AAWSAP DIRD, Antigravity for Aerospace Applications, March 2010

UNCLASSIFIED//1'8R: 81'fl@liltL I.I§& 8Ptb>f Defense Intelligence Reference Document Acquisition Threat Support 30 March 2010 !COD: 1 December 2009 DIA-08-1003-018 Antigravity for Aerospace Applications UNCLASSIFIED//FOR OFFl&IAL I.IS! 8HL I UNCLASSIFIED//F&R: GFFl61tl.L W&lii QtlL¥ Antigravity for Aerospace Applications Prepared by: Acquisition Support Division (DW0-3) Defense Warning Office Directorate for Analysis Defense Intelligence Agency Author: AAP Person 58 Administrative Note COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapon System Applications (AAWSA) Program. Comments or questions pertaining to this document should be addressed tolAAP Person 1 I AAWSA Program Manager, Defense Intelligence Agency, ATTN: CLAR/DWO-3, Bldg 6000, Washington, DC 20340-5100. UNCLASSIFIED/f,J;QA GFJ;IGlifil W&& 8HLV ii UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ Contents Foreword.................................................................................................................v I. Introduction ....................................................................................................... 1 II. Concepts for Antigravity Within Newtonian Physics .......................................... 2 Negating Newtonian Gravity .............................................................................. 2 Energy Estimate for Newtonian Levitation ......................................................... 3 III. Concepts for Antigravity Within General Relativity .......................................... 4 Antigravity via Gravitomagnetic Forces.............................................................. 4 Historical Foundations ................................................................................... 4 Forward's Dipole Gravitational Field Generator.............................................. 4 Felber's Relativistic Antigravity Effect................................................................ 7 Negative Energy-Induced Antigravity ................................................................ 9 Examples of Exotic or "Negative" Energy Found in Nature ........................... 10 Toy Model Estimate for Negative Energy-Induced Antigravity...................... 10 Cosmological Antigravity.................................................................................. 13 Pressure as a Source of Gravity.................................................................... 13 Vacuum Energy of Einstein's Cosmological Constant.................................... 13 Dark Energy ................................................................................................. 15 Antigravity Propulsion Application of Dark/Vacuum Energy ........................ 17 IV. Quantum Antigravity Propulsion Concepts ..................................................... 17 Antigravity via Quantum Vacuum Zero-Point Fluctuation Force ....................... 19 Antigravity via Nonretarded Quantum Interatomic Dispersion Force ............... 21 V. Conclusion: The Way Forward .......................................................................... 24 Appendix A ........................................................................................................... 29 Static Radial Electric & Magnetic Fields ............................................................ 29 Squeezed Quantum Vacuum ............................................................................. 29 Gravitationally Squeezed Electromagnetic Zero-Point Fluctuations.................. 30 UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f iii UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ Quantum Vacuum Field Stress: Negative Energy from the Casimir Effect ......... 31 Dynamical Casimir Effect: Moving Mirrors ........................................................ 32 References ........................................................................................................... 34 Figures Figure 1. Dipole Electric Field Generator ................................................................ 5 Figure 2. Diople Gravitational Field Generator........................................................ 6 Figure 3. Dipole Gravitational Field Generator: Inside-Out Whirling Dense Matter Torus ............................................................................................ 7 Figure 4. Illustration of the Casimir Effect........................................................... 31 Figure 5. Negative Energy Flux {Gold) Emanating From a Moving Mirror ............. 33 UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f iv UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ Antigravity for Aerospace Applications Foreword Antigravity effects can be implemented by manipulating spacetime. This paper reviews several different theoretical approaches for exploring the possibility of controlling gravity by generating forces that counteract, or otherwise modify, gravity for the purpose of aerospace propulsion. Einstein's General Theory of Relativity is the theoretical framework guiding this study. The paper also reviews other antigravity approaches via the interaction of quantum theory with gravitation. And it explores the question of which method or technique is best suited for aerospace applications and evaluates the make-or-break issues that limit them. UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f V UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ I. Introduction Gravity is the bane of aerospace transportation. The force of the Earth's gravitational field acts to pull all objects, whether in motion or at rest, downward towards the Earth's surface. Because aerospace transportation involves the motion of vehicles through the atmosphere and/or into space, propulsion engineers are always faced with the requirement that aerospace vehicles will have to carry enough propellant and associated tankage in order to provide enough propulsive thrust to overcome the downward pull of gravity and achieve rectilinear motion. Energy has to be expended by a propulsion system to overcome the force of gravity in addition to providing for rectilinear motion, and the majority of propulsive energy is dedicated to overcome gravity. The aerospace propulsion engineer is faced with two choices for the control of gravity in this regard: passive control and active control. Modern aerospace propulsion technology, which is based on accumulated scientific knowledge since recorded history, can only achieve the passive control of gravity whereby a given propulsion device must develop a thrust that will passively counteract the Earth's gravitational pull, lift a vehicle off the surface, and propel it through the air or into space. Newton's laws of motion and gravity require that the fuel fraction of any aerospace vehicle can never be less than that given by a simple function of the ratio of the vehicle's maximum speed to the speed of its rocket plume, jet, fan, or propeller wake. For example, this limit implies that a single-stage rocket that accelerates to escape velocity must be composed of more than 93 percent fuel. That is because a rocket must accelerate its working fluid from rest (relative to the rocket) up to its exhaust speed. Thus, exhaust speeds for aircraft and chemical rockets are limited by material science, chemical reaction rates, and engineering factors to only a few thousand meters per second. To