What would you consider intuitive? Whether it gives you empirically sound equations of motion is the only relevant issue when it comes down to judging the choice.Higgsono said:I know it's right because we get the right equations of motion from it, but can one understand it in a more intuitive way?
Orodruin said:What would you consider intuitive? Whether it gives you empirically sound equations of motion is the only relevant issue when it comes down to judging the choice.
This Lagrangian minimizes the path length, the shortest distance between two points is a straight line, a free particle moves in a straight line.Higgsono said:can one understand it in a more intuitive way?
The "deeper explanation" is the answer to the question "why does the Lagrangian look as it looks?". The somewhat "stupid" answer of course is, "because it works", which in physics means that it describes an aspect of nature in accordance with the observations associated with it.Higgsono said:Maybe intuitive is not the right word, but what I meant is some deeper explanation.
Higgsono said:I know it's right because we get the right equations of motion from it, but can one understand it in a more intuitive way?
Higgsono said:Maybe intuitive is not the right word, but what I meant is some deeper explanation.
A relativistic free particle is a concept in physics that describes the behavior of a particle with no external forces acting upon it and moving at speeds close to the speed of light. It takes into account the effects of relativity, such as time dilation and length contraction, on the particle's motion.
Action is defined as the integral of the Lagrangian (a function that describes the particle's motion) over a certain time period. For a relativistic free particle, the action is given by the relativistic version of the kinetic energy, which includes the particle's mass and its velocity.
Action is a fundamental concept in physics that helps us understand the behavior of particles and their interactions with their environment. In the case of a relativistic free particle, the action allows us to calculate the particle's trajectory and predict its future motion.
The principle of least action states that a physical system will follow the path that minimizes the action. In the case of a relativistic free particle, this means that the particle will follow the path that minimizes the relativistic kinetic energy, which is equivalent to the classical principle of least action in the limit of low speeds.
Yes, the concept of action can be extended to other physical systems, such as particles in electromagnetic fields or particles in quantum mechanics. In these cases, the action may take on different forms, but the principle of least action still applies.