Elementary particles and fermat's principle

In summary, photons and all elementary particles follow Fermat's principle of least time and the principle of extremal action in nature. This means that the quantity S = \int\!dt\, (T - V) is extremized over the history of the system, where T is kinetic energy and V is potential energy. In quantum mechanics, the probability of ending up at a certain point is determined by adding up all possible paths and weighing them with a phase factor, with the most dominant contribution coming from the path where S is an extremum. However, while their behavior is well approximated by classical paths, elementary particles ultimately follow quantum mechanical principles.
  • #1
spidey
213
0
Photons(light) follow the fermat's principle of least time...so do all elementary particles also follow fermat's principle of least time?..say electron,proton etc..
 
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  • #2
As far as we know, everything in nature (classically) follows the principle of extremal action. Meaning that a quantity, [itex]S = \int\!dt\, (T - V)[/itex] is extremized over the history of the system. Here T is kinetic energy and V is potential energy. For light, the action is usually simply equal to the time it takes to propagate from source to destination.

Quantum mechanically, to find the probability of ending up at some point, you add up every possible path, weighing each path with a phase factor of [itex]e^{i S}[/itex], and square the result. For the most part, paths interfere destructively because they all have wildly different phase factors. But for paths where [tex]S[/tex] is an extremum (minimum, maximum, saddle point), you end up with a lot of paths with the same phase factor, and these constructively interfere. So as long as quantum effects aren't too strong, the most dominant contribution to the probability comes from that path where [tex]S[/tex] is an extremum. This is simply the classical solution to the Euler-Lagrange equations of motion.

Fermat's principle played an important role in de Broglie's development of his wave theory as well as to the principle of extremal action.
 
  • #3
so you say for elementary particles like electrons also follows extremal action...the path traversed by all elementary particles is also extremal..is it correct
 
  • #4
Well... no. For the most part, their behaviour is well approximated by their classical paths, but we live in a quantum mechanical world and there's just no getting around that =)

Read up on path integrals if you like.
 

What are elementary particles?

Elementary particles are the fundamental building blocks of matter. They are the smallest known particles that make up all matter in the universe.

What is Fermat's principle?

Fermat's principle is a fundamental principle in optics that states that light will follow the path that takes the least amount of time to travel from one point to another.

What are fermions and bosons?

Fermions and bosons are two types of elementary particles. Fermions are particles with half-integer spin, such as electrons and quarks, while bosons are particles with integer spin, such as photons and W and Z bosons.

How do elementary particles interact?

Elementary particles interact through four fundamental forces: gravity, electromagnetism, strong nuclear force, and weak nuclear force. These interactions are mediated by other elementary particles, such as photons and gluons.

What is the importance of studying elementary particles and Fermat's principle?

Studying elementary particles and Fermat's principle allows us to gain a deeper understanding of the fundamental laws of the universe and the forces that govern it. This knowledge can also lead to advancements in technology, such as in the development of new materials and energy sources.

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