date, there is no technology that can achieve the active control of gravity. If one could eliminate or otherwise control the Earth's gravity field, then one has the ability to dramatically reduce the amount of propellant, its tankage, and the overall structural size and mass of an aircraft or rocket because there will no longer be any need for these to overcome the pull of Earth's gravity while transporting a payload across the globe or into space. Instead, aerospace vehicles will only need to have the propellant mass and infrastructure necessary to change their kinetic energy from rest to a final velocity necessary to achieve atmospheric flight or space orbit. The Earth's gravitational well will no longer have any impact on aircraft, launch vehicle, or spaceflight dynamics if one were to achieve active gravity control. Aerospace vehicles would merely "levitate" in air and their propulsion systems would be optimized for change-in-velocity missions. However, it is possible to envision a form of active gravity control propulsion that would not require a change in kinetic energy. One of the primary concepts for the goal of affecting gravity is "antigravity," which is a colloquial expression that specifically means the negation or repulsion of the force of gravity. A more general term that encompasses this notion and other possibilities is "gravity control." If antigravity exists, it can be exploited to counteract or nullify the gravitational pull, or attraction, of a planetary (or stellar) body that acts upon a much smaller body. Einstein's General Theory of Relativity gives a prescription for a variety of different antigravity generators. Even Newton's law of gravity offers several different classical prescriptions. Newton's law of gravity can be used to simply nullify the gravity field of one body acting on another body by using a clever arrangement of masses. The UNCLASSIFIED//FOA OFFI€1.t.k YS& 0,.k\f 1 UNCLASSIFIED/ fFOA OFFIEIA~ W&li QPI~¥ theoretical possibility of antigravity also appears in quantum gravity theories, cosmological vacuum or dark energy, and quantum field theory. This report reviews all of these topics. The report will also review the topics of gravity control that include the production of antigravity (self-lifting) forces induced by quantum vacuum zero-point energy and by nonretarded quantum interatomic dispersion forces in a curved spacetime (that is, in a background gravitational field). The reader should bear in mind that many of these concepts are nowhere near having any form of practicable engineering implementation. However, the report will provide theoretical estimates to guide the way toward technologica l implementation of antigravity. II. Concepts for Antigravity Within Newtonian Physics The basic form of Newton's law of gravity is given by the standard expression for the gravitational force {Fgrav) that mutually acts between two masses (Reference 1): (1) where the negative sign indicates that Fgrn" is a (mutual) force of attraction, G is Newton's universal gravitation constant (6.673 x 10-11 Nm2/kg 2), m 1 and m 2 are two interacting masses, and r is the radial distance between the two masses (note: MKS units are used throughout). Observe in Equation (1) that the force of gravity acting on a small test mass becomes stronger when the other (gravitating) mass is larger in magnitude or when the distance between them is very small, or both. Also recall that Equation (1) and Newton's second law of motion (F = ma) to define the magnitude of the gravitational acceleration a8 that acts on a small test mass m due to a larger (gravitating) mass M (Reference 1): GM a g = - ?­ (2) r- If Earth is chosen to be the larger gravitating mass so that M = M@ (5.972 x 1024 kg), then according to Equation (2) a small test mass m placed near the Earth's surface, whereby r~ R @ (6.378 x 106 m), will experience a downward gravitational acceleration of a g = g = 9.81 m/s2. NEGATING NEWTONIAN GRAVITY It is possible to design an antigravity machine that can nullify Earth's gravity field using Newton's law of gravity. One way to use Equation (1) to nullify the Earth's gravitational pull at a particular location would be to locate another planet of equal mass above that location (Reference 2,3). The forces from the two Earth masses will cancel each other out over a broad region between them . Everything within this broad region will be in free fall. However, this is not a practical solution for aerospace flight since there is no way to manipulate and control another planetary sized body. Along similar lines, Forward (Reference 2,3) suggested to consider using a ball of ultradense compact matter, corresponding to dwarf star or neutron star matter (~ 1011 - 1018 kg/m 3), having a diameter of 32 cm and a mass of 4 million metric tons. This ultradense ball will have a surface gravitational (attractive) force of 1-g. This small UNCLASSIFIED/ /FOA OFFI&il.t.k Y&li 8,.LY 2 UNCLASSIFIED/fFOA OFFIEIAL: U&i QPIL:¥ ultradense ball could be placed near the surface of the Earth and its 1-g gravity field will cancel the Earth's 1-g gravity field. All test objects placed in the broad region between the small ultradense ball and the Earth will thus be in free fall. Another option Forward (Reference 2-5) suggested would be to shape the compact ultradense matter into a disk that is 45 cm in diameter and 10 cm thick, and having the same mass and density as the small ultra dense ball. Its gravitational acceleration is a g = 4Gp,, where p is the mass density of the disk and t is its thickness. In this case, the disk will have a force of gravitational attraction that is the same on both sides, and it will be uniform near the center of the disk where the strength of the gravitational force will be 1-g. If this disk were to be placed very close above the Earth's surface, then there will be a gravitational force of 2-g above the disk (= 1-g due to the Earth's gravity field plus 1-g due to the top-side gravity field of the disk) while underneath the disk near its center there will be a gravity-free (or free fall) region because the Earth's gravity field underneath is canceled by the gravity field of the disk's bottom-side. While these are interesti ng antigravity machines, they are unfortunately not feasible from an engineering standpoint since one does not yet have the technology or means to create and handle ultradense compact matter. ENERGY ESTIMATE FOR NEWTONIAN LEVITATION An ideal propulsion breakthrough could take the form of the antigravity-based levitation of an aerospace vehicle within the Earth's atmosphere. Rockets like the Air Force DC-XA can hover above the ground for a time that is limited by the amount of rocket fuel available (Reference 6). But an ideal antigravity propulsion device should allow for the indefinite levitation of a vehicle above the Earth's surface. It is illustrative to estimate the energy required to levitate a 1-kg test mass above the Earth's surface. This will help quantify a potentially key engineering parameter for such a levitation system . A generic estimate can be found by considering the amount of energy per unit mass required to nullify the (magnitude) of the Earth's gravitational potential energy E1ev for a test mass m hovering at height It above the Earth's surface: E =GMffl m (J / ko) (3) lcv h b Equation (3) can also be derived by calculating how much energy is required to completely remove a test mass from the Earth's surface to