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We are all acquainted with the law of conservation of energy which says that energy remains conserved in an isolated system and this is a basic law of nature.

But what I want to ask is that is there any scope for disproving this famous law. What I think is that the law is too vast to leave space for contradictions.

Consider this from Feynman's lectures

In order to verify the conservation of energy, we must be careful that we have not put any in or taken any out. Second, the energy has a large number of different forms, and there is a formula for each one. These are: gravitational energy, kinetic energy, heat energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy. If we total up the formulas for each of these contributions, it will not change except for energy going in and out.

I am considering energy as a number which is calculated using vast number of formulas and essentially remains the same. Now, if some physicist some day finds that the number is not the same, according to me, he/she would most likely add some more items in this long list of forms of energy and that's how it would end.

I don't know whether I am right on wrong, but this is what I feel. Maybe because I consider energy just as a number which is always the same and it may not be the case. So firstly I want you to tell me what exactly energy is. I am unable to grasp it's connection with symmetries of this universe and if here hides the answer to my query, then I would like to know it later.

Secondly, I want to know how you as physicist can ever disprove this law. This would ofcourse require me to know, at the first place, what energy is.

I know that how mechanical energy is related to work, and have seen how this law helps us to solve a host of problems, but still the idea seems very much abstract and becomes incomprehensible when the general idea of energy conservation is introduced. This is most probably because I'm not sure on how something is approved to be considered as a form of energy. So I want your help with this and want to know your opinion and idea behind this abstract idea.

I tried my best to make myself clear.

Qmechanic
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Abhinav Dhawan
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    Possible duplicates: https://physics.stackexchange.com/q/19216/2451 , https://physics.stackexchange.com/q/3014/2451 and links therein. – Qmechanic Mar 07 '18 at 16:43
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    Feynman: "It is important to realize that in physics today, we have no knowledge of what energy is." – Jasper Mar 07 '18 at 16:45

1 Answers1

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It's quite easy to disprove the law of conservation of energy:

  • You can find a situation where the laws of physics cannot be described by (classical or quantum) lagrangian mechanics.
  • You can find a situation where the laws of physics change over time, i.e. where doing an experiment at time $t$ and doing the same identical experiment at time $t+\Delta t$ produces a different result.

If you do that, then you're on your way to breaking the conservation law.

If you don't do either of those, then Noether's theorem guarantees that there will be a conserved Noether charge that corresponds to the symmetry under time translations, and generally speaking that conserved charge can always be called an energy.

(To be a bit more clear for the technically minded: to disprove the conservation of energy it is necessary to tick at least one of the two bullet points above, but they're not sufficient, either ─ you still have your work cut out even after you've done it, but one core fundamental barrier has now been removed. However, doing away with either of those two features of physical law is so far removed from our current understanding of nature that it's pretty pointless to speculate about how you might proceed after you've cleared that barrier.)

Emilio Pisanty
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  • What do you mean by " a conserved Noether charge"? – Abhinav Dhawan Mar 07 '18 at 16:49
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    Noether's theorem tells you that if you have a continuous symmetry of the system, then you have a quantity (known as a Noether charge) that is conserved by the system's evolution (and it also gives you an explicit expression for that Noether charge). No matter what it comes out to be or what strange system you're dealing with, if a quantity $Q$ is the conserved Noether charge that corresponds to a symmetry under time translations, then the name 'energy' will always be appropriate for it. – Emilio Pisanty Mar 07 '18 at 16:58
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    @EmilioPisanty In your first two bullet points, you didn't disprove the law of conservation of energy. The latter has some hypotheses that aren't realised in the former. Therefore, the bullet points don't disprove anything: the "theorem" isn't applicable to them. The "theorem" itself is safe and sound. – AccidentalFourierTransform Mar 07 '18 at 17:17
  • @AccidentalFourierTransform Care to be a bit more specific as to what these "some hypotheses" actually are? – Emilio Pisanty Mar 07 '18 at 18:46
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    @EmilioPisanty That kind of depends on the precise theorem you want to work with. For example, in standard point-particle mechanics (in the simplest case where there are no constraints or the like), a necessary and sufficient condition for $\frac{\mathrm dH}{\mathrm dt}=0$ is that $\frac{\partial L}{\partial t}=0$. More general theorems can be enunciated. In any case, the theorem has conditions. In the case above, that the system admits a Lagrangian description with time independent Lagrangian. You cannot disprove the theorem by picking a system that violates the conditions. – AccidentalFourierTransform Mar 07 '18 at 18:59
  • @AccidentalFourierTransform You're kind of battling the converse of what I really want to say here, which is that you can't break conservation of energy without breaking the hypotheses of any relevant theorems, i.e. it's a necessary condition, not sufficient. However, since those necessary conditions are already prohibitive, expanding them into sufficient conditions is pretty pointless in my view. – Emilio Pisanty Mar 07 '18 at 19:08