What is the Abstract Definition of Energy?

[Abstracted Universes]

I've looked at a couple of the suggested previous discussions. While the questions are similar, if not the same in essence, I have not found a good answer. Allow me to first give you some background as to what I am asking.

I have pondered this question day and night; it has often distracted me from coursework and other such tasks I need to complete. Unless I completely misunderstand the topic, energy is difficult to grasp intuitively. Now, yes I understand energy is a property of a particle or body. Yes, I understand that energy has formulaic definitions for many things in many subjects. Yes, I understand that energy "works" and does its job, whatever those mean. However, I am not looking for these answers. I am not looking for "energy is the capacity to do work". This is a recursive definition. Work is already energy, granted, sometimes it is only a fraction of the energy of a system, but it is already some of said energy.

So, what I'm looking for is an inherent, intuitive, and abstract definition of energy. A definition that can be applied to most, if not all situations. Please do not respond that "this isn't possible" unless you have absolute proof that it is. Not only will this definition help me in my own discovery, but it could very well help many students who are trying to understand the topic.
I look forward to your responses and interesting discussion.​

 

[Vanadium 50]

OK, so you know what energy is, and you want to know what it is "really". If we answered that, couldn't you then ask what it is "really really" and then "really really really"?

You know what it is. It sounds like you have some sort of philosophical dissatisfaction with that, but it doesn't change anything. That's what it is.

 

[DennisN]

Hi, Abstracted Universes, and welcome to PF!
To me, "energy is the capacity to do work" is actually both intuitive and abstract. I would say that the best way to get an understanding of energy is learning physics and doing different exercises/solving problems that involves energy in classical mechanics (at first, at least). There are a lot of other concepts in physics that initially may be difficult to grasp intuitively like e.g. force, momentum etc and I'd say the same for those, that is, the way to get the intuition is solving various types of problems.

 

[Abstracted Universes]

First off, I'd like to thank you both for your answers. Second, I do have a philosophical problem with the way energy's defined. Allow me to tell you why:
#1: As I said above, and explained, its definition is recursive.
#2: I cannot extract a meaning of "energy" from its units alone. You may say that this is because its units are complex (not like imaginary complex, of course, but like convoluted complex), however, here's an example of complex units that make intuitive sense when stared at for a while:
At first, the universal gas constant, $R_\rm{u}$, has units $\frac {\rm{J}} {\rm{ mol ⋅ °K}}$ which can really be thought of as $\left( \frac {\rm{J}} {\rm{mol}}\right)⋅\frac 1 {°K}$. The last representation can be read "Joules per Mole, per Kelvin" this is relatively easy to understand... while there is an energy unit there, you get the point.
Certain complex units can be re-perceived in such a way they make realistic sense. I could assess a situation and point to the universal gas constant when I saw it. When I originally re-saw this constant, I had a little "awe" moment. When something like that has been plaguing me, I almost always have an awe moment, like a rush of clarity. At no point in my study of energy have I had such an awe moment. This leads me to believe that I do not understand it to its fullest as this feeling is associated with most all my other learning/discovery experiences. Needless to say, for otherwise I would not be posting this to a forum and would rather continue mulling it over myself, I think this awe moment does have an important meaning in learning. I'm not saying that I think this needs to me made easier. I think it is easier than I can see. Like the awe moment is right in front of me, in front of all of us.
And finally; I can tell you that the GPE of a 5 kg object at 20 m from the surface of the Earth is 980 J, and that this means that, I guess, it has the stored the capacity of 980 J of work. I have a vague notion of what this means, but its not "ahah". Its not completely without hand-wavy-ness.
Maybe I do just need to do more exercises, but so far, through out physical science in middle school, chemistry, and physics in high school, I have not found any revelation from the exercises. Maybe you can recommend to me a text that will help me understand this better, or if you've thought of something different, I'd love to hear that too.
Thanks again for your answers.

 

[russ_watters]

So, what I'm looking for is an inherent, intuitive, and abstract definition of energy. A definition that can be applied to most, if not all situations. Please do not respond that "this isn't possible" unless you have absolute proof that it is.
...
#2: I cannot extract a meaning of "energy" from its units alone.

Physics (science) doesn't seek to provide "meaning" and it isn't abstract; it seeks to answer quantitative questions. So the definitions of energy and work are mathematical, only mathematical and only mean what the math says. Unsatisfying? You're going to have to get over that, because that is all there is.

 

[Dale]

I am not looking for "energy is the capacity to do work". This is a recursive definition.

