DTIC Copy AFRL-PR-ED-TR-2003-0034 AFRL-PR-ED-TR-2003-0034 Teleportation Physics Study Eric W. Davis Warp Drive Metrics 4849 San Rafael Ave. Las Vegas, NV 89120 August 2004 Special Report APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AIR FORCE RESEARCH LABORATORY AIR FORCE MATERIEL COMMAND EDWARDS AIR FORCE BASE CA 93524-7048 REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188
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Davis 5e. TASK NUMBER 0159 5f. WORK UNIT NUMBER 549907 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NO. Warp Drive Metrics 4849 San Rafael Ave. Las Vegas, NV 89120 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) Air Force Research Laboratory (AFMC) AFRL/PRSP 10 E. Saturn Blvd. Edwards AFB CA 93524-7680 12. DISTRIBUTION / AVAILABILITY STATEMENT 11. SPONSOR/MONITOR’S REPORT NUMBER(S) AFRL-PR-ED-TR-2003-0034 Approved for public release; distribution unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT
This study was tasked with the purpose of collecting information describing the teleportation of material objects, providing a description of teleportation as it occurs in physics, its theoretical and experimental status, and a projection of potential applications. The study also consisted of a search for teleportation phenomena occurring naturally or under laboratory conditions that can be assembled into a model describing the conditions required to accomplish the transfer of objects. This included a review and documentation of quantum teleportation, its theoretical basis, technological development, and its potential applications.
The characteristics of teleportation were defined and physical theories were evaluated in terms of their ability to completely describe the phenomena. Contemporary physics, as well as theories that presently challenge the current physics paradigm were investigated. The author identified and proposed two unique physics models for teleportation that are based on the manipulation of either the general relativistic spacetime metric or the spacetime vacuum electromagnetic (zero-point fluctuations) parameters.
Naturally occurring anomalous teleportation phenomena that were previously studied by the United States and foreign governments were also documented in the study and are reviewed in the report. The author proposes an additional model for teleportation that is based on a combination of the experimental results from the previous government studies and advanced physics concepts. Numerous recommendations outlining proposals for further theoretical and experimental studies are given in the report. The report also includes an extensive teleportation bibliography. 5. SUBJECT TERMS teleportation; physics, quantum teleportation; teleportation phenomena; anomalous teleportation; teleportation theories; teleportation experiments; teleportation bibliography 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON Franklin B. Mead, Jr. 19b. TELEPHONE NO (include area code) a. REPORT b. ABSTRACT c. THIS PAGE Unclassified Unclassified Unclassified A 88 (661) 275-5929 Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. 239. 18 NOTICE
USING GOVERNMENT DRAWINGS, SPECIFICATIONS, OR OTHER DATA INCLUDED IN THIS DOCUMENT FOR ANY PURPOSE OTHER THAN GOVERNMENT PROCUREMENT DOES NOT IN ANY WAY OBLIGATE THE US GOVERNMENT. THE FACT THAT THE GOVERNMENT FORMULATED OR SUPPLIED THE DRAWINGS, SPECIFICATIONS, OR OTHER DATA DOES NOT LICENSE THE HOLDER OR ANY OTHER PERSON OR CORPORATION; OR CONVEY ANY RIGHTS OR PERMISSION TO MANUFACTURE, USE, OR SELL ANY PATENTED INVENTION THAT MAY RELATE TO THEM. FOREWORD This Special Technical Report presents the results of a subcontracted study performed by Warp Drive Metrics, Las Vegas, NV, under Contract No.
F04611-99-C-0025, for the Air Force Research Laboratory (AFRL)/Space and Missile Propulsion Division, Propellant Branch (PRSP), Edwards AFB, CA. The Project Manager for AFRL/PRSP was Dr. Franklin B. Mead, Jr. This report has been reviewed and is approved for release and distribution in accordance with the distribution statement on the cover and on the SF Form 298. This report is published in the interest of scientific and technical information exchange and does not constitute approval or disapproval of its ideas or findings. //Signed// _______________________________________ FRANKLIN B.
MEAD, JR. Project Manager //Signed// ______________________________________ RONALD E. CHANNELL Chief, Propellants Branch //Signed// PHILIP A. KESSEL Technical Advisor, Space and Missile Propulsion Division //Signed// AFRL-ERS-PAS-04-155 RANNEY G. ADAMS III P ublic Affairs D irector This Page Intentionally Left Blank Table of Contents Section Page 1. 0 INTRODUCTION…. ……………………………………………………………………………… …. 1 1. 1 Introduction….. ………………………………………………………………………………. …… 1 1. 2 The Definitions of Teleportation…… ………………………………………………………… ……. 1 2. 0 vm -TELEPORTATION…………………. ………………………………. …………………………… 3 2. 1 Engineering the Spacetime Metric…….. …………………………………………………………… 3 2. 1. 1 Wormhole Thin Shell Formalism…………………………………………………… ………. 3 2. 1. 2 “Exotic” Matter-Energy Requirements…. ………………………………………….. …… …11 2. 2 Engineering the Vacuum………………………………………………………………………….. 11 2. 2. 1 The Polarizable-Vacuum Representation of General Relativity………………………… …20 2. 3 Conclusion and Recommendations……………………………………………………………. …26 3. 0 q-TELEPORTATION….. ……….. …………………….. ……………………………………………30 3. 1 Teleportation Scenario…………………………………………………. …………………. …….. 0 3. 2 Quantum Teleportation……………………………………………………………………… ……32 3. 2. 1 Description of the q-Teleportation Process………………………………………………… 34 3. 2. 2 Decoherence Fundamentally Limits q-Teleportation………………………………………38 3. 2. 3 Recent Developments in Entanglement and q-Teleportation Physics…. ………………….. 38 3. 3 Conclusion and Recommendations…………………….. ………………………………. ……….. 46 4. 0 e-TELEPORTATION…… ……… …….. ……………………………………………………………… 50 4. 1 Extra Space Dimensions and Parallel Universes/Spaces…. ……………………………………… 50 4. 2 Vacuum Hole Teleportation………………………………………………………………………52 4. Conclusion and Recommendations………………………………………………………….. …… 53 5. 0 p-TELEPORTATION…… …………… …. ……………………………………………………………55 5. 1 PK Phenomenon.. ………………………………………. …. …………………………………….. 55 5. 1. 1 Hypothesis Based on Mathematical Geometry………………………………………. …….. 60 5. 2 Conclusion and Recommendations……………………………………………………………… ………………. 61 6. 0 REFERENCES….. …….. ………………………………………………………. …… ……………. …63 APPENDIX A – A Few Words About Negative Energy………….. …………………. ……………… ….. 73 A. 1 A General Relativistic Definition of Negative or Exotic Energy……………………………….. 3 A. 2 Squeezed Quantum States and Negative Energy………………. …………………………. ……. 73 APPENDIX B – TH? µ Methodology……. ….. ………. …………………………. ……………….. ……… 75 Approved for public release; distribution unlimited. iii List of Figures Figure Page Figure 1. Diagram of a Simultaneous View of Two Remote Compact Regions (? 1 and ? 2) of Minkowski Space Used to Create the Wormhole Throat ?? , Where Time is Suppressed in This Representation…………….. ………………………. ……………………………………5 Figure 2. The Same Diagram as in Figure 1 Except as Viewed by an Observer Sitting in Region ? Who Looks Through the Wormhole Throat ?? and Sees Remote Region ? 2 (Dotted Area Inside the Circle) on the Other Side………………………………………………………. 6 Figure 3. A Thin Shell of (Localized) Matter-Energy, or Rather the Two-Dimensional Spacelike Hypersurface ?? (via (2. 3)), Possessing the Two Principal Radii of Curvature ? 1 and ? 2…. ….. 8 Figure 4. A Schematic of Vacuum Quantum Field Fluctuations (a. k. a. Vacuum Zero Point Field Fluctuations) Involved in the “Light-by-Light” Scattering Process That Affects the Speed of Light…………………………………………………………………………………………13 Figure 5.
