Why the least action: a fact or a meaning ?

1. Jun 28, 2006

lalbatros

Have some people tried to find a meaning to the principle of least action that apparently underlies the whole physics? I know of one attempt, but not convincing to me (°). A convincing attempt, even modest, should suggest why it occurs, what is/could be behind the scene and how it might lead us to new discoveries.

The link from QM/Schroedinger to CM/Newton is a clear explanation for the classical least action. But the surpirse is that least action can be found nearly everywhere, even as a basis for QFT (isn't it?).

Michel

(°) this is how I understood the book by Roy Frieden "Science from fisher information"

2. Jun 28, 2006

eljose

Feynmann gave a beatiful "justification2 or explanation of this principle when dealing with Path integral..if you have:

$$\int D[\phi]e^{iS[\phi]/\hbar}$$

then the classical behavior h-->0 so only the points for wich the integrand have a maximum or a minimum contribute to the integration in our case the maximum or minimum is given by the equation $$\delta S =0$$ wich is precisely the "Principle of Least action"... Unfortunately following Feynmann there is no variational principles in quantum mechanics.

3. Jun 30, 2006

lalbatros

eljose,

http://www.ece.rutgers.edu/~maparke...apts/Ch05-Dynamics/Ch05Sec05SchrodEqLagr.pdf"

Other systems surprisingly also have a Lagragian and a least action principle:
http://www.lns.cornell.edu/spr/2003-06/msg0052131.html"

Clearly this is an exception: this pictural explanation for the CM least action derived from the stationary phase limit of QM. Least action is seen nearly everywhere. This is why I asked the PF if there is explanation or a meaning behind that.

Would it be possible that a very wide range of differential equations can be reformulated as a least action principle? Then the explanation would be general mathematics, and the meaning would not be much of physics. This would translate my question to something like "why is physics based on differential equations?".

Or is there more to learn on physics from the LAP ?

Michel

Last edited by a moderator: Apr 22, 2017