Energy is not a substance, not something in the sense of “some thing”. Energy often appears to be a substance that flows, for example if charging a battery or an electrical capacitor. When charging, also electrons flow into these devices, but as many electrons flow out of the device. Nevertheless, there is something flowing into the device, namely energy. Moreover, the charged electrical capacitor is a tiny little bit more massive, more heavy than before, because an amount of energy E has always the mass m given by the famous equation E = m c2. Therefore, when charging a battery for example, energy did flow – there is no doubt about it, also because there is no doubt about the direction that the energy flowed into. Add that energy is almost always ‘conserved’, which means that energy is usually not destroyed, and it is understandable that energy seems to be an indestructible substance for many. However, discussing ‘space plungers’ and general relativity shows that energy is not conserved. Now let us consider first the energy of movement, called ‘kinetic energy’, in order to see independently that energy is not a substance, not holy golden cow urine.

If I push two shopping carts away from me toward the left and right, it seems that some of the energy in the food I ate flows through my arms into the carts. The carts now have kinetic energy, relative to me and relative to each other. It is moreover true that I lost as much energy as the carts now have relative to me. I lost that much energy somehow “through” (the action of) my arms. However, it is a mistake to think that energy is a substance flowing through my arms into the carts. I and the shopping carts are on the deck of a ship and the ship is moving to the right. The cart that I pushed toward the left away from me was therefore slowed down relative to somebody on the shore, stationary on land while the ship sails by. That cart, the cart toward the left, therefore lost kinetic energy.

Therefore, relative to observers on land, the energy flowed from the left cart into me. If energy were a substance, perhaps like water made from “tiny little things” such as water molecules, those little things either went from me to the left cart or from that cart to me. However, the “flow of energy”, its direction and size, depends on whether we describe the situation relative to the ship or relative to the shore. As long as the energy is mostly a mathematical expression on paper, there is no problem, but “real things” go one way or the other (of course, “real” is used in many different ways and quite usually fundamentally meaningless).

Do not think that perhaps we cannot describe also the kinetic energy here in terms of energy flows. We can. The problem is only that relative to me, the energy flowed from me to the left cart, but relative to the shore, it flowed from that cart into me. Therefore, there was no substance or even just particular kinds of information that flowed that would be the chemical energy in my arms that somehow turned into kinetic energy in the carts! Now how can that be if the chemical energy is some sort of substance? It seems easy: the chemical energy turns into the energy of spring-like molecules in my muscles and so on. But tell me, where and how does it turn into kinetic energy? Or replace me with a spring squeezed in between the shopping carts. As the spring relaxes and therefore pushes the carts apart, how does the energy in the spring, which can be thought of as being in the squeezed molecular electric fields, turn into the kinetic energy? What goes from where into which direction?

There is an answer: Special relativity theory shows that the moving body’s length is somewhat contracted, and the energy of the squeezed fields in the spring can indeed be described as having been transferred into the squeezed state of the contracted moving body. So, the circumstance of being contracted flowed (geometrically in space-time). However, many who claim knowing relativity theory refuse this answer as misleading or even totally wrong, because they often think that whoever talks like I just did also believes that the contraction is not “merely relativistic”, that velocities are not relative but instead velocities in a substance-like space (‘ether’). We will return to this topic, but for now I emphasize that our arguing against kinetic energy being a substance does not involve modern relativity theory! All that is necessary are Galileo’s 1632 insights into the relativity of motion, because that is where the ‘Principle of Relativity’ (POR) originated, not with modern relativity theory (also Feynman pointed this out).

Once more: That kinetic energy is relative to the observer (and therefore not a substance) is known, or could have been known, since (at least) Galileo’s insights into the relativity of motion in 1632, no matter whether or not Galileo or even still Newton personally thought that earth is a mere ship while space is a shore of godly significance – I am not interested in the history of who thought in which way or how the language of most of the people we can still read about is to be properly interpreted given that Galileo for example was clearly not allowed to speak freely. I am interested in how we can understand fundamental issues with the least amount of theoretical input today.

The chemical energy turned into facts about how everything moves relative to each other. Not just carts moving relative to me. Also the heat produced in my arms is molecules moving relative to each other. So, there is again a flow of energy into a certain direction, for example when the extra heat in my arm leaves into the surrounding air. But what flows? The circumstance that things move faster relative to each other! What goes into a battery? Electro-magnetic fields between charges such as electrons. However, in descriptions that are widely held to be “more fundamental”, those fields are made from ‘photons’. Those photons are mostly ‘virtual’, meaning in some sense not “real”, but also real photons do not exist as independent things by themselves – saying that photons are “particles of light” is very misleading. Photons are not packages of energy. Photons are never stationary, and their energy changes with the velocity of the observer. So we arrive again not at substances but at circumstances, how things move relative to each other.

The same holds for the potential energy in form of chemical bonds in the battery. All such potential energy can be described as the interaction of ‘virtual particles’ with each other. Energy has in some sense disappeared, has been ‘eliminated’ as the philosopher may say (‘eliminativism’, regarding energy or consciousness), because wherever you think the energy currently is, for example in a certain photon, you can move along with it and therefore have that energy be as close to nothing as you wish relative to you. Kinetic or potential, energy is always potential (and kinetic). For example, your kinetic energy relative to me is the potential for me to take energy out of your movement, perhaps charging a battery a little with it. You see here that the Chinese word for energy, 能量 (néngliàng), or “capacity of potential(capability)”, conveys this interpretation. Energy is in the facts of how things are to each other – there is no substance that is conserved but symmetries.

An Exercise to see whether you understand - should be solved without caring much about the equations: Energy Conservation, Kinetic Energy as Potential Energy I push two shopping carts apart as discussed, giving them each the same velocity v relative to me, and therefore the same kinetic energy E. The total energy given to them is therefore 2E. If the carts were to collide (I could for example have them on bent tracks), this energy will be turned into heat inside the carts, and some sound energy, but all together being precisely 2E.
       However, kinetic energy is proportional to the square of the velocity: E = m v2/2. The relative velocity of one cart relative to the other is 2v. Therefore, the kinetic energy of one cart relative to the other is 4E, twice the energy I put into them! How can that be? Why is the produced heat in the collision not equivalent to 4E? (After all, the carts collide; they do not care about how I move relative to them!)

The above is an outtake of an introduction to a chapter on explaining energy as curvature from S. Vongehr: “Fundamental Science for Applied and Social Science Students.” Lecture Notes, Nanjing University (2018)