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(Spacetime Metric) Engineering HarlodJBIS, Vol. E. 63,Puthoff pp.82-89, 2010 ADVANCED SPACE PROPULSION BASED ON VACUUM (SPACETIME METRIC) ENGINEERING HAROLD E. PUTHOFF Institute for Advanced Studies at Austin, 11855 Research Blvd., Austin, Texas 78759, USA. Email: [email protected] A theme that has come to the fore in advanced planning for long-range space exploration is the concept that empty space itself (the quantum vacuum, or spacetime metric) might be engineered so as to provide energy/thrust for future space vehicles. Although far-reaching, such a proposal is solidly grounded in modern physical theory, and therefore the possibility that matter/ vacuum interactions might be engineered for space-flight applications is not a priori ruled out [1]. As examples, the current development of theoretical physics addresses such topics as warp drives, traversable wormholes and time machines that provide for such vacuum engineering possibilities [2-6]. We provide here from a broad perspective the physics and correlates/ consequences of the engineering of the spacetime metric. Keywords: Space propulsion, metric engineering, spacetime alteration, warp drives, wormholes, polarizable vacuum 1. INTRODUCTION The concept of “engineering the vacuum” found its first ex- regarding global thermodynamic and energy constraints. Fur- pression in the physics literature when it was introduced by thermore, it is likely that energetic components of potential Nobelist T.D. Lee in his textbook Particle Physics and Intro- utility involve very small-wavelength, high-frequency field struc- duction to Field Theory [7]. There he stated: “The experimen- tures and thus resist facile engineering solutions. With regard to tal method to alter the properties of the vacuum may be called perturbation of the spacetime metric, the required energy densi- vacuum engineering…. If indeed we are able to alter the vacuum, ties predicted by present theory exceed by many orders of then we may encounter new phenomena, totally unexpected.” magnitude values achievable with existing engineering tech- This legitimization of the vacuum engineering concept was niques. Nonetheless, one can examine the possibilities and based on the recognition that the vacuum is characterized by implications under the expectation that as science and its at- parameters and structure that leave no doubt that it constitutes tendant derivative technologies mature, felicitous means may an energetic and structured medium in its own right. Foremost yet be found that permit the exploitation of the enormous, as- among these are that (1) within the context of quantum theory yet-untapped potential of engineering so-called “empty space,” the vacuum is the seat of energetic particle and field fluctua- the vacuum. tions, and (2) within the context of general relativity the vacuum is the seat of a spacetime structure (metric) that encodes the In Section 2 the underlying mathematical platform for inves- distribution of matter and energy. Indeed, on the flyleaf of a tigating spacetime structure, the metric tensor approach, is book of essays by Einstein and others on the properties of the introduced. Section 3 provides an outline of the attendant vacuum we find the statement “The vacuum is fast emerging as physical effects that derive from alterations in the spacetime the central structure of modern physics” [8]. Perhaps the most structure, and Section 4 catalogs these effects as they would be definitive statement acknowledging the central role of the exhibited in the presence of advanced aerospace craft technolo- vacuum in modern physics is provided by 2004 Nobel Prize gies based on spacetime modification. winner Frank Wilczek in his recent book The Lightness of Being: Mass, Ether and the Unification of Forces [9]: 2. SPACETIME MODIFICATION – METRIC TENSOR APPROACH “What is space? An empty stage where the physical world of matter acts out its drama? An equal participant Despite the daunting energy requirements to restructure the that both provides background and has a life of its own? spacetime metric to a significant degree, the forms that such Or the primary reality of which matter is a secondary restructuring would take to be useful for space-flight applica- manifestation? Views on this question have evolved, and tions can be investigated, and their corollary attributes and several times have changed radically, over the history of consequences determined - a “Blue Sky,” general-relativity- science. Today the third view is triumphant.” for-engineers approach, as it were. From such a study the signatures that would accompany such advanced-technology Given the known characteristics of the vacuum, one might craft can be outlined, and possible effects of the technology reasonably inquire as to why it is not immediately obvious how with regard to spacetime effects that include such phenomena to catalyze robust interactions of the type sought for space- as the distortion of space and time can be cataloged. This would flight applications. To begin, in the case of quantum vacuum include, among other consequences, cataloging effects that processes there are uncertainties that remain to be clarified might be potentially harmful to human physiology. 