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Polarizable Vacuum and the Schwarzschild Solution
Abstract
The PV model is examined for a solution that is mathematically equivalent to the Schwarzschild solution of Einstein's equations for general relativity. A simple solution is found and the resulting Lagrangian density and equation of motion are presented for further investigation.
... The Schwarzschild metric component is then interpreted as the Refractive Index of the vacuum surrounding a spherical, homogeneous mass, "M" centred at the origin of the coordinate system. [1] Moreover, if we include an Electromagnetic (EM) "source" term, such as a charge "q", located at the origin of the coordinate system, Eq. (2) becomes, ...
... In all cases, the solutions were found to be identical to those found under GR. Therefore, this Revised PV Model [1,2] may provide some insight into alternative models of Quantum Gravity in flat space-time, without the need for the cumbersome geometrical interpretation of background space-time. All that is required is a consistent application of the Refractive Index "c/K", to a typical scalar field theory. ...
... Including the Reissner-Nordstrom solution, identical to GR.[1,2]. ...
Presented herein is a revision of the time-independent solutions of the equations of motion for the Refractive Index, in the Polarizable Vacuum (PV) Model. It is demonstrated that these equations may be used to obtain solutions and equations of motion for the metric component functions, identical to General Relativity (GR). The equations of motion in this Revised PV Model are easier to solve than the equations of GR as they do not require Tensor mathematics or geometrical interpretations to be understood.
... Fortunately, Puthoff [4] developed an alternative representation of General Relativity (GR) termed e Polarizable-Vacuum (PV) Model of Gravity. Since then, Depp et al. [5,6] and Desiato [7] have shown the PV Model of Gravity to be isomorphic to GR by satisfying the Schwarzschild and Reissner-Nordstrom solutions. ...
... e Polarizable-Vacuum Model of Gravity developed by Puthoff [4], the isomorphic work presented by Dep et al. [5,6], and the form of the Gravitational Refractive Index implicitly asserted by Desiato [7] with CMBR Temperature observations (viii) e SMoC "Ω Λ + ΔΩ Λ " limit violates the SMoC "H 0 + ΔH 0 " limit (ix) e existence of a Massive Photonic Dark Energy Field is implied (x) e Massive Photonic Dark Energy Field is responsible for Accelerated Cosmological Expansion (xi) e effect of Accelerated Cosmological Expansion is to "pull" time dilation in the "opposite direction," acting to "stretch time" (xii) H 0 � 67.1181 (km/s/Mpc) ± 0.0269 (km/s/Mpc) (xiii) t 0 � 14.5685 (Gyr) ± 5.849 (Myr) ...
A derivation of Cosmological Age explicitly constrained by Cosmic Microwave Background Radiation (CMBR) is presented, demonstrating that the correct value of Cosmological Age is equal to the Hubble Age. It is shown that utilizing “z = 0” for Cosmological Redshift in the Present Epoch introduces a fundamental flaw into Cosmological Age calculations. However, this flaw is captured and corrected by the Polarizable-Vacuum (PV) Model of Gravity developed by Puthoff, suggesting that the Dark Energy Field exists as a massive photonic field. Consequently, it is demonstrated that for a Dark Energy Driven description of Accelerated Cosmological Expansion, Cosmological Redshift takes a negative value in the Present Epoch.
... K is the index of refraction, l is an arbitrary constant, and F(K) is an arbitrary scalar function. In a previous publication (2) the author showed that the above Lagrangian density exactly reproduced the Schwarzschild solution of Einstein's equations for general relativity when ...
In a previous publication the author showed that the PV model of Dicke with a modified Lagrangian density produced a solution that is mathematically equivalent to the Schwarzchild solution of Einstein's equations for general relativity. In this paper it is shown that the same PV model with modified Lagrangian also gives an exact solution to the charged mass point metric of Reissner and Nordstrom.
... Schwarzschild solution of GR, [13] and in the PV Model. [14, 15] Where, ...
