How fundamental is Law of Conservation of Energy?

[I_am_learning]

Is it just as fundamental as Newtons Law of Motion or it is deeper than that?
I mean, is it like-
No matter what invention and discoveries you come up in future, no matter which theories fail and which emerge, this Law of Conservation of Energy shall always stand above all.

 

[russ_watters]

It's pretty fundamental, yeah.

 

[browncat]

I first answer to "the critic" and, later on I'll address to the short answer of russ_watters

This question is very important and deserves a special respect. You see, the critic, I've asked myself also the very same question and found a book by Bruce Lindsay, called: "energy: historical development of the concept", in which it discusses the strange concept of energy and the arrival to the conservation of energy.

It's pretty amazing, and the principle had to be verified in every science. One might think it is simply an obvious tautology, because: "hey, aren't we defining energy in such a way that, after a transition, IT DOES conserve?". But the answer is obvious: if such transition is reversed, and the limitations imposed by the second principle of thermodynamics can be reduced to a minimum (that is, if the losts in heat are reduced to a minimum), then we can almost have a reversible process and such reversibility is a statement of conversation of energy, as a conceptual thing.
The arrival to the theorem of work-energy, and hence the very first steps in understanding these principles are presented in a very artificial way in normal textbooks, so the most critic people ask about it: "how in hell can that be?? It suggests hidden truths!", and indeed. But when I look backwards to the point when I had that very same question, I realize the problem is due to the typical "shortness" (I won't take it as "mediocrity") of textbooks: the typical deduction of this theorem, and the theorem itself, is only a mathematical representation of the next sentence: "Hey! When we lift a body up, or when we exert a force on it, something changes; and if we take the process back in a way were we don't have heat loses, no matter the mechanism and no matter the details of the machine that let's us go backwards, then we'll get to the very same beginning, and will be able to start again".

Note: You've got it right: I take Reversibility as a main help to interpret the Principle of Conservation of Energy. It DOESN'T MEAN that irreversible processes (i.e., with heat loses) don't conserve energy: they DO, as every process does, but when heat losses enter the game the arguments are much more subtle, and therefore I'm using only the simplified ideality of reversible process.

Best regards to The_Critic, and continue being such critic, HARD TO FIND FRIENDS LIKE THAT, who ask themselves: "WHY IN HELL?".

D.
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It's pretty fundamental, yeah.

I'm truly sorry, russ_watters, but could you please avoid lowering the level of the site "www.physicsforums.org" through avoiding giving this non-argumentative kind of answers, and hence somewhat disrespectful to our friend who asks? The only way you could shut me up, would be by correcting and amplifying your answer to our friend in a way that HE judges as satisfactory.

Regards,

D.
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[Jokerhelper]

I'm truly sorry, russ_watters, but could you please avoid lowering the level of the site "www.physicsforums.org" through avoiding giving this non-argumentative kind of answers, and hence somewhat disrespectful to our friend who asks? The only way you could shut me up, would be by correcting and amplifying your answer to our friend in a way that HE judges as satisfactory.

 

[Feldoh]

It's fundamental in the sense that experimentally we've never observed a spontaneous increase in energy.

If you ever find yourself with a measured increase in energy typically the first place you should look is how you are defining your system.

As an example: a case like this might be looking at a car on a track. If you just look at kinetic and potential energy it might appear that the car is slowing down, but if you expand the system to include heat energy you will see that energy is, in fact conserved to a much more accurate measure.

All of this isn't to say that energy conservation is some fundamental truth, just that we haven't found a contradiction experimentally. Perhaps one day energy will be found to not be conserved.

 

[NEILS BOHR]

well now it seems as it is quite obvious and its like woho why is he askin that quesn??

but yeah it may take a few experiments to disprove it but then for now it is indeed one of the most fundamental law of nature!

 

[harcel]

It is not just an experimental fact. In fact, some experiments seemed to violate conservation of energy (CoE) and people spend a lot of time and money in seeing how this could be explained, as CoE is supposed to be universal, as long as we define energy deccently.

From Noether's theorem it follows that with every symmetry in Nature, there comes a conservation law. CoE goes hand in hand with the fact that the laws of physics are invariant under translations in time (this means that fundamental physics now is the same as it has always been, and that it always will be the same). Similarly, conservation of momentum goes together with translations in space (i.e. physics here is the same as elsewhere). This makes CeO very fundamental and not just some phenomenological oddity.

Cheers, Harcel

 

[I_am_learning]

All of this isn't to say that energy conservation is some fundamental truth, just that we haven't found a contradiction experimentally. Perhaps one day energy will be found to not be conserved.

Then the law is just as much 'pretty' fundamental as we consider any other law that is yet to be dis-proven experimentally, (like Newtons laws)
I thought, in deep level, it was like saying, 2=2, which can never be disproved. I think I was wrong, now.

Also, as browncat suggested, in engineering applications such as electrical, we readily accept this law and without regard to internal mechanism we simply have -> Energy Input = Energy Output.
I mean, without using any explicit circuit equations even in the complex circuit, we use this law to simplify matters.
I was just wondering, what if this law should fail for a particular circuit parameter, because, we haven't proved this law for that circuit.
Or is it that, the law is again experimentally supported when we see that the light glows just as calculated (based on that law)

 

[lalbatros]

Nobody knows about inventions and discoveries in the future.
If someone knew about it now, these inventions and discoveries would not be "from the future".
Therefore, it is obvious that one can only discuss the past and the present.

