. Biography “Ludwig Boltzmann – Wikipedia.” 
https://en.wikipedia.org/wiki/Ludwig_Boltzmann

117. Deeper Dive “Why is a minute divided into 60 seconds, an hour into 60 minutes.” 5 Mar. 2007,
https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/

118. Deeper Dive “absolute zero | Definition & Facts | Britannica.” 18 Jan. 2019,
https://www.britannica.com/science/absolute-zero