Exploring the Power of Action: A Physics Student's Journey

[robousy]

Hi all,

I'm a 2nd year physics grad student and have recently found this great forum.

I've taken a course on classical mechanics but never really appreciated why action is such a useful concept. I've noticed people talking about action a lot in things like string theory and it seems that action is more fundamental (?) or more useful (?) than simply the Lagrangian or the Hamiltonian but I do not see why.

If anyone could say a few words about why it is so useful to know the action ... and what you would then DO with it - then I would be very appreciative. (ie. what you can DO with the Lagrangian is stick it into the euler lagrange eqtns to get the eqtns of motion - what can you 'do' with the action).

Thanks in advance.

robousy

 

[Doc Al]

This site says it better than I could: http://en.wikipedia.org/wiki/Action_(physics)

Admin edit: fixed link. I'm not sure why it was broken in the first place -- I might need to make sure the url parser vB code is working properly.

 

[GSXR750]

Hello robousy,

I'm glad you found this forum and thank you for bringing up the topic of action in physics. As a physics grad student, I can understand your curiosity and confusion about the concept of action. Let me try to shed some light on it for you.

Action is a fundamental concept in physics that helps us understand the behavior of systems in motion. It is defined as the integral of the Lagrangian over time, and it has a deep connection with the principle of least action, which states that a system will always take the path of least action in its motion.

Now, why is this concept so useful and powerful in physics? Well, first of all, it provides us with a more general and elegant way to describe the dynamics of a system compared to the traditional methods of using equations of motion. By using the principle of least action, we can derive the equations of motion for any physical system, whether it is classical mechanics, quantum mechanics, or even string theory.

Moreover, the concept of action allows us to study and understand the behavior of complex systems, such as those found in string theory. In these systems, the Lagrangian and Hamiltonian formalisms may not be sufficient, but the principle of least action and the concept of action provide a powerful tool to explore and analyze their dynamics.

So, what can we do with the action? Well, as you mentioned, we can use it to derive the equations of motion for a system. But that's not all. The action also helps us understand the symmetries and conservation laws in a system. For example, the conservation of energy can be derived from the time translation symmetry of the action.

In summary, the concept of action is a powerful tool in physics that allows us to understand the behavior of complex systems and derive their equations of motion. It has a deep connection with the principle of least action and provides a more elegant and general approach to studying the dynamics of systems in motion.

I hope this helps clarify the importance and usefulness of action in physics. Keep exploring and asking questions, and I'm sure you'll continue to unravel the power of this concept in your studies. Best of luck in your physics journey.