infinity. This calculation is more in line with the analogy to nullify the effect of gravitational energy. And Equation (3) also represents the energy required to stop a test mass at the levitation distance h if it were falling in from infinity with zero initial velocity. Setting h ;::i Re and m = 1 kg in Equation (3), the result is E1ev = 62.5 MJ/kg. This is 2.05 times the kinetic energy required to put the test mass into low Earth orbit {LEO). However, this estimate will require some adjustment that depends upon the type of theory and its technological implementation. That is because the operational energetics of a putative antigravity propulsion system must be considered in conjunction with E1cv , UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f 3 UNCLASSIFIED/ fFOA OFFIEIA~ W&li QPI~¥ III. Concepts for Antigravity Within General Relativity In the Sections that follow the known types of antigravity that can be derived from Einstein's General Theory of Relativity are described and summarized, which is the modern relativistic theory of gravity. ANTIGRAVITY VIA GRAVITOMAGNETIC FORCES Historical Foundations Heaviside (Reference 7) (in 1883), Einstein (prior to the 1916 publication of his General Theory of Relativity), Thirring (Reference 8,9), and Thirring and Lense (Reference 10) (see also, Reference 11) showed that general relativity theory provides a number of ways to generate non-Newtonian gravitational forces via the splitting of gravitation into electric and magnetic field type components. These forces can be used to counteract the Earth's gravitational field, thus acting as a form of antigravity. General relativity theory predicts that a moving source of mass-energy can create forces on a test body which are similar to the usual centrifugal and Coriolis forces, although much smaller in magnitude. These forces create accelerations on a test body that are independent of the mass of the test body, and the forces are indistinguishable from the usual Newtonian gravitational force. The Earth's gravitational field can be counteracted by generating these forces in an upward direction at some spot on the Earth. Forward (Reference 12) linearized Einstein's general relativistic field equation and developed a set of dynamic gravitational field relations similar to Maxwell's electromagnetic field relations. The resulting linearized gravitational field relations are a version of Newton's law of gravitation that obeys special relativity. The linearized gravitational field relations show that there is a unique correspondence between the gravitational field and the electric field. For example, the Newtonian gravitational field of an isolated mass is the gravitational analog to the electric field of an isolated electric charge. Likewise, there is an analogy to a magnetic field contained within the linearized gravitational field relations. In Maxwellian electrodynamics, a magnetic field is due to the flow of an electric charge or an electric current. In other words, the electric field surrounding an electric charge in motion will appear as a magnetic field to stationary observers. If the observers move along with the charge, they see no relative motion, and so they will only observe the charge's electric field. Thus, the magnetic field is simply an electric field that is looked at in a moving frame of reference. In an analogous fashion, the linearized gravitational field relations show that if a (gravitational) mass is set into motion and forms a mass current, then a new type of gravitational field is created that has no source and no sink. This is called the Lense-Thirring effect, or rotational frame dragging effect, in which rotating bodies literally drag spacetime around themselves. Forward's Dipole Gravitational Field Generator Forward (Reference 13,14) used the linearized gravitational field relations plus aspects of the Lense-Thirring effect to develop models for generating antigravity forces. One example of an antigravity generator is based on a system of accelerated masses whose mass flow can be approximated by the electrical current flow in a wire-wound torus. UNCLASSIFIED/ /FOA OFFI&il.t.k Y&li 9,.LY 4 UNCLASSIFIED/ fFOA OFFIEIAk W&i 0Pilk¥ According to Maxwellian electrodynamics, an electric current flowing through a wire that is wrapped around a torus (or ring) causes a magnetic field to form inside the torus. If the current (I) in the wire increases with time, then the magnetic field B inside the torus also increases with time. This time-varying magnetic field in turn creates a dipole electric field E, as shown in Figure 1. The magnitude of the electric field at the center of the torus is given by: (4) where µo is the vacuum electromagnetic permeability constant (4n x 10-7 H/m), N is the total number of turns of wire wound around the torus, i is the time rate-of-change of the electric current flowing through the wire, r is the radius of one of the loops of wire, and Rt is the radius of the torus. Figure 1. Dipole Electric Field Generator (Reference 14) In a similar fashion, Forward's antigravity device is a dipole gravitational field generator. As shown in Figure 2, a mass flow T through a pipe wound around a torus induces a Lense-Thirring field P to form inside the torus. If the mass flow is accelerated, then the P-field increases with time, and thus a dipole gravitational field G is created. The magnitude of the anti-gravitational field at the center of the torus is given by: (5) UNCLASSIFIED/ /FOA OFFI&IAb Yi&: 8,.bY 5 UNCLASSIFIED/fFOA OFFIEIAk W&i 0Pilk¥ where rio is the vacuum "gravitational permeability" constant(= 16nG/c2 = 3. 73 x 10-26 m/kg), 1 N is the total number of turns of pipe wound around the torus, 'ft. is the time rate-of-change of the mass current flowing through the pipe, r is the radius of one of the loops of pipe, R1 is the radius of the torus, and c is the speed of light (3 x 108 m/s) (Reference 14). One should note the striking similarity between Equations (4) and (5) for the dipole electric and dipole gravitational fields. Figure 2. Diople Gravitational Field Generator {Reference 14} Using Equation (5), Forward (Reference 13,14) showed that there would be a need to accelerate matter with the density of a dwarf star through pipes as wide as a football field wound around a torus with kilometer dimensions in order to produce an antigravity field (at the center of the torus) of G ~ 10-10a acc , where a acc is the acceleration of the (dwarf star density) matter through the pipes. The tiny factor 10-10 is composed of the even smaller rio, which is the reason why very large systems are required to obtain even a measurable amount of acceleration. To counteract the Earth's gravitational field of 1-g requires an antigravity field of 1-g (vectored upward), and thus the dwarf star density material within the pipes must achieve a acc = 1011 m/s2 in order to accomplish this effect. Forward (Reference 5) also identified a configuration comprised of a rotating torus of dense matter that turns inside-out like a smoke ring as another type of dipole gravitational field generator. As shown in Figure 3, an inside-out turning ring of very dense mass (M) will create an upward force (of acceleration a) in the direction of the (constant) mass motion (Mv, vis the mass velocity). This is also a feature of the 1 The vacuum "gravitational permittivity" constant is (Reference 12): yo= (41tGJ-' = 1.19 x 109 kg-s2/m3• UNCLASSIFIED//FOA OFFI&IAb Yi&: 8,.bY 6 