# What is Energy? A Definition and Controversy

Estimated Read Time: 6 minute(s)
Common Topics: energy, definition, object, defined, definitions

## Summary

• The article addresses the fundamental question, “What is energy?” and explores why discussions about energy can be challenging.
• It introduces the Newtonian mechanics definition of energy, which defines energy as the capacity of a system to do work and work as a force applied over a distance.
• The concept of kinetic energy, derived from the laws of Newtonian mechanics, is explained as the energy associated with the motion of an object.
• The work-energy theorem is mentioned, which states that the net work done on a rigid object is equal to the change in its kinetic energy.
• The article acknowledges that energy has different definitions in thermodynamics, Lagrangian mechanics, and quantum mechanics, all of which can be related to each other.
• It highlights how conversations about energy often go wrong, including when questioners seek a more complex or hidden explanation beyond the defined quantity of energy.
• The misconception of energy as a tangible “stuff” with independent existence is discussed, emphasizing that energy is merely a defined quantity used to describe a system, similar to other physics-defined quantities like mass and charge.
• The importance of using consistent definitions to avoid confusion in physics discussions is emphasized, even though different contexts may have subtly different meanings for the same term.
• The article concludes by emphasizing that energy’s usefulness lies in its conservation and its relationships with other essential physical quantities.

## What is energy?

Energy is a fundamental concept that refers to the capacity of a system to do work. It is a scalar quantity, meaning it has magnitude but no specific direction. Energy is a crucial concept in understanding the behavior of the physical world, and it comes in various forms, each with its unique properties.

1. Kinetic Energy (KE): This is the energy of an object in motion. The kinetic energy of an object depends on both its mass and its velocity. The formula for kinetic energy is KE = (1/2) * m * v^2, where “m” is the mass of the object, and “v” is its velocity.
2. Potential Energy (PE): This is the energy that is associated with the position or configuration of an object. Gravitational potential energy, for example, depends on an object’s height above the ground. The formula for gravitational potential energy is PE = m * g * h, where “m” is the mass, “g” is the acceleration due to gravity, and “h” is the height.
3. Mechanical Energy: This is the sum of kinetic and potential energy in a mechanical system. According to the law of conservation of mechanical energy, in the absence of non-conservative forces (like friction), the total mechanical energy of a system remains constant.
4. Thermal Energy: This is the internal energy of a system due to the random motion of its particles. It’s often associated with temperature and is a fundamental concept in thermodynamics.
5. Chemical Energy: Chemical reactions involve the rearrangement of atoms and molecules, and this process is associated with changes in energy. The energy stored in the chemical bonds of molecules is referred to as chemical energy.
6. Electromagnetic Energy: This includes energy associated with electromagnetic waves, such as light, radio waves, and X-rays. It can also be in the form of electrical or magnetic energy.
7. Nuclear Energy: This is the energy associated with changes in the structure of atomic nuclei. Nuclear reactions release a significant amount of energy.

## 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 that 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 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 to 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 an 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 that “has” the mass, the same thing holds with energy.  Sometimes questioners mistakenly think of light (photons) as being “pure energy”, but the 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.

Tags:
44 replies
1. Dale says:

Several speculative posts and responses have been deleted and this thread is now closed.

2. Mark Harder says:

[QUOTE=”Islam Hassan, post: 5124304, member: 336879″]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[/QUOTE]

Shouldn’t we extend that list? There are thermodynamic potentials and associated generalized forces related to generalized gradients of the thermodynamic potentials. Thermodynamic potentials include internal energy, enthalpy, free energy and others.

Of course, thermodynamic energies are a bit more complicated than the mechanical energies that generate mechanical forces, in that they include the mysterious, vaguely defined energy called ‘heat’. Heat is not a true potential. Nor is it something that ‘flows’, an outdated usage left over from the phlogiston theory of heat, which held that the stuff that raised temperatures was this massless invisible fluid that flowed from hot bodies to cool ones. Nor is it a single, differentiated form of energy like the mechanical potentials. In fact, it can be in the form of any of them. Perhaps it’s best defined as the sum of all the energies that increase as the temperature of a system is increased. Maybe heat is thermo’s equivalent of mechanical kinetic energy, an energy that exchanges one PE for another. Heat an iron bar, for example, and it will radiate light, so the heat given to the bar must have been transmuted into quantum jumps in the electronic energy of the iron atoms, which then is lost as electromagnetic energy in the form of photons.

