Most of my students can trot out the standard definition of energy: “the ability to do work”. If asked to categorize ‘types’ of energy, they will default to the two broad categories of potential energy and kinetic energy. This says something about the effectiveness of the education system in secondary school science in conveying these notions. It may also reveal the analogies that have been found useful to describe energy phenomena to schoolkids. But it may also be a hint of how a reductionist Newtonian mechanics has permeated our view of nature.
I wonder how energy was described before this renaissance of physics and its accompanying mathematical tools. When putting on our ‘science hats’, we might scorn the ancient ideas that seem tinged with magic and mysticism, and yet embrace them when packaged as Force-wielding Jedi masters in the Star Wars saga. The scientific view we have imbibed implies detachment. We observe. We experiment. We are separated from the object of our study.
Our categorization of the two broad categories of potential and kinetic energy may be a consequence of this detached worldview. Let’s take the easier one first. If asked what kinetic energy is, my students will undoubtedly say “energy due to motion” and can even trot out a formula (E = ½ mv2) to calculate it. There are two internal labels attached to the object: it has a mass (assumed as a constant for now) and it has a velocity at a particular instant of time. With some prompting, my chemistry students would likely classify thermal energy (the various motion of molecules) and photon energy (the vibration of waves) as types of kinetic energy, in addition to their classical mind’s-eye picture of atoms moving in space. Electrons within an atom are in constant motion – so they should also possess some kinetic energy. In any case, all these are conceived as being solely “internal” to the moving object.
Potential energy, on the other hand, is more nebulous to students. Most of them would be able to recite the vague mantra that it is “energy due to position or state”. Exactly what that means is illustrated by specific examples, of which there are many. Gravitational and electrostatic potential energy are two that are well-known to students, as is the idea of energy “stored” in (Hooke’s Law) springs. There’s more vagueness when it comes to thinking about chemical energy (“stored in chemical bonds”) or nuclear energy (“stored in nuclei?”); and soon potential energy is a catch-all for anything that can “store” energy before being turned into motion. It’s potential. Not actual. Yet. Sounds oddly Aristotelian. In any case, there’s something “systemic” about potential energy – you have to consider the object, not in isolation, but where it is placed within a larger system. This may give rise to forces that act on the system that “tell” it what happens in the next instance or time-step.
Students will trot out multiple formulas for different situations to calculate potential energy. On occasion, a curious student will wonder why there are so many different ones, and we can proceed into a discussion of systems and reference states. This introduces a certain arbitrariness – after all we, the observers, have chosen to define the reference states thereby allowing us to come up with a formula or equation. The student experiences a little discomfort but then doesn’t worry too much, and the nagging thought of arbitrariness disappears. While I’ve referred to “students” liberally in the last several paragraphs, I should make clear that I too am a student who sometimes behaves in similar ways to my students. I’m briefly puzzled, and then something else that I have to do invades my mind, and the ephemeral strange feeling evaporates away.
Even as I’m teaching quantum chemistry, that sense of division between the potential energy and the kinetic energy remain – at least in the way we frame how to solve the Schrodinger equation for the models that we’ve introduced (particles-in-boxes, oscillators, rotors, atoms with nuclei and electrons). Odd ideas of wave-particle duality show up. We substitute Newtonian determinism for Born probabilities, but haven’t really changed the underlying paradigm. Although there are glimpses that potential energy and kinetic energy are coupled – the electron doesn’t fall into the nucleus of a hydrogen atom with Heisenberg’s Uncertainty Principle kicking in.
I was a little disheartened after grading my most recent G-Chem exams. A number of students seemed rather confused about how to solve a photoelectric effect problem. Instead of thinking conceptually about the different entities and their associated energies, it looks like they just tried to plug numbers into equations they could think of, even though I had explicitly stressed in class the importance of utilizing the conceptual picture and not to play the equation hunting-game which easily leads one astray. Maybe it was the pressure of being in an exam that caused their minds to fog. I was also less than impressed by the vagueness of explaining why atomic emission lines are observed. Granted, it can be a tricky concept. An electron is losing potential energy as it “drops” from a higher energy state to a lower one, and that energy is converted to a photon emitted from the atom. Some students conflated parts of their explanation with the photoelectric effect, suggesting to me that they didn’t quite understand the distinction between the two.
What would a pre-renaissance observer make of rainbows? A sign from God? Or a sign of gold? Leprechaun magic has some appeal, I suppose. In any case, there is an appeal to an external cause that increases the “size” of possibly existing entities. This is opposite to the scientific reductionist’s answer to why rainbows are observed. My reflex is to discuss the physical nature of light rather than leprechauns, but I wonder if my reflexive thoughts are honed by too narrowly framing the possibilities. Maybe this works for “simple” things such as rainbows, but fails when it comes to “complex” entities such as organisms. But rainbows and organisms are still part of a larger ecosystem to which they owe their existence. The way we frame our discussion of energy, the representative models we use, and why it can all be so confusing, perhaps hints at something more profound. If only I could grasp it.
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