UNCLASSIFIED/fFOA OFFIEIAL: U&i QPIL:¥ Lense-Thirring effect. Forward's linearization analysis generalizes all of these effects into the following two key ingredients that are required to produce antigravity forces: 1) any mass with a velocity and an acceleration exerts many different general relativistic forces on a test mass, and 2) these forces act in the direction of the velocity and in the direction of the acceleration of the originating mass. In summary, these forces are equivalent to gravitational forces, which can be used to cancel the Earth's gravitational field. Figure 3. Dipole Gravitational Field Generator: Inside-Out Whirling Dense Matter Torus (Reference 5) One can also view this genre of devices as a gravity catapult machine in which the machine pushes a body away using its general relativistic antigravity forces to impart a change in velocity. A space launch operator on the ground wanting to send a payload up into orbit would just ratchet up the strength of the (upward-directed) antigravity field to some value above 1-g, and after pressing the release button the payload accelerates up and away into orbit. These devices could also be placed in Earth orbit, stationed anywhere within the solar system, or even distributed throughout the galaxy in order to establish a network of gravity catapults. Space travelers could begin their trip by being launched from the catapult on the Earth's surface, and when they reach space they would jump through various catapults as needed to reach their destination. FELBER'S RELATIVISTIC ANTIGRAVITY EFFECT Felber (Reference 15) used the Schwarzschild solution of Einstein's general relativistic field equation to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. His analysis gives a relativistically exact (strong gravitational field condition) calculation showing that a mass, which radially approaches or recedes from a payload at a relative velocity of Vcrir > c/3 112 ( vc,i1 = critical velocity), will gravitationally repel the payload as seen by distant inertial observers. In other words, any source mass, no matter how large or small it is or how far away it is from a test body (payload), will produce an antigravity field when moving at any constant velocity above Vent • UNCLASSIFIED//FOA OFFI€1.t.k Y&li 8,.LY 7 UNCLASSIFIED/fFOA OFFIEIAk W&i 0Pilk¥ The exact relativistic strong-field condition that establishes the lower limit criterion for vcr;r to induce antigravity repulsion of a payload (as measured by distant inertial observers in the rest frame of the source or in the initial rest frame of the payload) is given by (Reference 15): (6) In this expression, y = (I - p2)- 112 is the standard relativistic Lorentz transformation factor which is a function of the normalized relativistic velocity parameter p= vie, 'I'= 'l'(r) = I ­ (2GM/rc2) is the goo (or time-time) component of the static Schwarzschild spacetime metric2 of a source (or central) body of mass M, Lis the constant specific angular momentum of a ballistic payload of mass m, and r is the radial distance of the approaching/receding payload from M. One can solve the inequality in Equation (6) for p (or v) under the condition that a payload far from M, such that r » b (b is the periapsis distance of the payload from M) and r » GM!c2 , and find that the payload will become gravitationally repelled by M whenever y2 > 3/2 or p > 3-112. In order to derive an exact solution, Felber considered the case for which M » m so that the energy and momentum delivered to the payload has a negligible back-reaction on the source body's motion. And he found that a strong gravitational field is not required for antigravity propulsion because a weak-field solution achieves the same results. Felber discovered another interesting facet about this new relativistic antigravity effect. He found that there is also an antigravity field that repels bodies in the backward direction with a strength that is one-half the strength of the antigravity field in the forward direction. Thus a stationary body will repel a test body that is radially receding from it at any v > vcri,, To delineate the propulsion benefit from this technique, Felber determined that the maximum velocity ( vpmax-wf) that can be imparted to a payload initially at rest by the weak (gravitational) field of a larger source mass moving toward the payload at constant V > Vcrit is Vpmax-wf « c[P - (3Pt 1]. For the strong-field case, the maximum velocity (vpma,-,r) that can be imparted to the payload (initially at rest) by the larger source mass moving toward the payload at any constant v is vpma,-,r = pc. Felber's analysis includes examples where he uses black holes for the large source mass. This form of antigravity propulsion is not too surprising because Misner et al. (Reference 16), Ohanian and Ruffini (Reference 17), and Ciufolini and Wheeler (Reference 18) report that general relativistic calculations show that the time­ independent Kerr (spinning black hole) gravitational field exhibits an inertial frame dragging effect similar to gravitational repulsive forces in the direction of a moving mass at relativistic velocities. This and Felber's exact solution are among the genre of Lense-Thirring type effects that produce antigravity forces. It is interesting to note that even though general relativity theory admits the generation of antigravity forces at relativistic velocities (Reference 19), they have not been seen in laboratory experiments 2 A spacetime metric (ds2 ) is a Lorentz-invariant distance function between any two points in spacetime that is defined by ds2 = g""dx1'dx' , where g," is the metric tensor which is a 4x4 matrix that encodes the geometry of spacetime and dx" is the infinitesimal coordinate separation between two points. The Greek indices (µ,v = 0...3) denote spacetime coordinates, ><° ...x3, such that x 1...x 3 = space coordinates and ><°= time coordinate. The Schwarzschild metric is: ds2 = - (1 - 2GM/cir)c2dt2 + (1 - 2GM/c2r )"1dr2 + r2(d02 + sin 20dcp2) . The corresponding metric tensor is a diagonal matrix: g,,. = diag[- (1 - 2GM/c2r), (1 - 2GM/c2r)"1, r2, r2sin20). (r, O,cp) are the usual spherical polar coordinates in 3-dimensional space. UNCLASSIFIED//FOA OFFI&IAb Yi&: 8,.bY 8 UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ because repulsive force terms are second and higher-order in the source mass velocity. To invent a relativistic driver for a captured astronomical body in order to use it to launch payloads into relativistic motion presents a large technical challenge for future experimenters. For this reason, this paper will not consider this concept any further. However, it does serve the useful purpose of illustrating the unusual antigravity forces that can appear in Einstein's general relativity theory. NEGATIVE ENERGY-INDUCED ANTIGRAVITY Negative energy density and negative pressure are acceptable results both mathematically and physically in general relativity and quantum field theories, and negative energy/pressure manifests as gravitational repulsion (that is, antigravity). Negative energy is also known as a form of "exotic matter." In classical physics the energy density of all observed forms of matter (fields) is non­ negative. What is exotic about negative energy is that it must have negative energy density and/or negative flux (Reference 20). The energy density is "negative" in the sense that a given (exotic) matter field must have an energy density, PE(= pc2, where p is the rest-mass density), that is less than or equal to its pressures/tensions, p1 (Reference 21,22). 