Is Energy Only What We Think It Is?

[Dale]

DaleSpam submitted a new PF Insights post

What is Energy?

Continue reading the Original PF Insights Post.

 

[nasu]

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

 

[Greg Bernhardt]

Nice first entry @DaleSpam!

 

[anorlunda]

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

 

[Unified28]

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.

 

[baudrunner]

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

 

[Dale]

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.

 

[anorlunda]

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 something, 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.

 

[Greg Bernhardt]

Good distinction!

 

[Dale]

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.

 

[Dale]

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.

 

[HallsofIvy]

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.

 

[bhobba]

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 can't 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

 

[Jeff Rosenbury]

(sorry, I don't know how to do Latex in PF4.)

Is there a tutorial somewhere?

 

[Jeff Rosenbury]

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.

 

[nasu]

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.

 

[Khashishi]

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

 

[Islam Hassan]

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:

• 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.

IH

 

[Unified28]

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:

• 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.

IH

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

 

[Dale]

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

 

[Bret V]

DaleSpam submitted a new PF Insights post

What is Energy?

Continue reading the Original PF Insights Post.

In a word, energy is "Potential"

 

[Jimster41]

Very lucid. More philosophical than I expected

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.

 

[bhobba]

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

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.

Added later:
Whoops - as Shyan pointed out it was Hilbert.

Thanks
Bill

 

[ShayanJ]

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

Just a historical correction!
Hilbert asked her to look into it, not Einstein. Einstein only received the results in a letter and was amazed.

 

[bhobba]

Just a historical correction! Hilbert asked her to look into it, not Einstein. Einstein only received the results in a letter and was amazed.

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

 

[Dale]

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

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

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.

 

[bhobba]

That also happens to be my favorite definition.

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

Thanks
Bill

 

[Dale]

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.

 

[bhobba]

No, I think several other definitions are valid also. Also if you are doing a non Lagrangian theory then you need something else anyway.

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.

Thanks
Bill

 

[DirkMan]

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

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.

Added later:
Whoops - as Shyan pointed out it was Hilbert.

Thanks
Bill

And how does Noether define energy ? I couldn't figure it out reading those links.

 

[bhobba]

And how does Noether define energy ? I couldn't figure it out reading those links.

Its the conserved Noether charge from time symmetry.

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

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 can't define energy in GR in a straightforward way - because in GR you have space-time curvature:
http://motls.blogspot.com.au/2010/08/why-and-how-energy-is-not-conserved-in.html

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

 

[Jimster41]

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.

 

[DirkMan]

Thanks
Bill

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 ?

 

[bhobba]

Is it nonsense what I'm thinking ?

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

 

[anorlunda]

Dalespam,

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