The Quantum Quandary

Author: Kristina Lenn

Editors: Alex Taylor, Zuleirys Santana-Rodriguez, and Whit Froehlich

My absolute favorite movie is The Imitation Game with Benedict Cumberbatch and Keira Knightley, and I love this movie for these reasons:

  1. The lesson of not giving in to naysayers is showcased throughout the movie.
  2. As a computationalist, I am proud to see my field obtain more visibility in the public eye.
  3. And duh – Benedict Cumberbatch!

However, one of my favorite scenes in the movie is when school-age Alan Turing is walking with his only friend, Christopher. Alan’s perceived oddities make him a target of ridicule among his classmates, but Christopher makes this very poignant statement: “Sometimes it is the people no one imagines anything of who do the things that no one can imagine.”

History is filled with people deemed by others as misfits who overcame considerable odds to leave their marks on this world: Helen Keller, who, although blind and deaf, helped found the American Civil Liberties Union; Maya Angelou, a woman of color born to a Missouri family just before the Great Depression, who wrote the New York Times bestseller I Know Why the Caged Bird Sings; Srinivasa Ramanujan, who, despite his poor background and deep aversion to proofs, became a Fellow of the Royal Society. Given this tried-and-true spirit of human nature, it makes sense that the matter which creates us would follow suit. Or perhaps it is the other way around.

Think about the world around us. Pondering the cosmos is what many scientists and philosophers do at some point in their careers. The realization that we are minuscule compared to everything else that occupies this universe is both exhilarating and terrifying. And yet almost everything in it is affected by something that is ten trillion trillion times lighter than a feather (that’s 10 with 24 zeros after it)! This particle lived in obscurity until the end of the 19th century when it challenged two hundred years of established physical theory. It was the challenger; the champion was one of the most famous scientists history has ever known.

 

Physical foundations

Sir Isaac Newton is considered a household name in the scientific community. Known as the father of Classical Mechanics, Newton formulated many of the physical laws that govern our world such as gravity and the three laws of motion. These are expounded upon in his infamous book, Philosophiae Naturalis Principia Mathematica, the first edition of which is housed in the Wren Library of Trinity College at Cambridge. (Interestingly, one of Ramanujan’s notebooks is also housed there.) Additionally, Newton is credited with developing the mathematical branch of calculus.

principia

Newton’s magnum opus details the foundations of classical mechanics and begins to hint at the calculus he would later develop to further describe mechanical motions. Source.

 

Newton’s laws of motion are the backbone of classical mechanics, or Newtonian physics. The first law introduces the concept of inertia, which means that unless some outside force interacts with an object, that object will either remain at rest or remain in motion. The second law says that the force acting on an object is equal to that object’s mass multiplied by its acceleration (how fast it is speeding up or slowing down). The third law explains that when a force acts upon an object, a force of equal magnitude acts in the opposite direction.  For example, an object sitting on a table exerts a force on the table (the object’s weight); the table exerts a force of equal magnitude on the object, called the normal force.

 

Atomic rebels

These laws went unchallenged for approximately two hundred years; however, they fail for certain instances, one of which is atomic structure. An atom contains some of the smallest particles ever discovered, one of which is the electron, discovered by J. J. Thomson. This particle determines the charge of an atom. If an electron is removed from a neutral atom, the atom will become positive. If an electron is added, the atom will become negative.

At the center of the atom is its nucleus, discovered by Ernest Rutherford who was one of Thomson’s students, which is a central mass that contains two different subatomic particles. One of those particles, the proton, was also discovered by Rutherford and carries a positive charge. Protons are what give each atom its identity; for instance, hydrogen has one proton and helium has two. If another proton were added to helium, it would no longer be helium; it would be lithium.

 

atomicModel.png

Atomic model of three atoms: hydrogen, lithium, and carbon. Numbers indicate how many protons there are in the nucleus and the most outward shell holds the valence electrons. Source: Sarah Kearns

 

One of Rutherford’s students, James Chadwick, discovered the subatomic particle that coexists with protons in the nucleus: the neutron, which is of neutral charge. For example, carbon by definition has six protons and can have six neutrons. However, it can also have more than six neutrons or less than six. Neutrons determine the isotope of an element. Atoms of the same element but with different numbers of neutrons are called isotopes. While protons and neutrons are essential to an atom’s function, it is the electron that determines many of matter’s properties.

Electrons determine how a reaction will proceed; how solid crystals are arranged; if a material will conduct heat and/or electricity; and how high a material’s melting and boiling points are. One of the smallest things in the universe, this cosmological underdog, controls the design and function of medications, the body’s metabolism, and even blood flow. However, this particle cannot be described by classical mechanics. According to these laws, as electrons move and give off energy, they would eventually crash into the nucleus. But this situation is impossible.

