Explaining Reality with Imaginary Numbers
You may have heard the term Quantum. By definition, quantum means “the minimum value of a physical property involved in an interaction” (Anne Marie Helmenstine). However, in physics, quantum means a discrete packet of physical property (Britannica). Quantum mechanics has been around for the last two centuries, and –subjectively– is one of the most interesting branches of physics. Quantum mechanics is well known, probably more so in recent years with new developments. Maybe you have heard of quantum computers or other technology and thus heard the term.
Perhaps you may also have heard about Schrödinger’s cat. It is often used in the discussions regarding our understanding of quantum mechanics (Wikipedia). How we cannot know whether the cat is dead or alive until we look and observe, and how both possibilities coexist when the box is not observed. This analogy depicts a paradox.
Unlike the mechanics we are used to, quantum mechanics deals with the behavior of particles at the scale of atomic and subatomic, such as these particles and their interaction with electromagnetic radiation (Britannica). On this smaller scale, the physics we use every day is not enough to explain the behavior of particles. Their interactions in this scale differ from what would happen. In quantum mechanics, objects may act like little balls or waves that travel.
In quantum mechanics, light and matter show the characteristics of both waves and particles –just like the comparison between waves or balls that helps us visualize. Therefore, every matter has a wavelength. However, the wavelength of the object is inversely proportional to the mass of the object (Quantum Mechanics and the Schrödinger Equation). Because of that, as the mass gets smaller, the greater the wavelength gets, and vice versa. This explains the dual characteristics of electrons or the notion that electrons can act like waves and particles both. To explain the wave-like properties of electrons, the Schrödinger Equation is used.
However, we already established that quantum mechanics is unlike the traditional physics we are used to. Therefore, it should be kept in mind that while we are dealing with formulae regarding quantum mechanics, such as the Schrödinger Equation, we often come across imaginary numbers and deal with complex numbers. However, what is an imaginary number? An imaginary number is the square root of negative 1. The imaginary number, i, was created in order to solve equations. Most people have already been acquainted with this number in high school since it helps us solve the equation x squared equals negative 1. On the other hand, a real number and an imaginary number combined are called complex numbers, these numbers contain a real part and an imaginary part. These numbers can be a part of an equation, and we often come across them in quantum mechanics. And if they didn’t exist, we wouldn’t be able to solve the equations (“Necessity of Complex Numbers.”).
Overall, I believe that it is incredibly interesting to see that something that happens in real life is explained with numbers that are not real and, on the contrary, are imaginary. Imaginary numbers are called imaginary since we cannot utilize them in any aspect of life, yet, there is a space for them in quantum mechanics.
Anne Marie Helmenstine, Ph.D. “What Quantum Really Means in Science.” ThoughtCo, ThoughtCo, 9 Aug. 2019, https://www.thoughtco.com/definition-of-quantum-in-chemistry-605914.
“Quantum.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., https://www.britannica.com/science/quantum.
“Schrödinger's Cat.” Wikipedia, Wikimedia Foundation, 5 Oct. 2022, https://en.wikipedia.org/wiki/Schrödinger's_cat.
“Quantum Mechanics.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., https://www.britannica.com/science/quantum-mechanics-physics.
Quantum Mechanics and the Schrödinger Equation, YouTube, 2 May 2017, https://www.youtube.com/watch?v=O6g-7rUgrdg. Accessed 7 Oct. 2022.
MIT. “Necessity of Complex Numbers.” YouTube, MIT OpenCourseWare, 5 July 2017, https://www.youtube.com/watch?v=f079K1f2WQk.
Image Source: Procsilas Moscas, CC BY 2.0 <https://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons