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DIA Defense Intelligence Reference Document DIA-08-1003-015 (29 March 2010), prepared under the AAWSA program, surveys how engineering the spacetime metric could in principle yield propulsion, time-rate, mass, and gravity effects for advanced aerospace craft.
DIA AATIP Defense Intelligence Reference Documents (38 DIRDs), FOIA Release, DIRD_15-DIRD_Advanced_Space_Propulsion_Based_on_Vacuum_Spacetime_Metric_Engineer.pdf
DIA Defense Intelligence Reference Document DIA-08-1003-015 (29 March 2010), prepared under the AAWSA program, surveys how engineering the spacetime metric could in principle yield propulsion, time-rate, mass, and gravity effects for advanced aerospace craft.
This 17-page UNCLASSIFIED/FOUO paper, dated 29 March 2010 with an information cutoff of 1 December 2009, was produced for the Defense Intelligence Agency's Advanced Aerospace Weapon System Applications (AAWSA) Program. It applies the metric tensor formalism of general relativity to catalog physical effects (time dilation, frequency shift, energy scaling, length change, effective velocity of light, effective mass, and gravity/antigravity) that would arise in a spacetime-altered region around a notional craft. The author grounds the work in mainstream theoretical physics, citing Nobelist T. D. Lee on 'vacuum engineering' and Frank Wilczek on the vacuum as 'the central structure of modern physics,' while acknowledging that required energy densities 'exceed by many orders of magnitude values achievable with existing engineering techniques.' Table 1 lays out, for a 'Spacetime-Engineered Metric (g00 > 1, |g11| < 1),' clocks running faster, blueshifted emissions, expanded rulers, superluminal effective light velocity, decreased effective mass, and antigravitational behavior.
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.p.4
The vacuum is fast emerging as the central structure of modern physicsp.4
the required energy densities predicted by present theory exceed by many orders of magnitude values achievable with existing engineering techniques.p.5
a technology exists that can control and manipulate (that is, engineer) the spacetime metric to advantage.p.6
Note that the effect on the metric due to charge Q differs in sign from that due to mass m, leading to what in the literature has been referred to as electrogravitic repulsionp.7
matter tells space how to curve, and space tells matter how to move.p.11
an individual who has spent time within such a temporally modified field would, when returned to the normal environment, find that more time had passed than could be experientially accounted for.p.12
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UNCLASSIFIED/FOR OFFICIAL USE ONLY Defense Intelligence Reference Document Acquisition Threat Support 29 March 2010 ICOD: 1 December 2009 DIA-08-1003-015 Advanced Space Propulsion Based on Vacuum (Spacetime Metric) Engineering UNCLASSIFIED/FOR OFFICIAL USE ONLY
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UNCLASSIFIED/FOR OFFICIAL USE ONLY Advanced Space Propulsion based on Vacuum (Spacetime Metric) Engineering Prepared by: (b)(3):10 USC 424 Defense Intelligence Agency Author: (b)(6) Administrative Note COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency, (b)(3):10 USC 424 Advanced Aerospace Weapon System Applications (AAWSA) Program. Comments or questions pertaining to this document should be addressed to (b)(3):10 USC 424;(b)(6) AAWSA Program Manager, Defense Intelligence Agency, ATTN: (b)(3):10 USC 424 Bldg 6000, Washington, DC 20340-5100. i UNCLASSIFIED/FOR OFFICIAL USE ONLY
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UNCLASSIFIED/FOR OFFICIAL USE ONLY relative to the reference frame of background space, energy bonds of materials strengthened (that is, hardened) relative to the background environment, a decrease in effective mass vis-à-vis the environment, an accelerated timeframe that would permit rapid trajectory changes relative to the background rest frame without undue internal stress, and the generation of gravity-like forces of arbitrary geometry—all on the basis of restructuring the vacuum spacetime variables. As avant garde as such features appear to be, they are totally in conformance with the principles of general relativity as currently understood. A remaining challenge is to develop insight into the technological designs by which such vacuum restructuring can be generated on the scale required to implement the necessary spacetime modifications. Despite the challenges, sample calculations as presented herein indicate the direction of potentially useful trends derivable on the basis of the application of GR principles as embodied in a metric 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 