3. anorlunda says:

[QUOTE=”afcsimoes, post: 5126985, member: 514004″]Please explain. Time is measured by clocks. A clock is something where periodic changes occurs. When there are no changes there are no time? But if I MUST have a clock to measure the time…[/QUOTE]

Think of causality, cause before effect. Before and after express concepts of time. We only need clocks to measure the quantity if time.

4. Neandethal00 says:

[QUOTE=”bhobba, post: 5127283, member: 366323″]That’s one reason why the definition I gave based on Noethers theorem IMHO is the best – it avoids all this stuff.

Yes its real energy, just as real as kinetic, or any other kind of energy.

Energy is simply a quantity required because the laws of physics do not change with time, or to be even more exact, required by an inertial frame – but detailing that will take us too far from the purpose of this thread. Start a new thread about the laws of physics and inertial frames if it interests you.

Thanks
Bill[/QUOTE]
Thanks Bill for all the links you posted above on Noethers Theorem. Isn’t it sad so many brilliant minds like Emmy Noethers go unknown in history of science. Even though I have to read them a few more times to understand her theorem, but its conclusion has touched the area from which I made the statement about Potential Energy.
In uncertainty principle I noticed there is a relation between energy and time.

5. bhobba says:

[QUOTE=”Neandethal00, post: 5127281, member: 265414″][B]Is Potential Energy Real Energy? [/B]In my opinion the answer is NO. A stationary object has no energy.[/QUOTE]

That’s one reason why the definition I gave based on Noethers theorem IMHO is the best – it avoids all this stuff.

Yes its real energy, just as real as kinetic, or any other kind of energy.

Energy is simply a quantity required because the laws of physics do not change with time, or to be even more exact, required by an inertial frame – but detailing that will take us too far from the purpose of this thread. Start a new thread about the laws of physics and inertial frames if it interests you.

Thanks
Bill

6. Neandethal00 says:

[QUOTE=”DaleSpam, post: 5122374, member: 43978″]DaleSpam submitted a new PF Insights post

[URL=’https://www.physicsforums.com/insights/what-is-energy/’]What is Energy?[/URL]

[URL=’https://www.physicsforums.com/insights/what-is-energy/’]Continue reading the Original PF Insights Post.[/URL][/QUOTE]

I do not want to start a new thread, I think this Energy thread is the right place to ask a new question.

[B] Is Potential Energy Real Energy? [/B]

In my opinion the answer is NO. A stationary object has no energy.

7. afcsimoes says:

[QUOTE=”anorlunda, post: 5122640, member: 455902″]If time is defined as “the way to order events from past to present to future”, then no events implies no time[/QUOTE]
Please explain. Time is measured by clocks. A clock is something where periodic changes occurs. When there are no changes there are no time? But if I MUST have a clock to measure the time…

8. anorlunda says:

Dalespam,

Can nuclear energy or chemical energy be expressed as capacity to do work, without converting to mechanics first?

9. bhobba says:

[QUOTE=”DirkMan, post: 5126721, member: 556592″]Is it nonsense what I’m thinking ?[/QUOTE]

Nonsense isn’t quite the way I would put it – its simply a bit complex and not easy to grasp without math.

As simply as I can put it, there is this theorem, called Noethers Theorem, that says if the laws governing a system do not change with time, then a quantity exists that also does not change in time ie is conserved. It, by definition, is called energy.

Thanks
Bill

10. DirkMan says:

[QUOTE=”bhobba, post: 5126491, member: 366323″]
Thanks
Bill[/QUOTE]
So I have read that blog, and also the comments. If I understand it at the simple most basic level, energy is conserved because of time, that is if we have X energy in a system at time t0 , and we have energy increasing towards Y at time t1 , we can have that conserved because we can imagine rewinding back the time evolution of the energy in the system as decreasing from Y to X , and if we add up the increase and decrease we get the same X. Is it nonsense what I’m thinking ?

