AAWSAP DIRD Advanced Space Propulsion Based on Vacuum Spacetime Metric Engineering March 29 2010
⚠ Texto extraído por OCR de la fuente oficial — puede contener errores de reconocimiento. El documento original es la autoridad.
UNCLASSIFIED/ fFOR OFFI&il.t.k WIiii 8Plklf
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 OfflelAL 1:191!!! eHtY
UNCLASSIFIED/ /F8fl 8FFIOIAL ~SE er•LY
Advanced Space Propulsion based on Vacuum (Spacetime
Metric) Engineering
Prepared by:
Acquisition Support Division (DW0-3)
Defense Warning Office
Directorate for Analysis
Defense Intelligence Agency
Author:
AAP Person 57
Administrative Note
COPYRI GHT WARNING: Further dissemination of the photographs in this publication is not authorized.
Th is product is one in a series of advanced t echnology reports produced in FY 2009
under the Defense Intell igence Agency, Defense Warning Office's Advanced Aerospace
Weapon System Applications (AAWSA) Program . Comments or questions pertaining to
this document should be addressed to lAAP Person 1 !,
AAWSA Program
Manager, Defense Intell igence Agency, ATTN: CLAR/ DWO-3, Bldg 6000, Washington,
DC 20340-5100 .
UNCLASSIFIED//FQR: &FFIGlilJL W&li &tlli?f
UNCLASSIFIED//POR OPPICIAL l191!! OIILI
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
UNCLASSIFIED/ /FOR 8FPl@IAL tt:!I!! OHL t
UNCLASSIFIED/ ,'FOR 8ffl@IAL l!tSI! OHL¥
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: OFFI&ilal.k Wii ,u1k¥
UNCLASSIFIED/ /POlt Offl@IAL WSli OP.LY
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/ /FOA OFFl&illik: W&li 0 .. LY
UNCLASSIFIED/ ,'FOR OFFI@IAL YSE OHL¥
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 spacefl ight 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 gµ ., is given by
ds 2 = g µvdx"dx" {l)
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)
c/s 2 = c2 dt 2 - (dx2 +dy2 +dx 2 ) (2)
where the identification dx 0 = cdt , dx' = dx, dx 2 = dy , dx3 = dz is made, with metric
tensor coefficients g00 = 1, g I I = g 22 = g 33 = - 1, gµ v = 0 for µ --t= v.
For spherical coordinates in ordinary Minkowski flat spacetime
ds 2 = c2 dt 2 -dr2 - r 2 d0 2 - r 2 sin 2 0dql (3)
where dx 0 = cc/t , dx' = dr, dx 2 = d0, dx 3 =d(f), with metric tensor coefficients g 00 =1,
g 11 = -1, g22 = -r2 , g 33 = -r 2 sin 2 0, gµv = O for µ -t; v.
As an example of spacetime alteration, in a spacetime altered by the presence of a
spherical mass distribution mat the origin (Schwarzschild-type solution), the above can
be transformed into (Reference 10)
1
UNCLASSIFIED/ /FOR OFFI&I.t.k Wliliii 8Nk¥
UNCLASSIFIED/ /POI\ orr1e1At l:ISE 8Ptklf
with the metric tensor coefficients gµ v 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)
with the metric tensor coefficients gµv 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 t he metric tensor can be generated for arbitrarily engineered
spacetimes, characterized by an appropriate set of spacetime variables d.x:11 and metric
tensor coefficients g µ 11 • 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 dxµ and time intervals dt, defined in a flat Minkowski spacetime, the spacetime
of common experience. In spacetime-altered regions, dx;i 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 ✓-8µ v dxµ and time
intervals .j'i;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
reg ion result in an altered velocity of light, from an eng ineering 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. 8FFl@IAL U91! f>flt I
UNCLASSIFIED/ /FOR 8Ffl@IAL tl.!I!! er•t a
TIMEINTERVAL, FREQUENCY, ENERGY
Begin by considering the case where ~ < 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 ..[i";;dt < dt; thus an interval of time dt between two events in an undistorted
spacetime remote 1 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,
.[i";;;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
M/
emissions) that takes a time !:::.t in unaltered spacetime slows to !).t ➔ .ji;, when
occurring within the altered spacetime. Conversely, under conditions (for example,
metric engineering) for which Ji;; > 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 w is given by m➔ m.Jg;; , our second entry in
Table 1. This accounts, for example, for the redshifting of atomic emissions from dense
masses where ..[i";; < 1. Conversely, under conditions for which Ji;; > 1, blueshifting of
emissions would occur. In addition, given that quanta of energy are given by E = hm,
energy scales with Jg;; , as does frequency, E ➔ E.jg;,, our third entry in the table.
