UNCLASSIFIED//FOR OFFICIAL USE ONLY Defense Intelligence Reference Document Acquisition Threat Support M arch 2010 1 Decem ber 2009 .-08-1003-015 Advanced Space Propulsion Based on Vacuum (Spacetime Metric) Engineering UNCLASSI FIED //FOR OmCIAL USE ONLY U N CLASSI FIE D//TOR OFFICIAL UOC ONL¥ Advanced Space Propulsion based on Vacuum (Spacetime Metric) Engineering Prepared by: Acquisition Support Division (DWO-3) Defense Warning Office Directorate for Analysis Defense Intelligence Agency Author: A A P P erson 57 A dm inistrative N ote 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 2 009 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 to[AAP Person 1 ~|, AAWSA Program Manager, Defense Intelligence Agency, ATTN: CLAR/DWO-3, Bldg 6000, Washington, DC 2 0340-5 100. i UNCLASSIFIED/ /FOR OFFICIAL U66 ONL¥ UNCLASSIFIED//FOA OFFICIAL USE ONET Contents Advanced Space Propulsion Based on Vacuum (Spacetime Metric) Engineering ....iii Preface and Introduction............................................... iii I. Spacetime Modification - Metric Tensor Approach.................................................1 II. Physical Effects as a Function of Metric Tensor Coefficients................................2 Time Interval, Frequency, Energy............................ 3 Spatial Interval..................................................................................................4 Velocity of Light in Spacetime-Altered Regions................................................4 Refractive Index Modeling.................................. 5 Effective Mass in Spacetime-Altered Regions..................................................6 Gravity/Antigravity "Forces"....................................................................... 6 III. Significance of Physical Effects Applicable to Advanced Aerospace Craft Technologies as a Function of Metric Tensor Coefficients.........................................6 Time Alteration..................................................................................... 6 Spatial Alteration............................................................... 8 Velocity of Light/Craft in Spacetime-Altered Regions..........................................8 Refractive Index Effects................................................................... 9 Effective Mass in Spacetime-Altered Regions........................................................9 Gravity/Antigravity/Propulsion Effects....................................... 10 IV. Discussion...........................................................................................................11 Figures Figure 1. Blueshifting of Infrared Heat Power Spectrum..........................................7 Figure 2. Light-Bending in a Spacetime-Altered Reigon...........................................9 Figure 3. Alcubierre Warp Drive Metric Structure..................................................11 Tables Table 1. Metric Effects on Physical Processes in an Altered Spacetime as Interpreted by a Remote (Unaltered Spacetime) Observer.................4 ii UN CLASSI FI ED//rOR OFFICIAL USE OHLY UNCLASSIFIED//FOR OFFICIAL UOC ONLY Advanced Space Propulsion Based on Vacuum (Spacetime Metric) Engineering Preface and Introduction A theme that has come to the fore in advanced planning for long-range space exploration in the future is the concept that empty space itself (the quantum vacuum, or spacetime metric) might be engineered 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 spaceflight applications is not a priori ruled out (Reference 1). Given the current development of mainstream theoretical physics on such topics as warp drives and traversable wormholes that provides for such vacuum engineering possibilities (References 2-6), provided in this paper is a broad perspective of the physics and consequences of the engineering of the spacetime metric. The concept of "engineering the vacuum" found its first expression in the mainstream physics literature when it was introduced by Nobelist T. D. Lee in his textbook P article P h ysics an d In trodu ction to Field Th eory (Reference 7). There he 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 new phenomena, totally unexpected." This legitimization of the vacuum engineering concept was based on the recognition that the vacuum is characterized by parameters and structure that leave no doubt that it constitutes an energetic and structured medium in its own right. Foremost among these are that (1) within the context of quantum theory, the vacuum is the seat of energetic particle and field fluctuations and (2) within the context of general relativity, the vacuum is the seat of a spacetime structure (metric) that encodes the distribution of matter and energy. Indeed, on the flyleaf of a book of essays by Einstein and others on the properties of the vacuum, there is the statement, "The vacuum is fast emerging as the central structure of modern