A Schematic of the Casimir Effect Cavity/Waveguide………………………………………… 15 Figure 6. Classical Facsimile Transmission (Modified IBM Press Image)………………………………35 Figure 7. Quantum Teleportation (Modified IBM Press Image)…………………………………………36 Figure 8. Quantum Teleportation (From www. aip. org)…………………………………………………………………… 43 Approved for public release; distribution unlimited. iv List of Tables Table Page Table 1. Metric Effects in the PV-GR Model When K > 1 (Compared With Reference Frames at Asymptotic Infinity Where K = 1)…………………………………………………………… 21 Table 2. Metric Effects in the PV-GR Model When K < 1 (Compared With Reference Frames at Asymptotic Infinity Where K = 1)……………………………………………………………… 22 Table 3. Substantial Gravitational Squeezing Occurs When ? ? 8? rs (For Electromagnetic ZPF)………… 28 Approved for public release; distribution unlimited. v Glossary AEC AFRL AU BBO CGS CIA DARPA DEC DIA DNA DoD EPR ESP eV FRW FTL IBM INSCOM IR MeV MKS NEC NLP NMR NSA PK PPN PRC PV-GR QED QISP R&D SAIC SEC SRI USSR UV WEC ZPE ZPF Average Energy Condition Air Force Research Laboratory Astronomical Unit Beta (? -Barium Borate Centimeter-Gram-Second Central Intelligence Agency Defense Advanced Research Projects Agency Dominant Energy Condition Defense Intelligence Agency Deoxyribo Nucleic Acid Department of Defense Einstein, Podolsky and Rosen Extrasensory Perception Electron Volt Friedmann-Robertson-Walker Faster-Than-Light International Business Machines Intelligence and Security Command Infrared Mega-Electron Volt Meter-Kilogram-Second Null Energy Condition Neuro-Linguistic Programming Nuclear Magnetic Resonance National Security Agency Psychokinesis Parameterized Post-Newtonian Peoples Republic of China Polarizable-Vacuum Representation of General Relativity Quantum Electrodynamics Quantum Information Science Program Research and Development Science Applications International Corporation Strong Energy Condition Stanford Research Institute Union of Soviet Socialist Republics Ultraviolet Weak Energy Condition Zero-Point Energy Zero-Point Fluctuations Approved for public release; distribution unlimited. vi Acknowledgements This study would not have been possible without the very generous support of Dr. Frank Mead, Senior Scientist at the Advanced Concepts Office of the U. S. Air Force Research Laboratory (AFRL) Propulsion Directorate at Edwards AFB, CA. Dr. Mead’s collegial collaboration, ready assistance, and constant encouragement were invaluable to me. Dr.
Mead’s professionalism and excellent rapport with “out-of-the-box” thinkers excites and motivates serious exploration into advanced concepts that push the envelope of knowledge and discovery. The author owes a very large debt of gratitude and appreciation to both Dr. David Campbell, Program Manager, ERC, Inc. at AFRL, Edwards AFB, CA, and the ERC, Inc. staff, for supporting the project contract and for making all the paperwork fuss totally painless. Dr. Campbell and his staff provided timely assistance when the author needed it, which helped make this contract project run smoothly. There are two colleagues who provided important contributions to this study that I wish to acknowledge.
First, I would like to express my sincere thanks and deepest appreciation to my first longtime mentor and role model, the late Dr. Robert L. Forward. Bob Forward was the first to influence my interests in interstellar flight and advanced breakthrough physics concepts (i. e. , “Future Magic”) when I first met him at an AIAA Joint Propulsion Conference in Las Vegas while I was in high school (ca. 1978). The direction I took in life from that point forward followed the trail of exploration and discovery that was blazed by Bob. I will miss him, but I will never forget him. Second, I would like to express my sincere thanks and appreciation to my longtime friend, colleague and present mentor, Dr.
Hal Puthoff, Institute for Advanced Studies-Austin, for our many discussions on applying his Polarizable VacuumGeneral Relativity model to a quasi-classical teleportation concept. Hal taught me to expand my mind, and he encourages me to think outside the box. He also gave me a great deal of valuable insight and personal knowledge about the Remote Viewing Program. Last, I would like to offer my debt of gratitude and thanks to my business manager (and spouse), Lindsay K. Davis, for all the hard work she does to make the business end of Warp Drive Metrics run smoothly. Eric W. Davis, Ph. D. , FBIS Warp Drive Metrics Las Vegas, NV Approved for public release; distribution unlimited. vii Preface
The Teleportation Physics Study is divided into four phases. Phase I is a review and documentation of quantum teleportation, its theoretical basis, technological development, and its potential application. Phase II developed a textbook description of teleportation as it occurs in classical physics, explored its theoretical and experimental status, and projected its potential applications. Phase III consisted of a search for teleportation phenomena occurring naturally or under laboratory conditions that can be assembled into a model describing the conditions required to accomplish the disembodied conveyance of objects. The characteristics of teleportation were efined, and physical theories were evaluated in terms of their ability to completely describe the phenomenon. Presently accepted physics theories, as well as theories that challenge the current physics paradigm were investigated for completeness. The theories that provide the best chance of explaining teleportation were selected, and experiments with a high chance of accomplishing teleportation were identified. Phase IV is the final report. The report contains five chapters. Chapter 1 is an overview of the textbook descriptions for the various teleportation phenomena that are found in nature, in theoretical physics concepts, and in experimental laboratory work.
Chapter 2 proposes two quasi-classical physics concepts for teleportation: the first is based on engineering the spacetime metric to induce a traversable wormhole; the second is based on the polarizable-vacuum-general relativity approach that treats spacetime metric changes in terms of equivalent changes in the vacuum permittivity and permeability constants. These concepts are theoretically developed and presented. Promising laboratory experiments were identified and recommended for further research. Chapter 3 presents the current state-of-art of quantum teleportation physics, its theoretical basis, technological development, and its applications. Key theoretical, experimental, and applications breakthroughs were identified, and a series of theoretical and experimental research programs are proposed to solve technical problems and advance quantum teleportation physics. Chapter 4 gives an overview of alternative teleportation concepts that challenge the present physics paradigm.