Depending on the value of .Ji: 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/ j POI\ OPPIEIICL tl.!I!! BHLY
UNCLASSIFIED/ /FOR OFFI@IAL 1::191!! 8HLY
Table 1. Metric Effects on Physical Processes in an Altered Spacetime as
Interpreted by a Remote (Unaltered Spacetime) Observer
Variable Typical Stellar Mass Spacetime-Engineered
(goo < 1, lg11 I > 1) Metric
(g(X) > 1, lg11 I < 1)
. M ➔ tit/ ji:i Processes (for example, Processes (for example,
Time Interval 00 clocks) run slower clocks) run faster
w ➔ wji;; Redshift toward lower Bluesh ift toward higher
Frequency 00 frequencies frequencies
E ➔ E.ji;; Energy states lowered Energy states raised
Enerqv 00
Objects (for example, Objects (for example,
Spa t .,a 1 !::.r ➔ t::.r/~ rulers) shrink rulers) expand
Velocity vL = c ➔ c.Jgoo / - 811 Effective vL < c Effective vL > c
Mass m= E/ c2 ➔ (-gIJ.Ji:;)m Effective mass increases Effective mass decreases
Gravitational "force"
"Gravitational" "Antig ravitationa I"
f(goo ,81 1)
Spatial Interval
Again, by considering the case typical for an altered spacetime metric in the vici nity of,
say, a stellar mass, then ~ > 1 for the radia l dimension x 1 = r, as expressed by the
second term in Equation ( 4 ). Therefore, local measurements with physical rulers within
the altered spacetime yield a spatial interval ~ d r > 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 th is one can rightly infer that, relatively speaking, rulers (atom ic
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, atom ic
orbit) that possesses a measure !::.r in unaltered spacetime shrinks to !::..r ➔ t::.r/ ~
when placed with in the altered spacetime . Conversely, under conditions for which
~ < 1, objects wou ld expand-thus the fourth ent ry for the table of physical effects.
Velocity of Light in Spacetime-Altered Regions
Interior to a spacetime reg ion altered by, say, a dense mass (for example, a black
hole), the locally measured velocity of light c in, say, the x 1 = r direction is given by the
ratio of locally measured (proper) distance/time intervals for a propagating light signal
( Reference 13).
; .J-g,1 dr
V = --- = C (6)
L ..{i;;dt
4
UNCLASSIFIED/ /FOR OFFI@IAL l::ISE OHL¥
UNCLASSIFIED/ /Pelt err1e1J11t l!ISl!!! 8HL'I
From a viewpoint exterior to the region, however, from the above one finds that the
remotely observed coordinate ratio measurement yields a different value
(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.Jg 00 /-g I 1 < 1. Conversely,
under (metric engineering) conditions for which .Jg /-g > 1, the velocity of light-and
00 11
exotic-technology craft velocities that 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
(8)
where n is an effective refractive index of the (spacetime-altered) vacuum. This widely
known result has resu lted 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/.Jµ 0c0 ,
where µ 0 and &0 are the magnetic permeability and dielectric permittivity of undistorted
vacuum space (µ 0 = 4Jr x 10-7 H/m and &0 = 8.854 x l0- 12 F/m) . The generation of an
effective refractive index n = .j- g 11 / g 00 =t:- I by technological means can from an
engineering viewpoint be interpreted as manipulation of the vacuum parameters µ 0 and
&0 . In GR theory, such variations in µ 0, &0 and hence the velocity of light, c, are often
treated in terms of a "THsµ" 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.
5
UNCLASSIFIED/ /FOR OFFI@IAI: WSE OHl:l/
UNCLASSIFIED/ /FOR OFFI@IAk WSI: OPtklf
Effective Mass in Spacetime- Altered Regions
In a spacetime-altered region, E = mc 2 still holds in terms of local ("proper coord inate")
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( - g 11 )/-Jg;;;, provid ing a
sixth entry for our table. Depending on the values of g00 and g 11 , 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 th is case
as expressed in Equation ( 4) above. Therefore, in terms of the metric coefficients,
lg I
gravitational attraction in this case derives from the cond ition that g 00 < 1, 11 > 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 g 11 could be reversed would be
considered (loosely) as antigravitational in nature. A seventh entry in Table 1
represents these features of metr ic sign ificance .
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/ fg; re lative to the remote observer. Near a dense mass, for example, -Jg;;;< 1, and
6
UNCLASSIFIED/ /FOR [email protected] WSI: OHk\f
UNCLASSIFIED/ j FOR OFFICI"L U.!I! Grit I
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
with in such a temporally modified field wou ld, 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 wh ich Ji::>
1, t ime flow with in the altered spacetime reg ion would appear sped up
to an externa l observer, while to an internal observer externa l time flow would appear
to be in slow mot ion. A corollary would be that within the spacetime-altered region,
normal environmental sounds from outside the reg ion might cease to be registered,
since externa l sounds could under these conditions redshift below the auditory range.
