Samuel Leventhal, University of Utah
Physics
The uncertainty existing within the scientific community as to why quantum mechanics (QM) behaves as it does comes from the fact there exists no mathematically sound approach for deriving the postulates of QM. It is the purpose of our research to present a derivation for the postulates of QM through the theory of Scale Relativity (SR), followed by a search for physical signatures of SR in the mechanics of celestial bodies. The construction of SR is based on an extension of the relativity principle to scale transformations coupled with a loss of differentiability. Our first paper presents the derivation of QM through scale relativity. During the SR derivation we also show fundamental qualities of QM, such as the presence of complex numbers in state functions. Lastly, the seemingly unrelated behaviors between relativity and quantum phenomena are shown a single mathematical formulation, only to change form due to scale. The new resolution variable within the adapted Schrodinger equation allows it to become applicable to macroscopic scales allowing us to look at large scale mechanics for signs of SR. Gravitation being scale invariant leads it to be a perfect candidate for experimental purposes. Our second paper investigates whether or not celestial bodies, formed by chaotic gravitational structuring, obey the properties of a Schrodinger equation dependent on the Keplerian potential. If so SR implies solar systems would form along probability distributions predicted by the square magnitude of the Schrodinger-Keplerian wave equation. In theory a planets probability distribution would depend on discrete variables, denoted orbital rank, n=n. In search for SR it is sufficient to see if planets tend to have orbital ranks near integer values. We start by calculating the orbital ranks within various solar systems, followed by testing whether the accumulation of planets’ rank near integer values is a probable event. To test this we take the squared difference between the calculated rank and the nearest integer. As a result we are able to test how likely orbital structuring will be discrete. Our results show a strong certainty that orbital rank is likely to accumulate near integer values.