These concepts are based on the existence of parallel universes/spaces and/or extra space dimensions. The theoretical and experimental work that has been done to develop these concepts is reviewed, and a recommendation for further research is made. Last, Chapter 5 gives an in-depth overview of unusual teleportation phenomena that occur naturally and under laboratory conditions. The teleportation phenomenon discussed in the chapter is based on psychokinesis (PK), which is a category of psychotronics. The U. S. military-intelligence literature is reviewed, which relates the historical scientific research performed on PK-teleportation in the U. S. China and the former Soviet Union. The material discussed in the chapter largely challenges the current physics paradigm; however, extensive controlled and repeatable laboratory data exists to suggest that PK-teleportation is quite real and that it is controllable. The report ends with a combined list of references. Approved for public release; distribution unlimited. viii 1. 0 INTRODUCTION 1. 1 Introduction The concept of teleportation was originally developed during the Golden Age of 20th century science fiction literature by writers in need of a form of instantaneous disembodied transportation technology to support the plots of their stories.
Teleportation has appeared in such SciFi literature classics as Algis Budry’s Rogue Moon (Gold Medal Books, 1960), A. E. van Vogt’s World of Null-A (Astounding Science Fiction, August 1945), and George Langelaan’s The Fly (Playboy Magazine, June 1957). The Playboy Magazine short story led to a cottage industry of popular films decrying the horrors of scientific technology that exceeded mankind’s wisdom: The Fly (1958), Return of the Fly (1959), Curse of the Fly (1965), The Fly (a 1986 remake), and The Fly II (1989). The teleportation concept has also appeared in episodes of popular television SciFi anthology series such as The Twilight Zone and The Outer Limits.
But the most widely recognized pop-culture awareness of the teleportation concept began with the numerous Star Trek television and theatrical movie series of the past 39 years (beginning in 1964 with the first TV series pilot episode, The Cage), which are now an international entertainment and product franchise that was originally spawned by the late genius television writer-producer Gene Roddenberry. Because of Star Trek everyone in the world is familiar with the “transporter” device, which is used to teleport personnel and material from starship to starship or from ship to planet and vice versa at the speed of light. People or inanimate objects would be positioned on the transporter pad and become completely disintegrated by a beam with their atoms being patterned in a computer buffer and later converted into a beam that is directed toward the destination, and then reintegrated back into their original form (all without error! ). Beam me up, Scotty” is a familiar automobile bumper sticker or cry of exasperation that were popularly adopted from the series. However, the late Dr. Robert L. Forward (2001) stated that modern hard-core SciFi literature, with the exception of the ongoing Star Trek franchise, has abandoned using the teleportation concept because writers believe that it has more to do with the realms of parapsychology/paranormal (a. k. a. psychic) and imaginative fantasy than with any realm of science. Beginning in the 1980s developments in quantum theory and general relativity physics have succeeded in pushing the envelope in exploring the reality of teleportation.
A crescendo of scientific and popular literature appearing in the 1990s and as recently as 2003 has raised public awareness of the new technological possibilities offered by teleportation. As for the psychic aspect of teleportation, it became known to Dr. Forward and myself, along with several colleagues both inside and outside of government, that anomalous teleportation has been scientifically investigated and separately documented by the Department of Defense. It has been recognized that extending the present research in quantum teleportation and developing alternative forms of teleportation physics would have a high payoff impact on communications and transportation technologies in the civilian and military sectors.
It is the purpose of this study to explore the physics of teleportation and delineate its characteristics and performances, and to make recommendations for further studies in support of Air Force Advanced Concepts programs. 1. 2 The Definitions of Teleportation Before proceeding, it is necessary to give a definition for each of the teleportation concepts I have identified during the course of this study: Approved for public release; distribution unlimited. 1 Teleportation – SciFi: the disembodied transport of persons or inanimate objects across space by advanced (futuristic) technological means (adapted from Vaidman, 2001). We will call this sfTeleportation, which will not be considered further in this study. Teleportation – psychic: the conveyance of persons or inanimate objects by psychic means. We will call this p-Teleportation.
Teleportation – engineering the vacuum or spacetime metric: the conveyance of persons or inanimate objects across space by altering the properties of the spacetime vacuum, or by altering the spacetime metric (geometry). We will call this vm-Teleportation. Teleportation – quantum entanglement: the disembodied transport of the quantum state of a system and its correlations across space to another system, where system refers to any single or collective particles of matter or energy such as baryons (protons, neutrons, etc. ), leptons (electrons, etc. ), photons, atoms, ions, etc. We will call this q-Teleportation. Teleportation – exotic: the conveyance of persons or inanimate objects by transport through extra space dimensions or parallel universes.
We will call this e-Teleportation. We will examine each of these in detail in the following chapters and determine whether any of the above teleportation concepts encompass the instantaneous and or disembodied conveyance of objects through space. Approved for public release; distribution unlimited. 2 2. 0 vm-TELEPORTATION 2. 1 Engineering the Spacetime Metric A comprehensive literature search for vm-Teleportation within the genre of spacetime metric engineering yielded no results. No one in the general relativity community has thought to apply the Einstein field equation to determine whether there are solutions compatible with the concept of teleportation.
Therefore, I will offer two solutions that I believe will satisfy the definition of vmTeleportation. The first solution can be found from the class of traversable wormholes giving rise to what I call a true “stargate. ” A stargate is essentially a wormhole with a flat-face shape for the throat as opposed to the spherical-shaped throat of the Morris and Thorne (1988) traversable wormhole, which was derived from a spherically symmetric Lorentzian spacetime metric that prescribes the wormhole geometry (see also, Visser, 1995 for a complete review of traversable Lorentzian wormholes): ds 2 = ? e 2? ( r ) c 2 dt 2 + [1 ? b(r ) r ]? 1 dr 2 + r 2 d ? 2 (2. 1), here by inspection we can write the traversable wormhole metric tensor in the form g?? ? ? e 2? ( r ) 0 ? 0 [1 ? b(r ) r ]? 1 =? ? 0 0 ? ? 0 0 ? 0 0 r2 0 ? ? 0 ? ? 0 ? r 2 sin 2 ? ? ? 0 (2. 2) using standard spherical coordinates, where c is the speed of light, ? ,? ? (0 = t, 1 = r, 2 = ? , 3 = ? ) are the time and space coordinate indices (-? < t < ? ; r: 2? r = circumference; 0 ? ? ? ?; 0 ? ? ? 2? ), d? 2 = d? 2 + sin2? d? 2, ? (r) is the freely specifiable redshift function that defines the proper time lapse through the wormhole throat, and b(r) is the freely specifiable shape function that defines the wormhole throat’s spatial (hypersurface) geometry. Such spacetimes are asymptotically flat.