physics" (Reference 8). Perhaps the most definitive statement acknowledging the central role of the vacuum in modern physics is provided by 2004 Nobelist Frank Wilczek in his book Th e Ligh tn ess of B ein g: M ass, Eth er an d th e U n ification of Forces (Reference 9): "What is space? An empty stage where the physical world of matter acts out its drama? An equal participant that both provides background and has a life of its own? Or the primary reality of which matter is a secondary manifestation? Views on this question have evolved, and several times have changed radically, over the history of science. Today the third view is triumphant." Given the known characteristics of the vacuum, one might reasonably inquire why it is not immediately obvious how to catalyze robust interactions of the type sought for spaceflight applications. For starters, in the case of quantum vacuum processes, uncertainties regarding global thermodynamic and energy constraints remain to be clarified. Furthermore, it is likely that energetic iii UNCLASSI FIED/ / FOR OFFIGIAh USE QNh¥ UNCLASSIFIED//FOR OFFICIAL USE ONLY components of potential utility involve very-small-wavelength, high-frequency field structures and thus resist facile engineering solutions. With regard to perturbation of the spacetime metric, the required energy densities predicted by present theory exceed by many orders of magnitude values achievable with existing engineering techniques. Nonetheless, one can examine the possibilities and implications under the expectation that as science and its attendant derivative technologies mature, felicitous means may yet be found that permit the exploitation of the enormous, as-yet-untapped potential of engineering so-called "empty space," the vacuum. This paper introduces the underlying mathematical platform for investigating spacetime structure, the metric tensor approach. It then outlines the attendant physical effects that derive from alterations in the spacetime structure. Finally, the paper examines these effects as they would be exhibited in the presence of advanced aerospace craft technologies based on spacetime modification. iv UNCLASSI FIED//FOR OFFICIAL USE ONEY UNCLASSIFIED//rOR OFFICIAL UDE OML¥ I. Spacetime Modification - Metric Tensor Approach Despite the daunting energy requirem ents to restructure the spacetim e m etric to a significant degree, one can investigate the form s that such restructuring would take to be useful for spaceflight applications and determ ine their corollary attributes and consequences. Thus we em bark on a " Blue Sky," general-relativity-for-engineers approach, as it were. As a m athem atical evaluation tool, the m etric tensor that describes the m easurem ent of spacetim e intervals is used. Such an approach, well known from studies in general relativity (G R ), has the advantage of being m odel independent— that is, it does not depend on knowledge of the specific m echanism s or dynam ics that result in spacetim e alterations but rather only assum es that a technology exists that can control and m anipulate (that is, engineer) the spacetim e m etric to advantage. Before discussing the predicted characteristics of such engineered spacetim es, beginning in Section III, a brief m athem atical digression for those interested in the m athem atical structure behind the discussion to follow is introduced. As a brief introduction, the expression for the four-dim ensionai line elem ent J.?2 in term s of the m etric tensor g^. is given by ds2 = g^dx^dx' (1) where sum m ation over repeated indices is assum ed unless otherwise indicated. In ordinary M inkowski flat spacetim e, a (four-dim ensional) infinitesim al interval ds is given by the expression (in Cartesian coordinates) ds2 = c2dt2 - (dx2 + dy2 + dx2) where the identification dx° = cdt, dx' = dx, dx2 - dy, dx2 -dz is m ade, with m etric tensor coefficients ^= 1, gH = g22 = ^ = ~b ^= 0 for 0^v- For spherical coordinates in ordinary M inkowski flat spacetim e ds2 = c2dt2-dr2 — r2d0 2 — r2 sin2 3d(p2 (2) (3) where ^°= £f^ , ^' = ^r, ^A = d0 1 dx3 = d(p, with m etric tensor coefficients ^ = 1, Sn^b gi2=-r‘, g33= -r2wa20, g^O for//*v. As an exam ple of spacetim e alteration, in a spacetim e altered by the presence of a spherical m ass distribution m at the origin (Schwarzschild-type solution), the above can be transform ed into (R eference 10) 1 - Gm ) rc2 1 + Gm /rc2; c2dr \-Gm /rc2 1 + Gm j rc2 dr2 -(1 + G m /rc'}r2[d0 2 + sin2 0d< p2} (4) 1 UNCLASSI FIED//WR OFFICIAL USE QNh¥ UNCLASSIFIED//TOW OFFICIAL UDE ONLY with the m etric tensor coefficients g^. m odifying the M inkowski flat-spacetim e intervals dt, dr, and so forth, accordingly. As another exam ple of spacetim e alteration, in a spacetim e altered by the presence of a charged spherical m ass distribution (2,m )at the origin (R eissner-N ordstrom -type solution), the above can be transform ed into (R eference 11) ds1 = 1 - Gm i rc~ 