No, it isn't a recursive definition, nor is it circular (which is probably what you meant). Energy is the capacity to do work, and work is F.d. There is nothing circular about that.

There are other definitions of energy useful for different specialties, but within any given specialty the relevant definition is valid and non circular.

Unless I completely misunderstand the topic, energy is difficult to grasp intuitively.

Intuitiveness is pretty subjective. It is certainly very intuitive to me.

Work is already energy, granted, sometimes it is only a fraction of the energy of a system, but it is already some of said energy.

No, this is not correct.

#1: As I said above, and explained, its definition is recursive.

As above, it is neither recursive nor circular.

So, what I'm looking for is an inherent, intuitive, and abstract definition of energy. A definition that can be applied to most, if not all situations.

Then I would look into a definition related to Noether's theorem. I would define energy as the conserved quantity associated with time translation symmetry of the Lagrangian.

 

[Drakkith]

I can tell you that the GPE of a 5 kg object at 20 m from the surface of the Earth is 980 J, and that this means that, I guess, it has the stored the capacity of 980 J of work. I have a vague notion of what this means, but its not "ahah". Its not completely without hand-wavy-ness.

The GPE isn't stored in the object nor is stored in the Earth. It's stored in the Earth-object system.

 

[Orodruin]

At first, the universal gas constant, RuRuR_\rm{u}, has units Jmol⋅°KJmol⋅°K\frac {\rm{J}} {\rm{ mol ⋅ °K}} which can really be thought of as (Jmol)⋅1

There is no such thing as °K, it is just K.

 

[A.T.]

So, what I'm looking for is an inherent, intuitive, and abstract definition of energy.

This just leads to questions about definitions of "inherent", "intuitive", and "abstract".

I don't think there is much more to say, than stated here by Feynman:
http://www.feynmanlectures.caltech.edu/I_04.html

 

[olek]

Sorry, but I couldn't stay silent when I saw your question :-)

I would look into a definition related to Noether's theorem.

Thumbs up for that. IMHO it's the best answer outthere. It seems like total energy (called the hamiltonian) is just one of mathematical "parameters" of a system that undergoes some process, and it happens to be conserved in time, because of the assumption that the outcome of this process does not depend on the particular moment of time that process starts. Well, does it sound more or less convoluted? Keep in mind that to this day there are no observations of a process that doesn't conserve the total energy of a system (with the possible exclusion of the Big Bang of course), so defining energy as the very thing that is always conserved makes a lot of sense. It also suggests that energy is somehow connected with time.

This is classical mechanics. From quantum we deduce that energy and time are otherwise connected with an uncertainty principle (and there are imaginary numbers involved which opens quantum mechanics to strange interpretations). When quantum fields come into play a process can borrow energy from the physical vacuum in order to return it later on (which makes it finally conserved, but how does it know to do that if it's supposed to be inherently random - right?).

Furthermore, mass can transform into energy and energy into mass. So in order for the energy to be conserved we need to agree that mass somehow is energy. Since Einstein we know how much of it, but nobody knows how this transformation "really" happens.

I'm not sure if the conservation of energy even holds when time itself is not eternal, or time is not appropriately differentiable, i.e. granular or something like that.

You're going to have to get over that, because that is all there is.

Not cool. You did get over it - good for you. Do not discourage others from seeking better answers. How do you know that it's all there is?

The definition of what energy is "really" seems to annoy physicists, but it shouldn't. It's essential and they know it. So don't stop looking.

 

[Drakkith]

Not cool. You did get over it - good for you. Do not discourage others from seeking better answers. How do you know that it's all there is?

We don't. But Russ almost certainly means that it's all we know right now. Seeking an answer beyond what we know right now is pointless because we don't know the answer! This is not to discourage anyone from asking questions, it's to point them in the right direction and say, "Hey, this path leads nowhere right now. Go that way!"

The definition of what energy is "really" seems to annoy physicists, but it shouldn't. It's essential and they know it. So don't stop looking.

The reason it annoys people is that what something "really" is often implies that all of our current definitions and mathematical formulas aren't good enough and are missing something. Many also believe that because they don't have an easy time grasping something, then that means that our current understanding just ins't good enough. This thread is a perfect example. The OP is looking for an easy answer to something that is inherently abstract and often difficult to understand. Energy, while having a very simple definition, shows up almost everywhere and often in different forms than what you'd expect. For example, how many people actually understand that voltage is a measure of energy, not force? I'd be willing to bet that a huge amount of people don't. Then you have things like the uncertainty principle in quantum physics, mass-energy equivalence in relativity, and many other things where energy seems to be some mystical substance that we don't "really" understand.