The Einstein field equation requires that a localized source of matter-energy be specified in order to determine the geometry that the source induces on the local spacetime. We can also work the Einstein equation backwards by specifying the local geometry in advance and then calculate the matter-energy source required to induce the desired geometry. The Einstein field equation thus relates the spacetime geometry terms comprised of the components of the metric tensor and their derivatives (a. k. a. the Einstein tensor) to the local matterenergy source terms comprised of the energy and stress-tension densities (a. k. a. the stress-energy tensor). The flat-face wormhole or stargate is derived in the following section. 2. 1. Wormhole Thin Shell Formalism The flat-face traversable wormhole solution is derived from the thin shell (a. k. a. junction condition or surface layer) formalism of the Einstein equations (Visser, 1989; see also, Misner, Thorne and Wheeler, 1973). We adapt Visser’s (1989) development in the following discussion. The procedure is to take two copies of flat Minkowski space and remove from each identical regions of the form ? ? ? , where ? is a three-dimensional compact spacelike hypersurface and ? is a timelike straight line (time axis). Then identify these two incomplete spacetimes along the timelike boundaries ?? ? ?. The resulting spacetime Approved for public release; distribution unlimited. 3 s geodesically complete and possesses two asymptotically flat regions connected by a wormhole. The throat of the wormhole is just the junction ?? (a two-dimensional space-like hypersurface) at which the two original Minkowski spaces are identified (see Figures 1 and 2). Approved for public release; distribution unlimited. 4 Figure 1. Diagram of a Simultaneous View of Two Remote Compact Regions (? 1 and ? 2) of Minkowski Space Used to Create the Wormhole Throat ?? , Where Time is Suppressed in This Representation (adapted from Bennett et al. , 1995) Approved for public release; distribution unlimited. 5 Figure 2. The Same Diagram as in Figure 1 Except as Viewed by an Observer Sitting in Region ? Who Looks Through the Wormhole Throat ?? and Sees Remote Region ? 2 (Dotted Area Inside the Circle) on the Other Side Approved for public release; distribution unlimited. 6 The resulting spacetime is everywhere Riemann-flat except possibly at the throat. Also, the stressenergy tensor in this spacetime is concentrated at the throat with a ? -function singularity there. This is a consequence of the fact that the spacetime metric at the throat is continuous but not differentiable, while the connection is discontinuous; thus causing the Riemann curvature to possess a ? -function singularity (causing undesirable gravitational tidal forces) there. The magnitude of this ? function singularity can be calculated in terms of the second fundamental form on both sides of the throat, which we presume to be generated by a localized thin shell of matter-energy. The second fundamental form represents the extrinsic curvature of the ?? hypersurface (i. e. , the wormhole throat), telling how it is curved with respect to the enveloping four-dimensional spacetime. The form of the geometry is simple, so the second fundamental form at the throat is calculated to be (McConnell, 1957): K i ± j ?? 0 0 ? = ± ? 0 ? 1 ? 0 0 ? ?0 0 ? = ± ? 0 1 ? 1 ? 0 0 ? 0? ? 0? ?2 ? ? 0 ? ? 0 ? 1 ? 2 ? ? (2. 3), where i,j = 0,1,2 and Kij± is the second fundamental form. The full 4? 4 matrix K?? has been reduced to 3? form, as above, for computational convenience because the thin shell (or hypersurface) is essentially a two-surface embedded in three-space. The overall ± sign in equation (2. 3) comes from the fact that a unit normal points outward from one side of the surface and points inward on the other side. We hereafter drop the ± sign for the sake of brevity in notation. The quantities ? 0, ? 1, and ? 2 measure the extrinsic curvature of the thin shell of local matter-energy (i. e. , the stuff that induces the wormhole throat geometry). Since the wormhole throat is a space-like hypersurface, we can exclude time-like hypersurfaces and their components in the calculations. Therefore we set ? = 0 in equation (2. 3) because it is the time-like extrinsic curvature for the time-like hypersurface of the thin shell of matter-energy. As seen in equation (2. 3) ? 1 and ? 2 are simply related to the two principal radii of curvature ? 1 and ? 2 (defined to be the eigenvalues of Kij) of the two-dimensional spacelike hypersurface ?? (see Figure 3). It should be noted that a convex surface has positive radii of curvature, while a concave surface has negative radii of curvature. Approved for public release; distribution unlimited. 7 Figure 3. A Thin Shell of (Localized) Matter-Energy, or Rather the Two-Dimensional Spacelike Hypersurface ?? (via (2. )), Possessing the Two Principal Radii of Curvature ? 1 and ? 2 Approved for public release; distribution unlimited. 8 It is a standard result of the thin shell or junction condition formalism that the Einstein field equation may be cast in terms of the surface stress-energy tensor Sij of the thin matter-energy shell localized in ?? (note: we are exploiting the symmetry of the wormhole with respect to interchange of the two flat regions ? 1 and ? 2): Si j = ? c4 ( K i j ? ? i j K k k ) (2. 4), 4? G where G is Newton’s gravitational constant and ? ij is the (three-dimensional) unit matrix. Kkk is the trace of equation (2. 3): K k k = Tr K i j = and 1 ?1 + 1 (2. 5) ?2 i j K kk ? 1 1 ? + ? ?1 ? 2 ? =? 0 ? ? ? 0 ? ? 0 1 ?1 + 0 1 ?2 ? ? ? ? 0 ? ? 1 1 ? + ? ?1 ? 2 ? ? 0 (2. 6). Substituting (2. 3) and (2. 6) into (2. 4) gives (after simplification): 1 ? 1 ?? +? 1 2 c4 ? i ? 0 S j= 4? G ? ? 0 ? ? 0 1 ? 2 0 ? 0 ? ? 0 ? ? 1 ? 1 ? ? ? (2. 7). The thin matter-energy shell’s surface stress-energy tensor may be interpreted in terms of the surface energy density ? and principal surface tensions ? 1 and ? 2: ? ?? ? Si j = ? 0 ? 0 ? 0 ?? 1 0 0 ? ? 0 ? ?? 2 ? ? (2. 8). Thus we arrive at the Einstein field equation by equating (2. 8) and (2. 7) and multiplying both sides by –1: Approved for public release; distribution unlimited. ?? 0 ? ? 0 ? 1 ? 0 0 ? 1 ? 1 ?? +? 0? 1 2 c4 ? ? ? 0 0 ? =? 4? G ? ?2 ? ? ? 0 ? ? 0 1 ? 2 0 ? 0 ? ? 0 ? ? 1 ? 1 ? ? ? (2. 9), which gives the final result ? =? c4 ? 1 1 ? ? + ? 4? G ? ?1 ? 2 ? c4 1 ? 1 = ? 4? G ? 2 (2. 10a) (2. 10b) (2. 10c). ?2 = ? c4 1 4? G ? 1 These are the Einstein equations. Equations (2. 10a-c) imply that (for ?? convex) we are dealing with negative surface energy density and negative surface tensions. This result is in fact the primary matterenergy requirement for traversable wormholes, as was proved by Morris and Thorne (1988), and later by Visser (1995), within the paradigm of classical Einstein general relativity.
The negative surface tension (= positive outward pressure, a. k. a. gravitational repulsion or antigravity) is needed to keep the throat open and stable against collapse. The reader should not be alarmed at this result. Negative energies and negative stress-tensions are an acceptable result both mathematically and physically, and they manifest gravitational repulsion (antigravity! ) in and around the wormhole throat. One only needs to understand what it means for stress-energy to be negative within the proper context. In general relativity the term “exotic” is used in place of “negative. ” The effects of negative energy have been produced in the laboratory (the Casimir Effect is one example).