1 + Gm / rc1 Q~G4k;^ r‘(l + Gm / rc2 } c" dt1 \ Gm rc: _ Q G 4^~t:< lc4 J + Gm /rc2 r(\ + Gm rr ] (5) -^l+ Gm /rc2^ r2 [d0 2 + sin2 0d< p2} with the m etric tensor coefficients ^ again changed accordingly. N ote that the effect on the m etric due to charge Q differs in sign from that due to m ass m , leading to what in the literature has been referred to as electrogravitic repulsion (R eference 12). Sim ilar relatively sim ple solutions exist for a spinning m ass (Kerr solution) and for a spinning electrically charged m ass (Kerr-N ewm an solution). In the general case, appropriate solutions for the m etric tensor can be generated for arbitrarily engineered spacetim es, characterized by an appropriate set of spacetim e variables dr''and m etric tensor coefficients^,. Of significance now is to identify the associated physical effects and to develop a table of such effects for quick reference. W e begin by sim ply cataloging m etric effects— that is, physical effects associated with alteration of spacetim e variables— saving for Section IV the significance of such effects within the context of advanced aerospace craft technologies. II. Physical Effects as a Function of Metric Tensor Coefficients In undistorted spacetim e, m easurem ents with physical rods and clocks yield spatial intervals dx^ and tim e intervals dt, defined in a flat M inkowski spacetim e, the spacetim e of com m on experience. In spacetim e-altered regions, dxf‘ and dt are still chosen as natural coordinate intervals to represent a coordinate m ap, but now local m easurem ents with physical rods and clocks yield spatial intervals J^g^dx*' and tim e intervals ^g^dt, so-called proper coordinate intervals. From these relationships a table of associated physical effects to be expected in spacetim e regions altered by either natural or advanced technological m eans can be generated. G iven that, as seen from an unaltered region, alteration of spatial and tem poral intervals in a spacetim e-altered region result in an altered velocity of light, from an engineering viewpoint such alterations can in essence be understood in term s of a variable refractive index of the vacuum (see Section III below) that affects all m easurem ent. 2 UNCLASSI FIED/ / FOR OFFICIAL USE ONLT UNCLASSIFIED//FOR OFFICIAL USE 8KW TIME INTERVAL, FREQUENCY, ENERGY Begin by considering the case where -fg// < 1, typical for an altered spacetim e m etric in the vicinity of, say, a stellar m ass, as expressed by the leading term in Equation (4). Local m easurem ents with physical clocks within the altered spacetim e yield a tim e interval y[g^dt< dt', thus an interval of tim e dt between two events in an undistorted spacetim e rem ote1 from the m ass— say, 10 seconds— would be judged by local (proper) m easurem ent from within the altered spacetim e to occur in a lesser tim e interval, y[g//dt < dt — say, 5 seconds. From this one can rightly infer that, relatively speaking, clocks (atom ic processes and so forth) within the altered spacetim e run slower. G iven this result, a physical process (for exam ple, interval between clock ticks, atom ic em issions) that takes a tim e St in unaltered spacetim e slows to St ^ St/ ^g^ when occurring within the altered spacetim e. Conversely, under conditions (for exam ple, m etric engineering) for which Jg^ >1, processes within the spacetim e-altered region are sped up. Thus the first entry for a table of physical effects (see Table 1) is m ade. 1 An observer at " infinity." G iven that frequency m easurem ents are the reciprocal of tim e duration m easurem ents, the associated expression for frequency co is given by to — > tOy/g™ , our second entry in Table 1. This accounts, for exam ple, for the redshifting of atom ic em issions from dense m asses where ^ < 1. Conversely, under conditions for which ^g^ > 1, blueshifting of em issions would occur. In addition, given that quanta of energy are given by E = lw, energy scales with Jg//, as does frequency, E -> Ey/g~, our third entry in the table. Depending on the value of ^in the spacetim e-altered region, energy states m ay be raised or lowered relative to an unaltered spacetim e region. 3 UNCLASSI FIED//FOR OFFICIAL USE ONLY UNCLASSIFIED//FOR OFFICIAL USE ONLY Table 1. Metric Effects on Physical Processes in an Altered Spacetime as Interpreted by a Remote (Unaltered Spacetime) Observer Variable Typical Stellar Mass Uoo^ ISuM Spacetime-Engineered Metric (&»H fc| ^1‘'1% ™ Processes (for exam ple, clocks) run slower Processes (for exam ple, clocks) run faster Frequency " ^^V ^w R edshift toward lower frequencies Blueshift toward higher frequencies Energy E^E^8™ Energy states lowered Energy states raised Spatial ^r^^l^ Objects (for exam ple, rulers) shrink Objects (for exam ple, rulers) expand V elocity 17 = c ^ c^^/~^" Effective vL < c Effective vL > c M ass m = E/c2 -+ (-g,, /y[g^]m Effective m ass increases Effective m ass decreases G ravitational " force" ./ (# 00 ’ ^11 ) " G ravitational" " Antigravitational" Spatial Interval Again, by considering the case typical for an altered spacetim e m etric in the vicinity of, say, a stellar m ass, then -/-g^ >1 for the radial dim ension x' = r, as expressed by the second term in Equation (4). Therefore, local m easurem ents with physical rulers within the altered spacetim e yield a spatial interval y/^g^dr > dr; thus a spatial interval dr between two locations in an undistorted spacetim e— say, rem ote from the m ass— would be judged by local (proper) m easurem ent from within the altered spacetim e to be greater. From this one can rightly infer that, relatively speaking, rulers (atom ic spacings and so forth) within the altered spacetim e are shrunken relative to their values in unaltered spacetim e. G iven this result, a physical object (for exam ple, atom ic orbit) that possesses a m easure Ar in unaltered spacetim e shrinks to Ar->Ar/^gu when placed within the altered spacetim e. Conversely, under conditions for which y/-g^ < 1, objects would expand— thus the fourth entry for the table of physical effects. Velocity of Light in Spacetime-Altered Regions Interior to a spacetim e region altered by, say, a dense m ass (for exam ple, a black hole), the locally m easured velocity of light c in, say, the x1 = r direction is given by the ratio of locally m easured (proper) distance/tim e intervals for a propagating light signal (R eference 13). UNCLASSI FIED //FOR OFFICIAL USE ONLY UNCLASSIFIED//FOR OFFICIAL USE ONLY From a viewpoint exterior to the region, however, from the above one finds that the rem otely observed coordinate ratio m easurem ent yields a different value VL= --L dt dr (7) Therefore, although a local m easurem ent with physical rods and clocks yields c, an observer in an exterior reference fram e rem ote from the m ass speaks of light " slowing down" on a radial approach to the m ass owing to the ratio^/-^, < 1. Conversely, under (m etric engineering) conditions for which y[g^J-g^ > 1, the velocity of light— and exotic-technology craft velocities that obey sim ilar form ulas— would appear superlum inal in the exterior fram e. This gives our fifth entry for the table of physical effects. Refractive Index Modeling G iven that velocity-of-light effects in a spacetim e-altered region, as viewed from an external fram e, are governed by Equation (7), it is seen that the effect of spacetim e alteration on light propagation can be expressed in term s of an optical refractive index n, defined by (8) where n is an effective refractive index of the (spacetim e-altered) vacuum . This widely known result has resulted in the developm ent of refractive index m odels for G R (R eferences 14-17) that have found application in problem s such as gravitational lensing (R eference 18). The estim ated electric or m agnetic field strengths required to generate a given refractive index change given by standard G R theory (the Levi-Civita Effect) can be found in (R eference 19). In engineering term s, the velocity of light c is given by the expressionc = l//^^, where ;/() and ^0 are the m agnetic perm eability and dielectric perm ittivity of undistorted vacuum space (//0 = 4,tx10 H/m and f0 = 8.854xl0“12 F/m ). The generation of an effective refractive index n = yj-g^Jgw t 1 by technological m eans can from an engineering viewpoint be interpreted as m anipulation of the vacuum param eters//0 and f0 . In G R theory, such variations in ^0 , sn and hence the velocity of light, c, are often treated in term s of a "THsp" form alism used in com parative studies of gravitational theories (R eference 20). As discussed below, a num ber of striking effects can be anticipated in certain engineered spacetim e regions. 5 UNCLASSI FIED/ / FOR OFFICIAL USE ONLY UNCLASSIFIED//rOR OFFICIAL USE ONLY Effective Mass in Spacetime-Altered Regions In a spacetim e-altered region, E-m c1 still holds in term s of local (" proper coordinate" ) m easurem ents, but now energy E and the velocity of light c take on altered values as observed from an exterior (undistorted) spacetim e region. R eference to the definitions for E and c in Table 1 perm its one to define an effective m ass as seen from the exterior undistorted region as therefore taking on the value m ^>m (-gn)/Jg^, providing a sixth entry for our table. Depending on the values of g0(land glt, the effective m ass m ay be seen from the viewpoint of an observer in an undistorted spacetim e region to have either increased or decreased. Gravity/Antigravity "Forces" Strictly speaking, from the G R point of view, there are no gravitational " forces" but rather (in the words of G R theorist John W heeler) " m atter tells space how to curve, and space tells m atter how to m ove." (R eference 21) As a result, N ewton's law of gravitational attraction to a central m ass is therefore interpreted in term s of the spacetim e structure as expressed