Why is energy so difficult to understand?

As mentioned before one of the complicating factors is that theoretical scientists tend to complicate subjects instead of simplifying them. And today mathematics prevail over natural philosophy.

‘If you can’t explain it simply, you don’t understand it well enough,’
Albert Einstein.

A little strange, because Einstein’s theory of general relativity is the hardest scientific theory to explain in simple terms!

Energy is a very difficult concept to work with because of the conservation (theories) laws and the theories on thermodynamics.

Among modern scholarship the most influential interpretation by far of the appearance of energy conservation between 1830 and 1850 is Thomas S. Kuhn’s classic essay, “Energy Conservation as an Example of Simultaneous Discovery,” which in turn has stimulated a number of thoughtful alternative approaches to the problem. Kuhn’s principal interest was not, however, to write another history of the emergence of the principle of conservation of energy; instead, he sought to identify “the sources of the phenomenon called simultaneous discovery.” He argued that between 1832 and 1854 twelve scientists—above all, Julius Robert Mayer, James Prescott Joule, Ludwig Colding, and Hermann von Helmholtz—“grasped for themselves” the essential “elements” of the concept of energy and its conservation, and he asked why these “elements” became accessible at that time, thereby seeking to identify not the innumerable “prerequisites” of the principle of energy conservation but rather only what he called the “trigger factors.” In particular, he identified three such factors: the “concern with engines,” the “availability of the conversion processes,” and the “philosophy of nature.” (Professor Fabio Bevilacqua, 1990)

Professor Hermann von Helmholtz is a scientist who has spent an important part of his career on the science of energy.

‘Energy’ issues dominate social, political, technological, military discussions and events. However, it is not at all clear if its various meanings are acceptable aspects of its polysemic nature or the result of deep confusion. Is there a way to clarify the field?
(Professor Fabio Bevilacqua, 2014, Energy: learning from the past)

The work of Von Helmholtz on this subject is beautifully described by Professor Fabio Bevilacqua in “Helmholtz’s Ueber die Erhaltung der Kraft: The Emergence of a Theoretical Physicist”.

Von Helmholtz introduced the term ‘the sum of tension forces’, soon after renamed ‘potential energy’. Here energy and its conservation acquire a first definite (mechanical) meaning: while a variation of potential energy corresponds to a variation of kinetic energy, in every instant the sum of potential and kinetic energy is constant.
(Bevilacqua 2014)

Brucke, a friend and colleague of Helmholtz, plays an important role: in 1874 he asserts that “all living organisms, including humans, are essentially energy-systems to which, no less than to inanimate objects, the principle of the conservation of energy applies”
(Bevilacqua 2014)

Brucke his opinion is very important here as it directs us to the fact that all nature is a giant mechanical (energy) system.

James Clerk Maxwell is well known for his book his book, “Theory of Heat”. Also his work shows the complexity of the conservation laws of heat and force.

“The whole science of heat is founded on Thermometry and Calorimetry, and when these operations are understood we may proceed to the third step, which is the investigation of those relations between the thermal and the mechanical properties of substances which form the subject of thermodynamics. The whole of this part of the subject depends on the consideration of the Intrinsic Energy of a system of bodies, as depending on the temperature and physical
state, as well as the form, motion, and relative position of these bodies. Of this energy, however, only a part is available for the purpose of producing mechanical work, and though the energy itself is indestructible, the available part is liable to diminution by the action of certain natural processes, such as conduction and radiation of heat, friction, and viscosity”.

“We now see the appropriateness of the name kinetic energy, which we have hitherto used merely as a name for the product 1/2mv2. For the energy of a body may be
defined as the capacity which it has of doing work, and is measured by the quantity of work which it can do. The kinetic energy of a body is the energy which it has in virtue of being in motion, and we have just shown that its value may be found by multiplying the mass of the body by half the square of the velocity”

“That part which is due to their relative position depends upon the work which the various forces would do if the bodies were to yield to the action of these forces. This is called the Sum of the Tensions by Helmholtz, in his celebrated memoir on the ‘Conservation of Force.’ Thomson called it Statical Energy, and Rankine introduced the term Potential Energy, a very felicitous name, since it not only signifies the energy which the system has not in possession, but only has the power to acquire, but it also indicates that it is to be found from what is called (on other grounds) the Potential Function”.

“It is proved in treatises on dynamics that if, in any system of bodies, the force which acts between any two bodies is in the line joining them, and depends only on their distance, and not on the way in which they are moving at the time, then if no other forces act on the system, the sum of the potential and kinetic energy of all the bodies of the system will always remain the same. This principle is called the Principle of the Conservation of Energy; it is of great importance in all branches of science, and the recent advances in the science of heat have been chiefly due to the application of this principle”.

“The reason for believing heat not to be a substance is that it can be generated, so that the quantity of it may be increased to any extent, and it can also be destroyed, though this operation requires certain conditions to be fulfilled”.

“The reason for believing heat to be a form of energy is that heat may be generated by the application of work, and that for every unit of heat which is generated a certain
quantity of mechanical energy disappears. Besides, work may be done by the action of heat, and for every foot-pound of work so done a certain quantity of heat is put out
of existence”.

“Now when the appearance of one thing is strictly connected with the disappearance of another, so that the amount which exists of the one thing depends on and can be calculated from the amount of the other which has disappeared, we conclude that the one has been formed at the expense of the other, and that they are both forms of the
same thing. Hence we conclude that heat is energy in a peculiar form”.

These fragments from The Theory of Heat, shows indeed that it is far from easy to label both force and heat as a form of energy. Also Maxwell leaves the origin of heat unspoken.

…“It is important to realize that in physics today we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way”
…. “It is an abstract thing in that it does not tell us mechanisms or reasons for the various formulas” …. “If we had all the formulas for all kinds of energy, we could analyze how many processes should work without having to go into the details”
…. “We do not understand the conservation of energy. We do not understand energy as a certain number of little blobs.” …. “Unlike Dennis’ blocks, there can be any amount of energy, at least as presently understood.”

Professor Richard Feynman 1963