The meaning of transferring energy and storing energy
I am taking a free online course on introductory physics, and I am having difficulty understanding the concept of energy. I believe a lot of the difficulty comes from the choice of words used, when talking about energy, so I hope you can confirm or deny or elaborate on my points below. I am a mathematician by training, but a layman in physics, so my questions and thoughts below are from that standpoint.
First off, if I raise an object some distance above ground-level, then I do work on the object, and one of the phrases that is being used is that I transfer energy to that object. My question is if is there an actual flow of energy coming from me to the object? Am I giving my energy away to the object?
I think the answer is no, and that the phrase “transfer of energy” just means that the energy that I spend or lose is equal to the energy that the object gains because of our interaction. (It may be unclear what exactly I mean by “flow of energy”, but I imagine something similar to water flowing from a place with a high water level to a place with a lower water level).
Second, when lifting an object and talking about gravitational potential energy, the phrases the energy is stored in the object or energy is held by the object is often used. Some webpages qualify that the energy is actually stored in the gravitational field, and not in the object itself. 927
Similarly, when a spring is compressed, the spring is said to store potential energy, and some webpages say that the energy is stored in the bonds between its atoms.
My understanding is that a field is just the presence of a force, and as such, it should not have the ability to “store” anything? And in the same vein, do atomic bonds have the ability to store energy?
The thoughts that I have had so far, which make more sense to me, are this: The way we talk about energy is a convenience, which does not necessarily match how the energy concept really works. Energy is neither stored nor transferred. Rather, energy is a derived quantity, which is interesting because it is preserved within a closed system. From the state of a given object (i.e. given its speed, or its position in a field, or tensions within itself etc.), we may calculate a quantity that we call the object's energy. If the state of the object is changed, this may result in a change of the energy for the object, and if so, this increment or decrement in energy will match a decrement or increment of energy in the rest of the system, which can be useful in determining the new state of the system. 927