Philosophy behind writing the article:

The modern theories like quantum mechanics, general relativity give results which match the experimental observations. However, the problem with the modern theories seems to be that, there is no attempt to draw a classical picture of the physical reality and mathematics (with some postulates) itself is supposed to represent the reality.

Therefore, the author has attempted to draw a classical picture of the basic particle like electron in the earlier works published in AIP Advances in 2011 and Canadian Journal of Physics in 2017, based on the mathematics and postulates of these theories.

In this article, it is attempted to understand the classical geometrical picture of the curved space-time. The space-time is curved can be initially treated as a mathematical assumption. Once, you assume that this is also the actual physical picture, then you have to change the geometrical definition of vectors and the geometrical picture of space is modified.

It may be noted that the “bilocal vectors” based classical treatment can give all the desired results but this picture has some geometrical difficulties. It becomes impossible to write the conventional vectors including the unit vectors, making it difficult to even draw a coordinate system. Therefore, it is required to suggest a new definition of “local vectors” as discussed in Ref. 1 (Gravitation by Misner...) of the article. But, this definition raises some new concerns.

Therefore, drawing a classical geometrical picture of curved space-time still remains difficult.