Inadequacy of Classical Logic in Classical Harmonic Oscillator and the Principle of Superposition

Abhishek Majhi (1) , Ramkumar Radhakrishnan (2)

1 Indian Statistical Institute [Kolkata]
2 Sardar Vallabhbhai National Institute of Technology [Surat]

In course of the development of modern science, inadequacy of classical logic and Eastern philosophy have generally been associated only with quantum mechanics in particular, notably by Schroedinger, Finkelstein and Zeilinger among others. Our motive is to showcase a deviation from this prototypical association. So, we consider the equation of motion of a classical harmonic oscillator, and demonstrate how our habit of writing the general solution, by applying the principle of superposition, can not be explained by remaining within the bounds of classical logic. The the law of identity gets violated. The law of non-contradiction and the law of excluded middle fail to hold strictly throughout the whole process of reasoning consequently leading to a decision problem where we can not decide whether these two 'laws' hold or not. We discuss how we, by habit, apply our intuition to write down the general solution. Such intuitive steps of reasoning, if formalized in terms of propositions, result in a manifestation of the inadequacy of classical logic. In view of our discussion, we conclude that the middle way (Mulamadhyamakakarika), a feature of Eastern philosophy, founds the basis of human reasoning. The essence of the middle way can be realized through self-inquiry (Atmavichar), another crucial feature of Eastern philosophy, which however is exemplified by our exposition of the concerned problem. From the Western point of view, our work showcases an example of Hilbert's axiomatic approach to deal with the principle of superposition in the context of the classical harmonic oscillator. In the process, it becomes a manifestation of Brouwer's views concerning the role of intuition in human reasoning and inadequacy of classical logic which were very much influenced by, if not founded upon, Eastern philosophy.

Domaines: Physique [physics]

Abhishek Majhi, Ramkumar Radhakrishnan. Inadequacy of Classical Logic in Classical Harmonic Oscillator and the Principle of Superposition. 2022. ⟨hal-03556334⟩