Wednesday, February 22, 2017
SHOULD WE USE TENSORS? IS IT MATHEMATICAL?
Mathematics tells us how much a system changes when any or all of its parameters change. The changes are related to numbers. The change can be due to accumulation and/or reduction of numbers linearly (between similars) or non-linearly (between partly similars). Mathematics has another property: it can only be operated between similars: we cannot add 3 apples and 2 oranges, but can add them as fruits. Measurement is a comparison between similars, out of which one is called the unit. The object to be measured is scaled up or down to give the result of measurement in scalar quantities. For this reason, we can multiply a vector with a scalar, which only increases the magnitude, but leaves the direction unchanged. Here the scalar represents a higher force that is applied to increase the velocity. This principle in not violated in any operation and is universally valid. But tensor violates this principle. If we want to change both the magnitude and the direction of the force, It must be addition of a different force from a different angle. Then it should be treated as vector addition as per standard formula. Why should we use imported terminology of Tensor of Rank 0, 1, 2, 3, etc? Can anyone explain to me why scalars must not be called so and called Tensor of rank 0? Why Tensor of rank 1 have 3 components? If these are related to Cartesian coordinates, how do we define a Dyad, which is a Tensor of rank 2 with magnitude and two directions with 9 components? What are the two directions and the 9 components stand for? Similarly, for a Triad, which is a Tensor of rank 3, what are the 3 directions and 27 components stand for? What about Tensor of rank 4,5,...n? What they are called and what is their physical explanation? It has been used to brainwash billions of people for generations. Let us try to understand it: whether it is science or fiction based on a riddle?