# The principle of least action and diffraction

• StrawberrySaturn
In summary, the conversation discusses a paragraph from the Feynman lectures regarding light and its behavior. It questions how particles determine the path of least action and whether they are able to sense neighboring paths. Diffraction is mentioned as a phenomenon that occurs when light is unable to test all possible paths. The speaker then asks about the relevance of refraction in this example. Feynman suggests that light behaves in a certain way, but it has no motives or plans. The conversation concludes by mentioning the importance of accuracy in scientific models.

#### StrawberrySaturn

When reading through one of the feynman lectures (http://www.feynmanlectures.caltech.edu/II_19.html) there was a paragraph that said:

"In the case of light we also discussed the question: How does the particle find the right path? From the differential point of view, it is easy to understand. Every moment it gets an acceleration and knows only what to do at that instant. But all your instincts on cause and effect go haywire when you say that the particle decides to take the path that is going to give the minimum action. Does it ‘smell’ the neighboring paths to find out whether or not they have more action? In the case of light, when we put blocks in the way so that the photons could not test all the paths, we found that they couldn’t figure out which way to go, and we had the phenomenon of diffraction."

My question is how exactly diffraction result from light not knowing which is the path of least action. Is he saying that the light waves spread out and take every path? I thought that refraction would be more relevant to his example, when light hits a glass block it travels through it at an angle that results in the quickest travel time.

Too anthropomorphic, I think. Light behaves a certain way 'as if it knew' what to do. It has no motives or plans. We have invented laws and equations that predict (not explain) what it does.
There are often alternative explanations for phenomena and people argue and worry to death about which one 'is correct' when what really counts is the 'accuracy' of each model.

## 1. What is the principle of least action?

The principle of least action is a fundamental principle in physics that states that a physical system will take the path or motion that minimizes the action, which is the integral of the Lagrangian over time. In simpler terms, it means that the path taken by a physical system is the one that requires the least amount of energy.

## 2. How does the principle of least action relate to diffraction?

The principle of least action can be applied to the phenomenon of diffraction in optics. When light passes through a small opening, it bends and spreads out, creating a diffraction pattern. According to the principle of least action, the path taken by the light is the one that minimizes the action, which in this case is the time it takes for the light to reach the screen. This results in the characteristic diffraction pattern.

## 3. What is the mathematical equation for the principle of least action?

The mathematical equation for the principle of least action is known as the Euler-Lagrange equation, which is derived from the Lagrangian function. It states that the path taken by a physical system must satisfy the condition of the first variation of the action being equal to zero.

## 4. How is the principle of least action used in physics?

The principle of least action is a fundamental principle that is used to describe a wide range of physical systems, from classical mechanics to quantum mechanics. It is used to determine the motion of objects and particles, as well as the behavior of light and other electromagnetic waves.

## 5. Can the principle of least action be violated?

The principle of least action is a fundamental law of physics and has been proven to accurately describe the behavior of physical systems. However, there are some cases where it may not hold true, such as in extreme conditions like in the presence of strong gravitational fields. In these cases, more complex theories like general relativity must be used.