In short, negative energy arises from Heisenberg’s quantum uncertainty principle, which requires that the energy density of any electromagnetic, magnetic, electric or other fields must fluctuate randomly. Even in a vacuum, where the average energy density is zero, the energy density fluctuates. This means that the quantum vacuum can never remain truly empty in the classical sense of the term. The quantum picture of the vacuum is that of a turbulent plenum of virtual (i. e. , energy non-conserving) particle pairs that spontaneously pop in and out of existence. The notion of “zero energy” in quantum theory corresponds to the vacuum being filled with such fluctuations going on. This issue is further elaborated on and clarified in greater detail in Appendix A.
We will also revisit this in Section 2. 2. Finally, it should be noted that for the analysis in this section we assumed an ultrastatic wormhole [i. e. , g00 ? 1 ? ?(r) = 0 in equation (2. 1)] with the “exotic” matter-energy confined to a thin layer, and we dispensed with the assumption of spherical symmetry. We can now build a wormhole-stargate and affect vm-Teleportation such that a traveler stepping into the throat encounters no exotic matter-energy there. This will require that our wormhole be flat shaped. To make the wormhole flat requires that we choose the throat ?? to have at least one flat face (picture the thin shell in Figure 3 becoming a flat shell).
On that face the two principal radii of curvature become ? 1 = ? 2 = ? as required by standard geometry. Substituting this into equations (2. 10a-c) gives ? = ? 1 = ? 2 = 0 (2. 11), Approved for public release; distribution unlimited. 10 which is a remarkable result. A further consequence of this is that now Kij = 0, thus making the Riemann curvature and stress-energy tensors (Riemann: R?? ~ K?? ; stress-energy: T?? ~ K?? ) at the throat become zero such that the associated ? -function singularities disappear there. This means that a traveler encountering and going through such a wormhole will feel no tidal gravitational forces and see no exotic matter-energy (that threads the throat).
A traveler stepping through the throat will simply be teleported into the other remote spacetime region or another universe (note: the Einstein equation does not fix the spacetime topology, so it is possible that wormholes are inter-universe as well as intra-universe tunnels). We construct such a teleportation stargate by generating a thin shell or surface layer of “exotic” matterenergy much like a thin film of soap stretched across a loop of wire. 2. 1. 2 “Exotic” Matter-Energy Requirements Now we have to estimate the amount of negative (or exotic) mass-energy that will be needed to generate and hold open a vm-Teleportation wormhole. A simple formula originally due to Visser (1995) for short-throat wormholes using the thin shell formalism gives: M wh rthroat c 2 =? G rthroat 1 meter r = ? (0. 09 M Jupiter ) throat 1 meter = ? (1. 3469 x1027 kg ) (2. 12), where Mwh is the mass required to build the wormhole, rthroat is a suitable measure of the linear dimension (radius) of the throat, and MJupiter is the mass of the planet Jupiter (1. 90? 1027 kg). Equation (2. 12) demonstrates that a mass of –0. 709 MJupiter (or –1. 3469? 1027 kg) will be required to build a wormhole 1 meter in size. As the wormhole size increases the mass requirement grows negative-large, and vice versa as the wormhole size decreases. After being alarmed by the magnitude of this, one should note that Mwh is not the total mass of the wormhole as seen by observers at remote distances.
The non-linearity of the Einstein field equations dictates that the total mass is zero (actually, the total net mass being positive, negative or zero in the Newtonian approximation depending on the details of the negative energy configuration constituting the wormhole system). And finally, Visser et al. (2003) have demonstrated the existence of spacetime geometries containing traversable wormholes that are supported by arbitrarily small quantities of exotic matter-energy, and they proved that this was a general result. In Section 2. 3 we will discuss how or whether we can create such a wormhole in the laboratory. 2. 2 Engineering the Vacuum Engineering the spacetime vacuum provides a second solution that also satisfies the definition of vmTeleportation. The concept of “engineering the vacuum” was first introduced to the physics community by Lee (1988).
Lee stated: “The experimental method to alter the properties of the vacuum may be called vacuum engineering…If indeed we are able to alter the vacuum, then we may encounter some new phenomena, totally unexpected. ” This new concept is based on the now-accepted fact that the vacuum is characterized by physical parameters and structure that constitutes an energetic medium which pervades the entire extent of the Approved for public release; distribution unlimited. 11 universe. We note here the two most important defining properties of the vacuum in this regard (Puthoff et al. , 2002): Within the context of quantum field theory the vacuum is the seat of all energetic particle and field fluctuations.
Within the context of general relativity theory the vacuum is the seat of a spacetime structure (or metric) that encodes the distribution of matter and energy. We begin our look into this concept by examining the propagation of light through space. We know from quantum field theory that light propagating through space interacts with the vacuum quantum fields (a. k. a. vacuum quantum field fluctuations). The observable properties of light, including the speed of light, are determined by these interactions. Vacuum quantum interactions with light lead to an effect on the speed of light that is due to the absorption of photons (by the vacuum) to form virtual electronpositron pairs followed by the quick re-emission (from the vacuum) of the photon (see Figure 4).
The virtual particle pairs are very short lived because of the large mismatch between the energy of a photon and the rest mass-energy of the particle pair. A key point is that this process makes a contribution to the observed vacuum permittivity ? 0 (and permeability µ0) constant and, therefore, to the speed of light c [c = (? 0µ0)? 1/2]. Approved for public release; distribution unlimited. 12 Figure 4. A Schematic of Vacuum Quantum Field Fluctuations (a. k. a. Vacuum Zero Point Field Fluctuations) Involved in the “Light-by-Light” Scattering Process That Affects the Speed of Light (from Chown, 1990) Approved for public release; distribution unlimited. 13 The role of virtual particle pairs in determining the ? (µ0) of the vacuum is analogous to that of atoms/molecules in determining the relative permittivity ? (and µ) of a dielectric material. We know that the absorption/re-emission of photons by atoms/molecules in a transparent medium (note: there are no strongly absorbing resonances, so the atoms/molecules remain in their excited states for a very short time before re-emitting photons) is responsible for the refractive index of the medium, which results in the reduction of the speed of light for photons propagating through the medium. This absorption/re-emission process is also known in physics as a scattering process. We know from experiment that a change in the medium leads to a change in ? µ), thus resulting in a change of the refractive index. The key point arising from this analogy is that a modification of the vacuum produces a change in ? 0 (µ0) resulting in a subsequent change in c, and hence, a corresponding change in the vacuum refraction index. Scharnhorst (1990) and Latorre et al. (1995) have since proved that the suppression of light scattering by virtual particle pairs (a. k. a. coherent light-by-light scattering) in the vacuum causes an increase in the speed of light accompanied by a decrease in the vacuum refraction index. This very unique effect is accomplished in a Casimir Effect capacitor cavity (or waveguide) whereby the vacuum quantum field fluctuations (a. k. a. ero-point fluctuations or ZPF) inside have been modified (becoming anisotropic and non-translational invariant) to satisfy the electromagnetic boundary conditions imposed by the presence of the capacitor plates (or waveguide walls). The principal result of this modification is the removal of the electromagnetic zero-point energy (ZPE) due to the suppression of vacuum ZPE modes with wavelengths longer than the cavity/waveguide cutoff (? 0 = 2d, where d = plate separation; see Figure 5). This removal of free space vacuum ZPE modes suppresses the scattering of light by virtual particle pairs, thus producing the speed of light increase (and corresponding decrease in the vacuum refraction index).
We know from standard optical physics and quantum electrodynamics (QED) that the optical phase and group velocities can exceed c under certain physical conditions, but dispersion always ensures that the signal velocity is ? c. But recent QED calculations (see, Scharnhorst, 1990 and Latorre et al. , 1995) have proved that in the Casimir Effect system, the dispersive effects are much weaker still than those associated with the increase in c so that the phase, group and signal velocities will therefore all increase by the same amount. Note that, in general, no dispersion shows up in all of the modified vacuum effects examined by investigators. Approved for public release; distribution unlimited. 14 Figure 5. A Schematic of the Casimir Effect Cavity/Waveguide (from Chown, 1990) Approved for public release; distribution unlimited. 15
Examples demonstrating the increase in light speed (decrease in vacuum refraction index) via the Casimir Effect vacuum and other modified vacuum effects, as well as those effects producing a decrease in light speed (increase in vacuum refraction index), are described as follows. The vacuum modification effect on the speed of light described in the previous paragraph is (Scharnhorst, 1990): c?? ? 11 e4 ? ( = c0 = ? 0 = µ0 = 1) = ? 1 + 6 ? c0 ? 2 i(45) 2 (me a) 4 ? ? 11? 2 2 1 ? = ? 1 + >1 ? 4 ? ? 8100 (me a ) ? (2. 13), where c? * is the (modified) speed of light propagation perpendicular to the Casimir Effect capacitor plates, c0 is the speed of light in free space (3? 108 m/s in MKS units), me is the electron mass, ? s the fine structure constant (? 1/137), e is the electron charge (e2 = 4?? in quantum field theory natural units), a is the plate separation, h is Planck’s reduced constant, and ? 0 is the vacuum permittivity constant. The condition h = c0 = ? 0 = µ0 = 1 stresses that (2. 13), and all the equations that follow, are in quantum field theory natural units. The speed of light and vacuum refraction index measured parallel to the plates is unchanged from their free space values (c|| = c0, n|| = n0 = 1). The modified vacuum refraction index measured perpendicular to the plates is (Scharnhorst, 1990): ? 11 e4 ? n? = ? 1 ? 6 c0. But c? * > c0 and n? > 1 when a > ? s expected, since we are now allowing all of the vacuum ZPE modes to re-enter the Casimir cavity in this case. We now survey the additional examples of modified vacuums which increase/decrease light speed (from Latorre et al. , 1995): For light (photons) propagating in a Friedmann-Robertson-Walker (FRW) vacuum (i. e. , a homogeneous and isotropic Robertson-Walker gravitational background with Friedmann cosmology): c? ? 11 ? + p? = ? 1 + ? G r 2 ? > 1 c0 ? 45 me ? ( = c0 = ? 0 = µ 0 = 1) (2. 15), where c* is the modified vacuum speed of light, G is Newton’s constant, ? r is the energy density and p is the pressure of a radiation-dominated universe (p = ? r/3).
Here the speed of light is increased. For light (photons) propagating in a homogeneous and isotropic thermal vacuum: c? ? 44? 2 2 T 4 ? ? = ? 1 ? ? c0 on causality. As this topic is beyond the scope of this study, I will make three points in this regard: 1) There are no grounds for microcausality violations in accordance with Drummond and Hathrell (1980). 2) A new definition of causality is in order for FTL (fasterthan-light) phenomena. 3) Investigators have found that time machines (a. k. a. closed timelike curves) do not affect Gauss’s theorem, and thus do not affect the derivation of global conservation laws from differential ones (Friedman et al. , 1990).
The standard conservation laws remain globally valid while retaining a natural quasi-local interpretation for spacetimes possessing time machines (for example, asymptotically flat wormhole spacetimes). Thorne (1993) states that it may turn out that causality is violated at the macroscopic scale. Even if causality is obeyed macroscopically, then quantum gravity might offer finite probability amplitudes for microscopic spacetime histories possessing time machines. Li and Gott (1998) found a self-consistent vacuum for quantum fields in Misner space (a simple flat space with closed timelike curves), for which the renormalized stress-energy tensor is regular (in fact zero) everywhere. This implies that closed timelike curves could exist at least at the level of semi-classical quantum gravity theory.
Therefore, FTL causality paradoxes are just a reflection of our ignorance or inadequate comprehension of the physics of chronology and causality. In this section we have shown how “vacuum engineering” can modify the speed of light, and how this can, in principle, lead to vm-Teleportation. The vacuum modification concepts summarized above lead us to a formal theory that implements the concept of vacuum engineering within a framework that parallels general relativity theory. This theory is called the Polarizable-Vacuum Representation of General Relativity. In the next section we will introduce and summarize this theory. 2. 2. 1 The Polarizable-Vacuum Representation of General Relativity The polarizable-vacuum representation of general relativity (a. k. a.
PV-GR) treats the vacuum as a polarizable medium of variable refractive index (Puthoff, 1999a, 2002a, b; Puthoff et al. , 2002) exemplifying the concept of the vacuum modification (or vacuum engineering) effects surveyed and discussed in the previous section. The PV-GR approach treats spacetime metric changes in terms of equivalent changes in the vacuum permittivity and permeability constants (? 0 and µ0), essentially along the lines of the “TH? µ” methodology (see Appendix B for a brief description of this) used in comparative studies of alternative metric theories of gravity (Lightman and Lee, 1973; Will, 1974, 1989, 1993; Haugan and Will, 1977).
Such an approach, relying as it does on parameters familiar to engineers, can be considered a “metric engineering” approach. Maxwell’s equations in curved space are treated in the isomorphism of a polarizable medium of variable refractive index in flat space (Volkov et al. , 1971); the bending of a light ray near a massive body is modeled as due to an induced spatial variation in the refractive index of the vacuum near the body; the reduction in the velocity of light in a gravitational potential is represented by an effective increase in the refractive index of the vacuum, and so forth. This optical-engineering approach has been shown to be quite general (de Felice, 1971; Evans et al. , 1996a, b). Approved for public release; distribution unlimited. 0 As recently elaborated by Puthoff (1999a, 2002a, b; Puthoff et al. , 2002) the PV-GR approach, which was first introduced by Wilson (1921) and then developed by Dicke (1957, 1961), can be carried out in a self-consistent way so as to reproduce to appropriate order both the equations of general relativity and the match to the standard astrophysics weak-field experimental (PPN parameters and other) tests of those equations while posing testable modifications for strong-field conditions. It is in application that the PVGR approach demonstrates its intuitive appeal and provides additional insight into what is meant by a curved spacetime metric.
Specifically, the PV-GR approach treats such measures as the speed of light, the length of rulers (atomic bond lengths), the frequency of clocks, particle masses, and so forth, in terms of a variable vacuum dielectric constant K in which the vacuum permittivity ? 0 transforms as ? 0 > K? 0 and the vacuum permeability transforms as µ0 > Kµ0 (see also, Rucker, 1977). In a planetary or solar gravitational potential K = exp(2GM/rc02) ; 1 (M is a local mass distribution, r is the radial distance from the center of M) while K = 1 in “empty” or free asymptotic space (Puthoff, 1999a, 2002a, b; Puthoff et al. , 2002). In the former case, the speed of light is reduced, light emitted from an atom is redshifted as compared with a remote static atom (where K = 1), clocks run slower, objects/rulers shrink, etc. See Table 1. Table 1.
