# What is Energy?

## 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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44 replies
1. 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

2. 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.

3. 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…

4. anorlunda says:

Dalespam,

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

5. 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

6. 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 ?

7. 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.

8. 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

9. 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.

10. 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

11. 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.

12. 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

13. 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.

14. 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

15. 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.

16. 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

17. 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.

18. 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”

19. Dale says:

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

20. 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.