Researchers at the Resonance Project both publish scientific papers in the context of the Hawaii Institute of Unified Physics and release layman papers and articles related to these publications.

Please visit the Publications section of the HIUP.org website.

#### Quantum Gravity and the Holographic Mass

**Haramein, N. (2012). Quantum Gravity and the Holographic Mass, Physical Review & Research International, ISSN: 2231-1815, Page 270-292**

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We find an exact quantized expression of the Schwarzschild solution to Einstein’s field equations utilizing spherical Planck units in a generalized holographic approach. We consider vacuum fluctuations within volumes as well as on horizon surfaces, generating a discrete spacetime quantization and a novel quantized approach to gravitation. When applied at the quantum scale, utilizing the charge radius of the proton, we find values for the rest mass of the proton within 0.069×10^{-24}gm of the CODATA value and when the 2010 muonic proton charge radius measurement is utilized we find a deviation of 0.001×10^{-24}gm from the proton rest mass. We identify a fundamental mass ratio between the vacuum oscillations on the surface horizon and the oscillations within the volume of a proton and find a solution for the gravitational coupling constant to the strong interaction. We derive the energy, angular frequency, and period for such a system and determine its gravitational potential considering mass dilation. We find the force range to be closely correlated with the Yukawa potential typically utilized to illustrate the exponential drop-off of the confining force. Zero free parameters or hidden variables are utilized.

Keywords : Quantum gravity; holographic principle; Schwarzschild solution; proton charge radius; strong interaction; Yukawa potential.

#### The Schwarzschild Proton

**Haramein, N. (2010). The schwarzschild proton, AIP Conference Proceedings, CP 1303, ISBN 978-0-7354-0858-6, pp. 95-100.**

This manuscript received a Best Paper Award in the field of “Physics, Quantum Mechanics, Relativity, Field Theory, and Gravitation” at CASYS’09 (Computing Anticipatory Systems) in Belgium.

Abstract: We review our model of a proton that obeys the Schwarzschild condition. We find that only a very small percentage (~10^{-39}%) of the vacuum fluctuations available within a proton volume need be cohered and converted to mass-energy in order for the proton to meet the Schwarzschild condition. This proportion is equivalent to that between gravitation and the strong force where gravitation is thought to be ~10^{-38} to 10^{-40} weaker than the strong force. Gravitational attraction between two contiguous Schwarzschild protons can accommodate both nucleon and quark confinement. We calculate that two contiguous Schwarzschild protons would rotate at c and have a period of 10^{-23}s and a frequency of 10^{22} Hz which is characteristic of the strong force interaction time and a close approximation of the gamma emission typically associated with nuclear decay. We include a scaling law and find that the Schwarzschild proton data point lies near the least squares trend line for organized matter. Using a semi-classical model, we find that a proton charge orbiting at a proton radius at c generates a good approximation to the measured anomalous magnetic moment.

#### Scale Unification – A Universal Scaling Law for Organized Matter

**Haramein, N., Rauscher, E.A., and Hyson, M. (2008). Scale unification: a universal scaling law. Proceedings of the Unified Theories Conference. ISBN 9780967868776**

Abstract: From observational data and our theoretical analysis, we demonstrate that a scaling law can be written for all organized matter utilizing the Schwarzschild condition, describing cosmological to sub-atomic structures. Of interest are solutions involving torque and Coriolis effects in the field equations. Significant observations have led to theoretical and experimental advancement describing systems undergoing gravitational collapse, including vacuum interactions. The universality of this scaling law suggests an underlying polarizable structured vacuum of mini white holes/black holes. We briefly discuss the manner in which this structured vacuum can be described in terms of resolution of scale analogous to a fractal-like scaling as a means of renormalization at the Planck distance. Finally, we describe a new horizon we term the “spin horizon” which is defined as a result of a spacetime torque producing boundary conditions in a magnetohydrodynamic structure.

#### Spinors, Twistors, Quaternions, and the “Spacetime” Torus Topology

**Rauscher, E.A., and Haramein, N., (2007). Spinors, twistors, quaternions, and the “spacetime” torus topology, International Journal of Computing Anticipatory Systems, 1373-5411.**

Abstract: The dual torus topology occupies a central role in the spinor, twistor and quaternionic formulation. This topology appears to be ubiquitous in astrophysical and cosmological phenomena and is predicted by the U4 bubble of the affine connection in the HarameinRauscher solution to Einstein’s field equations. The geometric structure of the complexified Minkowski space is associated with the twistor algebra, spinor calculus, and the SUn groups of the quaternionic formalism. Hence quantum theory and relativity are related mathematically through the dual torus topology. Utilizing the spinor approach, electromagnetic and gravitational metrics are mappable to the twistor algebra, which corresponds to the complexified Minkowski space. Quaternion transformations relate to spin and rotation corresponding to the twistor analysis.