An additional implication of t ime 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, observ ing the external
environment to be in relat ive slow motion, it wou ld not be surprising to consider that
one's relatively modest changes in motion would appear abrupt to an external observer.
Based on the second ent ry in Table 1 (frequency), yet another implication of an
accelerated timeframe due to craft-associated metric engineering that leads t o
Ji::> 1, frequencies associated with the craft would fo r a remote observer appear to
be blueshifted. Corollary to observation of such a craft is the possibility that there
wou ld be a brightening of luminosity due to the heat spectrum blueshifting up into the
visible portion of the spectrum (see Figure 1).
inf1 red
visible
l
:.. M
(shifted infrared)
41 ~
$ 3:
0 visible 0
Q. Q.
~CJ
l"
C
CJ
41 41
0. 0.
V) V)
Frequency w Frequency w
Figure 1. Blueshifting of Infrared Heat Power Spectrum
With regard to the third ent ry in Table 1 (energy), in a spacetime-altered region,
energy scales as Ji: relative to a remote observer in an undistorted spacetime. I n the
vicinity of a dense mass where Jg;;< 1, the consequent reduction of energy bonds
correlates with observed redsh ifts of emission. For engineered spacetimes associated
with advanced craft technology in wh ich ,Ji;;;> I (accelerated timeframe case), a
2 In t he ca se of approach to a black hole, to stop altogether.
7
UNCLASSIFIED/ /FOR. OFFlelJltt t:ISI! OHL'I
UNCLASSIFIED/ /FOR 0FFI€1Ak Ulili ,u1k¥
craft's material properties would appear "hardened" relative t o the environment owing
to the increased bind ing energies of atoms in its material structure. Such a craft cou ld,
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 l/ Fi::. In the vicin ity of a
dense mass M , > 1, in which case an object within the altered spacetime region
appears to a remote observer t o have shrunk. As a corollary , metric eng ineering
associated with an advanced aerospace craft to produce this effect could in principle
result in a large craft with a spacious interior appea ring to an external observer to be
relatively small. Additional dimensiona l 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;_ = 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 v1
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 signa l
approaches a dense mass (for example, a black hole.) In an engineered spacetime in
which g 00 > 1, lg11 1< 1, however, the effective velocity of light v~ 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 ➔ .J g 00 /-g 11v -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. Th is opens
up the possibility of transport at superluminal velocities (as measured by an external
observer) without violation of the velocity-of-light constraint with in the spacetime
altered region, a feature attractive for interstellar travel. Th is is the basis for discussion
of warp drives and wormholes in the GR literature (References 2-6). Therefore,
although present t echnological 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. 8PFISI.t.k U&li 0Plk¥
UNCLASSIFIED/ /P81t errl@IAL l!ISI!!! 8HL'I
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 bend ing 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 I
space (well-defined boundaries, light
trapped within, bending or term ination
in mid-space). Additional observations
might include apparent changes in size
,~
or shape (changes in lensing Figure 2. Light-Bending in a Spacetime-Altered
Region
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.
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/ /P81t err1e11et U:!I!!! ()fl[ I
UNCLASSIFIED/ /POil OFFIEJIAk W&lii QNL¥
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 eng ineering. 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 t ime 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,, v) 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 OFFI&I.t.k W&li ONkY
UNCLASSIFIED/ /FOR. err1e1At l:191!! er•t I
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
' See Reference 1 for a comprehensive introduction to the subject with contributions from lead scientists from
around the globe.
11
UNCLASSIFIED/ ,'FOR OFFI@IAI: WSE OHl:l/
UNCLASSIFIED/ /P91t 9Ffl@IAL l:ISIE 8HLY
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-a-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-l ike 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 eng ineering 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 examp le, a series of essays in the compendium Frontiers of Propulsion Science, Eds. M. G. Mill is 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. 5. 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. 5. Morris, K. 5. 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 5 . M. Mahajan, A. Qadir and P. M. Valanju, " Reintroducing the concept of 'force' into relativity theory," II Nuovo
Cimento 65B, 404 (1981).
13 R. Klauber, "Physical components, coordinate components, and the speed of light," www.arXiv :gr-qc/0105071 vl
(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. 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 polarizab le 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. 5. Thorne and J. A. Wheeler, Gravitation, Freeman, San Francisco (1973), p. 5.
22 E.W. Davis, " Chapter 15: Faster-than-Light Approaches in Genera l 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/ /FOA OFFICiI.\k Wliliii O,.k¥
Fuente: archivo UAP oficial del gobierno de EE.UU. (dominio público) · war.gov/ufo ↗ · ver en el archivo de Nodriza