11. Jimster41 says:

I was blissfully aware of it. It ‘s the way Susskind presents the Lagrangian, and Hamiltonian in his first (excellent) “Theoretical Minimum”.
I agree. It is as elegant as observation gets…

The reference for time, as we have it. The asymmetry of energy density?

Wow, I actually enjoyed that Motl essay.

12. bhobba says:

[QUOTE=”DirkMan, post: 5126397, member: 556592″]And how does Noether define energy ? I couldnt figure it out reading those links.[/QUOTE]

Its the conserved Noether charge from time symmetry.

If that’s gooblygook you have to know the theorem:
[URL]http://phys.columbia.edu/~nicolis/NewFiles/Noether_theorem.pdf[/URL]

The situation is this. The theorem states given any symmetry then there exists a conserved quantity. For time symmetry, ie the laws of physics do not change with time, that is defined as energy, so from its very definition is conserved. Its beauty is not only does it define what it is, it explains why it’s conserved.
‘if the Lagrangian is invariant under time translations, that is if it does not depend explicitly on time, then the Hamiltonian of the system is conserved In most physically relevant cases the value of the Hamiltonian is the total energy. We thus discovered that the conservation of energy is a direct consequence of the invariance of the Lagrangian under time translations. Under stable conditions, if you perform a lab experiment today or tomorrow you expect to get the same results. This fact alone implies that energy is conserved.’

The other advantage is it works in mechanics or field theory. It explains why you cant define energy in GR in a straightforward way – because in GR you have space-time curvature:
[URL]http://motls.blogspot.com.au/2010/08/why-and-how-energy-is-not-conserved-in.html[/URL]

Its usually only encountered in advanced treatments, but most when they first see it are simply dumbfounded – its implications are very deep. As Shyan pointed out when Einstein found out about it he was just as amazed.

The other interesting thing about it, is I have found most philosophy types are blissfully unaware of it.

Thanks
Bill

13. DirkMan says:

[QUOTE=”bhobba, post: 5126277, member: 366323″]I have read the replys, and still I cant see why the definition Noether sorted out isn’t the correct one:
[URL]http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html[/URL]

Not only does it define precisely what it is, it explains why its conserved, and even why the concept of energy becomes problematical in GR.

In fact that’s why Einstein asked Emmy Noether to look into it because of the issues in GR.

Whoops – as Shyan pointed out it was Hilbert.

Thanks
Bill[/QUOTE]
And how does Noether define energy ? I couldnt figure it out reading those links.

14. bhobba says:

[QUOTE=”DaleSpam, post: 5126302, member: 43978″]No, I think several other definitions are valid also. Also if you are doing a non Lagrangian theory then you need something else anyway.[/QUOTE]

Of course – there is no right or wrong answer here. Its just the modern version using Noether is so beautiful and elegant.

Actually I think that’s a future insights paper.:smile::smile::smile::smile::smile::smile:

Thanks
Bill

15. Dale says:

Although they are not my favorites, I think several other definitions are valid also. Also if you are doing a non Lagrangian theory then you need something else anyway.

16. bhobba says:

[QUOTE=”DaleSpam, post: 5126294, member: 43978″]That also happens to be my favorite definition.[/QUOTE]

I got that feeling – I am just surprised it didnt garner a lot of support in this thread.

Thanks
Bill

17. Dale says:

[QUOTE=”bhobba, post: 5126277, member: 366323″]I have read the replys, and still I cant see why the definition Noether sorted out isn’t the correct one:
[URL]http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html[/URL]

Not only does it define precisely what it is, it explains why its conserved, and even why the concept of energy becomes problematical in GR.

In fact that’s why Einstein asked Emmy Noether to look into it because of the issues in GR.

Thanks
Bill[/QUOTE]That also happens to be my favorite definition. As I said in the commentary, I don’t think that conversations about energy degenerate due to the definition (whichever one you choose), they degenerate for more human reasons.