premature to even guess about an optimum strategy, let alone attempt to form a critical path for the engineering development of such technologies. Nonetheless, only through rigorous inquiry into such concepts can one hope to arrive at a proper assessment of the possibilities inherent in the evolution of advanced spaceflight technologies. ¹ See, for example, a series of essays in the compendium Frontiers of Propulsion Science, Eds. M. G. Millis and E. W. Davis, AIAA Press, Reston, Virginia (2009). ² M. Alcubierre, "The warp drive: Hyper-fast travel within general relativity," Class. Quantum Grav. 11, p. L73 (1994). ³ H. E. Puthoff, "SETI, the velocity-of-light limitation, and the Alcubierre warp drive: An integrating overview," Physics Essays 9, p. 156 (1996). ⁴ M. S. Morris and K. S. Thorne, "Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity," Am. J. Phys. 56, pp. 395-412 (1988). ⁵ M. Visser, Lorentzian Wormholes: From Einstein to Hawking, AIP Press, New York, 1995. ⁶ M. S. Morris, K. S. Thorne and U. Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys. Rev. Lett. 61, p. 1446 (1988). ⁷ T. D. Lee, Particle Physics and Introduction to Field Theory, Harwood Academic Press, London (1988). ⁸ The Philosophy of Vacuum, Eds. S. Saunders and H. R. Brown, Clarendon Press, Oxford (1991). ⁹ F. Wilczek, The Lightness of Being: Mass, Ether and the Unification of Forces, Basic Books, New York (2008). ¹⁰ A. Logunov and M. Mestvirishvili, The Relativistic Theory of Gravitation, Mir Publ., Moscow (1989), p. 76. ¹¹ Op. cit., p. 83. ¹² S. M. Mahajan, A. Qadir and P. M. Valanju, "Reintroducing the concept of 'force' into relativity theory," Il Nuovo Cimento 65B, 404 (1981). ¹³ R. Klauber, "Physical components, coordinate components, and the speed of light," www.arXiv:gr-qc/0105071 v1 (18 May 2001). ¹⁴ F. de Felice, "On the gravitational field acting as an optical medium," Gen. Rel. and Grav. 2, 347 (1971). ¹⁵ K. Nandi and A. Islam, "On the optical-mechanical 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. Quant. Grav. 22, 1905 (2005). ¹⁸ X.-H. Ye and Q. Lin, "A simple optical analysis of gravitational lensing," J. Modern Optics 55, no. 7, 1119 (2008). ¹⁹ H. E. Puthoff, E. W. Davis and C. Maccone, "Levi-Civita effect in the polarizable vacuum (PV) representation of general relativity," Gen. Relativ. Grav. 37, 483 (2005). ²⁰ A. P. Lightman and D. P. Lee, "Restricted proof that the weak equivalence principle implies the Einstein equivalence principle," Phys. Rev. D 8, 364 (1973). ²¹ C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, Freeman, San Francisco (1973), p. 5. ²² E. W. Davis, "Chapter 15: Faster-than-Light Approaches in General Relativity," Frontiers of Propulsion Science, Progress in Astronautics and Aeronautics Series, Vol. 227, eds. M. G. Millis and E. W. Davis, AIAA Press, Reston, VA, pp. 473 (2009). 12 UNCLASSIFIED/FOR OFFICIAL USE ONLY
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UNCLASSIFIED/FOR OFFICIAL USE ONLY Defense Intelligence Reference Document Acquisition Threat Support 29 March 2010 ICOD: 1 December 2009 DIA-08-1003-015 Advanced Space Propulsion Based on Vacuum (Spacetime Metric) Engineering UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY Advanced Space Propulsion based on Vacuum (Spacetime Metric) Engineering Prepared by: (b)(3):10 USC 424 Defense Intelligence Agency Author: (b)(6) Administrative Note COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency, (b)(3):10 USC 424 Advanced Aerospace Weapon System Applications (AAWSA) Program. Comments or questions pertaining to this document should be addressed to (b)(3):10 USC 424;(b)(6) AAWSA Program Manager, Defense Intelligence Agency, ATTN: (b)(3):10 USC 424 Bldg 6000, Washington, DC 20340-5100. i UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY
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
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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 Particle Physics and Introduction to Field Theory (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 The
Lightness of Being: Mass, Ether and the Unification 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
UNCLASSIFIED/FOR OFFICIAL USE ONLYUNCLASSIFIED/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 UNCLASSIFIED/FOR OFFICIAL USE ONLY
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I. Spacetime Modification – Metric Tensor Approach
Despite the daunting energy requirements to restructure the spacetime metric to a
significant degree, one can investigate the forms that such restructuring would take to
be useful for spaceflight applications and determine their corollary attributes and
consequences. Thus we embark on a "Blue Sky," general-relativity-for-engineers
approach, as it were.
