# Can the Principle of Least Action Unify Different Branches of Physics?

• I
• Delta2
In summary, the principle of least action can be used to derive Newton's 2nd law in classical mechanics and two of Maxwell's equations. It is also used in quantum physics and relativity to derive fundamental laws. In general relativity, all forces, including electromagnetic and gravity, can be derived from corresponding terms of actions. In quantum mechanics, the principle is generalized to Feynman's path integral, which sums over all paths. Ultimately, the principle of least action is the only action in physics.
Delta2
Gold Member
TL;DR Summary
Does the principle of least action unifies physics in a way that we can say that all the fundamental laws of physics (e.g Newton's 2nd law, Maxwell's equations) we know. can be derived from the principle of least action?
From what I know Newton's 2nd law in classical mechanics can be derived from the principle of least action. Also from what I know, two of the Maxwell's equations (those that contain the time derivatives, i.e. Maxwell-Faraday law and Maxwell-Ampere law) also can be derived from the principle of least action. Of course the action defined is different in these two cases.

I don't know if this can be expanded in quantum physics and relativity, if also there the fundamental laws can be derived from the principle of minimizing some -depending on the case- action.

So is the principle of least action offering some sort of unification of the different branches of physics?

I have the textbook of Dirac on general relativity. There all kind of forces including electromagnetic and gravity are derived from corresponding terms of actions.

Classical version of action principle comes from quantum action principle or integral path method.

atyy and Delta2
In QM, it has to be generalized to Feynman's path integral that sums over all paths. When doing the "saddle-point" approximation to the path integral, we recover the classical principle of extremizing the action.

fresh_42 and Delta2
As we all know...Physics is where the action is!

hutchphd
Actually its mostly where the action isn't

hutchphd said:
Actually its mostly where the action isn't
Touche'

But isn't the least action ultimately the only action?

## What is the principle of least action?

The principle of least action, also known as the principle of stationary action, is a fundamental concept in physics that states that the path taken by a system between two points in time is the one that minimizes the action, which is a mathematical quantity that represents the difference between the system's kinetic and potential energies.

## How does the principle of least action relate to classical mechanics?

The principle of least action is a foundational principle in classical mechanics, as it provides a way to determine the motion of a system without explicitly solving the equations of motion. It is based on the idea that nature tends towards the most efficient or economical path, and this principle can be used to derive the equations of motion for a given system.

## What are the applications of the principle of least action?

The principle of least action has numerous applications in physics, particularly in classical mechanics and quantum mechanics. It is used to derive the equations of motion for systems such as particles, fluids, and fields, and it is also used in the study of optics, electromagnetism, and relativity.

## How is the principle of least action related to the Hamiltonian and Lagrangian formulations of mechanics?

The principle of least action is closely related to the Hamiltonian and Lagrangian formulations of mechanics. In fact, the principle can be used to derive both the Hamiltonian and Lagrangian equations of motion, which are alternative formulations of classical mechanics that are often more convenient to use in certain situations.

## Is the principle of least action a fundamental law of physics?

The principle of least action is not considered a fundamental law of physics, but rather a principle or postulate that is based on observations and has been verified through experiments. It is a powerful tool that is used to understand the behavior of systems in classical mechanics, but it is not applicable in all situations and is not considered a universal law like the laws of thermodynamics or conservation of energy.

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