Exploring the Principle of Least Action in Physics

[adoion]

hi,

please if somebody could explain why anybody would consider the "action" and is there any proof that the minimal action actually gives the correct route of a problem?

 

[Dr.D]

It is considered because it works.

If you are asking what motivated Hamilton in the first place, well, that is a tough question. He had a lot of time on his hands since his job as Irish Royal Astronomer was not very demanding.

 

[adoion]

It is considered because it works.

If you are asking what motivated Hamilton in the first place, well, that is a tough question. He had a lot of time on his hands since his job as Irish Royal Astronomer was not very demanding.

hehe I bet he did but I think that Lagrange did most of the important work on this subject.

 

[anorlunda]

I recommend Prof. Leonard Susskind's video lectures on Classical Physics. You can find them on youtube or itunes.

He derives the principle of least action on the blackboard using the calculus of variations. He also shows where the Euler-Lagrange equation comes from and how we use that to derive the laws of motion. If I remember correctly, he also shows how to derive Noerther's Theorem from the calculus of variations.

Susskind is a great teacher. The video production quality is excellent. I've been having fun for the past 18 months by spending 15 minutes per day working through his 165 online lectures.

 

[adoion]

I recommend Prof. Leonard Susskind's video lectures on Classical Physics. You can find them on youtube or itunes.

He derives the principle of least action on the blackboard using the calculus of variations. He also shows where the Euler-Lagrange equation comes from and how we use that to derive the laws of motion. If I remember correctly, he also shows how to derive Noerther's Theorem from the calculus of variations.

Susskind is a great teacher. The video production quality is excellent. I've been having fun for the past 18 months by spending 15 minutes per day working through his 165 online lectures.

great, thanks a lot on that info that's exactly what I needed. Susskind is a funny guy :)

 

[ShayanJ]

He derives the principle of least action on the blackboard using the calculus of variations. He also shows where the Euler-Lagrange equation comes from and how we use that to derive the laws of motion. If I remember correctly, he also shows how to derive Noerther's Theorem from the calculus of variations.

That's wrong! You can't derive the principle of least action using calculus of variations.
The principle of least action states that of all possible evolutions of a system, the one that is realized is the one for which the action is stationary. Now people ask how should we make the action stationary? Here comes the calculus of variations!

The principle of least action dates back to the days that people thought about science in a way that was too concerned with theology. They said because god does things the best way, the economic way, so in the things that happen in nature, something is minimum and somehow they found that something to be action. Then it appeared that this is actually a very useful way so the method remained without those theological things! So basically we say its correct because it works.

 

[Dale]

So basically we say its correct because it works.

When it comes right down to it, that is the reason that we do anything in physics.

 

[ShayanJ]

When it comes right down to it, that is the reason that we do anything in physics.

And that's exactly what students should learn. Physicists are trying to understand what's happening inside a black box-the universe-and they only can do different things to it and see how it reacts. Then they build models somehow that if they do the same thing to that model, it reacts the same way. Then, the more actions on the black box and more reactions seen from it, the more complete the model becomes and more clearly we can see inside the black box. That's the whole business.
But it should be noted that this method doesn't guarantee that the model is exactly how the black box's inner structure is. It only assures we have something that behaves exactly as the black box. Its another question whether the model can be made exactly as the black box or not or how should it be done!