82 Advanced Space Propulsion Based on Vacuum (Spacetime Metric) Engineering The appropriate mathematical evaluation tool is use of the with the metric tensor coefficients gµv again changed accord- metric tensor that describes the measurement of spacetime inter- ingly. In passing, one can note that the effect on the metric due vals. Such an approach, well-known from studies in GR (general to charge Q differs in sign from that due to mass m, leading to relativity) has the advantage of being model-independent, i.e., what in the literature has been referred to as electrogravitic does not depend on knowledge of the specific mechanisms or repulsion [12]. dynamics that result in spacetime alterations, only that a technol- ogy exists that can control and manipulate (i.e., engineer) the Similar relatively simple solutions exist for a spinning mass spacetime metric to advantage. Before discussing the predicted (Kerr solution), and for a spinning electrically charged mass characteristics of such engineered spacetimes a brief mathematical (Kerr-Newman solution). In the general case, appropriate solu- digression is in order for those interested in the mathematical tions for the metric tensor can be generated for arbitrarily- structure behind the discussion to follow. engineered spacetimes, characterized by an appropriate set of µ spacetime variables dx and metric tensor coefficients gµv. Of As a brief introduction, the expression for the 4-dimensional significance now is to identify the associated physical effects 2 line element ds in terms of the metric tensor gµv is given by and to develop a Table of such effects for quick reference. 2 µ ν ds= gµν dx dx (1) The first step is to simply catalog metric effects, i.e., physi- cal effects associated with alteration of spacetime variables, where summation over repeated indices is assumed unless oth- and save for Section 4 the significance of such effects within erwise indicated. In ordinary Minkowski flat spacetime a (4- the context of advanced aerospace craft technologies. dimensional) infinitesimal interval ds is given by the expres- sion (in Cartesian coordinates) 3. PHYSICAL EFFECTS AS A FUNCTION OF METRIC TENSOR COEFFICIENTS ds2222=−++ c dt() dx dy 2 dz 2 (2) In undistorted spacetime, measurements with physical rods and where we make the identification dx0 = cdt, dx1 = dx, dx2 = dy, clocks yield spatial intervals dxµ and time intervals dt, defined dx3 = dz, with metric tensor coefficients g = 1, g = g = g in a flat Minkowski spacetime, the spacetime of common expe- 00 11 22 33 µ = -1, g = 0 for µ ≠ v. rience. In spacetime-altered regions, we can still choose dx µv and dt as natural coordinate intervals to represent a coordinate For spherical coordinates in ordinary Minkowski flat spacetime map, but now local measurements with physical rods and clocks yield spatial intervals dscdtdrrdr22222222=−−−θ sin θϕ d 2 (3) µ −gµν dx where dx0 = cdt, dx1 = dr, dx2 = dθ, dx3 = dϕ, with metric tensor and time intervals coefficients g = 1, g = -1, g = -r2, g = -r2 sin2 θ, g = 0 for 00 11 22 33 µv g dt µ ≠ v. 00 so-called proper coordinate intervals. From these relationships As an example of spacetime alteration, in a spacetime al- a Table can be generated of associated physical effects to be tered by the presence of a spherical mass distribution m at the expected in spacetime regions altered by either natural or ad- origin (Schwarzschild-type solution) the above can be trans- vanced technological means. Given that, as seen from an unal- formed into [10] tered region, alteration of spatial and temporal intervals in a spacetime-altered region result in an altered velocity of light, −1 from an engineering viewpoint such alterations can in essence 11−−Gm rc22 Gm rc ds2222=− c dt dr be understood in terms of a variable refractive index of the 22 11++Gm rc Gm rc vacuum (see Section 3.4 below) that affects all measurement. (4) 22 2 2 2 −+()()1sinGm rc r dθθϕ + d 3.1 Time Interval, Frequency, Energy The case where with the metric tensor coefficients gµv modifying the Minkowski flat-spacetime intervals dt, dr, etc., accordingly. g00 < 1 As another example of spacetime alteration, in a spacetime is considered first, typical for an altered spacetime metric in the altered by the presence of a charged spherical mass distribution vicinity of, say, a stellar mass – see leading term in Eq. (4). (Q, m) at the origin (Reissner-Nordstrom-type solution) the Local measurements with physical clocks within the altered above can be transformed into [11] spacetime region yield a time interval g00 dt< dt thus an interval of time dt between two events located in an 1− Gm rc2 QG244πε c ds222=+0 c dt undistorted spacetime region remote from the mass (i.e., an 22 1+ Gm rc rGmrc22()1+ observer at infinity) – say, ten seconds - would be judged by local (proper) measurement from within the altered spacetime −1 region to occur in a lesser time interval, 1− Gm rc2 QG244πε c −+0 dr 2 g dt< dt 22(5) 00 1+ Gm rc rGmrc221+ () - say, 5 seconds.
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