 

Enter quantum mechanics

Niels Bohr, another of Rutherford’s students, developed the Bohr model of the atom to explain how they are structured. This model describes electrons as revolving around the atom’s nucleus in discrete orbitals which maintain distance from the nucleus. This is similar to the heliocentric view of the galaxy: all planets revolve around the sun. The sun, which is larger than all the planets (just as the nucleus is the largest part of an atom), is at the center, and the eight planets (sorry, Pluto) orbit around the sun. Mercury is the closest and would be considered the ground-state orbital (the orbital with the lowest energy). Neptune would be the highest-energy orbital (the valence orbital). But one of the key differences between planetary motion, which is described by classical mechanics, and the electron is that planets remain in their orbits; electrons change theirs repeatedly.

The development of the Bohr model was the first breach in the dam of Newtonian mechanics; once this model was established, the development of quantum theory skyrocketed. In order to describe the electrons, they were assigned four quantum numbers, which indicate the location, shape, orientation, and energy of the orbital occupied by an electron. According to the Pauli exclusion principle, it is energetically unstable for two electrons to have the same quantum numbers, which means that each electron is unique.

While the behavior of the electron differs from a classical mechanics description, its mathematical formulation, the Schrodinger equation which is the backbone of all quantum mechanics calculations, describes a quantum system the same way Newton’s second law describes a classical system. However, knowing the electron’s speed and position is a more challenging endeavor. In a classical system, if one velocity and one position of a particle are known, all velocities and positions of the particle, both past and present, can be calculated. With an electron or any quantum particle, it is impossible to pinpoint every position and velocity at all times. Instead, the best approach is to calculate a probability; and the best friend of probability is uncertainty. Heisenberg’s uncertainty principle states that while a position or velocity of an electron at one time can be known, it is impossible to determine both at the same time.

schrodinger-cat.jpg

Schrodinger’s famous cat depicts the principle of superposition – where the cat is either alive or dead, depending on when the observer opens the box. Source

Another example of the electron’s contravention against classical mechanics is superposition. In classical mechanics, if a measurement is taken, it does not affect the outcome. For instance, if the length of a table were measured to be five feet, that length would remain the same before, during, and after the measurement. In quantum mechanics, the measurement determines everything! Superposition means that a quantum particle can exist in a combination of different states; when a measurement is taken, the particle will “collapse” into one specific state. (A famous illustration of this concept is Schrodinger’s cat.)

Other scientists who found shortcomings with Newtonian physics and paved the way for quantum mechanics include notable scientists such as Max Planck, who said that energy can have separate levels called quanta; Louis de Broglie, who proposed the wave-particle duality (all quantum objects, which includes light, are both matter and waves); Manhattan Project lead J. Robert Oppenheimer (another of J. J. Thomson’s students); and Richard Feynman, who, as Eileen Pollack describes in her article “The Mind of a Scientist,” was the “last living link to Einstein.”

 

Quantum revolution

All of these breakthroughs have led to invaluable technology. Quantum mechanics is the foundation for solid-state physics, which has led to the use of the semiconductor. These materials have led to the integrated circuit, which revolutionized technology by creating laptops and smartphones. Semiconductors have also impacted both the environment through solar cells (which convert sunlight to electricity and reduce the carbon dioxide emissions into the environment) and medicine through pacemakers, hearing aids, glucose monitors, MRIs, and robotic surgery.

quantumComputer.jpg

Quantum computing is still in its infancy, but once developed it could be used to untangle complicated chemical interactions, have more effective machine learning, and most importantly, find the best logistics for travel and deliveries. Source.

Another emerging field is that of quantum computing, which will allow calculations to be performed more quickly and accurately than even a supercomputer, such as the quantum computer designed by Google. Quantum computing utilizes the previously-described concept of superposition, allowing the computer to run many different calculations simultaneously. A typical computer is binary-based (meaning it stores information in a series of 0s and 1s). For a quantum computer, all possible binary combinations can exist together. Quantum computers also depend on entanglement, which means that for a set of interacting particles, the state of each particle cannot be ascertained independently. However, this entanglement can lead to decoherence, the eventual loss of quantum behavior; this results in classical calculations.

It’s an awesome thought that this minuscule particle, which remained unnoticed until a hundred twenty years ago, has helped society evolve to this point. The electron, smaller than a speck of dust and undetectable to the naked eye, is what gives the stars and the planets their uniqueness. The universe owes its existence to this tiny particle. What better inspiration do we have to strive toward our fullest potential?

“The misfits, the rebels, the troublemakers, the round pegs in the square holes, the ones who see things differently. They’re not fond of rules, and they have no respect for the status quo. You can quote them, disagree with them, glorify or vilify them. About the only thing you can’t do is ignore them. Because they change things – they push the human race forward.” Jobs



kristina_lennKristina Lenn is a Physical Chemistry and Scientific Computing Ph.D. student in the Geva Lab where she is analyzing the quantum dynamics behind charge transport in photosynthetic reaction centers. She received her B.S. in chemical engineering from Wayne State University and her M.S. in chemical engineering from Cornell University. She spent three years as a lecturer at Wayne State before starting her Ph.D. at Michigan. When she is not busy doing research or writing her next post for MiSciWriters, she is working with the Museum of Natural History as a Science Communications Fellow, volunteering for STEM outreach events, reading as many books as possible, playing friendly games of chess, and writing for her own blog, Chic Geek and Chemistry Freak.

Read all posts by Kristina here.

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