3 In many cases, these equations of state are also known to possess an energy density that is algebraically negative; that is, the energy density and flux are less than zero. It is on the basis of these conditions that this material property is called "exotic." The condition for ordinary, classical (non-exotic) forms of matter that one is familiar with in nature is that PE > pi and/or PE ~ 0. These conditions represent two examples of what are variously called the "standard" energy conditions: Weak Energy Condition (WEC: PE ~ 0, PE +Pi~ 0), Null Energy Condition (NEC: PE+ p1 ~ 0), Dominant Energy Condition (DEC), and Strong Energy Condition (SEC). These energy conditions forbid negative energy density between material objects to occur in nature, but they are mere hypotheses. Hawking and Ellis (Reference 23) formulated the energy conditions in order to establish a series of mathematical hypotheses governing the behavior of collapsed-matter singularities in their study of cosmology and black hole physics. More specifically, classical general relativity allows one to prove lots of general theorems about the behavior of matter in gravitational fields. The bad news is that real physical matter is not "reasonable" because the energy conditions are in general violated by semiclassical quantum effects (occurring at order 11) (Reference 22). 4 More specifically, quantum effects generically violate the average NEC (ANEC). Furthermore, it was discovered in 1965 that quantum field theory has the remarkable property of allowing states of matter containing local regions of negative energy density or negative fluxes (Reference 24). This violates the WEC, which postulates that the local energy density is non-negative for all observers. "Negative energy" has the unfortunate reputation of alarming physicists. This is unfounded since all the energy condition hypotheses have been experimentally tested in the laboratory and experimentally shown to be false - 25 years before their formulation (Reference 25). 3 Latin indices (e.g., i, j, k = 1...3) that are affixed to physical quantities denote the usual 3-dimensional space coordinates, x1... x3, indicating the spatial components of vector or tensor quantities. 4 Planck's reduced constant, 11 = 1.055 x 10-34 J.s. UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f 9 UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ Further investigation into this technical issue showed that violations of the energy conditions are widespread for all forms of both "reasonable" classical and quantum matter (Reference 26-30). Furthermore, Visser (Reference 22) showed that all (generic) spacetime geometries violate all the energy conditions. So the condition that PE > Pi and/or PE;::,: 0 must be obeyed by all forms of matter in nature is spurious. Violating the energy conditions commits no offense against nature. Negative energy has been produced in the laboratory and this will be discussed in the following sections. Examples of Exotic or "Negative" Energy Found in Nature The exotic (energy condition-violating) fields that are known to occur in nature are: • Static, radially-dependent electric or magnetic fields. These are borderline exotic, if their tension were infinitesimally larger, for a given energy density (Reference 23,31). • Squeezed quantum vacuum states: electromagnetic and other (non-Maxwellian) quantum fields (Reference 21,32). • Gravitationally squeezed vacuum electromagnetic (or other field) zero-point fluctuations (Reference 33). • Casimir effect; that is, the Casimir vacuum in flat, curved, and topological spaces (Reference 34-40). • Other quantum fields/states/effects. In general, the local energy density in quantum field theory can be negative due to quantum coherence effects (Reference 24). Other examples that have been studied are Dirac field states: the superposition of two single particle electron states and the superposition of two multi-electron­ positron states (Reference 41,42). In the former (latter), the energy densities can be negative when two single (multi-) particle states have the same number of electrons (electrons and positrons) or when one state has one more electron ( electron-positron pair) than the other. Cosmological inflation (Reference 22), cosmological particle production (Reference 22), classical scalar fields (Reference 22), the conformal anomaly (Reference 22), and gravitational vacuum polarization (Reference 26-29) are among many other examples that also violate the energy conditions. Since the laws of quantum field theory place no strong restrictions on negative energies and fluxes, then it might be possible to produce exotic phenomena such as faster-than-light travel (Reference 43-45), traversable wormholes (Reference 21,22,46), violations of the second law of thermodynamics (Reference 47,48), and time machines (Reference 22,46,49). There are several other exotic phenomena made possible by the effects of negative energy, but they lie outside the scope of this report. See Appendix A for more technical details on items 1 through 4. Toy Model Estimate for Negative Energy-Induced Antigravity For the purpose of this report, the discussion will be confined to how negative energy can be used to produce antigravity for the simplest case of counteracting the Earth's gravitational field. To counteract or otherwise reduce gravity merely requires the deployment of a thin spherical shell (bubble) of negative energy around an aerospace UNCLASSIFIED//FOA OFFI&il.t.k Y&li 8,.LY 10 UNCLASSIFIED/fFOA OFFIEIAk W&i 0Pilk¥ vehicle. This particular case study will serve as a useful illustrative comparison with the Newtonian antigravity case discussed in Section II-A. Interest is only in the slow (non-relativistic) motion, weak (gravity) field regime that characterizes the physics of the Earth, Sun, other forms of solar system matter, most interstellar matter (excluding compact dense stars and black holes), and small test masses. In this case the time-time component of the Ricci curvature tensor (Rµv) is given by Roo z Gp/c2 z (7.41 x 10-28 )p m-2 . This is the primary quantity inside the general relativistic field equation5 that encodes and measures the curvature of spacetime around a source of matter and characterizes the weak or strong gravity field regime for all forms of astronomical mass density (p). For example, the Earth's mass density is 5,500 kg/m 3 so Roo z 4.08 x 10-24 m-2, which indicates that an extremely flat space surrounds the Earth and thus the system is within the weak field regime. Gravitational physics in the weak field regime is completely described by the standard Schwarzschild spacetime metric, which leads to the usual Newtonian and post­ Newtonian gravitational physics. Two simple approaches can be used to determine the negative energy density required to counteract the Earth's gravitational field: a) integrate the Einstein general relativistic field equation, orb) use an already derived result from general relativity that gives the repulsive force acceleration in terms of the spacetime metric components. For the first case, the generalized gravitational Poisson equation from the Einstein field equation is: (7) where the definition is used, PE*= rest-energy density+ compressional potential energy (a.k.a. pressure), goo= goo(r) is the time-time component of the metric tensor 8r,v, and Tr(Tµv) = P\, is