As a mathematical evaluation tool, the metric tensor that describes the measurement of
spacetime intervals is used. Such an approach, well known from studies in general
relativity (GR), has the advantage of being model independent—that is, it does not
depend on knowledge of the specific mechanisms or dynamics that result in spacetime
alterations but rather only assumes that a technology exists that can control and
manipulate (that is, engineer) the spacetime metric to advantage. Before discussing the
predicted characteristics of such engineered spacetimes, beginning in Section III, a
brief mathematical digression for those interested in the mathematical structure behind
the discussion to follow is introduced.
As a brief introduction, the expression for the four-dimensional line element ds² in
terms of the metric tensor g_μν is given by
ds² = g_μν dx^μ dx^ν (1)
where summation over repeated indices is assumed unless otherwise indicated. In
ordinary Minkowski flat spacetime, a (four-dimensional) infinitesimal interval ds is given
by the expression (in Cartesian coordinates)
ds² = c²dt² − (dx² + dy² + dz²) (2)
where the identification dx⁰ = cdt, dx¹ = dx, dx² = dy, dx³ = dz is made, with metric
tensor coefficients g₀₀ = 1, g₁₁ = g₂₂ = g₃₃ = −1, g_μν = 0 for μ ≠ ν.
For spherical coordinates in ordinary Minkowski flat spacetime
ds² = c²dt² − dr² − r²dθ² − r² sin² θ dφ² (3)
where dx⁰ = cdt, dx¹ = dr, dx² = dθ, dx³ = dφ, with metric tensor coefficients g₀₀ = 1,
g₁₁ = −1, g₂₂ = −r², g₃₃ = −r² sin² θ, g_μν = 0 for μ ≠ ν.
As an example of spacetime alteration, in a spacetime altered by the presence of a
spherical mass distribution m at the origin (Schwarzschild-type solution), the above can
be transformed into (Reference 10)
ds² = ((1 − Gm/rc²)/(1 + Gm/rc²)) c²dt² − ((1 − Gm/rc²)/(1 + Gm/rc²))⁻¹ dr² − (1 + Gm/rc²)² r² (dθ² + sin² θ dφ²) (4)
1
UNCLASSIFIED/FOR OFFICIAL USE ONLYUNCLASSIFIED/FOR OFFICIAL USE ONLY with the metric tensor coefficients g_μν modifying the Minkowski flat-spacetime intervals dt, dr, and so forth, accordingly. As another example of spacetime alteration, in a spacetime altered by the presence of a charged spherical mass distribution (Q,m) at the origin (Reissner-Nordstrom-type solution), the above can be transformed into (Reference 11) ds² = ((1 − Gm/rc² + Q²G/4πε₀c⁴) / (1 + Gm/rc² + Q²G/(r²(1 + Gm/rc²)²))) c²dt² − ((1 − Gm/rc² + Q²G/4πε₀c⁴) / (1 + Gm/rc² + Q²G/(r²(1 + Gm/rc²)²)))⁻¹ dr² (5) −(1 + Gm/rc²)² r² (dθ² + sin² θ dφ²) with the metric tensor coefficients g_μν again changed accordingly. Note that the effect on the metric due to charge Q differs in sign from that due to mass m, leading to what in the literature has been referred to as electrogravitic repulsion (Reference 12). 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 solutions for the metric tensor can be generated for arbitrarily engineered spacetimes, characterized by an appropriate set of spacetime variables dx^μ and metric tensor coefficients g_μν. Of significance now is to identify the associated physical effects and to develop a table of such effects for quick reference. We begin by simply cataloging metric effects—that is, physical effects associated with alteration of spacetime 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 spacetime, measurements with physical rods and clocks yield spatial intervals dx^μ and time intervals dt, defined in a flat Minkowski spacetime, the spacetime of common experience. In spacetime-altered regions, dx^μ and dt are still chosen as natural coordinate intervals to represent a coordinate map, but now local measurements with physical rods and clocks yield spatial intervals √−g_μν·dx^μ and time intervals √g₀₀ dt, so-called proper coordinate intervals. From these relationships a table of associated physical effects to be expected in spacetime regions altered by either natural or advanced technological means can be generated. Given that, as seen from an unaltered region, alteration of spatial and temporal intervals in a spacetime-altered region result in an altered velocity of light, from an engineering viewpoint such alterations can in essence be understood in terms of a variable refractive index of the vacuum (see Section III below) that affects all measurement. 