How do we know the principle of least action is true?

In summary, the conversation discusses the origin and motivation behind the principle of least action in physics, which is a mathematical abstraction of previously known concepts such as the shortest distance between two points and Newton's laws of motion. The discussion also mentions potential resources and further reading materials for those interested in learning more about this topic.
  • #1
Terilien
140
0
How do we know that it is true? Most people don't give me a very straightforward answer, but I don't like that. Lagrange must have gotten it from somwhere.
 
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  • #2
It gives the right answers. What more do you expect?
 
  • #3
How Was It Discovered!?
 
  • #4
In some sense, it's a mathematical abstraction of things we already knew [like "shortest distance between two points is a line", geometric optics, Newton's laws of motion]... and we take pleasure to find that newer theories [developed after (say) Lagrange] seem to fit into this scheme... for example, quantum mechanics.

Implicit in this discussion is how one finds action that yield the equations of motion.

If you are interested in Lagrange's motivation, that's more of a historical question... which might be answered in (say) https://www.amazon.com/dp/0486650677/?tag=pfamazon01-20.

You might find some starting points here in this wikipedia article
http://en.wikipedia.org/wiki/History_of_variational_principles_in_physics (standard caveats apply).

You might find this section from http://mitpress.mit.edu/SICM/ interesting
http://mitpress.mit.edu/SICM/book-Z-H-8.html#%_sec_1.1If you want something deeper, then you might have to look at (say) Arnold or Abraham-Marsden.
 
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  • #5
Terilien said:
How Was It Discovered!?

Back when I was an undergrad, my analytical mechanics TA briefly mentioned that the principle of least action arose from some sort of theological argument. Unfortunately I don't have any further details on that.
 
  • #6
another good book to learn these stuff is the "classical" Classical Mechanics book by Goldstein.

to understand these, need to get your mind around Hamilton's or D'Alembert principle
 

1. How do we define the principle of least action?

The principle of least action states that a physical system will always choose the path that minimizes the action, which is the integral of the Lagrangian function over time, between two given states. This principle is a fundamental concept in classical mechanics and is used to predict the behavior of physical systems.

2. What is the evidence for the principle of least action?

The principle of least action has been extensively tested and confirmed through experiments and observations in various fields of physics, including mechanics, electromagnetism, and quantum mechanics. The predictions made using this principle have been found to be accurate and in agreement with experimental results.

3. How does the principle of least action relate to other laws of physics?

The principle of least action is a foundational principle that underlies other laws of physics, such as Newton's laws of motion and Maxwell's equations of electromagnetism. It provides a more general framework for understanding the behavior of physical systems and can be used to derive other laws and equations.

4. What are the limitations of the principle of least action?

The principle of least action is a classical principle and does not apply to quantum systems. It also assumes that a system is in equilibrium and does not take into account non-conservative forces, such as friction. Additionally, it may not be applicable in extreme conditions, such as near the speed of light or in the presence of strong gravitational fields.

5. How do we know the principle of least action is true?

The principle of least action has been extensively tested and has been found to accurately predict the behavior of physical systems. It is also supported by mathematical proofs and is a fundamental principle in physics. However, like all scientific theories, it is subject to future revisions and improvements as our understanding of the universe continues to evolve.

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