the trace (sum of diagonal matrix elements) of the stress-energy-momentum tensor Tµv (a matrix quantity that encodes the density and flux of a matter source's energy and momentum). Using tensor identities and grinding the algebra, Equation (7) can be re­ written as v' 2 ,--::- _ 4rcG • \I-goo - -4-Pe (8) C 5 The Einstein field equation is: G". = R". - (1/2)g". R = -(87[G/c:')°fi"'' where G". is the Einstein curvature tensor and R = R"" (the matrix trace of R". ) is the Ricci scalar curvature. In simplest terms, this relation states that gravity is a manifestation of the spacetime curvature (G".) induced by a source of matter (T".). UNCLASSIFIED//FOA OFFI&IAb Yi&: 8,.bY 11 UNCLASSIFIED/fFOA OFFIEIAk W&i 0Pilk¥ where V2 is the standard Laplace differential operator. The left-hand-side of Equation (8) is the gravitational potential. Integrating Equation (8) once over a region of space exterior to a ball (or thin spherical shell) of rest-energy density to obtain lv.J-g00 (r)I = G~ = g (acceleration, m/s2 ) (9) r where the standard spherically symmetric spacetime (or Schwarzschild) coordinate system (t,r,0,<p) in which time t, radial space coordinate r, and angular space coordinates (0,<p) have their usual meaning is used. The second approach (case b) can be derived by recalling that in the exterior Schwarzschild spacetime around a central mass M (a ball or thin spherical shell) is ,---- GM ✓-g oo (r) =1-- (10) r Since the definition is given that g = Iv .J-g00 (r)I, then perform the radial derivative of Equation (10) and again arrive at Equation (9). Since from special relativity M = E/c2 (for a given rest-energy E), a negative energy state is identical to a negative mass state (Reference 50). Thus the mass Min Equation (9) can be replaced with the negative energy density - pE * = - p c2 = - Mc2/V by using the volume (V = 4nr28r) of a thin spherical shell of radius rand thickness 8r, and rearrange quantities to solve for PE* to get the final result: • - gc 2 PE= 41tG8r (11) -(1.05 X 1027 ) = or where g is now the acceleration due to gravity near the Earth's surface. If one desires to use other geometries (for example, torus, cylinder, prism, cone, and pyramid) instead of a thin spherical shell, then Equation (11) will admit minor numerical adjustments to accommodate the relevant geometrical factors associated with different geometrical volumes. Equation (11) gives the negative energy density required to generate a repulsive gravitational force that counteracts the Earth's gravity field from the surface all the way up to LEO (since g in LEO is only a few percent smaller than on the surface). Any realistic value that one chooses for the bubble wall thickness 8rwill give a negative energy density that will always be on the order of the equivalent negative energy density of a dwarf star or neutron star. The technical challenge to implement this kind of antigravity, however, is daunting. In the next section the case of a cosmological antigravity that is generated by a form of matter having a positive energy density and negative pressure is discussed. UNCLASSIFIED//FOA OFFI&IAb Yi&: 8,.bY 12 UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ COSMOLOGICAL ANTIGRAVITY It turns out that there is already a naturally occurring antigravity force that acts throughout the universe. Actually, this force acts upon the entire spacetime structure of the universe, and it is called cosmological inflation. Cosmological inflation causes the universe to expand at an ever accelerating rate. In what follows, the nature of this cosmological antigravity force and its potential aerospace propulsion application is examined. Pressure as a Source of Gravity Newtonian gravitation is modified in the case of a relativistic perfect-fluid (where p << PE cannot be assumed). The stress-energy tensor p v for this case is (Reference 16) : (12) where p is the fluid mass density, PE= pc2 is the fluid rest-energy density (or just energy density), p is the fluid pressure, u µ is the 4-velocity vector of the fluid, and gµ v is the metric tensor. The Einstein general relativistic field equation using the identity gµµ = 4 to obtain R =(8nG!c4)T, which is the Ricci curvature scalar can be contracted. And so Equation (12) becomes T = PE - 3p, which is just the trace of p•v. Since T = PE - 3p, a modified Newtonian gravitational Poisson equation is produced: (13) where ~ is the gravitational potential. It should be noted that the energy density and pressure are kept as separate terms as opposed to Equations (7) and (8) in the previous section. Equation (13) means that a gas of particles all moving at the same speed u has an effective gravitational mass density of p(l + ii2/c2). Thus, for example, a radiation-dominated fluid generates a gravitational attraction twice as strong as one predicted by Newtonian gravity theory according to Equation (13). Vacuum Energy of Einstein's Cosmological Constant A major consequence of the Einstein field equation is that pressure p becomes a source of gravitational effects on an equal footing with the energy density PE• One consequence of the gravitational effects of pressure is that a negative-pressure equation of state that achieves PE + 3p < O in Equation (13) will produce gravitational repulsion (that is, antigravity). The Einstein field equation that includes a cosmological constant A is: (14) where Gµv is the Einstein curvature tensor. The A term, as it appears in Equation (14), represents the curvature of empty space. Now if one moves this term over to the right­ hand-side of Equation (14), which has become widespread practice in modern times, then UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f 13 UNCLASSIFIED/fFOA OFFIEIAk W&i 0Pilk¥ (15) whereby this term now behaves like the stress-energy tensor of the vacuum, Tv~; , which acts as a gravitational source: T r,v - Ac4 r,v (16) vac - 87tG g One should note that the absence of a preferred frame in special relativity means that r;.; must be the same (that is, isotropic or invariant) for all observers. There is only one isotropic tensor of rank 2 that meets this requirement: riµv (the Minkowski flat spacetime metric tensor in locally inertial frames). So in order for r;.; to remain invariant under Lorentz transformations, the only requirement is that it must be proportional to ri µv . But this generalizes in a straightforward way from inertial coordinates to arbitrary coordinates by replacing ri µv with gµv, thus justifying the curved spacetime metric tensor in Equation (16). By comparing Equation (16) with the perfect­ fluid stress-energy tensor in Equation (12), one finds that the vacuum looks like a perfect fluid with an isotropic pressure P vac opposite in sign to the energy density P v•c • Therefore, the vacuum must possess a negative-pressure equation of state (according to the first law of thermodynamics): P vac = -Pvac (17) The vacuum energy density should be constant throughout spacetime, since a gradient would not be Lorentz invariant. So by substituting Equation ( 17) into PE + 3p, the following is produced P vac + 3 P vac = P vac + 3 ( - P vac ) (18) =-2Pvac < 0. The vacuum equation of state is therefore manifestly negative. Last, when incorporating pvac into the Einstein field equation as a gravitational source term, and comparing its corresponding (Lorentz invariant) stress-energy tensor P vacg•" ' with Equation (16), then the usual identification (or definition) is made that: Ac4 (19) P