2 UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY TIME INTERVAL, FREQUENCY, ENERGY Begin by considering the case where √g₀₀ < 1, typical for an altered spacetime metric in the vicinity of, say, a stellar mass, as expressed by the leading term in Equation (4). Local measurements with physical clocks within the altered spacetime yield a time interval √g₀₀ dt < dt; thus an interval of time dt between two events in an undistorted spacetime remote¹ from the mass—say, 10 seconds—would be judged by local (proper) measurement from within the altered spacetime to occur in a lesser time interval, √g₀₀ dt < dt—say, 5 seconds. From this one can rightly infer that, relatively speaking, clocks (atomic processes and so forth) within the altered spacetime run slower. Given this result, a physical process (for example, interval between clock ticks, atomic emissions) that takes a time Δt in unaltered spacetime slows to Δt → Δt/√g₀₀ when occurring within the altered spacetime. Conversely, under conditions (for example, metric engineering) for which √g₀₀ > 1, processes within the spacetime-altered region are sped up. Thus the first entry for a table of physical effects (see Table 1) is made. Given that frequency measurements are the reciprocal of time duration measurements, the associated expression for frequency ω is given by ω → ω√g₀₀, our second entry in Table 1. This accounts, for example, for the redshifting of atomic emissions from dense masses where √g₀₀ < 1. Conversely, under conditions for which √g₀₀ > 1, blueshifting of emissions would occur. In addition, given that quanta of energy are given by E = ℏω, energy scales with √g₀₀, as does frequency, E → E√g₀₀, our third entry in the table. Depending on the value of √g₀₀ in the spacetime-altered region, energy states may be raised or lowered relative to an unaltered spacetime region. ¹ An observer at "infinity." 3 UNCLASSIFIED/FOR OFFICIAL USE ONLY
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Table 1. Metric Effects on Physical Processes in an Altered Spacetime as
Interpreted by a Remote (Unaltered Spacetime) Observer
Variable | Typical Stellar Mass (g₀₀ < 1, |g₁₁| > 1) | Spacetime-Engineered Metric (g₀₀ > 1, |g₁₁| < 1)
Time Interval Δt → Δt/√g₀₀ | Processes (for example, clocks) run slower | Processes (for example, clocks) run faster
Frequency ω → ω√g₀₀ | Redshift toward lower frequencies | Blueshift toward higher frequencies
Energy E → E√g₀₀ | Energy states lowered | Energy states raised
Spatial Δr → Δr/√−g₁₁ | Objects (for example, rulers) shrink | Objects (for example, rulers) expand
Velocity v_L = c → c√g₀₀/−g₁₁ | Effective v_L < c | Effective v_L > c
Mass m = E/c² → (−g₁₁/√g₀₀)m | Effective mass increases | Effective mass decreases
Gravitational "force" f(g₀₀, g₁₁) | "Gravitational" | "Antigravitational"
Spatial Interval
Again, by considering the case typical for an altered spacetime metric in the vicinity of,
say, a stellar mass, then √−g₁₁ > 1 for the radial dimension x¹ = r, as expressed by the
second term in Equation (4). Therefore, local measurements with physical rulers within
the altered spacetime yield a spatial interval √−g₁₁ dr > dr; thus a spatial interval dr
between two locations in an undistorted spacetime—say, remote from the mass—would
be judged by local (proper) measurement from within the altered spacetime to be
greater. From this one can rightly infer that, relatively speaking, rulers (atomic
spacings and so forth) within the altered spacetime are shrunken relative to their
values in unaltered spacetime. Given this result, a physical object (for example, atomic
orbit) that possesses a measure Δr in unaltered spacetime shrinks to Δr → Δr/√−g₁₁
when placed within the altered spacetime. Conversely, under conditions for which
√−g₁₁ < 1, objects would expand—thus the fourth entry for the table of physical effects.
Velocity of Light in Spacetime-Altered Regions
Interior to a spacetime region altered by, say, a dense mass (for example, a black
hole), the locally measured velocity of light c in, say, the x¹ = r direction is given by the
ratio of locally measured (proper) distance/time intervals for a propagating light signal
(Reference 13).
v_L = √−g₁₁ dr / √g₀₀ dt = c (6)
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From a viewpoint exterior to the region, however, from the above one finds that the
remotely observed coordinate ratio measurement yields a different value
v_L^r = dr/dt = √g₀₀/−g₁₁ · c (7)
Therefore, although a local measurement with physical rods and clocks yields c, an
observer in an exterior reference frame remote from the mass speaks of light "slowing
down" on a radial approach to the mass owing to the ratio √g₀₀/−g₁₁ < 1. Conversely,
under (metric engineering) conditions for which √g₀₀/−g₁₁ > 1, the velocity of light—and
exotic-technology craft velocities that would obey similar formulas—would appear
superluminal in the exterior frame. This gives our fifth entry for the table of physical
effects.
