ADVANCED SPACE PROPULSION BASED ON VACUUM …

1 82 Harlod E. concept of engineering the VACUUM found its first ex-pression in the physics literature when it was introduced byNobelist Lee in his textbook Particle Physics and Intro-duction to Field Theory [7]. There he stated: The experimen-tal method to alter the properties of the VACUUM may be calledvacuum If indeed we are able to alter the VACUUM ,then we may encounter new phenomena, totally unexpected. This legitimization of the VACUUM engineering concept wasbased on the recognition that the VACUUM is characterized byparameters and structure that leave no doubt that it constitutesan energetic and structured medium in its own right. Foremostamong these are that (1) within the context of quantum theorythe VACUUM is the seat of energetic particle and field fluctua-tions, and (2) within the context of general relativity the vacuumis the seat of a spacetime structure (metric) that encodes thedistribution of matter and energy.

2 Indeed, on the flyleaf of abook of essays by Einstein and others on the properties of thevacuum we find the statement The VACUUM is fast emerging asthe central structure of modern physics [8]. Perhaps the mostdefinitive statement acknowledging the central role of thevacuum in modern physics is provided by 2004 Nobel Prizewinner Frank Wilczek in his recent book The Lightness ofBeing: Mass, Ether and the Unification of Forces [9]: What is SPACE ? An empty stage where the physicalworld of matter acts out its drama? An equal participantthat both provides background and has a life of its own?Or the primary reality of which matter is a secondarymanifestation? Views on this question have evolved, andseveral times have changed radically, over the history ofscience.

3 Today the third view is triumphant. Given the known characteristics of the VACUUM , one mightreasonably inquire as to why it is not immediately obvious howto catalyze robust interactions of the type sought for SPACE -flight applications. To begin, in the case of quantum vacuumprocesses there are uncertainties that remain to be clarifiedregarding global thermodynamic and energy constraints. Fur-thermore, it is likely that energetic components of potentialutility involve very small-wavelength, high-frequency field struc-tures and thus resist facile engineering solutions. With regard toperturbation of the spacetime metric, the required energy densi-ties predicted by present theory exceed by many orders ofmagnitude values achievable with existing engineering tech-niques.

4 Nonetheless, one can examine the possibilities andimplications under the expectation that as science and its at-tendant derivative technologies mature, felicitous means mayyet be found that permit the exploitation of the enormous, as-yet-untapped potential of engineering so-called empty SPACE , the Section 2 the underlying mathematical platform for inves-tigating spacetime structure, the metric tensor approach, isintroduced. Section 3 provides an outline of the attendantphysical effects that derive from alterations in the spacetimestructure, and Section 4 catalogs these effects as they would beexhibited in the presence of ADVANCED aerospace craft technolo-gies BASED on spacetime MODIFICATION METRIC TENSOR APPROACHD espite the daunting energy requirements to restructure thespacetime metric to a significant degree, the forms that suchrestructuring would take to be useful for SPACE -flight applica-tions can be investigated, and their corollary attributes andconsequences determined - a Blue Sky, general-relativity-for-engineers approach, as it were.

5 From such a study thesignatures that would accompany such ADVANCED -technologycraft can be outlined, and possible effects of the technologywith regard to spacetime effects that include such phenomenaas the distortion of SPACE and time can be cataloged. This wouldinclude, among other consequences, cataloging effects thatmight be potentially harmful to human SPACE PROPULSION BASEDON VACUUM (SPACETIME METRIC) ENGINEERINGJBIS, Vol. 63, , 2010 HAROLD E. PUTHOFFI nstitute for ADVANCED Studies at Austin, 11855 Research Blvd., Austin, Texas 78759, : 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 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].

6 As examples, the currentdevelopment of theoretical physics addresses such topics as warp drives, traversable wormholes and time machines thatprovide 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 : SPACE PROPULSION , metric engineering , spacetime alteration, warp drives, wormholes, polarizable vacuum83 ADVANCED SPACE PROPULSION BASED on VACUUM (Spacetime Metric) EngineeringThe appropriate mathematical evaluation tool is use of themetric tensor that describes the measurement of spacetime inter-vals. Such an approach, well-known from studies in GR (generalrelativity) has the advantage of being model-independent, ,does not depend on knowledge of the specific mechanisms ordynamics that result in spacetime alterations, only that a technol-ogy exists that can control and manipulate ( , engineer) thespacetime metric to advantage.