in term s of the m etric tensor coefficients, in this case as expressed in Equation (4) above. Therefore, in term s of the m etric coefficients, gravitational attraction in this case derives from the condition that g^ < 1 J# ,,! > 1. As for the possibility for generating " antigravitational forces," noted in equation (5), inclusion of the effects of charge led to m etric tensor contributions counter to the effects of m ass— that is, to electrogravitic repulsion. This reveals that conditions under which, say, the signs of the coefficients ^ and gu could be reversed would be considered (loosely) as antigravitational in nature. A seventh entry in Table 1 represents these features of m etric significance. III. Significance of Physical Effects Applicable to Advanced Aerospace Craft Technologies as a Function of Metric Tensor Coefficients As in Section III, m etric tensor coefficients define the relationship between locally and rem otely observed (that is, spacetim e-altered and unaltered) variables of interest as listed in Table 1, and in the process define corollary physical effects. Table 1 thereby constitutes a useful reference for interpreting the physical significance of the effects of the alteration of spacetim e variables. The expressions listed indicate specific spacetim e alteration effects, whether owing to natural causes (for exam ple, the presence of a planetary or stellar m ass) or as a result of m etric engineering by advanced technological m eans as m ight be anticipated in the developm ent and deploym ent of advanced aerospace craft. TIME ALTERATION W ith regard to the first table entry (tim e interval), in a spacetim e-altered region, tim e intervals are seen by a rem ote (unaltered spacetim e) observer to vary as ^/'Jsm relative to the rem ote observer. N ear a dense m ass, for exam ple, ^ < 1, and 6 UNCLASSIFIED//rOR OFFICIAL USE ONLY UNCLASSIFIED//TOW OFFICIAL USE ONLY therefore tim e intervals are seen as lengthening and processes as running slower,2 one consequence of which is redshift of em ission lines. Should such a tim e-slowed condition be engineered in an advanced aerospace application, an individual who has spent tim e within such a tem porally m odified field would, when returned to the norm al environm ent, find that m ore tim e had passed than could be experientially accounted for. 2 In the case of approach to a black hole, to stop altogether. Conversely, for an engineered spacetim e associated with an advanced aerospace craft in which Jg^ > 1, tim e flow within the altered spacetim e region would appear sped up to an external observer, while to an internal observer external tim e flow would appear to be in slow m otion. A corollary would be that within the spacetim e-altered region, norm al environm ental sounds from outside the region m ight cease to be registered, since external sounds could under these conditions redshift below the auditory range. An additional im plication of tim e speedup within the fram e of an exotic craft technology is that its flightpath that m ight seem precipitous from an external viewpoint (for exam ple, sudden acceleration or deceleration) would be experienced as m uch less so by the craft's occupants, From the occupants' viewpoint, observing the external environm ent to be in relative slow m otion, it would not be surprising to consider that one's relatively m odest changes in m otion would appear abrupt to an external observer. Based on the second entry in Table 1 (frequency), yet another im plication of an accelerated tim efram e due to craft-associated m etric engineering that leads to ^2 > 1, frequencies associated with the craft would for a rem ote observer appear to be blueshifted. Corollary to observation of such a craft is the possibility that there would be a brightening of lum inosity due to the heat spectrum blueshifting up into the visible portion of the spectrum (see Figure 1). infrared Frequencyw Figure 1. Blueshifting of Infrared Heat Power Spectrum W ith regard to the third entry in Table 1 (energy), in a spacetim e-altered region, energy scales as yfg^ relative to a rem ote observer in an undistorted spacetim e. In the vicinity of a dense m ass where T^o? < 1, the consequent reduction of energy bonds correlates with observed redshifts of em ission. For engineered spacetim es associated with advanced craft technology in which y[g^ >1 (accelerated tim efram e case), a 7 UN CLASSI FIED //FOK OFFICIAL USE ONLY UNCLASSIFIED//rOR OrriCIAL USE ONLY craft's m aterial properties would appear " hardened" relative to the environm ent owing to the increased binding energies of atom s in its m aterial structure. Such a craft could, for exam ple, im pact water at high velocities without apparent deleterious effects. SPATIAL ALTERATION The fourth entry in Table 1 (spatial m easure) indicates the size of an object within an altered spacetim e region as seen by a rem ote observer. The size of, say, a