Why is Energy Conserved in Classical Mechanics?

[ksoy]

Why energy is conserved??

I have been taught that energy is conserved since i started to learn about physics, but I am curious that why it is conserved?

Could anyone answer me??
Thank you very much

 

[Alkatran]

I have been taught that energy is conserved since i started to learn about physics, but I am curious that why it is conserved?

Could anyone answer me??
Thank you very much

The total amount of energy in the universe is constant. To do something you use energy, but you don't really "use" it (as in it disappears), you just change it into something else (like motion or heat).

Unless you don't mean how it's done, but actually "Why". Because that's like asking what the meaning of life is... I can give you a lot of answers but none of them are really right. But I guess this is where that principle that "If such and such hadn't been like that, we wouldn't exist."

If energy was just lost gained randomly.. you could go "poof" any second.

 

[arildno]

Just adding to Alkatran here:
That the total amount of energy in the universe is constant, is not derived from any fancy maths or obscure logic, but is laid down as a fundamental premise/axiom in physics.

This axiom is better known as the 1.law of thermodynamics.

 

[Gokul43201]

One could also "shift the blame." From Noether's Theorem, we can say that Energy is conserved because of the symmetry of time translation.

Whether we do a particular experiment today, or twenty years from now, the result should be the same. This is known as the symmetry of time translation, or temporal symmetry (NOT to be confused with the symmetry of time reversal). Noether's Theorem proves that from every symmetry (temporal, translational, rotational, etc.) there arises a conservation law (for energy, momentum, angular momentum, etc. respectively).

So this merely raises the new question: "why should there be temporal (or any other kind of) symmetry ?" There really is no good answer I can give to such a question.

In fact, lots of astrophysicists currently believe that during the inflationary stage of the Universe's growth you didn't have temporal symmetry - and as a result, Energy was NOT conserved. Even now, Quantum Mechanics allows for Energy Conservation to be violated within a small window and only for very short periods of time.

 

[ksoy]

So, I am just wondering, how does Noether's Theorem got to do with the development of modern day physics??

Thank you very much

 

[omin]

One confusion that can be cleared to help understand conservation of energy is to understand the fallacy of dissapperance, which means physical things vanish: a once existing object becomes non-existent.

For example, we are taught early in school that one take away one is zero, which could infer that the first one had itself taken from itself, which means it was canceled out, it dissapeared. This has never physically occured. You can move an object from one place and it will be said not to exist in that old place, but it will exist where it was moved. In the sense I have mentioned, you cannot take one from one. How would you take something from itself? It's just moving!

Dissapearance is positively based upon the concept of the displacement of an object to a place where one cannot sense it. Just because something is too far away, has divided into unseeable parts, accelerates to speed which makes it unseeable, or combines into some unrecognizable form doesn't mean it has become non-existent. It just means you don't sense it now.

Conservation of energy idea essentially says:
Existing things stay existing, but may be invloved in a change of form.
Existing things don't turn to non-existence.
Non-existence (whatever that is) doesn't turn into existence.

It's that simple.

 

[JohnDubYa]

Interesting thoughts, omin.

 

[Michael F. Dmitriyev]

One confusion that can be cleared to help understand conservation of energy is to understand the fallacy of dissapperance, which means physical things vanish: a once existing object becomes non-existent.

For example, we are taught early in school that one take away one is zero, which could infer that the first one had itself taken from itself, which means it was canceled out, it dissapeared. This has never physically occured. You can move an object from one place and it will be said not to exist in that old place, but it will exist where it was moved. In the sense I have mentioned, you cannot take one from one. How would you take something from itself? It's just moving!

Dissapearance is positively based upon the concept of the displacement of an object to a place where one cannot sense it. Just because something is too far away, has divided into unseeable parts, accelerates to speed which makes it unseeable, or combines into some unrecognizable form doesn't mean it has become non-existent. It just means you don't sense it now.

Conservation of energy idea essentially says:
Existing things stay existing, but may be invloved in a change of form.
Existing things don't turn to non-existence.
Non-existence (whatever that is) doesn't turn into existence.

It's that simple.

I agree. In my opinion the photon does not disappear in atom. It is inbuilt in a circulating wave increasing its frequency and, therefore, energy. It can be compared with a braided chain in which one part is added at preservation of the general length.

Michael

 

[krab]

...understand the fallacy of dissapperance, which means physical things vanish: a once existing object becomes non-existent.