Metric Effects in the PV-GR Model When K ; 1 (Compared With Reference Frames at Asymptotic Infinity Where K = 1; adapted from Puthoff et al. , 2002) Variable Determining Equation (subscript 0 is asymptotic value where K = 1) K;1 (typical mass distribution, M) speed of light ; c0 effective mass increases redshift toward lower frequencies clocks run slower lower energy states objects/rulers shrink attractive gravitational force modified speed of light c*(K) Modified mass m(K) modified frequency ? (K) modified time interval ? t(K) modified energy E(K) Modified length L(K) dielectric-vacuum “gravitational” forces F(K) c* = c0/K m = m0K3/2 ? = ? 0K? 1/2 ? t = ? t0K1/2 E = E0K? 1/2 L = L0K? /2 F(K) ? ?K When K = 1 we have the condition that c* = c0 (vacuum refraction index = 1), because the vacuum is free (or un-modified, and ? vac = 0) in this case. When K ; 1, as occurs in a region of space possessing a gravitational potential, then we have the condition that c* ; c0 (vacuum refraction index ; 1), because the modified vacuum has a higher energy density in the presence of the local mass distribution that generates the local gravitational field. This fact allows us to make a direct correspondence between the speed of light modification physics discussion in Section 2. 2 and the underlying basis for the physics of the PVGR model.
Under certain conditions the spacetime metric can in principle be modified to reduce the value of K to below unity, thus allowing for faster-than-light (FTL) motion to be physically realized. In this case, the local speed of light (as measured by remote static observers) is increased, light emitted from an atom is blueshifted as compared with a remote static atom, objects/rulers expand, clocks run faster, etc. See Table 2. We therefore have the condition that c* ; c0 (vacuum refraction index ; 1) because the modified vacuum has a lower energy density. In fact, Puthoff (1999a, 2002a) has analyzed certain special Approved for public release; distribution unlimited. 21 black hole metrics and found K ; 1 from the model. We will return to this theme later.
In what follows we briefly review and summarize the key points and equations from the development of the PV-GR model, and we refer the reader to Puthoff (1999a, 2002a, b) for more extensive discussion and derivations. Table 2. Metric Effects in the PV-GR Model When K ; 1 (Compared With Reference Frames at Asymptotic Infinity Where K = 1; adapted from Puthoff et al. , 2002) Variable Determining Equation (subscript 0 is asymptotic value where K = 1) K c0 effective mass decreases blueshift toward higher frequencies clocks run faster higher energy states objects/rulers expand repulsive gravitational force modified speed of light c*(K) modified mass m(K) modified frequency ? (K) modified time interval ? (K) modified energy E(K) modified length L(K) dielectric-vacuum “gravitational” forces F(K) c* = c0/K m = m0K3/2 ? = ? 0K? 1/2 ? t = ? t0K1/2 E = E0K? 1/2 L = L0K? 1/2 F(K) ? ?K We begin by recalling that in flat space electrodynamics, the electric flux vector D in a linear, homogeneous medium can be written D = ? E = ? 0E + P = ? 0 E + ? V E where ? is the permittivity of the medium, the polarization P corresponds to the induced dipole moment per unit volume in the medium whose polarizability per unit volume is ? V, and E is the electric field. The identical form of the last two terms naturally leads to the interpretation of ? 0 as the polarizability per unit volume of the vacuum.
The quantum picture of the vacuum, where it has been shown that the vacuum acts as a polarizable medium by virtue of induced dipole moments resulting from the excitation of virtual electron-positron particle pairs (Heitler, 1954), completely justifies the interpretation that the vacuum is a medium. Note that there are other virtual particle pairs in the vacuum that also contribute to this picture; however, it is the electron-positron pairs that dominate the others, as shown in Section 2. 2. The basic postulate of the PV-GR model for curved space conditions is that the polarizability of the vacuum in the vicinity of localized mass-energy distributions differs from its asymptotic free space value by virtue of vacuum polarization effects induced by the presence of the local mass-energy. Thus the postulate for the vacuum itself is (2. 26), D = ? E ? K ? 0E Approved for public release; distribution unlimited. 22 (2. 27), here K (a function of position) is the modified dielectric constant of the vacuum due to the induced vacuum polarizability changes under consideration. Equation (2. 27) defines the transformation ? = K? 0. Table 1 shows the various quantitative effects a polarizable vacuum (in the presence of positive massenergy distributions) has on the various measurement processes important to general relativity. The effects demonstrated in the middle and right columns demonstrate the basis of the polarizable vacuum approach to general relativity. Table 2 shows what effects are manifested when negative mass-energy distributions induce vacuum polarizability changes that lead to FTL phenomenon.
Experimental observations impose constraints on the model causing key physical constants to remain constant even with variable polarizability present in the local space. Puthoff (1999a, 2002a, b) has shown that the fine structure constant is constrained by observational data to remain constant within a variable polarizable vacuum, and this constraint actually defines the transformation µ = Kµ0. The elementary particle charge e is also taken to be constant in a variable polarizable vacuum because of charge conservation. And h remains a constant by conservation of angular momentum for circularly polarized photons propagating through the (variable polarizability) vacuum.
The remaining constant of nature is the speed of light, and although the tables showed how this was modified in variable polarizability vacuums, it is interesting to see how this modification comes about. In a modified (variable polarizability) vacuum the speed of light is defined, as it is in standard electrodynamics, in terms of the permittivity and permeability by: c? ? ( ? µ ) ?1 2 ? 1 2 = ( K ? 0 i K µ0 ) = ( K 2? 0 µ 0 ) = ?1 2 (2. 28), 1 ? 1 2 ( ? 0 µ0 ) K c = 0 K where the permittivity/permeability transformations and the free space (un-modified vacuum) definition for c0 were inserted. Note that (2. 28) can be re-written as c*/c0 = 1/K, and this is to be compared with (2. 22). Thus we see from (2. 8), and by comparison with (2. 22), that K plays the role of a variable refractive index under conditions in which the vacuum polarizability is assumed to change in response to general relativistic-type influences. One further note of interest is that the permittivity/permeability transformations also maintains constant the ratio µ0 µ , = ? ?0 which is the impedance of free space. This constant ratio is required to keep electric-to-magnetic energy ratios constant during adiabatic movement of atoms from one position in space to another of differing vacuum polarizability (Dicke, 1957, 1961). And this constant ratio is also a necessary condition in the TH? formalism for an electromagnetic test particle to fall in a gravitational field with a compositionindependent acceleration (Lightman and Lee, 1973; Will, 1974, 1989, 1993; Haugan and Will, 1977). Now we make the “crossover connection” to the standard spacetime metric tensor concept that characterizes conventional general relativity theory, as originally shown by Puthoff (1999a, 2002a, b). In flat (un-modified or free) space the standard four-dimensional infinitesimal spacetime interval ds2 is given (in Cartesian coordinates with subscript 0) by Approved for public release; distribution unlimited. 23 ds 2 = ? c0 2 dt0 2 + ? dxi 0 2 i =1 3 (2. 29), where i ? (1 = x, 2 = y, 3 = z).