Refractive Index Modeling
Given that velocity-of-light effects in a spacetime-altered region, as viewed from an
external frame, are governed by Equation (7), it is seen that the effect of spacetime
alteration on light propagation can be expressed in terms of an optical refractive index
n, defined by
v_L^r = c/n, n = √−g₁₁/g₀₀ (8)
where n is an effective refractive index of the (spacetime-altered) vacuum. This widely
known result has resulted in the development of refractive index models for GR
(References 14-17) that have found application in problems such as gravitational
lensing (Reference 18). The estimated electric or magnetic field strengths required to
generate a given refractive index change given by standard GR theory (the Levi-Civita
Effect) can be found in (Reference 19).
In engineering terms, the velocity of light c is given by the expression c = 1/√μ₀ε₀,
where μ₀ and ε₀ are the magnetic permeability and dielectric permittivity of undistorted
vacuum space (μ₀ = 4π × 10⁻⁷ H/m and ε₀ = 8.854 × 10⁻¹² F/m). The generation of an
effective refractive index n = √−g₁₁/g₀₀ ≠ 1 by technological means can from an
engineering viewpoint be interpreted as manipulation of the vacuum parameters μ₀ and
ε₀. In GR theory, such variations in μ₀, ε₀ and hence the velocity of light, c, are often
treated in terms of a "THεμ" formalism used in comparative studies of gravitational
theories (Reference 20).
As discussed below, a number of striking effects can be anticipated in certain
engineered spacetime regions.
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Effective Mass in Spacetime-Altered Regions
In a spacetime-altered region, E = mc² still holds in terms of local ("proper coordinate")
measurements, but now energy E and the velocity of light c take on altered values as
observed from an exterior (undistorted) spacetime region. Reference to the definitions
for E and c in Table 1 permits one to define an effective mass as seen from the exterior
undistorted region as therefore taking on the value m → m(−g₁₁)/√g₀₀, providing a
sixth entry for our table. Depending on the values of g₀₀ and g₁₁, the effective mass
may be seen from the viewpoint of an observer in an undistorted spacetime region to
have either increased or decreased.
Gravity/Antigravity "Forces"
Strictly speaking, from the GR point of view, there are no gravitational "forces" but
rather (in the words of GR theorist John Wheeler) "matter tells space how to curve, and
space tells matter how to move." (Reference 21) As a result, Newton's law of
gravitational attraction to a central mass is therefore interpreted in terms of the
spacetime structure as expressed in terms of the metric tensor coefficients, in this case
as expressed in Equation (4) above. Therefore, in terms of the metric coefficients,
gravitational attraction in this case derives from the condition that g₀₀ < 1, |g₁₁| > 1. As
for the possibility for generating "antigravitational forces," noted in equation (5),
inclusion of the effects of charge led to metric tensor contributions counter to the
effects of mass—that is, to electrogravitic repulsion. This reveals that conditions under
which, say, the signs of the coefficients g₀₀ and g₁₁ could be reversed would be
considered (loosely) as antigravitational in nature. A seventh entry in Table 1
represents these features of metric significance.
III. Significance of Physical Effects Applicable to Advanced
Aerospace Craft Technologies as a Function of Metric
Tensor Coefficients
As in Section III, metric tensor coefficients define the relationship between locally and
remotely observed (that is, spacetime-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 spacetime variables. The expressions listed indicate specific spacetime
alteration effects, whether owing to natural causes (for example, the presence of a
planetary or stellar mass) or as a result of metric engineering by advanced
technological means as might be anticipated in the development and deployment of
advanced aerospace craft.