Well, maybe we don't "really" understand what energy is, but I'd venture a guess and say that almost everyone who asks what something "really" is would get a perfectly satisfactory answer if they just kept digging into our current understanding instead of trying to throw it all out the window.

 

[Dale]

The definition of what energy is "really" seems to annoy physicists,

The question of what anything "really" is annoys scientists because it always comes with a claim that the standard scientific definition is insufficient. I.e. the complaint is that the scientific definition covers what the thing "is" but not what it "really is".

That is an annoying question because the qualifier "really" doesn't convey any information other than the writer's philosophical distaste for the existing definition. It is annoying because regardless of how complete the answer, the questioner can always respond with some variant of "yes, I know that's what it is but I want to know what it really is".

 

[russ_watters]

Not cool. You did get over it - good for you. Do not discourage others from seeking better answers. How do you know that it's all there is?

The definition of what energy is "really" seems to annoy physicists, but it shouldn't. It's essential and they know it. So don't stop looking.

The answers the others gave were good, but my opinion is a bit stronger and more direct: "Energy" isn't like gravity or mass. It isn't a thing that exists in the universe outside of humans but rather is a human bookkeeping construct. It's a definition, not a phenomena. So it means exactly what scientists/engineers say it means; nothing more.

Often the "more" people are looking for is way outside the scope of what energy (or even science!) is.

*With deference to @Drakkith; that isn't to say we might not find additional uses for it.

 

[olek]

Do I have something to add? Hmmm, always :-)

One could - philosophically - say that no answer "really" answers any question, but just shifts it into another domain, onto another level. Mathematics allows for an infinite number of such levels to be arbitrarily created, so...it can potentially go forever. I believe we all agree that this goes nowhere - as being nonphysical - so I propose to close this line of thought.

I'm still not too comfortable with the annoyance part since there's no valid claim made here attacking the current state of things (valid, i.e. some new evidence or pointing out some mathematical insonsistency). I've just recently got annoyed this way and was trying to talk a guy down from his wild, highly unfounded claims - and then - I felt very bad about it nad said to myself "never again". What I shoud've done is to point him in the direction of some more mathematics - that'll do it.

I get where the idea of energy being just a human construct comes from, but the same can be said about any other thing like location, momentum, mass, gravity - ultimately they are all human bookkeeping constructs. Are they not? Surely there's a difference between a definition and a phenomenon. A phenomenon is just a definition by example, a working hypothesis, a temporary definition, until it becomes obsolete, explained off by a set of other underlying phenomena. When we're querying a quantum system to give us specific answers (like energy), human tailored answers to questions that are significant to us humans, the system responds in a conforming way actually giving us one of the answers we're looking for. It doesn't mean the system had those answers in it before we asked for them. In fact the current understanding is that the answers we get (eigenvalues) are always forced by our questions (operators). Which bring us to the question whether any properties "really" exist. Ok, at this point I really should try to refrain from using the "really" word. But it's fun, isn't it?

 

[Dale]

there's no valid claim made here attacking the current state of things (valid, i.e. some new evidence or pointing out some mathematical insonsistency).

That would actually be far less annoying because then it would be a scientific question that could be addressed scientifically. Evaluating experimental evidence and theoretical self consistency is what scientists do.

 

[Abstracted Universes]

Well, thank you all for your responses. I definitely will look further into Noether's theorem. This has already given me some insight into what and how I need to understand it. By the way, I understand that the GPE is stored in the system and not the object. I suppose my brain associates it with the object because the Earth isn't going to go flying toward the 5 kg object. Anyway, thank you all again. I'm getting closer to being able to work with my understanding that the hand-wavy-ness is going away. And, I would disagree with the "bookkeeping" definition of energy. It is appearing, to me, to have a physically relevant and obviously observable quantification (and qualification) now.
Thanks again everyone!

 

[jbriggs444]

I would disagree with the "bookkeeping" definition of energy.

The bookkeeping answer grows on you. For instance, kinetic energy cannot be "real" and must be "bookkeeping" because it changes depending on your choice of reference frame.

Edit: To elaborate on this...

Suppose that I strike you in the face with my fist, resulting in a bloody nose. We can account for this as the energy in my moving fist striking your stationary head and being dissipated into the broken capillaries in your nose and in the residual motion of your head and my hand. Or we can account for it as the energy in your moving head striking my stationary fist and being dissipated into the broken capillaries in your nose and the residual motion of your head and my hand.

