DOW-UAP-D138, AAWSAP DIRD, Warp Drive, Dark Energy, and the Manipulation of Extra Dimensions, April 2010

This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD examines whether a warp-propulsion concept can be grounded in known theoretical physics by linking general-relativistic warp metrics with dark energy, Casimir effects, and higher-dimensional models from string theory and brane cosmology. The paper hypothesizes that if dark energy arises from vacuum effects and originates in extra dimensions, then a future technology capable of manipulating those dimensions might be capable of altering local spacetime expansion to generate a warp bubble. While framed as a method to mitigate the astronomical energy demands of more traditional warp models, the report acknowledges that this concept relies entirely on unverified assumptions; namely, the physical reality, stability, and macroscopic controllability of extra dimensions. Consequently, while the paper draws on mainstream theoretical physics concepts, the speculative chain linking them lacks empirical support and offers no viable engineering pathway toward a functioning propulsion system.

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Defense
Intelligence
Reference
Document
Acquisition Threat Support
2 April 2010
ICOD: 1 December 2009
DIA-08-1004-001
Warp Drive, Dark Energy, and
the Manipulation of Extra
Dimensions
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Warp Drive, Dark Energy, and the Manipulation of Extra
Dimensions
Prepared by:
Acquisition Support Division (DW0-3)
Defense Warning Office
Directorate for Analysis
Defense Intelligence Agency
Authors:
AAP Person 74, AAP Person 58
Administrative Note
COPYRIGHT WARN ING: 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, Defense Warning Office's Advanced Aerospace
Weapon System Applications (AAWSA) Program. Comments or questions pertaining to
l
this document should be addressed to !AAP Person 1 AAWSA Program
Manager, Defense Intelligence Agency, ATTN: CLAR/DWO-3, Bldg 6000, Washington,
DC 20340-5100.
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Contents
Introduction ............................................................................................................v
2. General Relativistic Warp Drives ........................................................................ 1
2.1 Warp Drive Requirements ............................................................................ 2
3. The Cosmological Constant ................................................................................ 4
3.1 Einstein's Equation and the Introduction of/\ .............................................. 4
4. Casimir Energy and the Quantum Vacuum.......................................................... 5
4.1 The Casimir Effect ........................................................................................ 6
5. Extra Space Dimensions ..................................................................................... 8
5.1 Kaluza-Klein Theory ..................................................................................... 8
5.2 Large Extra Dimensions.............................................................................. 10
5.3 Randall Sundrum Brane Models.................................................................. 11
5.4 Extra Dimension Summary ......................................................................... 12
6. Dark Energy as a Higher Dimensional Artifact .................................................. 12
7. Warp Drive and Higher Dimensional Manipulation ........................................... 15
7.1 Adjusting Higher Dimensions for Propulsions ............................................ 16
7.2 The Geometry of Extra Dimensions ............................................................ 17
7.3 Higher Dimensions and Stabilization .......................................................... 17
7.4 Elementary Warp Drive Calculations .......................................................... 20
7.5 Future Experiments.................................................................................... 22
7.6 The Development of the Technology .......................................................... 23
8. Summary.......................................................................................................... 24
Figures
Figure 1. York Extrinsic Time (9-) Plot..................................................................... 1
Figure 2. The Interior Region of Parallel Conducting Plates ................................... 7
Figure 3. Internal Structure of a Seemingly One-Dimensional Object .................... 9
Figure 4. Manipulated Extra Dimension ................................................................ 15
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Figure 5. Artist's Conception of a Futuristic Warp Drive Spacecraft ..................... 16
Figure 6. A Toroidal Higher Dimension ................................................................. 17
Figure 7. A Combination of Phenomenologically Viable Fields .............................. 19
Figure 8. False Vacuum Minima ............................................................................ 19
Figure 9. Thick and Thin Shell Warp Bubble ......................................................... 21
Tables
Table 1. Transit Times to Various Exotic Destinations at 100 Times the Speed of
Light .........................................................................................................vi
Table 2. Negative Energy Required for Warp Bubble (Larger Negative Energy) ..... 3
Table 3. Negative Energy Required for Warp Bubble ............................................ 22
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Warp Drive, Dark Energy, and the Manipulation of Extra
Dimensions
Introduction
If one is to realistically entertain the notion of interstellar exploration in
timeframes of a human lifespan, a dramatic shift in the traditional approach to
spacecraft propulsion is necessary. It has been known and well tested since
the time of Einstein that all matter is restricted to motion at sublight velocities
(<< 3 x 108 m/s, the speed of light, or c), and that as matter approaches the
speed of light, its mass asymptotically approaches infinity. This mass increase
ensures that an infinite amount of energy would be necessary to travel at the
speed of light, and, thus, this speed is impossible to reach and represents an
absolute speed limit to all matter traveling through spacetime.