It is proposed that gravitational fields may be interpreted as a variation in the relative available driving power (Watts) of the Electromagnetic, Zero-Point Field (ZPF). It is shown that variations in the relative available power are covariant with variations in the coordinate speed of light as measured by a distant observer in unaltered space-time. Gravitational time dilation and length contraction may then be interpreted as a loss of driving power from the ZPF. It is hypothesized that the loss of power is due to increased radiative damping of matter, resulting from an increase in the local relative energy density which promotes this process. The relative radiative damping factor affects the relative ground state energy of the quantum mechanical harmonic oscillator such that, the mean-square fluctuations in matter reproduce the behavior attributed to, and resulting from variations in the space-time metric of General Relativity (GR). From this principle, all of the variations observed by a distant observer that occur due to gravity, or space-time curvature under GR may be reproduced from the variable relative damping function acting on the harmonic oscillator. What is presented herein, is an engineering model for quantum gravity that puts gravity in the hands of engineers, who will understand this process and will potentially advance artificial gravity and anti-gravity technology from pure speculation, to achievable endeavors in our lifetime.
... The ratio, 2 0 2GM c R is the familiar gravitational potential found in the Schwarzschild solution of GR, [13] and in the PV Model. [14, 15] Where, ...
It is proposed that gravitational fields may be interpreted as a variation in the relative available driving power (Watts) of the Electromagnetic, Zero-Point Field (ZPF). It is shown that variations in the relative available power are covariant with variations in the coordinate speed of light as measured by a distant observer in unaltered space-time. Gravitational time dilation and length contraction may then be interpreted as a loss of driving power from the ZPF. It is hypothesized that the loss of power is due to increased radiative damping of matter, resulting from an increase in the local relative energy density which promotes this process. The relative radiative damping factor affects the relative ground state energy of the quantum mechanical harmonic oscillator such that, the mean-square fluctuations in matter reproduce the behavior attributed to, and resulting from variations in the space-time metric of General Relativity (GR). From this principle, all of the variations observed by a distant observer that occur due to gravity, or space-time curvature under GR may be reproduced from the variable relative damping function acting on the harmonic oscillator. What is presented herein, is an engineering model for quantum gravity that puts gravity in the hands of engineers, who will understand this process and will potentially advance artificial gravity and anti-gravity technology from pure speculation, to achievable endeavors in our lifetime.
... • A gravitational field is interpreted as a variable refractive index that permeates all of space-time and determines the relative scale of rulers and clocks. [1,2,3] • A refractive index value less than 1, implies a relative speed of light which is faster than c. is faster than c. • It also implies a higher ground state energy, whilst simultaneously lowering the energy density due to inflation of the volume. • Understanding this helps engineers to conceptualize the function of exotic matter, and how it comes into play. ...
The Polarizable Vacuum Model is an alternative to General Relativity that is particularly well suited for engineering purposes. A gravitational field is interpreted as a variable refractive index that permeates all of space-time and determines the relative scale of rulers and clocks. A refractive index value less than 1 , implies a relative speed of light which is faster than c. It also implies a higher ground state energy, whilst simultaneously lowering the energy density due to inflation of the volume. Understanding this helps engineers to conceptualize the function of exotic matter, and how it comes into play. It is proposed here-in, that the variable refractive index results from a variation in the relative available driving power of the electromagnetic, zero-point field (ZPF). We then utilize this as the fundamental driving principle, to entertain how to go about engineering the warp drive.
... K is the index of refraction, l is an arbitrary constant, and F(K) is an arbitrary scalar function. In a previous publication (2) the author showed that the above Lagrangian density exactly reproduced the Schwarzschild solution of Einstein's equations for general relativity when ...
In a previous publication the author showed that the PV model of Dicke with a modified Lagrangian density produced a solution that is mathematically equivalent to the Schwarzchild solution of Einstein's equations for general relativity. In this paper it is shown that the same PV model with modified Lagrangian also gives an exact solution to the charged mass point metric of Reissner and Nordstrom.
