Foundations of Quantum Mechanics: The Connection Between QM and the Central Limit Theorem

Abstract

In this paper we unravel the connection between the quantum mechanical formalism and the Central limit theorem (CLT). We proceed to connect the results coming from this theorem with the derivations of the Schrodinger equation from the Liouville equation, presented by ourselves in other papers. In those papers we had used the concept of an infinitesimal parameter δx that raised some controversy. The status of this infinitesimal parameter is then elucidated in the framework of the CLT. Finally, we use the formal apparatus developed in our previous papers and the results of the present one to advance an alternative objective interpretation of quantum mechanics in which its relations with the classical framework are made explicit. The relations between our approach and those using the Wigner–Moyal transformation are also addressed.