The Origins of Mass
& The Nature of Gravity
Abstract

While Einstein field equations tell us that gravity is the result of the curvature of spacetime from a source term given as a stress energy tensor or mass-energy, it neither tells us the origin of this mass nor the nature of spacetime. Furthermore, it tells us that certain regions of spacetime can reach infinite curvature from an infinite energy density as in the singularity of a black hole. On the other hand, early exploration of quantum mechanics demonstrated that the electromagnetic quantum vacuum ground state is violently fluctuating resulting, when summing on all modes, in an infinite amount of energy. Here we demonstrate that this energy density is the source of mass and forces that ensue whether at the classical scale as in gravity, or at the quantum scale as in the confining force.

Utilizing the correlation functions, we examine Max Planck early discovery of zero-point energy (ZPE) in the context of the black body radiation of an oscillator. We find that ZPE, which diverges when all modes are considered resulting in an infinite electromagnetic energy density, is in fact in the order of the Planck density when considering General Relativity (GR) and quantum geometrodynamics providing a natural cut-off at the Planck scale. While in free space this energy density is not apparent at classical scale, in highly coherent phases like in resonant cavities, this energy density becomes significant and measurable for instance in the case of Casimir and dynamical Casimir effect. Furthermore, the consistency of the mathematical framework of quantum theory requires ZPE to maintain the non-commutativity of the operators, essential for particle stability.

Thereafter, when the correlation time, determining the coherency of the oscillating quantum vacuum fluctuations, is chosen as the characteristic time of the proton, we obtain precisely the energy density of the proton rest-mass demonstrating that the origin of mass clearly emerges from quantum vacuum fluctuations. This decoherence process of the vacuum energy defines a screening mechanism that determines the mass-energy of a system. This is similar to QFT in which the bare-mass and the bare-charge of particles, formally infinite, are shielded or screened by the quantum vacuum fluctuations “dressing” the particle, while in our case the vacuum fluctuations are the origin of the mass.

The current standard mechanism to define the source of the rest mass of the proton usually requires the strong nuclear force contribution to make up the deficiency of the Higgs mechanism which only predicts up to 5% of the proton rest mass. Furthermore, the fundamental origin of confinement (gluon) and the residual nuclear force (or strong force, meson) given by quantum chromodynamics (QCD) has no clear origin. Therefore, the origin of mass for matter in our universe remains an open issue notwithstanding dark matter and dark energy which is thought to be 95% of the mass-energy of the universe. Thus, current theoretical constructs only predict 0.2% of the mass-energy of the universe. Our computation finds a precise value for the hadronic mass and when applied to the cosmological scale predicts the critical density correctly without the need for dark energy or dark matter which clearly suggests that the nuclear confining force, analogous to the Casimir effect, and the universal mass-energy arise from the ZPE quantum vacuum fluctuations dynamics.

The current proton structure utilizes a quark-gluon plasma (QGP) fluid dynamic description resulting from the Brookhaven laboratory experiment. This fluid dynamics fundamental to the structure of hadrons is an integral part of QCD and as seen above it is critical to the hadronic mass-energy. We demonstrate that the origin of this QGP superfluid emerges from a deeper mechanism of the electromagnetic vacuum fluctuations (ZPE) acting as a Planck plasma where the elementary particles that constitute this fluid are Planck spherical units or PSU (equivalent to the Planck density).

The screening mechanism resulting from vacuum decoherence is equivalent to the action of a semi-permeable surface horizon enclosing the Planck plasma fluctuations in its volume reducing the available energy. Similarly to the holographic principle and Bekenstein conjecture utilized by Hawking and later ‘t Hooft to describe the entropy of a black hole, we pixelized the surface with PSU to describe its permeability. Considering the relationship between the interior energy and a first surface screening (holographic mass solution), we demonstrate an equivalence with the Schwarzschild solution to Einstein field equations. This decoherence represents the ZPE Planck plasma undergoing a phase transition resulting in a reduction of its energy density. Contrary to the classical approach, where one would expect the black hole formation to be the result of an accretion of infalling material to a critical limit, our result demonstrates that black hole formation is a natural manifestation of states of coherency in the quantum vacuum fluctuations.

When applying this first screening at the hadronic scale, we find an energy equivalent to the strong nuclear force directly related to the Planck force resulting from the gravitational force between two Schwarzschild protons. The treatment of particle in this manner is consistent with historical and present approaches from Einstein Rosen describing particles as wormhole bridges where “a particle being represented by a "bridge" connecting these [two] sheets.” [Einstein-Rosen 1935], or more recently when Susskind states in 2004 “One of the deepest lessons that we have learned over the past decade is that there is no fundamental difference between elementary particles and black holes.” [Susskind 2004], and Rees’ instanton described in his 1979 paper on the structure of the physical world [Eq9 Rees1979] where he defines the instanton as a black hole with a Planck length radius and a Planck mass.

When considering a second decoherence screening at the proton scale, we find our earlier result of an energy density equivalent to the rest-mass of the system. Such holographic approach was later applied to the electron to find its mass-energy, and also at the cosmological scale to find the critical density of the universe. Therefore, this scalable construct gives us a consistent mechanism across scales to define the emergence of mass and forces from quantum vacuum fluctuations having phase transitions and producing energy density gradients resulting in structure from matter to organize matter.

Carr, B. J., & Rees, M. J. (1979). The anthropic principle and the structure of the physical world. Nature, 278(5705), 605-612.

Einstein, A., & Rosen, N. (1935). The particle problem in the general theory of relativity. Physical Review, 48(1), 73.

Susskind, L. (2004). Cosmic natural selection. arXiv preprint hep-th/0407266.