7 Before discussing the predictedcharacteristics of such engineered spacetimes a brief mathematicaldigression is in order for those interested in the mathematicalstructure behind the discussion to a brief introduction, the expression for the 4-dimensionalline element ds2 in terms of the metric tensor g v is given by2dsgdx dx =(1)where summation over repeated indices is assumed unless oth-erwise indicated. In ordinary Minkowski flat spacetime a (4-dimensional) infinitesimal interval ds is given by the expres-sion (in Cartesian coordinates)222 2 2 2()dsc dtdxdydz= ++(2)where we make the identification dx0 = cdt, dx1 = dx, dx2 = dy,dx3 = dz, with metric tensor coefficients g00 = 1, g11 = g22 = g33= -1, g v = 0 for spherical coordinates in ordinary Minkowski flat spacetime222 22222 2sinds cdtdrrd rd = (3)where dx0 = cdt, dx1 = dr, dx2 = d , dx3 = d , with metric tensorcoefficients g00 = 1, g11 = -1, g22 = -r2, g33 = -r2 sin2 , g v = 0 for an example of spacetime alteration, in a spacetime al-tered by the presence of a spherical mass distribution m at theorigin (Schwarzschild-type solution) the above can be trans-formed into [10]()()

8 12222222222 22211111sinGm rcGm rcdsc dtdrGm rcGm rcGm rc rdd = ++ ++(4)with the metric tensor coefficients g v modifying the Minkowskiflat-spacetime intervals dt, dr, etc., another example of spacetime alteration, in a spacetimealtered by the presence of a charged spherical mass distribution(Q, m) at the origin (Reissner-Nordstrom-type solution) theabove can be transformed into [11]()()()()242222022221242202222222 2 2 2411141111sinQGcGm rcdsc dtGm rcrGmrcQGcGm rcdrGm rcrGmrcGm rcrdd =+ + + + + + ++(5)with the metric tensor coefficients g v again changed accord-ingly. In passing, one can note that the effect on the metric dueto charge Q differs in sign from that due to mass m, leading towhat in the literature has been referred to as electrograviticrepulsion [12].

9 Similar relatively simple solutions exist for a spinning mass(Kerr solution), and for a spinning electrically charged mass(Kerr-Newman solution). In the general case, appropriate solu-tions for the metric tensor can be generated for arbitrarily-engineered spacetimes, characterized by an appropriate set ofspacetime variables dx and metric tensor coefficients g v. Ofsignificance now is to identify the associated physical effectsand to develop a Table of such effects for quick first step is to simply catalog metric effects, , physi-cal effects associated with alteration of spacetime variables,and save for Section 4 the significance of such effects withinthe context of ADVANCED aerospace craft EFFECTS AS A FUNCTIONOF METRIC TENSOR COEFFICIENTSIn undistorted spacetime, measurements with physical rods andclocks yield spatial intervals dx and time intervals dt, definedin a flat Minkowski spacetime, the spacetime of common expe-rience.

10 In spacetime-altered regions, we can still choose dx and dt as natural coordinate intervals to represent a coordinatemap, but now local measurements with physical rods and clocksyield spatial intervalsgdx and time intervals00gdtso-called proper coordinate intervals. From these relationshipsa Table can be generated of associated physical effects to beexpected in spacetime regions altered by either natural or ad-vanced technological means. Given that, as seen from an unal-tered region, alteration of spatial and temporal intervals in aspacetime-altered region result in an altered velocity of light,from an engineering viewpoint such alterations can in essencebe understood in terms of a variable refractive index of thevacuum (see Section below) that affects all Interval, Frequency, EnergyThe case where001g<is considered first, typical for an altered spacetime metric in thevicinity of, say, a stellar mass see leading term in Eq.