spherical object is seen to have its radial dim ension, r, scale asl/^-g,, . In the vicinity of a dense m ass^-gn >1, in which case an object within the altered spacetim e region appears to a rem ote observer to have shrunk. As a corollary, m etric engineering associated with an advanced aerospace craft to produce this effect could in principle result in a large craft with a spacious interior appearing to an external observer to be relatively sm all. Additional dim ensional aspects, such as potential dim ensional changes, are discussed below in " R efractive Index Effects." VELOCITY OF LIGHT/CRAFT IN SPACETIME-ALTERED REGIONS Interior to a spacetim e-altered region, the locally m easured velocity of light, v, = c, is given by the ratio of (locally m easured) distance/tim e intervals for a propagating light signal, as expressed in Equation (6) above. From a viewpoint exterior to the region, however, the observed coordinate ratio m easurem ent can yield a different value v[ greater or less than c as given by the fifth entry in Table 1 (velocity). As an exam ple of a m easurem ent less than c, one speaks of light " slowing down" as a light signal approaches a dense m ass (for exam ple, a black hole.) In an engineered spacetim e in whichg00 >1, |gH|< l, however, the effective velocity of light v[ as m easured by an external observer can be > c. G iven that velocities in general in different coordinate system s scale as does the velocity of light— that is,v -> ^^/-^uV -for exotic propulsion an engineered spacetim e m etric can in principle establish a condition in which the trajectory of a craft approaching the velocity of light in its own fram e would be observed from an exterior fram e to exceed light speed— that is, exhibit m otion at superlum inal speed. This opens up the possibility of transport at superlum inal velocities (as m easured by an external observer) without violation of the velocity-of-light constraint within the spacetim e- altered region, a feature attractive for interstellar travel. This is the basis for discussion of warp drives and worm holes in the G R literature (R eferences 2-6). Therefore, although present technological facility is far from m ature enough to support the developm ent of warp drive and worm hole technologies (R eference 22), the possibility of developing such technologies in the future cannot be ruled out. In other words, effective transport at speeds exceeding the conventional speed of light could occur in principle, and therefore the possibility of reduced-tim e interstellar travel is not fundam entally ruled out by physical principles. 8 UNCLASSI FIED//TOR OmCIAL UGE ONEY UNCLASSIFIED//FOR OFFICIAL USE ONLY REFRACTIVE INDEX EFFECTS W hen considering m etric-engineered spacetim e associated with exotic propulsion, a num ber of corollary side effects associated with refractive index changes of the vacuum structure em erge as possibilities. Expected effects would m im ic known refractive index effects in general and can therefore be determ ined from known phenom ena. Indistinct boundary definition associated with " waviness" as observed with heat waves off a desert floor is one exam ple. As another, a light beam m ay bend (as in the G R exam ple of the bending of starlight as it grazes the sun; see Figure 2) or even term inate in m id-space. Such an observation would exhibit features that under ordinary circum stances would be associated with a high- refractive index optical fiber in norm al space (well-defined boundaries, light trapped within, bending or term ination in m id-space). Additional observations m ight include apparent changes in size or shape (changes in lensing m agnification param eters). Yet another possibility is the sudden " cloaking" or Figure 2. Light-Bending in a Spacetime-Altered Region " blinking out," which would at least be consistent with strong gravitational lensing effects that bend a background view around a craft, though other technical options involving, for exam ple, the use of m etam aterials, exist as well. EFFECTIVE MASS IN SPACETIME-ALTERED REGIONS As noted in the preceding sections, spacetim e alteration of energy and light-speed m easures leads to an associated alteration in the effective m ass of an object in a spacetim e-altered region as viewed from an external (unaltered) region. Of special interest is the case in which the effective m ass is decreased by application of spacetim e m etric engineering principles as m ight be expected in the case of m etric engineering for spaceflight applications (reference last colum n in Table 1). Effective reduction of inertial m ass as viewed in our fram e of reference would appear to m itigate against untoward effects on craft occupants associated with abrupt changes in m ovem ent. (The physical principles involved can also be understood in term s of associated coordinate transform ation properties as discussed above.) In any case, changes in effective m ass associated with engineering of the spacetim e m etric in a craft's environs can lead to properties advantageous for spaceflight applications. 