The two descriptions are equally valid. The invariant features of the incident were the initial relative velocity between head and hand and the final broken capillaries in the nose. The meaningful and "real" physics is in the invariants. The individual velocities, momenta and energies of head and hand are mere bookkeeping devices that we can use to calculate the invariants.

 

[russ_watters]

I'm still not comfortable with the annoyance part since there's no valid claim made here attacking the current state of things (valid, i.e. some new evidence or pointing out some mathematical insonsistency). I've just recently got annoyed this way and was trying to talk a guy down from his wild, highly unfounded claims - and then - I felt very bad about it nad said to myself "never again". What I shoud've done is to point him in the direction of some more mathematics - that'll do it.

At the very least the OP is saying either the current definition of "energy" is insufficient (circular, was the claim) or is being taught/explained poorly.

I get where the idea of energy being just a human construct comes from, but the same can be said about any other thing like location, momentum, mass, gravity - ultimately they are all human bookkeeping constructs. Are they not? Surely there's a difference between a definition and a phenomenon.

Some are, some aren't. Mass is a property of matter and gravity (or rather, a gravitational field gravitational field) is generated by that mass, so it's a phenomena. It's a thing that happens in nature that we try to describe. Location too (don't mistake units and coordinates for "being" location - they are a description of what is seen in nature).

But when I call energy a "bookkeeping construct", I mean it is a mathematical relationship between multiple actions/interactions/properties that turned-out to be useful, so we gave it a name so we could refer back to it. We've put names on a lot of mathematical relations, though the ones that are less useful aren't ones people remember. Consider velocity, acceleration, jerk, jounce...and then what? Physicists haven't put names on the next few derivatives of position with respect to time because they haven't found them to be very useful. Energy, it turns out, is very useful, so it has a name. But does that make it more "real" than the 6th derivative of velocity?

 

[russ_watters]

By the way, I understand that the GPE is stored in the system and not the object. I suppose my brain associates it with the object because the Earth isn't going to go flying toward the 5 kg object. ... And, I would disagree with the "bookkeeping" definition of energy. It is appearing, to me, to have a physically relevant and obviously observable quantification (and qualification) now.

I don't think you do understand that about GPE (or at least don't accept it) -- I think it goes to the heart of your problem. How do you reconcile your view with the fact (as said) that mechanical energy (potential and kinetic) are observer/frame dependent, making any object/system have an infinite number of different "energies"?

 

[sophiecentaur]

The question of what anything "really" is annoys scientists because it always comes with a claim that the standard scientific definition is insufficient. I.e. the complaint is that the scientific definition covers what the thing "is" but not what it "really is".

When that question is asked it is because the questioner has the wrong idea about what Science is all about. That applies to many people who have not been immersed in Science and Scientific Argument. It is annoying for many Scientists but we just have to accept that people can't believe that rearranging a few variables in a Mathematical formula can yield a meaningful answer. That is what Physics does. It's hard to avoid feeling excluded and resentful if the language you get your replies in means very little to you. "Really" is shorthand for "I can't understand the terms of the answer."
The answer is not to get mad but get educated.

 

[olek]

Mass is a property of matter and gravity (or rather, a gravitational field gravitational field) is generated by that mass, so it's a phenomena.

We've found that mass and gravity appear in the same equation, but it doesn't mean that one generates the other. Nothing is stopping us from defining mass as the negative gravitational flux over some small sphere divided by 4 pi G. Granted, assigning mass to matter as a property proved to be very useful, but I hope usefulness is not the only criteria we're after.

 

[Orodruin]

but I hope usefulness is not the only criteria we're after.

Of course it is. Being useful as a description of what we can observe is the entire point. Otherwise we are just doing maths.

 

[Drakkith]

We've found that mass and gravity appear in the same equation, but it doesn't mean that one generates the other. Nothing is stopping us from defining mass as the negative gravitational flux over some small sphere divided by 4 pi G.

You cannot arbitrarily redefine definitions without properly redefining everything that depends on, or leads to, those definitions. And what would be the point? You'd just end up explaining exactly what we already observe. The observable predictions of the theory wouldn't change one bit.

 

[Stephen Tashi]

So, what I'm looking for is an inherent, intuitive, and abstract definition of energy.​

Consider the distinction between "matter" and "mass". Physics textbooks often use the sloppy language that treats these ideas as equivalent. For example, a problem might say "A 2kg mass is resting on an inclined plane...". Something resting on an inclined plane could be a tea kettle or bowling ball. It could have the property of posessing a 2 kg mass, but it isn't the "mass" that is resting on the inclined plane. What's resting on the inclined plane is some form of "matter".

