My previous postings on quantum mechanics have emphasized its probabilistic nature and the role of uncertainty. Another important aspect of quantum mechanics, which I will discuss in today's concluding essay of the series, is how, under quantum mechanics, many properties must take on integer (i.e., whole-number or discrete) values.
According to a document from the Stanford Linear Accelerator Center (SLAC), specifically a section entitled, "Discrete Energy, Momenta, and Angular Momenta," here is how one could think of quantum mechanics:
To get some idea of how counter-intuitive this idea of discrete values is, imagine if someone told you that water could have only integer temperatures as you boiled it. For example, the water could have temperatures of 85º, 86º or 87º, but not 85.7º or 86.5º. It would be a pretty strange world you were living in if that were true.
In fact, according to the Wikipedia, the word quantum "is often used in the more specific sense which it has in physics, where a quantum refers to an indivisible, and perhaps elementary entity."
Perhaps the most interesting illustration of discrete, whole-number phenomena -- to me at least -- is the Bohr model of the atom (sometimes also known as the Rutherford-Bohr model), with electrons orbiting the nucleus like the planets orbiting the sun in the solar system. These orbits have discrete distances from the nucleus. According to an Environmental Protection Agency (EPA) document:
Each orbit around the nucleus represents an energy level, and electrons cannot exist in between orbits. Orbits closer to the nucleus have lower energy. If energy is added, an electron can be "excited" to jump to a higher energy level--an orbit farther from the nucleus. Eventually, though, the electron will return to its original state, and the atom will give off energy equal to the difference between the two orbits.
In some materials, the energy is given off as X-rays; other materials produce specific colors of visible light, or other types of electromagnetic energy.
The University of Colorado's Physics 2000 website has an interactive activity where you can click to move the electron to an orbit closer to or farther from the nucleus and see what happens. In this demonstration, when the electron moves to a more inner orbit, it gives up a photon (a particle of light, also known as a quantum of light). When it moves to a more outer orbit, it takes on a photon.
According to the aforementioned EPA document, the Rutherford-Bohr model was not perfect. However, Schrodinger (a name we've seen in the past) was able to propose some corrective modifications.
Frequently during this series, I've noted Albert Einstein's objections to many ideas that emerged from quantum mechanics. In fact, Einstein actually played a major role in launching quantum mechanics!
Washington University (St. Louis) physicist John Rigden argues in a Physics World article that, of the multiple landmark papers published by Einstein in 1905, the one characterizing light in terms of discrete particles is the one that really stands out:
The big idea in Einstein's March paper was his gentle suggestion that light consists of individual, discrete, localized and indivisible quantum particles. This blithely made, audacious claim contradicted a century of compelling empirical evidence, and it challenged the crowning achievement of 19th-century theoretical physics: the electromagnetic theory of light. It can be argued persuasively that Einstein's March paper was the start of quantum physics.