Introduction
In 1687, Isaac Newton presented his laws of motion and his law of universal gravitation in what is now referred to simply as The Principia. This remarkable work explained quite precisely the motions of the planets, the shape of the Earth, the tides, and the famous apple falling from a tree. This precision led to the thought that given the initial position and velocity of every particle in the universe, one could calculate the particles’ future positions and velocities for all time. This might suggest that God set the universe in motion according to a set of equations and thereby predetermines all physical events. This idea was referred to as “the clockwork universe” by some enlightenment thinkers.
Between 1900 and 1927, however, physicists conducted a series of experiments that probed the limits of applicability of Newton’s laws and ultimately lead to the development of quantum mechanics. Specifically, scientists sought to understand the nature of light and the structure of the atom. This article outlines the fundamental principles of quantum mechanics that developed during that time.
Wave-Particle Duality
Energy is not continuous: Light as a particle
Light has many wave-like properties. It refracts (bends) when it travels from one medium to another (from air into glass as with eyeglasses, for example), and it diffracts (bends, spreads out, and interferes with itself) when it passes through two closely spaced, narrow slits. In 1865, James Clerk Maxwell published a set of equations that described light as a wave. Those equations are still used to analyze visible light, radio waves, microwaves, and so forth.
Around 1900, however, Max Planck found that some light experiments could not be explained by treating light as the classical wave described by Maxwell. Maxwell’s equations did not place any restrictions on the possible energy values of the light at a given frequency (or color). Planck, however, found that the experimental results could only be explained if the light’s energy at a certain frequency was restricted to discrete values. Imagine the volume control knobs on two different radios – the first knob turns smoothly and can be set to any value one chooses (1½, 2.37, etc.), and the second knob “clicks” into place at integer values of 1, 2, 3, etc. The first knob is on a continuum, and the second knob is restricted to certain discrete values. When energy comes in discrete values, it referred to as being quantized, and thus the world of quantum mechanics was introduced.
Planck’s idea was further illustrated in 1905 when Albert Einstein published his paper on the Photoelectric Effect which described how light will knock electrons off a metal plate, but only if the frequency is high enough. For example, green light has a higher frequency than red light. For some materials, green light with a low intensity (not very bright) might knock electrons off the material, but red light will never knock off any electrons no matter how bright or intense the red light is. By analogy, one could imagine two hurdlers, one wearing green and the other wearing red. The hurdler in green (higher frequency) is able to leap over taller hurdles than the hurdler in red. No matter how many red hurdlers are sent down the track, none will ever jump over a green hurdle.
The photoelectric effect could only be explained by treating light as a collection of particles with discrete energies, now called photons. Brighter light is more photons, but higher frequency light (green) has more energy per photon. Planck and Einstein each won the Nobel prize in physics for their part in demonstrating that light has not only wave properties but also particle properties and light’s energy is restricted to certain discrete values.
Matter is not absolutely discrete: Electrons as a wave
Around the same time, chemists and physicists were working to understand the nature of electrons and the structure of the atom. Scientists considered the electron to be a small particle. However, in 1924, Louis de Broglie theorized that not only can light behave as both a wave and a particle, but so can matter, including electrons. In 1927, Clinton Davisson and Lester Germer proved the idea when their eponymous experiment showed that electrons could diffract (bend, spread out, and interfere), just like a light. The ability to diffract is a wave property. Electrons (a form of matter) have properties of both particles and waves.
Scientists had begun to realize that for very small (sub-microscopic) particles, Newton’s “classical” laws no longer applied. A new set of rules was needed, and quantum mechanics was born.
The Principles of Quantum Mechanics
In just a few short years, scientists had come to understand that light not only has wave properties but also has particle properties. Perhaps more surprisingly, electrons not only have particle properties but also have wave properties. Something completely new had been discovered for very small objects (roughly the size of an atom or less than approximately one billionth of a meter). How is this possible and what does it mean?
Superposition of waves into wave packets: When two waves interact, they can interfere constructively (adding together) or destructively (canceling one another). For example, two sound waves with slightly different frequencies will interfere to produce “beats” which musicians use to help tune their instruments. The beats are periodic fluctuations (themselves waves) in the volume of the sound. When two instruments are exactly in tune, the beats will disappear.
If MANY different waves with different frequencies are added together, they will interfere to form a wave packet (Figure 1). These wave packets can be used to describe objects as localized particles but with wave properties. In other words, this is how an object can behave as both a wave and a particle and it has several implications.
Uncertainty principle: The Heisenberg uncertainty principle states that for small particles, there is a minimum limit to how precisely the location and velocity of a small particle can be defined, and the precision of the two is inversely related (the better one is known, the worse the other is known).
As shown in Figure 1, very small particles have a wave-like nature, and the particles are, in fact, described as wave packets rather than as single points. This means that the location is not precisely defined. It is spread out over the length of the wave packet as marked by ∆x in Figure 1.
At the same time, the momentum of the particle (for simplicity, think velocity) depends on the wavelength of the wave packet (see Figure 1). However, since the wave packet is the superposition of many waves with many different wavelengths, the precise value of the wavelength of the wave packet is not well-defined.