It might or might not be true that a scientist would be annoyed if someone asks "What is mass,?". However, no scientist should be annoyed by the question "What is matter?". That line of investigation is still ongoing.

I think you are using the word "energy" in the same way that the word "matter" is used. You want it to be a word that describes some "real" phenomena of the world ( like a tea kettle) as opposed to a property-of-phenomena (like the mass of the tea kettle). If that is what you mean by "energy" then you have a legitimate question, but we are no more likely to answer "What is energy?" than to answer "What is matter?".

 

[A.T.]

I hope usefulness is not the only criteria we're after.

I hope otherwise.

 

[sophiecentaur]

I hope otherwise.

Usefulness as a descriptive tool is as much as we could hope for. What else could there be? The 'ultimate truth' as a concept is a bit too spiritual for my liking and it makes many assumptions that are based on a human viewpoint.

 

[rumborak]

I wouldn't call it "ultimate truth" for sure, but I personally can't deny that my interest in physics has at least one element which is the understanding of the deepest structures of reality. I know what you guys are trying to get across here of course, but I think your stance is maybe a bit too "ascetic", for lack of a better word :)

 

[sophiecentaur]

I think we (PF) are Erring on the safe side. The other direction is even more risky.
I could ask you what you mean by "reality". If it means describing everything acceptably in terms that you already understand then I think that would be of very limited use. All the major steps forward have involved new approaches. Why there should be any limit (="deepest") is questionable.

 

[Victor Ray Rutledge]

As an addendum to the question, If one considers absolute entropy as a state where a particle has 'no energy', then energy is a representation of the position of a given particle with respect to that state. In essence, I'm asking if the juxtaposition of position could be considered the 'energy' present. I realize that this needs tons of modification and much in the way of clarification, but it has a ring of truth, to me. If I'm wrong,(and I probably am) I'm sure some of you helpful people will not hesitate to clarify and correct.

 

[atommo]

I'll give my best shot at describing what energy is:

Anything in the universe emits some form of radiation- this means that at the point the thing exists there are vibrations/waves/whatever you want to call them. 'Energy' is these waves. The higher temperature a thing has, the more energy it contains so more waves are produced/emitted. When an object stops emitting/having waves, that object ceases to exist as there is no energy to sustain its existence.

Essentially 'energy' is a form of disturbance in an otherwise flat/silent medium.

Feel free to correct me if I sound too pseudo-sciencey.

 

[jbriggs444]

Essentially 'energy' is a form of disturbance in an otherwise flat/silent medium.

A brick on the top of a wall (*) has potential energy without involving any waves or medium.

(*) More pedantically, the brick+earth+wall system has and maintains this potential energy.

 

[CarlM]

I suppose my brain associates it with the object because the Earth isn't going to go flying toward the 5 kg object.

Yes it does. You just do not see it that way.

 

[Drakkith]

Anything in the universe emits some form of radiation- this means that at the point the thing exists there are vibrations/waves/whatever you want to call them. 'Energy' is these waves. The higher temperature a thing has, the more energy it contains so more waves are produced/emitted. When an object stops emitting/having waves, that object ceases to exist as there is no energy to sustain its existence.

That's not quite correct. Energy has a specific definition in physics, though it is a bit abstract and can take different forms. What you've written is not how energy is defined. Energy isn't required to sustain the existence of objects, though it may be required to sustain a specific state of an object.
Give this article a read: https://en.wikipedia.org/wiki/Energy

Note that the precise definition is a mathematical one. All of the other text is simply an attempt to explain an abstract concept non-mathematically.

 

[sophiecentaur]

I used to tell the (14 yr old) kids that "Energy is what makes things happen. Without energy being used, nothing happens". Then I would sit back and wait for the class to come up with things they though proved me wrong (always good fun for kids). I managed to come up with an answer that showed what I meant. Except "OK Sir, what about dying?" The BS level used to up a bit at that point.

 

[member 563992]

What about symmetry breaking? I'm not sure if there's anything more fundamental to it but I always go back to the vacuum ground state. We also say there that it's the lowest form of energy however it seems a bit "funny" if you'd try not to keep entropy into discussion. What's bothering me is the spontaneous symmetry breaking with which I guess everyone is familiar with this data: http://www.fnal.gov/pub/today/images/images08/iSGTW050908.jpg

But I may be talking non sense in the end as I'm a complete ignorant on the mathematics of all of this anyways. For some reason I'd love to see beyond the CMB (gravitational waves) and hoping for an answer over there.