Montessori High School
Capstone Publication
2022-2023
Wesley Wolheter......................3
Contents
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Quantum Accessibility
INTRODUCTION
Maria Montessori said “The goal of early childhood education should be to activate the child’s own natural desire to learn.” Even though I haven’t been in Montessori education all my life, I have had systems around me that stimulated my desire to learn. And when I was immersed in Montessori culture, that seed of desire was able to grow. One way I was able to grow my natural desire to learn was through libraries. My eighth grade year I was perusing the library and I found a book called We Have No Idea. It was a book about questions that science, specifically physics, couldn’t explain about the universe. I was hooked, and Oak Farm’s Montessori environment allowed me to pursue learning more, which led to my current passion for research and quantum mechanics. For my capstone project, I wanted to help inspire that desire in other students. I did that through a series of lessons and follow up shelf works that guided students through the basics of quantum mechanics in hopes of igniting their innate desire to learn.
Lesson One
My first lesson was an overview of quantum mechanics and the difference between it and classical physics. Quantum mechanics is the branch of physics used to describe the behavior of submolecular particles, including electrons, photons, and quarks (Mann, 2022). The ideas behind quantum mechanics were first developed in 1900 by physicist Max Planck and his work on blackbody radiation, electromagnetic radiation emitted from a body of matter that absorbs all wavelengths of electromagnetic radiation. He discovered that energy could only be absorbed or discharged in distinct packets. The smallest of these amounts he called “quanta” (“Planck’s Quantum Theory”, 2022). This meant that as a form of electromagnetic radiation, light was made up of these packets. This went against the general consensus that light and other forms of electromagnetic radiation was made of waves of varying energy and wavelengths (Mann, 2022). Five years later, Albert Einstein expanded on Planck’s ideas to explain the photoelectric effect, a phenomenon of metal emitting electrons while absorbing energy from these packets of light, which he called photons (Squires, 2022). Several years later, physicist Neil Bohr took the ideas of both Planck and Einstein to create his model of atoms. He also first discovered the property of electrons called wave-particle duality and is considered the father of quantum mechanics (Loeffler, 2018). Physicists who came after him like Werner Heisenberg and Erwin Schrodinger would build on his ideas to create modern quantum mechanics (Mann, 2022).
All these effects are what make quantum mechanics so different from classical physics. In classical physics, you can know an object’s initial state, as well as what is acting on it, you can predict how it will behave. But due to the inherent uncertainty in quantum mechanics, it is impossible to predict how any one particle will act. The quantum nature of subatomic particles also means certain properties can only have certain amounts, not in between them, the quantum (Cesare, 2019). Quantum mechanics also allows for things that seem impossible to happen, like quantum tunneling (Lea, 2020). My lesson introduced the history of quantum mechanics and how it differentiates from classical mechanics. The shelf work was a list of statements that the students had to sort between quantum mechanics and classical physics to help reinforce the ideas they learned.
Lesson Two
My second lesson was on the wave-particle duality of subatomic particles. Before Plank and Einstein hypothesized that light was made of particles, the scientific consensus was that light was a wave. Physicist Tomas Young performed an experiment called the Interference Experiment. In it he sent light through two slits onto a screen. The pattern of light created on the screen was created by the waves coming through each of the slits interacting with each other and either increasing or decreasing depending on the type of interference (Squires, 2022). But when Planck hypothesized that electromagnetic waves could be made into packets, this disrupted that idea. Einstein took the idea and used it to 3
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explain the photoelectric effect. Only certain wavelengths of light resulted in the effect on metal. He discovered that if light was quantized, it would explain the effect (Mann, 2022). When Young’s experiment was repeated, but with low levels of photons, individual photons spread seemingly random across the sheet. But as the intensity of light was increased, the individual photons formed the pattern expected of a wave (Ohtake). This is why while you can’t predict where an individual photon will appear, you can predict where it has a probability of appearing.
My lesson involved discussing Young’s experiment in depth. This experiment is crucial to understanding one of the basic concepts of quantum mechanics. The following shelf work will involve explaining the experiment to another student not involved in the lessons. By teaching someone else, I hoped to cement their understanding.
Lesson Three
The next lesson was about Hesienberg’s uncertainty principle. Werner Heisenberg’s principle about how much scientists can know about a particle’s properties. At its most basic, Heisenberg’s uncertainty principle is that you can’t know both a particle’s momentum and position. The simplest explanation for this is that at the quantum level, the very act of measuring one changes the other. Another way of looking at it is that this is part of the wave-particle duality of particles. A wave has a set momentum, but is spread out, whereas a particle has a set place, but uncertain momentum. Therefore the more you figure out a wave’s position the less you can figure about its momentum, and it starts acting like a particle, and vise-versa for particles (Lea, 2020). My lesson involved sharing this information with the students and the following shelf work was a simple worksheet involving answering questions about position and momentum.
Lesson Four
My fourth lesson was about quantum entanglement. Quantum entanglement is a phenomenon in which properties of particles, usually spin, will become connected to each other. Scientists are currently unaware how particles become entangled (Emspack, 2022). But scientists are sure it happens. And while it may seem impossible, entanglement has restrictions that prevent it from violating relativity (Caltech, 2023). My lesson explained quantum entanglement and the following shelf work was a simple walkthrough of the experiments scientists use to explore quantum entanglement.
Conclusion
Through these lessons, I hope that some of the students will find as much passion as I did. And maybe another student will find a different passion, and teach someone else about it. I hope that Montessori’s words take place through these lessons.
Works Cited
Cesare, Chris. “Quantum vs. Classical.” The Quantum Atlas, Joint Quantum Institute, 2019, https://quantumatlas. umd.edu/entry/quantum-classical/.
Emspak, Jesse. “Quantum Entanglement: A Simple Explanation.” Space.com, Space, 16 Mar. 2022, https://www.space. com/31933-quantum-entanglement-action-at-a-distance.html.
Lea, Rob. “Certainly Uncertain: What’s Heisenberg’s Uncertainty Principle.” ZME Science, 28 Sept. 2020, https://www. zmescience.com/science/physics/heisenberg-uncertainty-principle-095235/.
Loeffler, John. “Niels Bohr’s Quantum Mechanics and Philosophy of Physics.” Interesting Engineering, Interesting Engineering, 18 Nov. 2018, https://interestingengineering.com/science/niels-bohrs-quantum-mechanics-andphilosophy-of-physics.
Mann, Adam, and Robert Coolman. “What Is Quantum Mechanics?” LiveScience, Purch, 4 Mar. 2022, https://www. livescience.com/33816-quantum-mechanics-explanation.html.
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Ohtake, Yoshiyuki, et al. “The Wave-Particle Duality of Photons.” Photon Terrace, Hamamatsu Photonics K.K., https:// photonterrace.net/en/photon/duality/.
“Planck’s Quantum Theory: Quantization Of Energy.” BYJUS, BYJU’S, 5 July 2022, https://byjus.com/chemistry/ planks-quantum-theory/.
Squires, Gordon Leslie. “Quantum Mechanics”. Encyclopedia Britannica, 22 Aug. 2022, https://www.britannica.com/ science/quantum-mechanics-physics.
“What Is Entanglement and Why Is It Important?” Caltech Science Exchange, Caltech, 2023, https://scienceexchange. caltech.edu/topics/quantum-science-explained/entanglement.
Whiteson, Daniel, and Jorge Cham. We Have No Idea: A Guide to the Unknown Universe. Riverhead Books, 2018.
Link to video of Wesley’s presentation
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