TIME ALTERATION
With regard to the first table entry (time interval), in a spacetime-altered region, time
intervals are seen by a remote (unaltered spacetime) observer to vary as
1/√g₀₀ relative to the remote observer. Near a dense mass, for example, √g₀₀ < 1, and
6
UNCLASSIFIED/FOR OFFICIAL USE ONLYUNCLASSIFIED/FOR OFFICIAL USE ONLY therefore time intervals are seen as lengthening and processes as running slower,² one consequence of which is redshift of emission lines. Should such a time-slowed condition be engineered in an advanced aerospace application, an individual who has spent time within such a temporally modified field would, when returned to the normal environment, find that more time had passed than could be experientially accounted for. Conversely, for an engineered spacetime associated with an advanced aerospace craft in which √g₀₀ > 1, time flow within the altered spacetime region would appear sped up to an external observer, while to an internal observer external time flow would appear to be in slow motion. A corollary would be that within the spacetime-altered region, normal environmental sounds from outside the region might cease to be registered, since external sounds could under these conditions redshift below the auditory range. An additional implication of time speedup within the frame of an exotic craft technology is that its flightpath that might seem precipitous from an external viewpoint (for example, sudden acceleration or deceleration) would be experienced as much less so by the craft's occupants. From the occupants' viewpoint, observing the external environment to be in relative slow motion, it would not be surprising to consider that one's relatively modest changes in motion would appear abrupt to an external observer. Based on the second entry in Table 1 (frequency), yet another implication of an accelerated timeframe due to craft-associated metric engineering that leads to √g₀₀ > 1, frequencies associated with the craft would for a remote observer appear to be blueshifted. Corollary to observation of such a craft is the possibility that there would be a brightening of luminosity due to the heat spectrum blueshifting up into the visible portion of the spectrum (see Figure 1). [Figure 1: Two graphs side by side showing Spectral Power vs Frequency ω. Left graph shows infrared peak with visible marker to the right. Right graph shows visible (shifted infrared) peak shifted to the right.] Figure 1. Blueshifting of Infrared Heat Power Spectrum With regard to the third entry in Table 1 (energy), in a spacetime-altered region, energy scales as √g₀₀ relative to a remote observer in an undistorted spacetime. In the vicinity of a dense mass where √g₀₀ < 1, the consequent reduction of energy bonds correlates with observed redshifts of emission. For engineered spacetimes associated with advanced craft technology in which √g₀₀ > 1 (accelerated timeframe case), a ² In the case of approach to a black hole, to stop altogether. 7 UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY craft's material properties would appear "hardened" relative to the environment owing to the increased binding energies of atoms in its material structure. Such a craft could, for example, impact water at high velocities without apparent deleterious effects. SPATIAL ALTERATION The fourth entry in Table 1 (spatial measure) indicates the size of an object within an altered spacetime region as seen by a remote observer. The size of, say, a spherical object is seen to have its radial dimension, r, scale as 1/√−g₁₁. In the vicinity of a dense mass √−g₁₁ > 1, in which case an object within the altered spacetime region appears to a remote observer to have shrunk. As a corollary, metric 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 small. Additional dimensional aspects, such as potential dimensional changes, are discussed below in "Refractive Index Effects." VELOCITY OF LIGHT/CRAFT IN SPACETIME-ALTERED REGIONS Interior to a spacetime-altered region, the locally measured velocity of light, v_L = c, is given by the ratio of (locally measured) distance/time intervals for a propagating light signal, as expressed in Equation (6) above. From a viewpoint exterior to the region, however, the observed coordinate ratio measurement can yield a different value v_L^r greater or less than c as given by the fifth entry in Table 1 (velocity). As an example of a measurement less than c, one speaks of light "slowing down" as a light signal approaches a dense mass (for example, a black hole.) In an engineered spacetime in which g₀₀ > 1, |g₁₁| < 1, however, the effective velocity of light v_L^r as measured by an external observer can be > c. Given that velocities in general in different coordinate systems scale as does the velocity of light—that is, v → √g₀₀/−g₁₁ v—for exotic propulsion an engineered spacetime metric can in principle establish a condition in which the trajectory of a craft approaching the velocity of light in its own frame would be observed from an exterior frame to exceed light speed—that is, exhibit motion at superluminal speed. This opens up the possibility of transport at superluminal velocities (as measured by an external observer) without violation of the velocity-of-light constraint within the spacetime- altered region, a feature attractive for interstellar travel. This is the basis for discussion of warp drives and wormholes in the GR literature (References 2-6). Therefore, although present technological facility is far from mature enough to support the development of warp drive and wormhole technologies (Reference 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-time interstellar travel is not fundamentally ruled out by physical principles. 