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This is a question that has bothered me for a long time

Is energy real or is it just a very useful mathematical construct?

I personally think its just a mathematical construct, its designed so that it is conserved. Forces and fields are fundamental and energy is derived from it. However I have no justification for this apart from intuition and a desire for the universe to behave in a certain way.

However I am interested in what others think.

I understand that this could be a discussion on the definition of "real", and so I will clarify. By real I mean "fundamental". Is Energy the reason for forces and fields are so on or is it just a tool we use?

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    $\begingroup$ This is a philosophical question. (Many, including Hawking, don't draw a meaningful distinction between something that's 'real' and a 'mathematical construct') $\endgroup$
    – lemon
    Commented Jun 2, 2017 at 8:35
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    $\begingroup$ Why would a force be more fundemental than energy? For conservative forces we can define force as a function of the potential energy: $\vec{F} = -\nabla V$; so historically energy was probably derived from force, but mathematically there's really no way to state one's more fundemental than the other $\endgroup$
    – QuirkyTurtle98
    Commented Jun 2, 2017 at 8:39
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    $\begingroup$ My point of view is that if it can be measured, then it's"real". $\endgroup$
    – valerio
    Commented Jun 2, 2017 at 9:09
  • $\begingroup$ Related/possible duplicate: physics.stackexchange.com/q/138972/50583, physics.stackexchange.com/q/3014/50583, physics.stackexchange.com/q/217495/50583 $\endgroup$
    – ACuriousMind ♦
    Commented Jun 2, 2017 at 11:29
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    $\begingroup$ Nice question and you are right to ask such question. Not having the possibility to answer it because the question is on hold I'll comment it in simple words. An electron is real and a photon is real. To give the electron a higher energy one has to accelerate it with the photon. So the photons are the exchange particles, they transport energy from one body to another body. Photons are pure energy, the energy is real. Kinetic and potential energy are statistical values and depend from the basis of the observator. Only my 5cent. $\endgroup$
    – HolgerFiedler
    Commented Jun 2, 2017 at 19:12

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I think you believe in the reality of mass, but correct me if I'm wrong. It's involved in the acceleration of material bodies which are subjected to whatever kind of the three basic forces (the e.m. force, the weak force, and the strong color force). The bigger the mass the smaller the acceleration (except in gravity where acceleration is independent of mass).

Now, as you know, $E=mc^2$, (or $E^2=m^2 c^4 + p^2 c^2$), and thus you may conclude that $E$ is something real.

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