# What is Energy?

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What is energy?

For some reason, this perfectly legitimate question seems to spawn far more than its share of bad threads. So what is energy and how do conversations about what it is go wrong?

Energy in Newtonian mechanics

The first definition of energy that is usually encountered is “energy is the capacity of a system to do work”.  Work is then defined as a force applied over a distance.  When an object with some speed collides with another object it can exert a force on that other object and move it some distance.  So a moving object has “the capacity to do work” which is energy, specifically called kinetic energy.

From the laws of Newtonian mechanics and these definitions it is possible to derive the work-energy theorem.  This theorem basically says that for a rigid object the net work done is equal to the change in kinetic energy.  Similarly, it is possible to derive other forms of energy, such as gravitational potential energy or elastic potential energy, and to show how those forms of energy can be converted to other forms or transferred from one system to another through work.

Energy in other contexts

There are other definitions of energy which are used in thermodynamics, Lagrangian mechanics, and quantum mechanics.  There are also proofs that demonstrate how energy in one context is related to energy in the other contexts.  Those other definitions are also often brought up in a discussion about What Is Energy, and many people have a preferred definition.  For simplicity, we will stick with the usual first textbook definition, in no way implying that it is preferable to any other definition.  The discussion below applies for all the other definitions as well.

How the conversation goes wrong

The first way that conversations about energy go wrong is that, when someone provides a definition, the questioner essentially says “No, it cannot be that easy, what is energy REALLY”.

It is that easy.  Energy is a defined quantity, and the definition tells you what it is.  It doesn’t matter if you ask “What is energy” or “What is energy really truly actually” the answer is the same: the definition.  For any word, X, the answer to “what is X” is the definition of X, and this includes energy.  Energy is simply a defined quantity, defined as above.  The reason that we are interested in energy is not that the definition is tricky or involves any hidden magic, but that it is useful.  It is useful because it is conserved and it is related to other useful quantities.

The second way that conversations about energy go wrong is when questioners have the impression that energy is some type of “stuff” that has its own independent existence and they seek to find out what material the “stuff” of energy is made of.  In some ways, this impression is well founded.  After all, energy is conserved and it can be moved from one system to another, just like you would expect from your everyday experience with “stuff”.

Energy is not a thing with independent existence.  It is just a defined quantity used to describe a system.  This is similar to mass, charge, momentum, and any other similar defined quantity that we use in physics.  Just like you cannot have “pure mass” independent of a system which “has” the mass, the same thing holds with energy.  Sometimes questioners mistakenly think of light (photons) as being “pure energy”, but light has momentum and other properties also.

The third way that conversations about energy go wrong is when a poster knows and understands the definition of energy (either the “capacity to do work” definition or one of the others not covered here), but refuses to accept it for some reason.

There is not much to say about this one.  We use definitions so that we can understand each other.  If someone refuses to use the same definition as other people, then confusion results.  In physics (as in the rest of life), often the same word is used with subtly different meanings in different contexts.  It is important to be familiar with the various different definitions when you are dealing with the different contexts mentioned above.  It certainly is not a problem to have a favorite definition and to explain why it is your favorite, but recognize that the other definitions have their place also.

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42 replies
1. HallsofIvy says:

I've always thought  of "Energy" as a book keeping device!  We start with the definition of "kinetic energy" along with "momentum".  Then we find situations in which Kinetic energy is not constant so we define potential energy to take up the slack.  But when friction comes into play the sum of those is not constant.  So we add "heat energy", etc.

2. Jeff Rosenbury says:

Some generally accepted scientific facts:

Mass-energy is conserved.
Work is force times displacement.
Neutrinos rarely interact with other matter.
Neutrinos can be created with a much higher probability than they can be detected.

By my logic this causes some difficulties for the definition of energy as the ability to do work, since neutrinos generally can’t do the amount of work their energy would indicate (since they mostly don’t interact).

Claiming one neutrino in 10^25 can do work doesn’t excuse the others for slacking.

But that’s just my understanding. Could someone point out where my error is?

3. Wes Tausend says:

… Very good insight, Dale. Thank you. I have a unconventional, but simple perspective of looking at basic energy, or rather kinetic energy (which I believe is technically the basis of all energy). And this kinetic energy is simply equal to mc², as the most basic of root definitions. I then regard other forms of energy in the universe as subtracted from this kinetic total. In other words, since kinetic energy is most often associated with motion, I imagine some matter must always be given up somewhere (exchanged for energy) i.e. "decelerated" if we will, to accelerate a particle of mass somewhere else… or in fact apply any form of energy anywhere. Wes…

4. HomogenousCow says:

I feel like calling something a "defined quantity" might make it sound like a useless or ad hoc measure to laymen.