8 UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY REFRACTIVE INDEX EFFECTS When considering metric-engineered spacetime associated with exotic propulsion, a number of corollary side effects associated with refractive index changes of the vacuum structure emerge as possibilities. Expected effects would mimic known refractive index effects in general and can therefore be determined from known phenomena. Indistinct boundary definition associated with "waviness" as observed with heat waves off a desert floor is one example. As another, a light beam may bend (as in the GR example of the bending of starlight as it grazes the sun; see Figure 2) or even terminate in mid-space. Such an observation would exhibit features that under ordinary circumstances would be associated with a high- refractive index optical fiber in normal space (well-defined boundaries, light trapped within, bending or termination in mid-space). Additional observations might include apparent changes in size or shape (changes in lensing magnification parameters). Yet another possibility is the sudden "cloaking" or "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 example, the use of metamaterials, exist as well. [Figure 2: Graph showing a curved line bending downward, representing light-bending in a spacetime-altered region.] Figure 2. Light-Bending in a Spacetime-Altered Region EFFECTIVE MASS IN SPACETIME-ALTERED REGIONS As noted in the preceding sections, spacetime alteration of energy and light-speed measures leads to an associated alteration in the effective mass of an object in a spacetime-altered region as viewed from an external (unaltered) region. Of special interest is the case in which the effective mass is decreased by application of spacetime metric engineering principles as might be expected in the case of metric engineering for spaceflight applications (reference last column in Table 1). Effective reduction of inertial mass as viewed in our frame of reference would appear to mitigate against untoward effects on craft occupants associated with abrupt changes in movement. (The physical principles involved can also be understood in terms of associated coordinate transformation properties as discussed above.) In any case, changes in effective mass associated with engineering of the spacetime metric in a craft's environs can lead to properties advantageous for spaceflight applications. 9 UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY GRAVITY/ANTIGRAVITY/PROPULSION EFFECTS In the GR ansatz gravitational-type forces derive from the spacetime metric, whether determined by natural sources (for example, planetary or stellar masses) or by advanced metric engineering. Fortunately for our consideration of this topic, discussion can be carried out solely based on the form of the metric, independent of the specific mechanisms or dynamics that determine the metric. As one exemplar, consider Alcubierre's formulation of a "warp drive," a spacetime metric solution of Einstein's GR field equation (References 2, 22). Alcubierre derived a spacetime metric motivated by cosmological inflation that would allow arbitrarily short travel times between two distant points in space. The behavior of the warp drive metric provides for the simultaneous 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 spacetime geometry. By appropriate structuring of the metric, the spacecraft can be made 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 spacetime-altered region. Furthermore, the Alcubierre solution showed that the proper (experienced) acceleration along the spaceship's path would be zero, and that the spaceship would suffer no time dilation—highly desirable features for interstellar travel. In order to implement 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 matter—that is, a quantum field having negative energy and/or negative pressure. Although the technical requirements for such are unlikely to be met in the foreseeable future (Reference 22), the exercise nonetheless serves as a good example for showcasing attributes associated with manipulation of the spacetime metric at will. The entire discussion of the possibility of generating a spacetime structure like that of the Alcubierre warp drive is based simply on assuming the form of a metric (that is, g_μν) that exhibits desired characteristics. In like manner, arbitrary spacetime metrics to provide gravity/antigravity/propulsion characteristics can in principle be postulated. What is required for implementation is to determine appropriate sources for their generation, a requirement that must be met before advanced spaceship technology based on vacuum engineering can be realized in practice. The difficulties, challenges, and options for meeting such requirements can be found in the relevant literature (Reference 22). 