Register to reply 
Why is the lagrangian extremized 
Share this thread: 
#1
Jul2913, 05:33 PM

P: 83

I've been reading a lot about path integrals lately, and I've found it fascinating to see at the quantum level how the extremal values of the lagrangian are basically the only ones that contribute when the action is large and therefore we get the classical path.
Something that continues to puzzle me, though, is why the lagrangian function in particular is extremized. Why should TV be the quantity that gets extremized instead of some other function? Is there any consensus view on this question? Thanks! 


#2
Jul2913, 06:39 PM

C. Spirit
Sci Advisor
Thanks
P: 5,427

We have to first find the functions that extremize the action by solving Lagrange's equations. Nothing is extremized a priori.



#3
Jul2913, 06:54 PM

HW Helper
P: 3,440

yes, it is the action that is extremized, not the Lagrangian. I think what copernicus meant is along the lines of "why should the action have a particular form?" Or similarly "why should the Lagrangian have a particular form?". I think the answer is pretty much that this 'form' encodes the physical properties, or laws, of our system. It is similar to asking "why is F=ma?" or "Why is the electromagnetic force proportional to the charge it is acting on?" It is the physical law that we are postulating. We have to start somewhere, with some kind of principle. And our choice of principle is often guided by simplicity and common sense. For example isotropy, invariance to time reversal, e.t.c.



Register to reply 
Related Discussions  
Looking for Lagrangian Systems with Higher Order Time Derivatives in the Lagrangian  Special & General Relativity  1  
Lagrangian for SO(10) GUT  Beyond the Standard Model  1  
Lagrangian... anyone know their Lagrangian mechanics?  Advanced Physics Homework  7  
I know F = ma, but how will a Lagrangian help me?  Classical Physics  10  
Lagrangian remains invariant under addition  Classical Physics  2 