This metric means that measuring rods and clocks are non-varying wherever one goes in spacetime to make measurements. However, this has been shown to be incorrect in general relativity theory, so the length and time transformations (between proper and coordinate values) given in the tables (middle columns) indicate that measuring rods and clocks do vary when placed in regions where K ? 1. Therefore, we replace the time and space differentials in (2. 29) with the length and time transformations in the tables into (2. 29), and derive the general relativistic spacetime interval ds 2 = ? 1 2 2 ? 3 ? c0 dt + K ? ? dxi 2 ? K ? i =1 ? (2. 30). Note that observers within a K ? region will always measure the speed of light to be c0. Equation (2. 30) defines an isotropic coordinate system, which is a common and useful way to represent spacetime metrics in general relativity studies. By inspection the metric tensor is written g?? ? ? 1 K ? 0 =? ? 0 ? ? 0 ? 0 K 0 0 0 0 K 0 0? ? 0? 0? ? K? ? (2. 31). The Lagrangian density for matter-field interactions in a vacuum of variable K is given by Puthoff (1999a, 2002a, b) as 2 ? ? ? v ? m0 c0 2 i? 3 ? 1? ? Ld = ? ? + q? ? qAi v ? (r ? r0 ) ? K ? ? c0 K ? ? ? 2 ? c4 1 ? 1 ? B2 1 ? ?K ? ? ? ? ? K ? 0E2 ? ? 0 (? K ) 2 ? ? ? 2 ? 2 ? 2 ? K µ0 ( c0 K ) ? ?t ? ? ? 32? G K ? ? ? (2. 32), here the first term is the Lagrangian density for a free particle of mass m0, charge q and 3-vector velocity v (v = |v|, 3-vector components are labeled by i) interacting with electromagnetic fields via the electromagnetic field 4-vector potential Aµ = (? , Ai) (note that ? 3(r – r0) is the delta function that locates the point particle at position r = r0); the second term is the Lagrangian density for the electromagnetic fields themselves, and the last term is the Lagrangian density for K (treated here as a scalar variable). This last term emulates the Lagrangian density for the gravitational field. Equation (2. 32) does not include any quantum gauge field interaction terms because it is beyond the scope of the present incarnation of the PV-GR approach to include them.
We can obtain the equations of particle motion in a variable dielectric vacuum by performing the standard variations of the Lagrangian density ? (? Ld dx dy dz dt) with respect to the particle variables. However, we are more interested in obtaining the “master equation” for K by varying the Lagrangian density with respect to K, and Puthoff (1999a, 2002a, b) gives the result: Approved for public release; distribution unlimited. 24 ?2 K ? 1 ( c0 K) 2 ?2 K ? t 2 ? ? 2 K 1 ? ? v ? 2 ? 3 ? m0 c0 8? G ? ?1 + ? =? 4 K ? ? ? ? (r ? r0 ) 2 2 c0 ? ? c0 K ? ? ? ? v ? ? ? ? 1? ? ? ? c0 K ? ? ? ( ) (2. 33). 2 ? c0 4 1 ? 1 ? B2 1 ? ?K ? ? ? 2? 2 + ? + K ? 0E ? ? (? K ) + ? ?? 2 ? 2 ? 2 ? K µ0 ( c0 K ) ? t ? ? ? ? 32? G K ? ? ?? This equation describes the generation of general relativistic vacuum polarization effects due to the presence of matter and fields. By inspecting the right-hand side of the equation, we observe that changes in K are driven by the mass density (1st term), electromagnetic energy density (2nd term), and the vacuum polarization energy density itself (3rd term). In fact, the 3rd term emulates the gravitational field selfenergy density. Note that the 2nd and 3rd terms in (2. 33) appear with opposite signs with the result that electromagnetic field effects can counteract the gravitational field effects. Puthoff found that (2. 3) gives 2 the solution K = exp(2GM/rc0 ) in the vicinity of a static spherically symmetric (uncharged) mass M (in the low velocity limit v 1 near mass concentrations. Of major importance to the present study are solutions giving K ; 1 so that teleportation can be realized. Puthoff has found one such solution by studying the case of a static spherically symmetric mass M with charge Q familiar from the study of the Reissner-Nordstr? m spacetime metric. In this case Puthoff found the result ? ? b2 ? a 2 K = ? cos ? r ? ? ? ? ? ? b2 ? a 2 a sin ? ?+ ? ? r b2 ? a 2 ? ? ?? ?? ?? ?? 2 (b 2 ; a2 ) (2. 34), where a2 = (GM/c02)2, b2 = Q2G/4?? 0c04, and r is the radial distance from the center of M. And in this case (2. 4) gives K ; 1, which shows that FTL solutions are available in the PV-GR approach (as they are also in the Einstein theory). (For a2 ; b2 the solution is hyperbolic-trigonometric and describes the standard Reissner-Nordstr? m metric where K ; 1. ) Generally speaking, in Einstein general relativity the Reissner-Nordstr? m metric can be manipulated along with two shells of electrically charged matter to form a traversable wormhole (Schein and Aichelburg, 1996). But there are two drawbacks to this. The first is that the scheme involves dealing with the collapsed state of the stellar matter that generates the metric (a. k. a. Reissner-Nordstr? black hole) along with the unpleasant side effects that are encountered, such as the crushing singularities and multiple (unstable) event horizons. Second, the traversable wormhole is an eternal time machine connecting remote regions of the same universe together. Now there are no black hole solutions found in the PV-GR model because in that approach stellar matter collapses smoothly to an ultra-dense state and without the creation of singularities and event horizons (Puthoff, 1999b). In either case, the Reissner-Nordstr? m metric does not offer a viable mechanism for vmTeleportation. We are more interested in examining other PV-GR cases (where K ; 1 or even K ; gigagauss magnetic fields, ? 016 Volt/cm electric field strengths, ;; terabar light pressures and ;; 1022 m/sec2 subatomic particle accelerations. These ultrahigh-intensity Approved for public release; distribution unlimited. 26 tabletop lasers are thus the ideal instrument with which to explore the fundamental physics underlying the two possible concepts for vm-Teleportation. There are several ideas on how to generate negative energy in the lab that could potentially be extracted and concentrated in the proper fashion to induce the traversable flat-face wormhole outlined in Section 2. 1. 1 or induce the K ; 1 condition (in the PV-GR model) outlined in Section 2. 2. 1.
The schemes for generating negative energy are: Casimir Effect (described in Section 2. 2): This is the easiest and most well known way to generate negative energy in the lab. The energy density ? Casimir = ? (? 2hc0/240)a? 4 within a Casimir capacitor cavity is negative and manifests itself by producing a force of attraction between the capacitor plates. This has been measured in the lab (see above references). Forward (1998) proposes a mechanism for the endless extraction of energy from the vacuum in a Casimir cavity by cyclic manipulation of the cavity dimensions. Moving Mirror: Negative quantum vacuum energy can be created by a single moving reflecting surface (a moving mirror).
If a mirror moves with increasing acceleration, then a flux of negative energy emanates from its surface