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Energy is not really defined formally in what it is but in how it changes

Energy is as a number we can assign to a system using certain carefully chosen formulas and we state that this number is constant no matter what change a closed system has gone through. And there are a lot of formulas for seemingly different kinds of energy .

-? First ,How is energy even classified into different kinds when we don't even have a proper concrete definition about what energy is ,like what's the basis for classification and how formulas are chosen such that the number they provide obeys the conservation law ,is it arbitrary like choosing a certain set of rules that everybody aggress on ,and in those set of rules this formula gives us a number that stays constant ?

-? What's its relation to force ,force causes acceleration ,so what does energy signifies here?

Is energy like something that forces only acts on to transfer from A to B and this transfer of eneryg is what essentially causes acceleration ,Is this how we are supposed to interpret the scenario ?

i.e Are we supposed to asssume that force only acts on energy that it only causes transfer of energy and that transfer is what that results in accelration ,Is this the interpretation of energy model?

Finally ,How should be interpret line like "an object or a system carries energy or contain energy" ? Are we supposed to interpret it as that some work was done that led to transfer of energy to this object or system ,and now this system \object can do work ,that it can transfer energy ?

Is this the correct interpretation ,if so ,Can you elaborate it ,I only have a vague sense as to what i mean by the above statement ,getting into detials leads to contradication ?

How should be interpret this kind of line for ex "electromagnetic radiation carries energy" ?

Anuj
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1 Answers1

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  • Energy is a property. It goes in the same category as "redness" not "roses". There is no such thing as "that energy over there", although we may use phrases like those as short-hand abbreviations for other concepts.

  • Energy is a property of mathematical objects which are part of models of reality, not a directly identifiable property of a part of reality, like the redness of a rose. Things like "the translation of the rose's center of mass in the selected rest frame" or "the configuration of the masses in the system which includes the rose" have energy. Physicists and physics textbooks are guilty of a great deal of potentially misleading short-hand here.

  • It is a quantitative property. We can represent it with a quantity: a number and a unit.

  • Energy is a scalar property. It doesn't have an associated direction, only a magnitude and a sign. It has this in common with money, which can come in assets (positive) and debt (negative).

  • Energy is a conserved property. If we keep track of all the mathematical objects in our model of the system, there is always the same quantity of energy.

If we put these together we have almost all the pieces of a definition:

"Energy is the conserved scalar quantitative property of mathematical objects which are part of models of reality..."

We just need to add one example of it, so that we can investigate any physical system for something like the example, and then go looking for how its characteristics change when we vary the value of the example. We could pick any number of things. Here's one:

"Energy is the conserved scalar quantitative property of mathematical objects which are part of models of reality, one example of which is a property associated with the translation with velocity $v$ of a point-mass $m$ whose quantity is $.5mv^2$."

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