Physics Help Forum What is the rigorous quantitative definition of the concept of "Energy"?

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Oct 29th 2016, 10:34 AM   #11

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 Originally Posted by HamedBegloo WHAT FINALLY I WANT IS A QUANTITATIVE DEFINITION OF ENERGY. I MEAN SOMETHING LIKE: $\displaystyle E := something$

That's what we are trying to tell you. There isn't one. But this is not a problem as there are many other concepts that don't have a specific definition, force, work, action, etc. are a few others. The quantities that appear on the other side of "E = " vary depending on what the physical system is composed of. To make things even worse, if we are talking about potential energies we also cannot set a scale that doesn't include an arbitrarily chosen position to set as a zero point. So even if we had such an equation we still would have ambiguity.

-Dan
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Oct 29th 2016, 11:29 AM   #12
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 Originally Posted by topsquark Please don't shout.
Sorry I didn't knew total capital writing means shouting(and recently searched the web and understood it). I just wanted to distinct my main point. So big apologies.

 Originally Posted by topsquark That's what we are trying to tell you. There isn't one. But this is not a problem as there are many other concepts that don't have a specific definition, force, work, action, etc. are a few others. The quantities that appear on the other side of "E = " vary depending on what the physical system is composed of. To make things even worse, if we are talking about potential energies we also cannot set a scale that doesn't include an arbitrarily chosen position to set as a zero point. So even if we had such an equation we still would have ambiguity. -Dan
But doesn't theories supposed to be designed in an axiomatic way.

I know Physics is not math but I know a physical theory is a mathematical framework that fits best with our descriptions of nature. On the other hand mathematics is always constructed in an "Axiom-Theorem" way for the propositions claimed and in a "Primitive notion-Well defined notion" way for the concepts introduced. So it's a real pain when you talk about a so important concept in a theory and have no precise definition of it. Yes I can talk about Work, Heat, Kinetic Energy, Potential Energy, Thermal Energy and so on but I know "Energy" as a whole concept should be defined. For example when we say "The energy of a system is conserved" we are talking about energy itself not its various forms. Maybe physicists are smart enough to conceptualise "Energy" without a rigorous definition but for a noob like me it doesn't work.

Last edited by HamedBegloo; Oct 29th 2016 at 11:42 AM.

 Nov 9th 2016, 12:51 PM #13 Senior Member   Join Date: Jun 2010 Location: NC Posts: 366 Force, energy, and other "defined terms" are also "constructs." A construct is a way or method of observation that is constructive to understanding. (convoluted eh?) Of course "force" is a construct. The term was argued for years before adopted. Double-entry bookkeeping is a grand example of construct. Count like "this" then like "that". Get the same? Jim topsquark likes this.
 Nov 10th 2016, 11:44 AM #14 Senior Member     Join Date: Jun 2016 Location: England Posts: 366 In post #10 you put forward Space, Time, Mass and Charge as primitive notions, why can't energy be a similar primitive? In post #9 Topsquark quoted the 4 vector for momentum, this places energy in the time-wise component of the momentum vector. I might suggest that energy and mass are actually different views of the same underlying fundamental property of existence. topsquark likes this. Last edited by Woody; Nov 10th 2016 at 11:58 AM.
Nov 13th 2016, 01:31 AM   #15
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 Originally Posted by Woody In post #10 you put forward Space, Time, Mass and Charge as primitive notions, why can't energy be a similar primitive?
Because it is (at least for me) not intuitive enough. I mean what is energy of a system/particle/wave/field? Where it is stored in the system? Can we even consider a locality for "Energy"? Is it a property of a system as a whole or is it generated by the properties of the particles inside the system?
But something like mass or charge: Simple scalar numbers we assign to a particle(a localized entity).

 Originally Posted by Woody In post #9 Topsquark quoted the 4 vector for momentum, this places energy in the time-wise component of the momentum vector. I might suggest that energy and mass are actually different views of the same underlying fundamental property of existence.
Again, I want the dialogue to be in the context of non-relativistic Newtonian mechanics.

 Originally Posted by THERMO Spoken Here Force, energy, and other "defined terms" are also "constructs." A construct is a way or method of observation that is constructive to understanding. (convoluted eh?) Of course "force" is a construct. The term was argued for years before adopted. Double-entry bookkeeping is a grand example of construct. Count like "this" then like "that". Get the same? Jim
Sorry, but I didn't understand what you meant. Can you explain more?

 Nov 13th 2016, 05:56 AM #16 Senior Member     Join Date: Jun 2016 Location: England Posts: 366 you are requesting that we don't include the current physics thinking in our replies. The whole point of relativity was to explain concepts that could not be explained by Newtonian physics. Perhaps the most famous feature of relativity is the fundamental link between mass and energy (E=mc^2). I think I would be correct in saying that this link is not (and cannot be) shown by Newtonian physics. It was exactly the difficulty of answering questions like the one you posted that required the introduction relativistic physics.

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