9 UNCLASSI FIED//FOR OFFICIAL USE ONET UNCLASSIFIED//FOR OFFICIAL USE ONhY GRAVITY/ANTIGRAVITY/PROPULSION EFFECTS In the G R ansatz gravitational-type forces derive from the spacetim e m etric, whether determ ined by natural sources (for exam ple, planetary or stellar m asses) or by advanced m etric engineering. Fortunately for our consideration of this topic, discussion can be carried out solely based on the form of the m etric, independent of the specific m echanism s or dynam ics that determ ine the m etric. As one exem plar, consider Alcubierre's form ulation of a " warp drive," a spacetim e m etric solution of Einstein's G R field equation (R eferences 2, 22). Alcubierre derived a spacetim e m etric m otivated by cosm ological inflation that would allow arbitrarily short travel tim es between two distant points in space. The behavior of the warp drive m etric provides for the sim ultaneous expansion of space behind the spacecraft and a corresponding contraction of space in front of the spacecraft (see Figure 3). The warp drive spacecraft would thus appear to be " surfing on a wave" of spacetim e geom etry. By appropriate structuring of the m etric, the spacecraft can be m ade to exhibit an arbitrarily large apparent faster-than-light speed as viewed by external observers without violating the local speed-of-light constraint within the spacetim e-altered region. Furtherm ore, the Alcubierre solution showed that the proper (experienced) acceleration along the spaceship's path would be zero, and that the spaceship would suffer no tim e dilation— highly desirable features for interstellar travel. In order to im plem ent a warp drive, one would have to construct a " warp bubble" that surrounded the spacecraft by generating a thin shell or surface layer of exotic m atter— that is, a quantum field having negative energy and/or negative pressure. Although the technical requirem ents for such are unlikely to be m et in the foreseeable future (R eference 22), the exercise nonetheless serves as a good exam ple for showcasing attributes associated with m anipulation of the spacetim e m etric at will. The entire discussion of the possibility of generating a spacetim e structure like that of the Alcubierre warp drive is based sim ply on assum ing the form of a m etric (that is,g ,) that exhibits desired characteristics. In like m anner, arbitrary spacetim e m etrics to provide gravity/antigravity/propulsion characteristics can in principle be postulated. W hat is required for im plem entation is to determ ine appropriate sources for their generation, a requirem ent that m ust be m et before advanced spaceship technology based on vacuum engineering can be realized in practice. The difficulties, challenges, and options for m eeting such requirem ents can be found in the relevant literature (R eference 22). 10 UNCLASSI FIED//FOR OFFICIAL USE ONLY UNCLASSIFIED//PeR OFFICIAL USE ONLY Figure 3. Alcubierre Warp Drive Metric Structure IV. Discussion This paper has considered the possibility— even likelihood— that future developm ents with regard to advanced aerospace technologies will trend in the direction of m anipulating the underlying spacetim e structure of the vacuum of space itself by processes that can be called vacuum engineering or m etric engineering. Far from being sim ply a fanciful concept, a significant literature exists in peer-reviewed, Tier 1 physics publications in which the topic is explored in detail.3 The analysis presented herein, a form of general relativity for engineers, takes advantage of the fact that in G R a m inim al-assum ption, m etric tensor approach can be used that is m odel-independent— that is, it does not depend on knowledge of the specific m echanism s or dynam ics that result in spacetim e alterations but rather only assum es that a technology exists that can control and m anipulate (that is, engineer) the spacetim e variables to advantage. Such an approach requires only that the hypothesized spacetim e alterations result in effects consonant with the currently known G R physics principles. In the m etric engineering approach, the application of the principles gives precise predictions as to what can be expected as spatial and tem poral variables are altered from their usual (that is, flat space) structure. Signatures of the predicted contractions and expansions of space, slowdown and speedup of tim e, alteration of effective m ass, speed of light and associated consequences, both as occur in natural phenom ena in nature and with regard to spacetim es specifically engineered for advanced aerospace applications, are succinctly sum m arized in Table 1. Of particular interest with regard to innovative form s of advanced aerospace craft are the features tabulated in the right-hand colum n of Table 1, features that presum ably describe an ideal craft for interstellar travel: an ability to travel at superlum inal speeds •See R eference 1 for a com prehensive introduction to the subject with contributions from lead scientists from around the globe. 