The law of energy conservation is one of the most fundamental laws, if not even the most fundamental.
That's the lesson of the past and the present.

Everytime energy looked as if it was not conserved, it turned out that the energy balance was not correct.
An additional item was identified and added to the balance.
This lead to almost all important discoveries in physics: from the nature of heat to photons and all the zoo of particles.

 

[russ_watters]

Then the law is just as much 'pretty' fundamental as we consider any other law that is yet to be dis-proven experimentally, (like Newtons laws)
I thought, in deep level, it was like saying, 2=2, which can never be disproved. I think I was wrong, now.

Actually, it is so fundamental that it is used as an assumption for the purpose of solving problems, very similar to 1+1=2. Most thermodynamics problems involve writing a CoE statement: Ein=Eout and using that statement to solve the problem, similar to what you said below.

In other words, we don't really try to prove CoE anymore, but rather use CoE to prove other things. That makes it pretty fundamental.

I was just wondering, what if this law should fail for a particular circuit parameter, because, we haven't proved this law for that circuit.

As explained above, you wouldn't use a circuit to test CoE, you'd use CoE to test the circuit. If you measured something and it didn't fit the CoE based prediction, you'd go look for your error, you wouldn't assume that CoE wasn't true for that situation.

That makes it pretty fundamental.

 

[D H]

Actually, it is so fundamental that it is used as an assumption for the purpose of solving problems, very similar to 1+1=2.

I agree with the latter sentiment, but not necessarily the former. It depends on what you mean by "fundamental". Fundamental, as in axiomatic? No. Conservation of energy derives from Noether's theorems. Fundamental, as in it is something that never has been observed to have been broken and that we think is never will be violated? Yes.

 

[lalbatros]

... Conservation of energy derives from Noether's theorems. ...

D H,

Noether's theorem has always fascinated me.
Therefore, I was almost going to mention it in my own answer to thecritic.
But I renounced to do so!

What does the Noether's theorem tell us regarding energy conservation?
It tells us that if the Hamiltonian is time-independent, then energy is conserved, isn't it?
Is that not a little bit like saying "if energy is conserved then energy is conserved" ?

In addition, the question by thecritic, could be rephrased in many different ways.
Like: "Is all fundamental physics hamiltonian physics?" and all the equivalent forms.

There is, of course, no general proof that energy conservation is an absolute truth that will never fail.
But as far as we consider the whole experimental range known today by physics, energy conservation is a truth.
That's how it goes with all truths in science: they have limits of applications that are more important to know than any truth itself.

 

[Feldoh]

It tells us that if the Hamiltonian is time-independent, then energy is conserved, isn't it?

It's not the Hamiltonian it's the Lagrangian of a system that has energy conservation if there is a time symmetry. I believe that the Hamiltonian is derived from time symmetry of the Lagrangian.

 

[Studiot]

... in engineering applications ... we readily accept this law and without regard to internal mechanism we simply have -> Energy Input = Energy Output.

~The Engineer's mantra has another term:

Input = Output plus Accumulation

 

[Feldoh]

Studiot has a good point. You need to also consider entropy. In any real life applications there is only a certain amount of useful energy that can be used.

 

[marcusl]

From Noether's theorem it follows that with every symmetry in Nature, there comes a conservation law. CoE goes hand in hand with the fact that the laws of physics are invariant under translations in time (this means that fundamental physics now is the same as it has always been, and that it always will be the same).

It's not the Hamiltonian it's the Lagrangian of a system that has energy conservation if there is a time symmetry. I believe that the Hamiltonian is derived from time symmetry of the Lagrangian.

Landau and Lifgarbagez make a distinction between symmetry, isotropy and homogeneity. They show that it is the homogeneity of time, that is, that a system behaves the same or an experiment gives the same result if run today as tomorrow, that leads to CoE. The demonstration involves showing that time-dependent behavior of the Lagrangian for a closed system is independent of absolute time. CoE results, and is as fundamental as time is homogeneous.

 

[Andy Resnick]

In addition to the deep connection between conservation laws and underlying symmetries (considering temporal homogeneity to be equivalent to symmetry under translations), there is also a deep connection between conservation laws and geometry: the so-called balance equations which are derived from the Reynolds transport theorem.

The Reynolds Transport theorem is a generalized continuity equation which balances the flow and forms an axiomatic basis for the conservation of mass, momentum, and energy. The derivation for energy balance is here:

http://en.wikiversity.org/wiki/Continuum_mechanics/Balance_of_energy

 

[Phrak]

Is Energy Conserved in General Relativity?

In special cases, yes. In general -- it depends on what you mean by "energy", and what you mean by "conserved".

--Michael Weiss and John Baez, here: http://www.xs4all.nl/~johanw/PhysFAQ/Relativity/GR/energy_gr.html"

 

[lalbatros]

It's not the Hamiltonian it's the Lagrangian of a system that has energy conservation if there is a time symmetry. I believe that the Hamiltonian is derived from time symmetry of the Lagrangian.

I think it doesn't matter if we talk Lagrangian or Hamiltonian.
I guess the Noether's theorem can be derived by both ways.
In quantum mechanics the traditional approach is the Hamiltonian, and the Noether's theorem refers to the commutator [H,S] where S is related to the symmetry. As far as energy is concerned, the conservation is simply related to H being time-independent. For momentum, it is related to [H,Lx] = 0, where Lx is the translation operator along a direction x.

(starting a new thread to be sure about that)

 

[Phrak]

I suggest both your Hamiltonians and Lagrangians are wrong, living on the wrong manifold.