ENGINEERING A BRIDGE BETWEEN QUANTUM ELECTODYNAMICS AND QUANTUM GRAVITY – AN ENGINEERING MODEL TODD J. DESIATO Statesville, NC 28625 [email protected] Abstract For engineering purposes, it is proposed that gravitational fields may be interpreted as a reduction in the relative available driving power (Watts) of the Electromagnetic, Zero-Point Field. It is shown that variations in the relative power are covariant with variations in the coordinate speed of light as measured by a distant observer, outside the gravitational field. Gravitational time dilation and length contraction may then be interpreted as a loss of power from the interaction between matter and the zero-point field. It is hypothesized that the loss of power is due to increased radiative damping within matter due to Larmor radiation. The relative radiative damping factor affects the relative ground state energy of the quantum mechanical harmonic oscillator such that, the mean-square fluctuations of matter reproduce the behavior attributed to and resulting from the space-time metric of General Relativity. From this principle the phenomenon observed by a distant observer that are due to gravity, may be reproduced from the variable relative damping factor acting on the quantum harmonic oscillator. Utilizing the technics of Nuclear Magnetic Resonance to stimulate Larmor radiation, experiments may be conducted which may pave the way for the creation of breakthrough technologies, such as, Artificial gravity, Anti-gravity and Warp Drive. Keywords: quantum engineering, quantum gravity, quantum electrodynamics, artificial gravity, anti-gravity, warp drive, electromagnetic zero-point field, general relativity, alternative models of gravity, breakthrough technology ENGINEERING A BRIDGE Updated - 3/27/20 1 Nomenclature gµν metric tensor where, µ and ν are indices in this context χ = (V-s) represents a scalar field of random magnetic flux quanta K = g11 / −g00 the relative coordinate dependent refractive index of the vacuum c0 = (m/s) the speed of light in vacuum as measured in a local inertial reference frame cK = c0 / K = (m/s) the relative coordinate speed of light as measured from outside the gravitational field Δx0 = (m) an interval along the x axis as measured in a local inertial reference frame Δx = Δx0 / K = (m) an interval along the x axis as measured from outside the gravitational field Δt0 = (s) an interval of time as measured in a local, inertial reference frame Δt = Δt0 K = (s) an interval of time as measured from outside the gravitational field q2 = (C) squared magnitude of the electrical charge quantum e ! = (J-s/rad) the reduced Planck's constant, h / 2π ε0 = (Farad/m) the dielectric permittivity of vacuum as measured in a local, inertial reference frame µ0 = (Henry/m) the dielectric permeability of vacuum as measured in a local, inertial reference frame G = (N-m2/kg2) the gravitational constant 1. INTRODUCTION Practically speaking, time is measured with a clock and space is measured with a ruler. Regardless of their unique construction, each is just a device used to compare with other similar devices at different sets of coordinates. An observer peering into the night sky uses his own devices to establish a coordinate system with which to compare his observations to identical devices at distant coordinates. He chooses for example, to observe the light emitted by distant supernovae and then compare it to the light emitted by other similar events at various locations, [1]. From this data and knowledge of the atomic reactions that generate these explosions, the distance to these events, and their motion relative to the observer is determined. There are other ways to achieve this of course. Clocks, rulers or supernovae are examples given to illustrate the point, that measurements are made using physical tools of our choosing which are composed of some form of matter. To date, it appears that all matter is subjected to the physical effects of gravity in the same way. In other words; all objects fall at the same rate such that; there are no absolute rulers, or absolute clocks that are impervious to the physical effects of gravity. ENGINEERING A BRIDGE Updated - 3/27/20 2 Working in the reference frame of a distant observer, space and time appear to be variables. General Relativity (GR) interprets these variables as space-time curvature when the local devices and the remote devices disagree. They disagree because matter experiences gravitational length contraction and time dilation in the presence of gravitational fields. This is not an illusion. Time dilation and length contraction are real, physical effects whose action can be described using elementary quantum mechanics, and the correct procedure to do so, which shall be shown here. The model presented here-in uses the reference frame of the distant observer to approximate GR as a scalar field, because it allows all observations to be consistently scaled without the need of complicated tensor coordinate transformations, as this is all that is required to