#### Collective Coherent Oscillation Plasma Modes in Surrounding Media of Black Holes and Vacuum Structure – Quantum Processes with Considerations of Spacetime Torque and Coriolis Forces

**Haramein, N., Rauscher, E. A. (2005). Collective coherent oscillation plasma modes in surrounding media of black holes and vacuum structure- quantum processes with considerations of spacetime torque and coriolis forces. Orinda: Beyond The Standard Model: Searching for Unity in Physics, 279-331.**

Abstract: The main forces driving black holes, neutron stars, pulsars, quasars, and supernovae dynamics have certain commonality to the mechanisms of less tumultuous systems such as galaxies, stellar and planetary dynamics. They involve gravity, electromagnetic, and single and collective particle processes. We examine the collective coherent structures of plasma and their interactions with the vacuum. In this paper we present a balance equation and, in particular, the balance between extremely collapsing gravitational systems and their surrounding energetic plasma media. Of particular interest is the dynamics of the plasma media, the structure of the vacuum, and the coupling of electromagnetic and gravitational forces with the inclusion of torque and Coriolis phenomena as described by the Haramein-Rauscher solution to Einstein’s field equations. The exotic nature of complex black holes involves not only the black hole itself but the surrounding plasma media. The main forces involved are intense gravitational collapsing forces, powerful electromagnetic fields, charge, and spin angular momentum. We find soliton or magneto-acoustic plasma solutions to the relativistic Vlasov equations solved in the vicinity of black hole ergospheres. Collective phonon or plasmon states of plasma fields are given. We utilize the Hamiltonian formalism to describe the collective states of matter and the dynamic processes within plasma allowing us to deduce a possible polarized vacuum structure and a unified physics.

#### The Origin of Spin: A Consideration of Torque and Coriolis Forces in Einstein’s Field Equations and Grand Unification Theory

**Haramein, N., and Rauscher, E. A. (2005). The orgin of spin: A consideration of torque and coriolis forces in Einstein’s field equations and grand unification theory. Beyond The Standard Model: Searching for Unity in Physics, 1, 153-168.**

Abstract. We address the nature of torque and the Coriolis forces as dynamic properties of the spacetime metric and the stress-energy tensor. The inclusion of torque and Coriolis effects in Einstein’s field equations may lead to significant advancements in describing novae and supernovae structures, galactic formations, their center supermassive black holes, polar jets, accretion disks, spiral arms, galactic halo formations and advancements in unification theory as demonstrated in section five. We formulate these additional torque and Coriolis forces terms to amend Einstein’s field equations and solve for a modified Kerr-Newman metric. Lorentz invariance conditions are reconciled by utilizing a modified metrical space, which is not the usual Minkowski space, but the U 4 space. This space is a consequence of the Coriolis force acting as a secondary effect generated from the torque terms. The equivalence principle is preserved using an unsymmetric affine connection. Further, the U 1 Weyl gauge is associated with the electromagnetic field, where the U4 space is four copies of U1. Thus, the form of metric generates the dual torus as two copies of U1 x U1, which we demonstrate through the S3 spherical space, is related to the SU2 group and other Lie groups. Hence, the S4 octahedral group and the cuboctahedron group of the GUT (Grand Unification Theory) may be related to our U 4 space in which we formulate solutions to Einstein’s field equations with the inclusion of torque and Coriolis forces.

#### American Physical Society (APS) Meetings

A Consideration of Torsion and Coriolis Effects in Einstein’s Field Equations

*Four Corners Fall October 24-25, 2003 Meeting ID: 4CF03 Arizona State University, Tempe, Arizona.*

The Quest for the Higgs Boson and the Planck Black Hole Production at the CERN Large Hadron Collider

Fundamental Dynamics of Black Hole Physics

*April Meeting 2002: Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American Astronomical Society April 20 – 23, 2002; Albuquerque Convention Center; Albuquerque, New Mexico.*

The Role of the Vacuum Structure on a Revised Bootstrap Model of the GUT Scheme

A Scaling Law for Organized Matter in The Universe

*Joint Fall Meeting of the Texas Sections of the APS and AAPT, and Zone 13 of the SPS October 4 – 6, 2001; Texas Christian University; Fort Worth, Texas.*