Applied Physics and Mathematics Annotation << Back MATHEMATICS-PHYSICS IDENTITY CHARLES K. RHODES A recent study has demonstrated that the calculation of the mass of a physical object can be equivalently achieved with two completely distinct modalities of analysis. One approach utilizes standard physical reasoning that involves particle mass values, corresponding interaction constants, and known traditional scaling relationships. The alternative method, that commences from the same initial data derived from the Fine Structure Constant α, follows a strictly computational pathway, based on the First Supplementary Law of Quadratic Reciprocity, from which it initially generates the Cosmological Constants {ΩΛ, Ωm, Ωl}, and subsequently produces the identical finding. In the latter mathematical/cryptographic case, it is also concretely shown that several additional quantitative relationships are produced that are entirely absent in the former procedure; two prominent results are (a) the identification of an Optimization and (b) the computation of the corresponding Fixed Point, a key dynamical property. Specifically, the physically based method yields the mass of the object sought, but the cryptographic approach places this mass value into an ordered information-rich array of other relationships to additional measured physical data. Hence, the result based on conventional physics is a minimal point finding; in contrast, the cryptographic picture yields an extensive quantitatively interlocking pattern. In sum, measurements of the Fine Structure Constant α and the Luminous Matter Fraction Ωl yield a quantitative determination of (1) the mass and distribution of an enormous Dark Matter object Md and (2) the tiny mass ms of the Sterile Neutrino νs; both can be seen to arise from a coherent analysis of the mass fractions of the Cosmic Domain. The mass of system Md is the neutrino equivalent of a White Dwarf Star at the Chandrasekhar Mass Limit. Furthermore, since previously established results precisely interrelate the full complement of the physical quantities of the {α, ΩΛ, Ωm, Ωl} tetrad, this striking quantitative predictive property now advances and holds equivalently for the entire membership of the {α, ΩΛ, Ωm, Ωl, Md, νs} sextet. Importantly, it is also determined that the proper Fermi-Dirac statistics associated with the structure of a White Dwarf system are intrinsically expressed as an identity through the arithmetic parity of the Sterile Neutrino νs mass number gβ -1 0(mod 2). The central key to these findings is the computation of the mass Md of a system that is composed of a number N of identical particles νs such that N ≥ 2; hence, the distinguishing particle attribute is the intrinsic statistical characteristic, thereby, rendering the outcome sensitive to the statistics of the constituents, in this case Fermi-Dirac. The presentation described herein involves N ~ 1089. These results thereby constitute a solid specific demonstration of the chief conclusion, specifically, that the mathematical/cryptographic and physically based analyses reciprocally yield absolutely identical fi ndings for Md and νs under the constraint of the statistical requirements for the particle νs. Therefore, these fi ndings clearly demonstrate that the two completely independent modes of computation are in perfect accord with the determination of their corresponding mass values, temperatures, and entropies. It is conjectured that the observed computational pattern that demonstrably aligns the corresponding mathematical/physical properties has its fundamental source in the mysterious details of the distribution of prime numbers. In this sense, we can regard the Distribution of Prime Numbers as the representation of the stupendously complex seminal code with which the basic physical data can be precisely enciphered. DOI: 10.25791/pfim.06.2018.330 Contacts: - Pp. 21-28.