For example, we are taught early in school that one take away one is zero, which could infer that the first one had itself taken from itself, which means it was canceled out, it dissapeared.

Math is a self-consistent system on its own. 1-1=0 cannot be argued with. On its own, it has no physical implications. It is abstract. Understanding physics is in large part understanding how to apply mathematics to the physical world. It seems, you do not have this understanding.

Conservation of energy idea essentially says:
Existing things stay existing, but may be invloved in a change of form.

Very vague. What for example do you define as a thing? Mass? Then what you say is wrong, since mass is not conserved. Energy? What you are saying is circular, therefore empty.

Energy is conservation means the following: We have found a way to calculate a quantity we call "energy"; it is related to the ability to do work; its utility lies in the fact that it is conserved. This is an observation. Gokul43201's comments are very to the point. You can "shift the blame". It does not answer the deep question, and I believe no answer exists. But thinking of energy conservation as time translation symmetry is very satisfying/instructive.

 

[Ivan Seeking]

I think Krab gives the best answer here. I once had a professor who became quite distressed at any question that began with the word "why". His objection was that Physics describes what happens; why is a question of philosophy. I personally think we can ask why until we reach the limit: The conservation laws. Unless and until we find something even more fundamental, once we reach the conservation principles we can only say what happens. No matter what advances we make, it seems that there will always be at least one "why" that can never be answered.

 

[omin]

Understanding physics is in large part understanding how to apply mathematics to the physical world.

I agree only that the physical world is applied to mathematics. The five senses represent the physical realm. Thoughts represent the fives senses. Theories represent thoughts. Math is a theory. Math soley represents the physical realm, even if it's the determined nueral activity of humans.

What do I define as a thing? Something physical. What is physical can be sensed by humans. Sense become thought, so we know indirectly what's physical. "Things" are what exist.

What is mass? Something that is sensed. It's a thing too. Mass may have stipulaive definitions, but there is nothing vague about the idea humans sense something and asserting it's existence with a representative grunt. If we sense it, it matters.

I am only trying to bring out a confusion that helped me understand the concept a bit more. The point was to say: things are not created or destroyed, with a little explanation that they just are, yet moving. I think that is the most important point to begin with on the concept of conservation of energy.

Your definition implies thing of interest to me, but I prefer simple explantions at the outset.

 

[omin]

...Physics describes what happens; why is a question of philosophy.

Why seems to ask for the previous state or cause. What seems to ask for a specific scope. Although I could word a why question as a what question.

1.Why did you do you write this comment? Because, there existed a previous comment about the subject and I also was motivated to respond to it.
2.What did I just do? I explained the cause and effect of a specific commentary.

I see your point on 'why' can be asked forever, because we can always ask a previous cause. 'What' brings us to answer what we know.

Why seems inductive and what seems deductive.

1.Why did it happen? Oh, probably because of these factors...
2.What happened? This I know, and what I don't know I can't mention...back to why.

Conservation is a what question. What is this energy that is conserved?

 

[Ivan Seeking]

Really I agree until we reach the last step. Then we can't make the why a what question. Note that you asked why energy is conserved. Now you ask what energy is.

Here we get into word games. Energy is a concept having a specific mathematical representation that when present has the ability to do work. What is work?

If I understand where you are going there may not be an answer. Consider the alleged Superstring. What are Strings made from? They're not made of anything; they're just strings. It gets no simpler than this. It seems that there may be concepts more fundamental than energy but I'm not qualified to speak on those terms - the sort of thing that Gokul43201 was talking about. Still, for all practical purposes energy is energy. It can do work. It is conserved. It can be calculated and it can take on many forms. That's about as good as it gets.

 

[Ivan Seeking]

Hey string people. Can the concept of energy be reduced to the vibration in a string?

 

[techwonder]

Don't you guys find it troubling though that the universe on the smallest of scales is allowed to not obey the conservation of energy law (Heisenberg) while we, at macroscopic scales, insist that it must be conserved? What I'm hinting at here is that we have a "when" issue rather than an "if" issue.

With regards to Noethers theorem: could it be construed that the unified force (four in one) does not need to observe any of these conservation laws?

 

[tomkeus]

In clasical mechanics energy conservation law can be proven as a consequence of nonexistence of absoulte beginning of time. As you know, in clasical mechanics you are free to put t_0 anytime you want, it won't change laws.