vac = S1tG Thus the terms "cosmological constant" and "vacuum energy" are essentially interchangeable in this perspective and mean the same thing (whereupon P vac = p.,..), which is seen in the present-day cosmological literature. UNCLASSIFIED//FOA OFFI&IAb Yi&: 8,.bY 14 UNCLASSIFIED/fFOA OFFIEIAL: U&i QPIL:¥ By substituting Equation (19) into Equation (17), one observes that a positive A will act to cause a large-scale repulsion of space (because this gives a negative vacuum pressure), whereas a negative A (giving a positive vacuum pressure) will cause a large­ scale contraction of space. Because A is a constant, the vacuum energy is a constant (that is, time independent) . This then implies a problem with energy conservation in an expanding universe since one expects that energy density decreases as a given volume of space increases, which is the case for the ordinary matter and cosmic microwave background that is observed in extragalactic space. In other words, the matter and radiation energy densities decay away as the universe expands while the vacuum energy density remains constant. The cure for this apparent energy conservation problem is the vacuum equation of state given by Equation (17) . A negative pressure is something like a tension in a rubber band. It takes work to expand the volume rather than work to compress it. The proof of this is as follows (Reference 51): the energy created in the vacuum by increasing (expanding) space by a volume element dV is PvacdV, which must be supplied by the work done by the vacuum pressure -pvac dV during the expansion of space, therefore /Jvac = - p vac , In other words, the work done by the vacuum pressure maintains the constant vacuum energy density as space expands. Therefore, the vacuum acts as a reservoir of unlimited energy that provides as much energy as needed to inflate any region of space to any given size at constant energy density. Dark Energy Dark energy is an easily misunderstood form of energy in cosmology. There are two sets of evidence pointing toward the existence of something else beyond the radiation and ( ordinary and dark) matter itemized in the overall cosmic energy budget. 6 The first comes from a simple budgetary shortfall. The total energy density of the universe is very close to critical. This is expected theoretically and it is observed in the anisotropy pattern of the cosmic microwave background (CMB). Yet, the total matter density inferred from observations is 26 percent of critical. 7 The remaining 74 percent of the energy density in the universe must be in some smooth, unclustered form that is dubbed "dark energy." The second set of evidence is more direct. Given the energy composition of the universe, one can compute a theoretical distance vs. redshift diagram. This relation can then be tested observationally. Riess et al. (Reference 52) and Perlmutter et al. (Reference 53) reported direct evidence for dark energy from their supernovae observations. Their evidence is based on the difference between the luminosity distance in a universe dominated by dark matter and one dominated by dark energy. They showed that the luminosity distance is larger for objects at high redshifts in a dark energy-dominated universe. Therefore, objects of fixed intrinsic brightness will appear fainter if the universe is composed of dark energy. The two groups measured the apparent magnitudes of a few dozen Type Ia supernovae at redshifts z ::; 0.9, which are known to be standard distance candles (meaning they have nearly identical absolute magnitudes at any cosmological redshift­ 6 Dark matter and dark energy are not to be confused. Dark matter is a non-luminous, non-absorbing, non­ baryonic form of matter that only interacts with all other forms of matter via gravitational and weak nuclear forces. Dark matter has a positive rest-energy density and a nearly negligible positive pressure. Thus, it has no beneficial application for breakthrough propulsion physics. 7 26% total matter density = 4% ordinary (baryonic) matter + 22% dark matter. 15 UNCLASSI FIED/ / FOA OFFI€1Ak Yi& 8,.k\f UNCLASSIFIED/fFOA OFFIEIAk W&i 0Pilk¥ distance).8 The supernovae data strongly disfavored (with high confidence) the flat matter-dominated (nm = 1, n /\ = 0) universe and the pure open universe (nm = 0.3, n /\ = 0) models.9 After this discovery, a lot of attention was paid to choosing an appropriate name for this new energy. "Quintessence" was one good choice because it expresses the fact that, after cosmological photons, baryons, neutrinos, and dark matter, there is a fifth essence in the universe. More recently, "dark energy" is used more often, with quintessence referring to the subset of models in which the energy density can be associated with a time-dependent scalar field or a time-dependent cosmological vacuum energy. In analyzing the cosmological modeling results suggested by the Type Ia supernovae data, it becomes apparent that the only form of dark energy budgeted for in the models is the cosmological constant. To consider other possibilities one evaluates the time evolution of the general relativistic conservation law for energy, VJ:= V,l ; = O, where v = 0 to signify time evolution and Vr, is the covariant derivative (or spacetime curvature gradient), in an expanding universe as applied to the cosmological constant (Reference 16): 8PE +~3PE + 3p] = O (20) at a where a is the scale factor of the universe and t& is the time derivative of a. Equation (20) is derived using Equation (12) in the case of a perfect isotropic fluid where there is no gravity and velocities are negligible such that u µ = (1, 0, 0, 0), and the energy density and pressure evolve according to the continuity and Euler equations. The only way Equation (20) can be satisfied with constant energy density is if the pressure is defined by Equation (17). One might imagine energy with a slightly different pressure and therefore energy evolution. Define the equation of state w: (21) A cosmological constant corresponds to w"' = wvac = -1, matter (ordinary and dark) to w mauer ::::: 0, and radiation to Wract = 1/3.10 The earlier Riess and Perlmutter supernovae data (fixing the universe to be flat) showed that values of Wcte > - 0.52 for dark energy are strongly disfavored. In fact, Riess and a team of collaborators (a.k.a. the "Higher-Z team") recently published new observational data and analysis that includes a much larger survey of Type Ia supernovae that are at much higher cosmological redshift (Reference 54). The measured spectra of ancient (z ~ 1, or up to 10 billion light-years distance or a look-back time of up to 10 billion years ago) and recent (z ~ 0.1, or ~ 1 billion light-years distance or a look-back time of ~ 1 billion years ago) were compared and showed that there was no evolutionary change in the physics that drives Type Ia supernovae explosions and their subsequent spectral luminosity output. This establishes 8 In cosmology, the redshi~ z serves as a surrogate for distance (in light-years) or look-back time. 9 O m = ratio of energy density contained in matter (as measured today) to the critical energy density; n A = Ovac = ratio of energy density in a cosmological constant to the critical energy density; Per= 3Hl /8rcG is the critical energy density, where Ho is the present-day Hubble expansion rate . 