Science Ecstasy

Imagine you have a big land piece and you want to build a beautiful mansion there. For this task you have to hire designers, masons, painter and all sort of workers. getting this work done from them is a pretty difficult task. And you suddenly you came across a machine that can do all sort of work alone. This is more or less same in the case of a lagrange The word Lagrangian can refer to a mathematical quantity or a description of a way/method to look at physical events. The Lagrangian method is normally contrasted with the Eulerian method. If you follow the motion of few moving things and devise equations to describe the motion and how the other attributes change along the path, then you are using the Lagrangian method. If you stick to ground and observe these moving things and again devise equations to describe the motion and the changes in the attributes of the moving objects, then you are using the Eulerian method. Like being in a plane and putting rules for its flight, or sitti...

The basic idea behind Feynman's sum-over-paths (or sum-over-histories) approach is as follows: Assume that a particle can travel between two points A and B by a - possibly infinite - number of different paths. Each one of these paths will have a certain probability associated with it. In quantum mechanical terms, these probabilities are encoded in the wavefunction that describes the particle, which assigns to each possible path a different probability amplitude ; the square modulus of this amplitude gives the corresponding probability.  The crucial point is that these different amplitudes have a wavelike nature, and as they spread through space they interfere with each other, their respective wave patterns either reinforcing or canceling each other out at various points. And if you sum over all the amplitudes of all the different paths, i.e. you sum-over-histories, then the different amplitudes will reinforce or cancel each other in such a way that the only path that survives this...