illustrate the engineering concepts to be conveyed. However, like a photograph displayed on a monitor appears to be a continuously smooth image when in fact it is pixelated at a scale that is below the resolution of our senses. Individual quantum oscillators behave in such a way that, in large numbers their averages reproduce the behavior of classical test particles on a curved space-time manifold, as directed by Einstein’s field equations of GR, [2]. Due to this quantum to classical correspondence, it is necessary to drop any expectation of using quantum field theory on a curved space-time manifold. In this model, space-time is considered to be perfectly flat background stage upon which the observations of curved space-time are an emergent property. As such, the simplified equations of physics done in flat space-time will be applied throughout. Engineers are clever, but aside from the calibration of the Global Positioning Satellite network, engineers really don’t know what to do with space-time curvature as a means to manipulate gravity. The Gravitic Caliper is not yet a tool in our toolbox. Likewise, referring to gravitational fields as a variable refractive index, as is done in the Polarizable Vacuum (PV Model) Representation of GR [3, 4, 5, 6, 7] adds some intuitive, pedagogical value to understanding gravitational fields, but does not address the pressing issue of; “What to do to create or mimic gravity?” What engineers require is a more practical set of tools to work with when dealing with the effects of gravitational fields, so that they can acquire a deeper understanding of the “Nuts and Bolts” regarding how gravity and matter interact. These tools are precisely what this paper will address. Space-time curvature is a useful mathematical description of the available data regarding gravity, but it is not the only useful interpretation of the data. The interpretation presented herein, describes gravitational time dilation and length contraction in the proximity of large gravitational bodies, as a physical effect acting on clocks and rulers at the quantum scale. This physical effect begins with a simple harmonic oscillator. Something most engineers should be familiar with. For the practical purposes of discussion, matter may be usefully approximated as being comprised of such oscillators, [8]. ENGINEERING A BRIDGE Updated - 3/27/20 3 If there is power dissipation (damping) occurring within the oscillator, eventually the oscillation will exponentially decay to its lowest energy state. In a passive electronic oscillator circuit for example, there may be a sinusoidal power supply (a.c. source) driving a resonant LC circuit, [9]. In the circuit there may be a resistance, R which dissipates power and damps the oscillation. Eventually, the source of power and the dissipation reach an equilibrium condition. In the case of matter, when a system of particles decays to its lowest energy state, it is in the ground-state. Where, the minimum energy is not zero, [8, 10]. The minimum energy is the equilibrium between a uniform zero-point field, (ZPF) which drives the oscillators, and a variable damping function which damps them. The damping function is dependent on the presence of a local mass-energy density, which stimulates radiative damping as Larmor radiation, resulting in the observed behavior of oscillators in a gravitational field. Where, they have a lower ground state energy than they would in an unperturbed ZPF. In other words; the damping function lowers the relative ground state energy below that which the ZPF establishes as the natural ground state in a vacuum far from any gravitational bodies. In GR, this reduction of the ground state energy is interpreted as gravity possessing negative energy, [11]. In section 2, the physical effects of gravitation are derived from the space-time metric and associated with the variable refractive index of the PV Model for illustration. In section 3, the quantum vacuum processes that determine the ground state equilibrium condition between matter and vacuum are discussed, in addition to the co-variant relationship between relative power and the relative coordinate velocity of light. In section 4, the relative radiative damping factor is derived and the connection to gravity is established. It is shown that the variable metric coefficients result from variations in the radiative damping factor that reduces the relative available power of the ZPF, making a test particle move in a way which may be interpreted as curved space-time. In sections 5, Inflated Matter is introduced as an alternative interpretation of Exotic Matter. Exotic Matter is defined as negative energy density and is in violation of the strong and weak energy conditions of GR. It is a state in which something is below the minimum energy density of the surrounding vacuum. The idea if inflated matter being that since volume increases faster than energy content, matter which is inflated to a larger scale has a lower energy density than mater which has been contracted by gravity.