If the wave packet is “squeezed” to find the position more precisely, the wavelength (and thus the velocity) becomes more uncertain. If you stretch out the wave packet to more precisely define the wavelength (and thus the velocity), position becomes more uncertain.
The observer effect: The observer effect says that the act of observing or measuring a system will change it to some extent. This can be understood by thinking about how objects are seen. When a person sees a large object like a baseball, their eyes are detecting the light (photons) reflected off that object. Anything that can be seen with the human eye is quite large and the photons of light do not move it.
However, when the object being observed is extremely small (for instance, the size of an atom), the photons striking the object will actually move the object when they reflect off of it. It is somewhat like throwing tennis balls at a basketball and determining the basketball’s location based on the reflection of the tennis balls. The impact of the tennis ball is going to move the basketball. To help mitigate this problem, scientists use a device called a scanning electron microscope which uses low-energy electrons to look at atoms. Because the electrons are lower in energy, they have less impact on the atom. Nonetheless, anytime something is observed, its position or velocity is changed to some degree. This is referred to as the observer effect.
Probability: In quantum mechanics, the mathematics which describes all of the possible locations of a particle is the mathematics of waves and probability. The probability of finding the particle in one location might be high and, in another location, might be low, but the important point is that there is more than one possible outcome when one looks for the location of a particle.
Multiple states until measured: In quantum mechanics, an electron can exist in a superposition of different possible “states.” A state could be thought of as all of its measurable properties, such as its location or its energy. Before a measurement is taken, one can predict the probability of the outcome of those measurements (one can predict what “state” the electron is in), but until the measurement is taken, the outcome is not known with certainty. Once the electron is observed or measured, the result becomes definite.
An illustration developed by Erwin Schrödinger helps explain this phenomenon: A cat is put in a sealed box with a radioactive substance, a detector, and a vial of poison. If the radioactive substance decays, the detector will trigger the release of the poison, killing the cat. The key here is that the decay of a radioactive atom is a quantum event governed by probability. In other words, one knows that the substance will decay, but one does not know EXACTLY when the decay will occur. According to quantum mechanics, before it is measured, the atom is in a superposition (combination) of both “decayed” and “not decayed” states. Because the cat’s fate is tied to the atom, the cat is also considered to be in a superposition—simultaneously alive and dead. The superposition only collapses, and the cat’s state becomes definite (either dead or alive), when a person opens the box and observes the system. Similarly, the definite state of an electron is only known when it is observed. Tunneling: Quantum tunneling is the phenomenon where a particle passes through a barrier that it classically shouldn’t have enough energy to overcome. This happens because quantum particles like electrons behave as waves, described by an equation that represents the probability of finding them in a certain location. Even when encountering a barrier, there can be some probability that the wave passes slightly through it, giving the particle a small but real chance of appearing on the other side (Figure 2). This phenomenon is utilized in a real-world device called a Scanning Tunneling Electron Microscope (STM) that can be used to provide images of surfaces down to the atomic level. It can even be used to manipulate individual atoms.
Summary of Quantum Mechanics
Through the study of light and very small particles such as electrons, physicists in the early twentieth century came to understand that for objects smaller than the size of an atom, Newton’s laws of classical physics no longer apply. Instead, the wave nature of matter starts to become apparent. This leads to a new understanding of the physical world governed by probabilities rather than certainties. Particles exist in multiple states at the same time and tunnel through barriers which they do not appear to have sufficient energy to overcome.
Part of what makes quantum mechanics so difficult is that it is generally impossible to observe for macroscopic objects (those objects that can be observed by the naked eye). Interestingly, however, the wave nature of matter does not cease to exist for these larger objects. For instance, it is possible to calculate the wavelength of a large object such as a baseball. The number is 10-34 meters (a 1 with thirty-three zeros in front of it). This cannot be measured or observed. For an electron, however, the wavelength is around 10-10 meters (a 1 with nine zeros in front of it) which is about the size of the atom and makes scanning electron microscopes possible. This means that the wavelength of an electron is approximately 1 septillion (or 1 trillion trillion) times larger than the wavelength of a baseball.
Theological Musings
As discussed at the start of this article, Newton’s classical laws of physics describe a deterministic and orderly universe where one could theoretically predict the future. By contrast, quantum mechanics describes a probabilistic and random universe. Albert Einstein himself found this troubling and in 1926, he famously wrote, “God does not play dice with the universe.” Yet after 100 years, the principles of quantum mechanics have been proven time and time again.
The principles of quantum mechanics suggest a world in which there is at least some degree of uncertainty. This in turn opens the door for a variety of theological musings. For instance, if there are multiple possible outcomes, then perhaps free will is choosing from among those outcomes. Maybe prayer, like the observer effect, is somehow a way to change the outcome. Maybe what appear to be “miracles” are simply the occurrence of low probability outcomes.
At the very least, thinking about quantum mechanics forces persons of faith to think about how God might act in a universe governed by probabilistic rather than deterministic laws.
The author thanks Prof. Rachele Dominguez of Randolph-Macon College for her helpful discussions and insights.