10 UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY [Figure 3: Three-dimensional mesh visualization showing a warped spacetime surface with labeled regions: "Warp Field" (elevated peak at center-left), "Flat Spacetime" (flat grid region at upper right), and "Gravity Field" (depression at lower right).] Figure 3. Alcubierre Warp Drive Metric Structure IV. Discussion This paper has considered the possibility—even likelihood—that future developments with regard to advanced aerospace technologies will trend in the direction of manipulating the underlying spacetime structure of the vacuum of space itself by processes that can be called vacuum engineering or metric engineering. Far from being simply 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 GR a minimal-assumption, metric tensor approach can be used that is model-independent—that is, it does not depend on knowledge of the specific mechanisms or dynamics that result in spacetime alterations but rather only assumes that a technology exists that can control and manipulate (that is, engineer) the spacetime variables to advantage. Such an approach requires only that the hypothesized spacetime alterations result in effects consonant with the currently known GR physics principles. In the metric engineering approach, the application of the principles gives precise predictions as to what can be expected as spatial and temporal variables are altered from their usual (that is, flat space) structure. Signatures of the predicted contractions and expansions of space, slowdown and speedup of time, alteration of effective mass, speed of light and associated consequences, both as occur in natural phenomena in nature and with regard to spacetimes specifically engineered for advanced aerospace applications, are succinctly summarized in Table 1. Of particular interest with regard to innovative forms of advanced aerospace craft are the features tabulated in the right-hand column of Table 1, features that presumably describe an ideal craft for interstellar travel: an ability to travel at superluminal speeds ³ See Reference 1 for a comprehensive introduction to the subject with contributions from lead scientists from around the globe. 11 UNCLASSIFIED/FOR OFFICIAL USE ONLY
UNCLASSIFIED/FOR OFFICIAL USE ONLY relative to the reference frame of background space, energy bonds of materials strengthened (that is, hardened) relative to the background environment, a decrease in effective mass vis-à-vis the environment, an accelerated timeframe that would permit rapid trajectory changes relative to the background rest frame without undue internal stress, and the generation of gravity-like forces of arbitrary geometry—all on the basis of restructuring the vacuum spacetime variables. As avant garde as such features appear to be, they are totally in conformance with the principles of general relativity as currently understood. A remaining challenge is to develop insight into the technological designs by which such vacuum restructuring can be generated on the scale required to implement the necessary spacetime modifications. Despite the challenges, sample calculations as presented herein indicate the direction of potentially useful trends derivable on the basis of the application of GR principles as embodied in a metric 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 premature to even guess about an optimum strategy, let alone attempt to form a critical path for the engineering development of such technologies. Nonetheless, only through rigorous inquiry into such concepts can one hope to arrive at a proper assessment of the possibilities inherent in the evolution of advanced spaceflight technologies. ¹ See, for example, a series of essays in the compendium Frontiers of Propulsion Science, Eds. M. G. Millis and E. W. Davis, AIAA Press, Reston, Virginia (2009). ² M. Alcubierre, "The warp drive: Hyper-fast travel within general relativity," Class. Quantum Grav. 11, p. L73 (1994). ³ H. E. Puthoff, "SETI, the velocity-of-light limitation, and the Alcubierre warp drive: An integrating overview," Physics Essays 9, p. 156 (1996). ⁴ M. S. Morris and K. S. Thorne, "Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity," Am. J. Phys. 56, pp. 395-412 (1988). ⁵ M. Visser, Lorentzian Wormholes: From Einstein to Hawking, AIP Press, New York, 1995. ⁶ M. S. Morris, K. S. Thorne and U. Yurtsever, "Wormholes, time machines, and the weak energy condition," Phys. Rev. Lett. 61, p. 1446 (1988). ⁷ T. D. Lee, Particle Physics and Introduction to Field Theory, Harwood Academic Press, London (1988). ⁸ The Philosophy of Vacuum, Eds. S. Saunders and H. R. Brown, Clarendon Press, Oxford (1991). ⁹ F. Wilczek, The Lightness of Being: Mass, Ether and the Unification of Forces, Basic Books, New York (2008). ¹⁰ A. Logunov and M. Mestvirishvili, The Relativistic Theory of Gravitation, Mir Publ., Moscow (1989), p. 76. ¹¹ Op. cit., p. 83. ¹² S. M. Mahajan, A. Qadir and P. M. Valanju, "Reintroducing the concept of 'force' into relativity theory," Il Nuovo Cimento 65B, 404 (1981). ¹³ R. Klauber, "Physical components, coordinate components, and the speed of light," www.arXiv:gr-qc/0105071 v1 (18 May 2001). ¹⁴ F. de Felice, "On the gravitational field acting as an optical medium," Gen. Rel. and Grav. 2, 347 (1971). ¹⁵ K. Nandi and A. Islam, "On the optical-mechanical 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. Quant. Grav. 22, 1905 (2005). ¹⁸ X.-H. Ye and Q. Lin, "A simple optical analysis of gravitational lensing," J. Modern Optics 55, no. 7, 1119 (2008). ¹⁹ H. E. Puthoff, E. W. Davis and C. Maccone, "Levi-Civita effect in the polarizable vacuum (PV) representation of general relativity," Gen. Relativ. Grav. 37, 483 (2005). ²⁰ A. P. Lightman and D. P. Lee, "Restricted proof that the weak equivalence principle implies the Einstein equivalence principle," Phys. Rev. D 8, 364 (1973). ²¹ C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, Freeman, San Francisco (1973), p. 5. ²² E. W. Davis, "Chapter 15: Faster-than-Light Approaches in General Relativity," Frontiers of Propulsion Science, Progress in Astronautics and Aeronautics Series, Vol. 227, eds. M. G. Millis and E. W. Davis, AIAA Press, Reston, VA, pp. 473 (2009). 12 UNCLASSIFIED/FOR OFFICIAL USE ONLY