10 Non-relativistic (ordinary and dark) matter has a very tiny positive pressure, p oc Temp/m (Temp is absolute temperature, m is mass), while a relativistic gas (of radiation) hasp = pE/3 > 0. UNCLASSIFIED//FOA OFFI&IAb Yi&: 8,.bY 16 UNCLASSIFIED/fFOA OFFIEIAL: U&i QPIL:¥ the efficacy of using Type Ia supernovae as a standard distance candle for cosmological dark energy surveys. The Higher-Z team's results also concluded, with 98 percent confidence, that wde = - 1.0, and that this is a perpetual constant (over at least 10 billion years time) (Reference 54). This result falsifies all quintessence models for cosmology. Therefore, a cosmological constant is consistent with the dark energy data to a high degree of precision and statistical confidence whereby one can now state that dark energy is the vacuum energy of Einstein's cosmological constant because wdc = wA = -1 (Reference 55,56). Equation (20) can be integrated to find the evolution of the dark energy density, Pde = PA, as a function of the cosmological scale factor a: (22) where a' is the dummy integration variable for the scale factor. Since wde = - 1 (= wA ) is a constant in Equation (22), then Pc,•. oc aexp[-3(1 + ~1,)] or Pde = P A oc a0. This is exactly what is expected on the basis of previous analysis in Section III-D-2. For a comparison with this result, one should note that pc2 oc a-3 for (ordinary and dark) matter and Prn<1 oc a-4 for radiation such that pc2 ➔ 0 and p,,d ➔ 0 as a ➔ oo while Pde = PA remains constant. Antigravity Propulsion Application of Dark/Vacuum Energy If one could somehow harness a local amount of dark/vacuum energy, then use can be made of its negative pressure property to produce an antigravity propulsion effect? To answer this question one can use the estimated value for Pde = PA:=:; 2.4poc2 ~ 10-9 J/m3, where po is the present-day value of the total cosmological mass density of (ordinary and dark) matter (Reference 54,57). Using this number one can work through the math and estimate that the total amount of dark/vacuum energy contained within our solar system amounts to the mass equivalent of a small asteroid. This means that its repulsive gravitational influence upon planetary orbital dynamics inside the solar system is completely inconsequential. Only on the extragalactic-to-cosmological scale will its repulsive gravitational property achieve strong enough influence over matter and spacetime. On this basis, one can conclude that it is highly unlikely, if not impossible, that one will be able to invent a technology in the near future that can acquire and exploit a near-cosmological amount of dark/vacuum energy to implement a useful antigravity propulsion system. IV. Quantum Antigravity Propulsion Concepts Quantum antigravity can be found within the very large genre of quantum gravity theories in which repulsive gravity terms appear as quantum corrections to the classical Newtonian gravitational force law. Generally, one can derive such correction terms by quantizing the Einstein general relativistic field equation or by starting with a particular type of quantum field theory (for example, supersymmetric field theory, quantized 5­ dimensional Kaluza-Klein unified field theories, quantum superstrings/D-Brane theory, quantum loops or knots, and Yang-Mills theories) and work backwards to find the corresponding gravity theory. The particular mathematical form and quantitative magnitude that quantum correction terms can have totally depends upon the UNCLASSIFIED//FOA OFFI€il.t.k Y&li 8,.LY 17 UNCLASSIFIED/fFOA OFFIEIAk W&i 0Pilk¥ quantization procedure and order of approximation used in a given quantum gravity theory. However, the linearized semi-classical quantum gravity theory is related to Einstein's classical nonlinear General Relativity Theory whereby the former uniquely implies the latter provided that the graviton, which exchanges the gravitational force between two massive particles or photons, is a pure spin-2 particle. In this theory, the stress-energy tensor of the source matter fields is quantized while gravitation (via the Einstein curvature tensor) is still treated classically. Semi-classical quantum gravity is a quantum field theory in curved spacetime that has been successful in reproducing a few of the predictions and many of the foundational precepts of General Relativity Theory. A particular example of what a quantum antigravity correction term looks like was derived in 1984 by R. L. Forward and the author, with instruction provided by R. P. Feynman and M. Scadron, during a summer quantum gravity seminar sponsored by the Hughes Research Labs in Malibu, CA. One began by studying the Feynman quantization procedure for the case of single-photon exchange between two charged particles, which tells us about the underlying nature and quantum corrections to the static Coulomb force. From this study discovered that the same is also true for the case of single­ graviton exchange between two massive spin-0 particles in connection with the static Newtonian force. By applying Feynman's quantization procedure (Reference 58-60) to the linearized Einstein field equation in the nonrelativistic limit, the following static graviton-exchange potential, V gr.,v (r), for two spin-0 particles undergoing a gravitational interaction can be derived: (23) where m1 and m 2 are the masses of the interacting particles, r is their radial separation, and 83(r) is the 3-dimensional Dirac 8-function with r the position vector of some reference point in space. The first term in Equation (23) is immediately recognized as the attractive Newtonian gravitational potential while the second quantum correction term is repulsive. Also, the second term is independent of the interacting particle masses and can only be measured for bound quantum s-states because the product of the coefficient 4n(Gli2/c2) ~ 10-94 with the 8-function gives only a minute physical effect at the atomic scale. The second term happens to be analogous to the usual quantum correction to the Coulomb or nuclear force. If the two particles were to have non-zero quantum spin, then Vgrav(r) will be modified by additional spin-orbit and spin-spin correction terms. Furthermore, there are additional velocity-dependent corrections to Vgrav(r) that generate the general relativistic post-Newtonian modifications of the classical equation of motion of a particle in a gravitational field. But the most important characteristic to observe about the quantum antigravity correction term in Equation (23) is that its magnitude is incredibly minute, only affecting bound quantum s-states. In general, quantum gravity correction terms at any level of approximation, whether gravitationally repulsive or attractive, will have coefficients ~G(li0/cK) (for 8, K > 1), and therefore will not have a measurable impact on any macroscopic system that embodies any form of propulsion. Because these quantum corrections are so minute, and because there is no single universally accepted quantum gravity theory to work with, investigators have had little reason to look into the potential application of quantum gravity correction terms to antigravity propulsion physics. UNCLASSIFIED//FOA OFFI&IAb Yi&: 8,.bY 18 UNCLASSIFIED/ fFOA OFFIEIA~ W&li QPI~¥ However, this isn't the entire story because there are many interesting quantum field theoretic phenomenon that exist outside of that which arises in quantum corrections to Newtonian gravity. In what follows, the recent discovery of antigravity forces that arise within both QED vacuum fluctuation and nonretarded quantum interatomic dispersion force theories i