5. nasu says:

Great, it should be used as a reference. :)
It applies to other “hot” topics, not just energy.

6. Unified28 says:

Energy does have it’s definition. However there is a reason why we can define energy the way we do which is unknown to physicists today.

7. baudrunner says:

I see that you are looking for creative answers, since a pretty good description exists online, for eg. [URL]https://en.wikipedia.org/wiki/Energy[/URL]

8. Dale says:

I do think that the sentence, “There are other definitions of energy which are used in thermodynamics, Lagrangian mechanics, and quantum mechanics. ” could have been broader to specifically mention, chemical, nuclear, EM and other forms of energy that are not thermodynamic, nor mechanics. (Wikipedia lists 16 forms of energy, I’ll bet there are still more.)

I wasn’t trying to list forms of energy. I was trying to list definitions of energy. For instance, using the mechanics definition you can define KE, elastic potential energy, and gravitational potential energy all as different forms of energy using the same definition.

9. anorlunda says:

Good post Dale, congratulations.

I do think that the sentence, “There are other definitions of energy which are used in thermodynamics, Lagrangian mechanics, and quantum mechanics. ” could have been broader to specifically mention, chemical, nuclear, EM, rest-mass-equivalent and other forms of energy that are not thermodynamic, nor mechanics. Those are all domains where work = force * distance is hard to apply, therefore making “the capacity to do work” definition problematical.
Also worthy of mention is that we can freely convert between all these forms and that conservation applies to the collective sum of all the forms.

You’re correct of course when you said, “Energy is not a thing with independent existence.” But there is something special about energy that IMO goes beyond other properties like mass or momentum. That is the intertwined concepts of energy and time. I am thinking of the Heisenberg expression for the rate of change for any observable B. (sorry, I don’t know how to do Latex in PF4.)

dB(t)/dt = (i/hbar) [H,B(t)]

where H is the Hamiltonian and B is any observable. This has always struck me as very profound. With zero H (zero energy), nothing can change ever. Without a nonzero d/dt of [U]something[/U], there can be no event of any kind. If time is defined as “the way to order events from past to present to future”, then no events implies no time. I read into that simple equation that the existence of energy is a prerequisite to the existence of time.

Forgive me for going off the deep end. I know your focus was on more basic concepts. Perhaps if the title was “What Is Energy in Mechanics?”, then I wouldn’t have gone so far astray.

10. Dale says:

Energy does have it’s definition. However there is a reason why we can define energy the way we do which is unknown to physicists today.

We can define energy the way we do because we can define any word anyway we want. By definition.

I think that you may mean that we don’t know why the laws of nature are such that energy is conserved. But that is quite a bit different from not knowing why we can define words.

11. Dale says:

it would be a scientifically correct mindset otherwise to not be afraid to answer questions about the nature of energy.

I agree, and in my experience on this forum such questions are answered clearly and directly. And then the discussion goes downhill from there.

12. bhobba says:

Energy does have it’s definition. However there is a reason why we can define energy the way we do which is unknown to physicists today.

BTW I agree with Dale.

But just for the sake of fleshing this out more why exactly cant energy be the conserved Noether charge related to time symmetry?

If that’s the case we know exactly what energy is and why its conserved.

Thanks
Bill

13. Jeff Rosenbury says:

My problem with the “Ability to do work” definition is that it abrogates the “energy is neither created nor destroyed” rule. The two are incompatible because one has to stretch the definition of “work” way too far to argue that the energy of a neutrino can do useful work. Yet there is clearly something very, very close to that definition going on. I certainly don’t have a better one.

It is interesting that any discussion of energy seems to rely on things outside the energy. An electron is a thing. A photon is a thing. Energy is an ability. Energy does not exist by itself, but only in relationship to something else.

14. nasu says:

Who said anything about useful work in the definition of energy?
There is no stretch in the definition of work. The neutrino can do work on the particle with which will interact in a neutrino detector.
And actually this is quite useful for the people working at the neutrino facilities. But utility is irrelevant.

15. Islam Hassan says:

If we ignore the different classical classifications of energy (heat energy, sound energy, etc) and take a fundamental view, can we say that all energy at the fundamental level is ultimately one of these four categories:
[LIST]
[*]Kinetic;
[*]Static, ie deriving from an object/particle’s position in a physical force field;
[*]Energy incarnated in mass; and
[*]Dark energy, which we know little about.
[/LIST]

IH