In Chapter 1: Objective & Subjective Reality the criterion for objectivity was defined as the consistency among all perceptions. Einstein’s stated this principle in mathematical terms as follows.
Natural laws must be covariant with respect to arbitrary continuous transformations of the co-ordinates.
We start in this book with the following postulate.
The UNIVERSE is a single system that is intrinsically continuous, harmonious and consistent.
Any perceived discontinuity among objects, disharmony among relatinships, or inconsistency among concepts hides some truth to be discovered.
Newton came up with fundamental concepts, such as, mass, force, inertia, and energy that applied to the macroscopic domain of matter. These concepts underwent drastic revision and expansion as the microscopic domain of field and quanta was discovered. New observations required the revision of even the concepts of space and time.
The science of physics thus examines all physical phenomena and comes up with a description that is consistent. As observations are refined through experimentation, hypotheses develop into theories, and theories lead to principles. This development follows a continual reduction of known and discovered inconsistencies.
The science of Physics uses the criterion of logical and mathematical consistency to investigate and build upon the objective reality of the universe.
Logic deals with consistency of real observations. Mathematics uses abstraction to further refine logical consistency. When mathematical results cannot be translated back into a consistent logic then mathematics itself has become inconsistent due to its assumptions and approximations.
When mathematical results are inconsistent with logic then mathematics has employed assumptions that are not consistent with reality.
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