The construction of mechanics. A new path to Newton's equations

TL;DR

This paper reconstructs Newtonian mechanics through logical principles and a constructive approach, emphasizing the role of fundamental beliefs, the observer, and the No Arbitrariness Principle, offering new insights into classical concepts like the velocity of light.

Contribution

It introduces a logical, constructive framework for deriving Newtonian mechanics, highlighting the foundational assumptions and the role of the observer, diverging from traditional axiomatic methods.

Findings

Reinterprets the constancy of light velocity as a consequence of Newtonian mechanics.

Highlights the importance of the No Arbitrariness Principle in classical mechanics.

Emphasizes the role of observer and foundational beliefs in the construction of physical theories.

Abstract

In the present essay we attempt to reconstruct Newtonian mechanics under the guidance of logical principles and of a constructive approach related to the genetic epistemology of J. Piaget and R. Garc\'ia \citep{piag89}. Instead of addressing Newton's equations as a set of axioms, ultimately given by the revelation of a prodigious mind, we search for the fundamental knowledge, beliefs and provisional assumptions that can produce classical mechanics. We start by developing our main tool: the No Arbitrariness Principle, that we present in a form that is apt for a mathematical theory as classical mechanics. Subsequently, we introduce the presence of the observer, analysing then the relation objective-subjective and seeking objectivity going across subjectivity. We take special care of establishing the precedence among all contributions to mechanics, something that can be better appreciated by considering the consequences of removing them: (a) the consequence of renouncing logic and the laws of understanding is not being able to understand the world, (b) renouncing the early elaborations of primary concepts such as time and space leads to a dissociation between everyday life and physics, the latter becoming entirely pragmatic and justified \emph{a-posteriori} (because it is convenient), (c) changing our temporary beliefs has no real cost other than effort. Finally, we exemplify the present approach by reconsidering the constancy of the velocity of light. It is shown that it is a result of Newtonian mechanics, rather than being in contradiction with it. We also indicate the hidden assumption that leads to the (apparent) contradiction.