... To find the line element in the PV as seen by an observer, the following substitutions to equation (1) should occur, dt o 2 . In cylindrical polar coordinates, the solutions are also consistent with GR. [5, 6] Substituting the coordinate velocities, dx / dt = 0, dy / dt = 0, dz / dt = v z , results in the ratio of proper time to coordinate time, as is typically found in SR. ...
When a space-time warp bubble is moving at velocity (i.e. v > c), Doppler shifted photons with energy tending to infinity, approach from the direction of motion. Event horizons form on the leading and trailing walls of the bubble. It is demonstrated herein that these phenomena mathematically arise from the application of shift-only space-time solutions; derived retrospectively from the geometrical interpretation of General Relativity. Moreover, it shall be demonstrated that these phenomena do not manifest in a properly formulated Polarizable Vacuum warp drive solution, IFF the refractive index within the space-time bubble is precisely controlled. This formalism is consistent within the analog gravity framework of the Polarizable Vacuum Model, [1-6] representing a variable speed of light interpretation of General Relativity.
Video available at: https://www.youtube.com/watch?v=H9OLXICP9_U
It is demonstrated that the transformation of observable quantities due to the space-time metric, are reproducible in the Standard Model of particle physics, and derivable from the constraints of the Heisenberg uncertainty principle.
The equivalence between obeying these constraints, and the effects attributed to the space-time metric using the Schwarzschild solution of GR and the PV Model of gravity are shown and tabulated.
The equivalence to the Radiative Damping Model of gravity is also shown, along with how these quantities can be controlled by the Maxwell Temporal Field.
This work opens the door for the control of gravity, and anti-gravity and offers the potential for warp drive propulsion technology and devices that can control the rate at which time passes.
2/27/2020 - In the paragraph leading up to equation (13), the formation was using R.A. d’Inverno's text, where he uses the 1st approximation in the path integration. As such, I expressed the speed of light as being inversely proportional to 1/sqrt(K(r, M)). This only holds for a 1st approximation, where sqrt(K(r, M)) ~ K(r, M) and are both approximately equal to 1. In general, throughout the rest of the paper, K(r, M) is correctly expressed as 1 / (1 - 2M/r), and the speed of light is proportional to 1/K(r, M). This use of the square root has caused some confusion regarding which form is correct. The correct form is found by solving the light-like line element for the coordinate speed of light, dr/dt, not dr/dtau. ______________________________________
The Polarizable Vacuum (PV) Model representation of General Relativity (GR) is used to show that an in-falling particle of matter will reach the central mass object in a finite amount of proper time, as measured along the world line of the particle, when using the PV Metric. It is shown that the in-falling particle passes through an event horizon, analogous to that found in the Schwarzschild solution of GR. Once it passes through this horizon, any light signal emitted outward by the in-falling particle will be moving slower than the in-falling particle, due to the reduced speed of light in this region. Therefore the signal can never escape this horizon. However, the light emitted by a stationary object below the horizon is exponentially red-shifted and can escape along the null geodesics, as was originally predicted by the PV Model. A static, non-rotating charge distribution is added to the central mass and the PV equivalent to the Reissner-Nordstrom metric is derived. It is illustrated that the dipole moment induced in a neutral, polarizable body, reduces the effects of gravity in the strong field region. We demonstrate the existence of the event horizon and how it may be affected by the presence of electric charge. v1 Final Release
Standard pedagogy treats topics in general relativity (GR) in terms of tensor formulations in curved space-time. An alternative approach based on treating the vacuum as a polarizable medium is presented here. The polarizable vacuum (PV) approach to GR, derived from a model by Dicke and related to the TH formalism used in comparative studies of gravitational theories, provides additional insight into what is meant by a curved metric. While reproducing the results predicted by GR for standard (weak-field) astrophysical conditions, for strong fields a divergence of predictions in the two formalisms (GR vs. PV) provides fertile ground for both laboratory and astrophysical tests to compare the two approaches.
DOI:https://doi.org/10.1103/RevModPhys.29.363