Derivation of the Uncertainty Relation from the fine structure constant: A derivation which just as well holds at the macroscopic level, wherefore uncertainties can be taken as finite differences of the given quantities


Yarman O. U., Yarman T.

, cilt.1, sa.1, ss.1-37, 2024 (Hakemsiz Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 1 Sayı: 1
  • Basım Tarihi: 2024
  • Dergi Adı:
  • Sayfa Sayıları: ss.1-37
  • İstanbul Üniversitesi Adresli: Evet

Özet


A straightforward derivation of Heisenberg’s Uncertainty Relation is presented starting from the established expression of the fine structure constant. Newfound link between these two universal relationships enriches the physical interpretation of reality as subject to a quantum mechanical regime at all levels. Macroscopic manifestation of the Uncertainty Principle is therefore shown to arise in the form of a discrete character for any electrical current driven by a flux of elementary charges. A new inequality governing the Uncertainty Principle for electricity at the macro-scale is hence proposed, and the results obtained are discussed. We furthermore demonstrate, in line with our undertaking, that “given finite difference quantities” are identical to, and thus interchangeable with, “well-defined uncertainty values”. Accordingly, possessed values acquired by finite difference quantities shall under no circumstances abolish related uncertainty characteristics. Our derivation of Heisenberg’s Uncertainty Relation from Sommerfeld’s original definition of the fine structure constant also evokes that the former too can well be stated as a definition, or vice versa. From such a perspective, The Uncertainty Relation can well be considered as simply a capstone re-formulation of the Planck constant – just like (Pressure x Volume / Temperature) happens to be the expression of the gas constant when written for gases. It is vital to recall that Yarman et al. have shown elsewhere how the macroscopic behaviour of a complex system, such as a gas enclosed in a container, is tethered to the Planck constant. In this sense, the current enterprise makes strictly no divisive distinction between the micro and the macro worlds.