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Joule’s device couples the gravitational potential of the weight with the thermal energy of the water in a tank. Newtonian mechanics had some subtle inconsistencies that modern (1900 modern) science was just beginning to notice.Special relativity helped fixed the heck out of that.The approximation is good enough that ye natural philosophers of olde can be forgiven for not noticing the tiny error terms.
So, energy is a sort of strict economy (total never changes) with many different currencies (types of energy).
It merely implies that if matter were to disappear, you’d need a certain amount of some other kind of energy to take its place (wound springs, books higher on shelves, warmer tea, other kind); and in order for new matter to appear, a prescribed amount of energy must also disappear.
Not in any profound way, but in a “when the pendulum swings up, it also slows down” sort of way.
Energy takes a heck of a lot of forms: kinetic, chemical, electrical, heat, mechanical, light, sound, nuclear, etc. For example, the energy stored in a (not overly) stretched or compressed spring is and the energy of the heat in an object is .
Now, these equations are true insofar as they work (like all true equations in physics). Energy is a value that we can calculate by adding up the values for all of the various energy equations (for springs, or heat, or whatever).
Among his other predictions, Einstein suggested (with some solid, consistent-with-experiment, reasoning) that the kinetic energy of a moving object should be , where the variables here are mass, velocity, and the speed of light (c).