# Energy a mathematical expression?!

by Phztastic
Tags: energy, expression, mathematical
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 Quote by Fredrik I wouldn't put it that way. It's not that the term "energy" can't be defined at all, it's just that it can't be defined in a theory-independent way. It has to be defined by a theory of physics, and different theories can (and do) define it in different ways. I wouldn't say that the idea that "energy is the ability to do work" is wrong. I would just say this: 1. It's not a definition. 2. It's a good way of thinking about the various types of energy that are defined in pre-relativistic classical mechanics. 3. It's not a good way of thinking about energy in quantum mechanics. 4. It's a guideline that we can use to choose which mathematical concepts in a new theory that should be given names that have the word "energy" in them.
1. Then what is it?
2. Energy? Or the definition?
3. Why? What about energy in QM?
4. Do explain!

In the common world... What is energy in both CM and QM? An ability? A property? What?
Or just a measuring tool for the amount of work?
Why use the idea of energy? Why do we need if?
Why not calculate the Work done and so be it?
What's the point of Potential energy?

What is our purpose of building mathematical models for energy and not knowing what "energy" is?!

The conservation principles are really mind boggling...
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 Quote by Phztastic 1. Then what is it? 2. Energy? Or the definition? 3. Why? What about energy in QM? 4. Do explain!
1. Explained by 2-4 (in the post you quoted), especially 4.
2. The statement that's not a definition.
3. In QM, the Hamiltonian is defined as the generator of translations in time, and we refer to its eigenvalues as "energy". "Work" is a less useful concept in the foundations of QM at least.
4. I thought that my statement was sort of self-explanatory, or at least that what I said before the list made the meaning clear.

 Quote by Phztastic In the common world... What is energy in both CM and QM? An ability? A property? What?
As I said, such terms are defined by theories. They are not defined "in the common world".

 Quote by Phztastic Or just a measuring tool for the amount of work? Why use the idea of energy? Why do we need if? Why not calculate the Work done and so be it? What's the point of Potential energy?
I'm not going to write 20 pages.

 Quote by Phztastic What is our purpose of building mathematical models for energy and not knowing what "energy" is?!
You're missing the point, those mathematical models (plus the experiments that tell us how good or bad their predictions are) are how we understand what energy is. If you want to understand energy, the only way to do it is to study its mathematical definitions in the relevant theories, and do some exercises.
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 Quote by Phztastic Why use the idea of energy? Why do we need if?
It is useful to make predictions.
 Emeritus Sci Advisor PF Gold P: 9,224 And power companies need it to know how much to overcharge you.

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