18. bhobba says:

[QUOTE=”Shyan, post: 5126291, member: 160907″]Just a historical correction! Hilbert asked her to look into it, not Einstein. Einstein only received the results in a letter and was amazed.[/QUOTE]

Thanks for the correction – yes that is the correct historical order of events.

Indeed every student when exposed to it is amazed once it sinks in a bit. Which is why I am surprised I am the only one putting forward it as what energy is. Its just so beautiful and elegant – you know it is the correct basis of what energy is – it just smells right.

Thanks
Bill

19. Shyan says:

[QUOTE=”bhobba, post: 5126277, member: 366323″]In fact that’s why Einstein asked Emmy Noether to look into it because of the issues in GR.[/QUOTE]
Just a historical correction!
Hilbert asked her to look into it, not Einstein. Einstein only received the results in a letter and was amazed.

20. bhobba says:

I have read the replys, and still I cant see why the definition Noether sorted out isn’t the correct one:
[URL]http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html[/URL]

Not only does it define precisely what it is, it explains why its conserved, and even why the concept of energy becomes problematical in GR.

In fact that’s why Einstein asked Emmy Noether to look into it because of the issues in GR.

Whoops – as Shyan pointed out it was Hilbert.

Thanks
Bill

21. Jimster41 says:

Very lucid. More philosophical than I expected :nb)

But, I liked the way this article sort of directly addresses the epistemological function of energy as a defined quantity applied to useful observations and other kinds of work. Dalespam is one of those teachers that I like especially for his calm clarity. His blackboard always feels well organized and patient, to me.

I think this article would have basically been perfect if it had just given a nod, in the process of clarifying what goes where (and what does not) to the awe that the deep questions about energy, as the functionally precise term of fundamental importance so clearly described, do and should inspire. Even if it said nothing else about those admittedly distracting mysteries.

They are the reason I am genuinely interested in the utility of the term.

22. Bret V says:

[QUOTE=”DaleSpam, post: 5122374, member: 43978″]DaleSpam submitted a new PF Insights post

[URL=’https://www.physicsforums.com/insights/what-is-energy/’]What is Energy?[/URL]

[URL=’https://www.physicsforums.com/insights/what-is-energy/’]Continue reading the Original PF Insights Post.[/URL][/QUOTE]
In a word, energy is “Potential”

23. Dale says:

Some posts have been removed. Please don’t post personal theories.

24. Unified28 says:

[QUOTE=”Islam Hassan, post: 5124304, member: 336879″]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[/QUOTE]

Obviously kinetic energy is the most fundamental in all cases. At least Wes Tausend was right about that.

25. 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

26. Khashishi says:

Like a lot of other terms in physics, the definition of energy depends on context.

27. nasu says:

Who said anything about [B]useful [/B]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.

28. 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.

29. Jeff Rosenbury says:

[QUOTE=”anorlunda, post: 5122640, member: 455902″] [I](sorry, I don’t know how to do Latex in PF4.)[/I]
[/QUOTE]

Is there a tutorial somewhere?

30. bhobba says:

[QUOTE=”Unified28, post: 5122620, member: 545238″]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.[/QUOTE]

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

31. Dale says:

[QUOTE=”Unified28, post: 5122775, member: 545238″]it would be a scientifically correct mindset otherwise to not be afraid to answer questions about the nature of energy.[/QUOTE]I agree, and in my experience on this forum such questions are answered clearly and directly. And then the discussion goes downhill from there.

32. Dale says:

[QUOTE=”Unified28, post: 5122620, member: 545238″]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.[/QUOTE]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.

33. 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 [I]work = force * distance[/I] 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]B[/B]. [I](sorry, I don’t know how to do Latex in PF4.)[/I]

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.

34. Dale says:

[QUOTE=”anorlunda, post: 5122591, member: 455902″]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.)[/QUOTE]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.

35. 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]

36. 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.

37. anorlunda says:

Whoops, unfinished post inadvertently posted. Replaced by a later post.

38. Greg Bernhardt says:

Nice first entry [USER=43978]@DaleSpam[/USER]!

39. nasu says:

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

40. HomogenousCow says:

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

41. 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…

42. 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?

43. 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.