Even if an engine were designed that could propel a spacecraft to an
appreciable fraction of light speed, travel to even the closest stars would take
many decades in the frame of reference of an observer on Earth. Although
these lengthy transit times would not make interstellar exploration impossible,
they would certainly dampen the enthusiasm of governments or private
individuals funding these missions. After all, a mission whose success is
perhaps a century away would be difficult to justify. In recent years, however,
physicists have discovered two loopholes to Einstein's ultimate speed limit:
the Einstein-Rosen bridge (commonly referred to as a "wormhole") and the
warp drive. Fundamentally, both ideas involve manipulation of spacetime itself
in some exotic way that allows for faster-than-light (FTL) travel.
Essentially, the wormhole involves connecting two potentially distant regions
of space by a topological shortcut. Theoretically, one would enter the
wormhole and instantaneously be transported to the exit located in a distant
region of space. Although no observational evidence of wormholes exists,
theoretically they can exist as a valid solution to general relativity.
The warp drive-the main focus this paper-involves local manipulation of the
fabric of space in the immediate vicinity of a spacecraft. The basic idea is to
create an asymmetric bubble of space that is contracting in front of the
spacecraft while expanding behind it. Using this form of locomotion, the
spacecraft remains stationary inside this "warp bubble," and the movement of
space itself facilitates the relative motion of the spacecraft. The most
attractive feature of the warp drive is that the theory of relativity places no
known restrictions on the motion of space itself, thus allowing for a
convenient circumvention of the speed of light barrier.
An advanced aerospace platform incorporating warp drive technology would
profoundly alter the capacity to explore-and potentially to colonize-the
universe. Because a warp drive is not limited by the speed of light, one can
only guess the top speeds such a technology might be capable of achieving.
For the sake of argument, let's consider the duration of trips taken by a
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spacecraft capable of 100c1 for an array of exotic destinations of possible
interest. As Table 1 shows, trips to the planets within our own solar system
would take hours rather than years, and journeys to local star system would
be measured in weeks rather than hundreds of thousands of years.
Table 1. Transit Times to Various Exotic Destinations
at 100 Times the Speed of Light
Destination Transit Time
Mars 193 seconds
Jupiter 36 minutes
Neptune 4 hours
Alpha Centauri 15 days
Epsilon Eridani 38 days
The Orion Nebula 1.3 years
Until recently, the warp drive was a concept reserved for science fiction.
However, a 1994 paper by Miguel Alcubierre placed the idea on a more solid
theoretical footing. Alcubierre (Reference 1) demonstrated that a specific
Lorentzian manifold could be chosen that exhibited bubble-like features
reminiscent of the warp drive from the popular Star Trek television series. The
bubble allowed for the surrounding spacetime to move at FTL speeds, and the
inhabitants of the bubble would feel no acceleration effects because spacetime
itself would be in motion instead of the spacecraft and its inhabitants.
A number of papers have emerged in recent years that build on this original
idea. However, these papers do not typically address how one might actually
create the necessary spacetime bubble. Our own research directly addresses
this question from a new and unique perspective and introduces a novel
paradigm shift in the field of warp drive study (Reference 2). More formally,
our work approaches the physics of warp drive from the perspective of
quantum field theory; this diverges from the more traditional approach to
warp drives, which utilizes the physics of general relativity. One of the
improvements the model introduces is a dramatic reduction in the overall
energy required to create such a phenomenon.
