Mathematical Time in Classical Mechanics - An Epistemological Perspective

The aim of this essay is to analyze the signification of the mathematical definition of time within the framework of the mathematical methods of classical mechanics. The strictly mathematical definition of time, starting from the requirements of classical mechanics, is at a level of abstractization the specific formalism of which together with the physical intuitive sense of time taken from classical mechanics give a scientific prospect and signification to time considered in this double scientific context. The mathematical time of classical mechanics is a fundamental concept of physics. Starting from the description of its complexity included in its physical-mathematical definition, the study attempts to make certain enlightening explications, followed by an analysis based on an algebraic approach. In this essay, the “algebraic view” on time represents a reference point for the philosophical perspective on the time. The algebraic approach to time proves the complexity of the problems and brings into attention new aspects and at the same time difficulties to be revealed from other viewpoints. After we have become familiar with it, this approach offers new themes for philosophic reflection. We do not refer to a breach between the philosophical and abstract formal views in issues related to time, we only specify the existence of some real distinctions between the two approaches.

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