11 UNCLASSI FIED//TOR OFFICIAL USE ONLY UNCLASSIFIED//FOR OFFICIAL USE OML¥ relative to the reference fram e of background space, energy bonds of m aterials strengthened (that is, hardened) relative to the background environm ent, a decrease in effective m ass vis-a-vis the environm ent, an accelerated tim efram e that would perm it rapid trajectory changes relative to the background rest fram e without undue internal stress, and the generation of gravity-like forces of arbitrary geom etry— all on the basis of restructuring the vacuum spacetim e variables. As avant garde as such features appear to be, they are totally in conform ance with the principles of general relativity as currently understood. A rem aining challenge is to develop insight into the technological designs by which such vacuum restructuring can be generated on the scale required to im plem ent the necessary spacetim e m odifications. Despite the challenges, sam ple calculations as presented herein indicate the direction of potentially useful trends derivable on the basis of the application of G R principles as em bodied in a m etric engineering approach, with the results constrained only by what is achievable practically in an engineering sense. The latter is, however, a daunting constraint. At this point in the consideration of such nascent concepts, given our present level of technological evolution, it is prem ature to even guess about an optim um strategy, let alone attem pt to form a critical path for the engineering developm ent of such technologies. N onetheless, only through rigorous inquiry into such concepts can one hope to arrive at a proper assessm ent of the possibilities inherent in the evolution of advanced spaceflight technologies. 1 See, for exam ple, a series of essays in the com pendium Frontiers of Propulsion Science, Eds. M . G . M illis and E. W . Davis, AIAA Press, R eston, V irginia (2009). 2 M . Alcubierre, " The warp drive: Hyper-fast travel within general relativity/' Class. Q uantum G rav. 11, p. L73 (1994). 3 H. E. Puthoff, " SETI, the velocity-of-light lim itation, and the Alcubierre warp drive: An integrating overview," Physics Essays 9, p. 156 (1996). 4 M . S. M orris and K. S. Thorne, " W orm holes in spacetim e and their use for interstellar travel: A tool for teaching general relativity/'Am . J. Phys. 56, pp. 395-412 (1988). 5 M . V isser, Lorentzian W orm holes: From Einstein to Hawking, AIP Press, N ew York, 1995. 6 M . 5. M orris, K. S. Thorne and U. Yurtsever, " W orm holes, tim e m achines, and the weak energy condition/' Phys. R ev. Lett. 61, p. 1446 (1988). 7 T. D. Lee, Particle Physics and Introduction to Field Theory, Harwood Academ ic Press, London (1988). 8 The Philosophy of V acuum , Eds. S. Saunders and H. R . Brown, Clarendon Press, Oxford (1991). 9 F. W ilczek, The Lightness of Being: M ass, Ether and the Unification of Forces, Basic Books, N ew York (2008). 10 A. Logunov and M . M estvirishvili, The R elativistic Theory of G ravitation, M ir Publ., M oscow (1989), p. 76. 11 Op. cit., p. 83. 12 S. M . M ahajan, A. Q adir and P. M . V alanju, " R eintroducing the concept of 'force' into relativity theory/' II N uovo Cim ento 65B, 404 (1981). 13 R . Klauber, " Physical com ponents, coordinate com ponents, and the speed of light," vl (18 M ay 2001). www.arXiv: gr-qc/0105071 14 F. de Felice, " On the gravitational field acting as an optical m edium ," G en. R ei. and G rav. 2, 347 (1971). 15 K. K. N andi and A. Islam , " On the optical-m echanical analogy in general relativity/' Am . J. Phys. 63, 251 (1995). 16 H. E. Puthoff, " Polarizable-vacuum (PV ) approach to general relativity," Found. Phys. 32, 927 (2002). 17 P. Boonserm et al., " Effective refractive index tensor for weak-field gravity," Class. Q uant. G rav. 22, 1905 (2005). 18 X.-H. Ye and Q . Lin, " A sim ple optical analysis of gravitational lensing," J. M odern Optics 55, no. 7, 1119 (2008). 19 H. E. Puthoff, E. W . Davis and C. M accone, " Levi-Civita effect in the polarizable vacuum (PV ) representation of general relativity," G en. R elativ. G rav. 37, 483 (2005). 20 A. P. Lightm an and D. P. Lee, " R estricted proof that the weak equivalence principle im plies the Einstein equivalence principle," Phys. R ev. D 8, 364 (1973). 21 C. W . M isner, K. S. Thorne and J. A. W heeler, G ravitation, Freem an, San Francisco (1973), p. 5. 22 E. W . Davis, " Chapter 15: Faster-than-Light Approaches in G eneral R elativity," Frontiers of Propulsion Science, Progress in Astronautics and Aeronautics Series, V ol. 227, eds. M . G . M illis and E. W . Davis, AIAA Press, R eston, V A, pp. 473 (2009). 12 U N CLASSI FI E D / /4OA^H4«MM«^N^