The roadmap to this new idea was the observation that spacetime is currently
known to be in a state of accelerated expansion, as demonstrated by the
redshifting of galaxies, and the belief that if the mechanism for this expansion
could be understood, then it might ultimately be controlled. A popular term
used by cosmologists today is "dark energy," an exotic and ubiquitous form of
energy that is believed to constitute over 70 percent of the matter-energy
content of the universe (Reference 3-6). One salient feature of dark energy is
its intrinsic ability to generate negative pressure, causing the fabric of space
to expand in the way that is currently observed (Reference 7).
1 This speed, while somewhat arbitrary, highlights the fact that our galaxy would become far more accessible if or
when one discovers how to surpass the speed of light barrier.
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Although we know what dark energy does, we do not yet fully understand its
nature. We do not understand why it exists or how it is created; we simply
know it provides an ever-present force on spacetime, causing the universe to
expand. Indeed, recent high-precision experimental observations indicate dark
energy may be a cosmological vacuum energy (Reference 8-10). These
observations are based on the magnitudes of high-redshift supernova and
have been a source of high research activity of late owing to the unexpected
discovery that the rate of expansion of the universe is increasing (commonly
referred to as accelerated expansion).
One tantalizing aspect of dark energy is that if it were fully understood, and if
a technology were developed that could generate and harness the exotic
effects of dark energy on the fabric of space, then a warp drive would be one
step closer to technological reality. While a full understanding of the true
nature of dark energy may be many years away, it is entirely feasible that
experimental breakthroughs at the Large Hadron Collider or developments in
the field of M-theory could lead to a quantum leap in our understanding of this
unusual form of energy and perhaps help to direct technological innovations.
Our own research focuses on gaining an understanding of the physical origin
of dark energy. By exploring novel ideas at the forefront of theoretical physics,
one is able to propose a physically viable model incorporating some of the
cutting-edge ideas emerging from string theory and quantum field theory. This
leads to a deeper understanding of the possible origin of dark energy and
allows consideration of a mechanism that would allow a sufficiently advanced
technology to control the dark energy density in any region of space, and thus
the expansion of space. This work has clear implications for the advancement
of warp drive research.
This paper is structured as follows: Section 2 reviews the more traditional
general relativistic warp drives, the energy required to create them, and the
physics required to understand them. Section 3 discusses the cosmological
constant, a term featured in Einstein's equation that regulates the contraction
and expansion of the spacetime. Section 4 introduces the Casimir energy,
which, under certain conditions, may be the phenomenon that physically
generates the cosmological constant. Section 5 discusses higher dimensions in
physics and their importance in the context of Casimir energy calculations.
Section 6 introduces the formulas that demonstrate that the Casimir energies
in higher dimensions may in fact be the dark energy that is responsible for the
accelerated expansion of the universe. Section 7 relates all the previous
concepts together and introduces the novel warp drive paradigm. Section 8
performs original calculations of the energy required to create a superluminal
warp drive. Finally, the paper speculates about the technological progress that
would be necessary to turn this model into a reality.
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2. General Relativistic Warp Drives
Alcubierre (Reference 1) derived a spacetime metric motivated by cosmological inflation
that would allow arbitrarily short travel times between two distant points in space. The
"warp drive" metric uses coordinates (t, x, y, z) and curve (or worldline) x = Xsh(t), y =
0, z = 0, lying in the t-x plane passing through the origin. Note that Xsh is the x-axis
coordinate position of the moving spaceship (or warp bubble) frame. The metric1
specifying this particular spacetime geometry is (Reference 1):
(2.1)
where c is the speed of light, Vsh(t) is the speed associated with the curve (or warp
bubble speed), and Tsh(t) is the Euclidean distance from the curve. The warp bubble
shape function f (rsh) is any smooth positive function that satisfies f (0) = 1 and
decreases away from the origin to vanish when Tsh > R for some distance R. The
geometry of each spatial slice is flat, and spacetime is flat where f (rsh) vanishes but is
curved where it does not vanish.
The driving mechanism of Equation (2.1) is the York extrinsic time, 9. This quantity is
defined as ( Reference 1):
S= v," x," df .
(2.2)
d,;"
C ~h
The 9 behavio