The S-Matrix (Scattering Matrix)

What is S-Matrix ?

        The 's' in S-Matrix stands for 'scattering'. The scattering matrix was formulated for point particles. It is helpful to predict what will happen when particles collide. On collision, how many particles will scatter at an angle with what amount of energy, is predicted by the elements of this matrix. The matrix is significant only if it has finite elements.


Why is Sky Blue ?

        When we look at the sky, what we see is actually the light that has been bounced off by the air molecules in the atmosphere. It is a general misconception that the light we see in the sky is the direct sunlight. Had it been the direct sunlight we would have seen the sky in white colour, as it is a blend of all seven fundamental components of colour found in nature. When the sunlight travels through the atmosphere it collides with molecules in the air (This shows the particle nature of light and hence justifies the use of S-Matrix). Since it is a case of particle collision, it is definite that the energy of both the particles will witness a change in the energy depending on the coefficient of restitution. The intensity with which the collision takes place is the answer for sky to be blue.


Why is Sun seen Red at Sunset ?
     The sun is seen red at the time of sunset due to a opposite effect. Sky is seen blue because of scattered blue component whereas sun is seen red because of non-scattered red component. At the time of sunset, the sun is near the horizon because of which the distance that light has to travel is larger. While travelling the particles of light collide with the particles of air. The number of collision increases due to increase in the path of light. As the light reaches its destiny- us, its components are scattered and only the red component is left.

Heisenberg Uncertainty Principle

 

   Diving into the world of sub atomic particles we come across the most important concept of the "Uncertainty" introduced by WERNER HEISENBERG, one of the founders of the "Quantum Mechanics" in the year 1927. He proposed that the exact position and the velocity of  an object cannot be known simultaneously. The equation describes a relation between the position and velocity/momentum of a microscopic body such as an electron.

        
   Heisenberg said that when the precision of measuring one quantity increases then, the precision of measuring the other quantity decreases. Consequently it can be seen that if we try to measure the position of an electron then we cannot precisely find its velocity. It is because of the fact that to make any measurement we need to see the particle for which we need light, that is a quanta (photon) is required to be aimed at the specimen particle. When the photon hits the particle then it bounces the particle out of its orbit hence changing its position/location. One may argue that we may someday overcome this problem with advanced technology in measuring instruments. But it may be here emphasised that the limitation of uncertainty is not due to the limitation of the present day technology, rather a limitation in nature as we need light (photon) to see. It seems as if nature itself has limited us with the power and conceals some of its secrets.