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Wormhole Induction Propulsion (WHIP)
Eric W. Davis, Ph.D.
National Institute for Discovery Science
1515 E. Tropicana Ave., Suite 400
Las Vegas, Nevada 89119
ABSTRACT
Space flight by means of wormholes is described whereby the
traditional rocket propulsion approach can be abandoned in favor of a new
paradigm involving the manipulation of spacetime. Maccone (1995) extended LeviCivita’s
1917 magnetic gravity solution to the Morris and Thorne (1988) wormhole
solution and claimed that static homogeneous magnetic/electric fields can
create spacetime curvature manifesting itself as a traversable wormhole.
Furthermore, Maccone showed that the speed of light through this curvature
region is slowed by the magnetic (or electric) induced gravitational field
there. Maccone’s analysis immediately suggests a way to perform laboratory
experiments whereby one could apply a powerful static homogeneous magnetic
field in a vacuum, thereby creating spacetime curvature, and measure the speed
of a light beam through it. Magnetic fields employed in this scenario must
achieve magnitudes > 10^{10} Tesla in order for measurable
effects to appear. Current magnetic induction technology is limited to static
fields of ~ several x 10^{3} Tesla. However, destructive
chemical (implosive/explosive) magnetic field generation technology has
reached peak rateofrise field strengths of ~ 10^{9} Tesla/sec.
It is proposed that this technology be exploited to take advantage of the high
rateofrise field strengths to create and measure spacetime curvature in the
lab.
INTRODUCTION
Rapid interplanetary and interstellar space flight by means
of spacetime wormholes is possible, in principle, whereby the traditional
rocket propulsion approach can be abandoned in favor of a new paradigm
involving the use of spacetime manipulation. In this scheme, the light speed
barrier becomes irrelevant and spacecraft no longer need to carry large mass
fractions of traditional chemical or nuclear propellants and related
infrastructure over distances larger than several astronomical units (AU).
Travel time over very large distances will be reduced by orders of magnitude.
Einstein published his General Theory of Relativity (GTR) in 1915. In 1917,
physicist Tullio LeviCivita read a paper before the Academy of Rome about
creating artificial gravitational fields (spacetime curvature) by virtue of
static homogeneous magnetic or electric fields as a solution to the GTR
equations. This paper went largely unnoticed. In 1988, Morris and Thorne
published an exact solution to the GTR equations which describe the creation
of traversable wormholes in spacetime by virtue of exotic (massenergy
r c^{2} < stressenergy
t ) matterenergy fields (see
figures 1 and 2). Visser (1995) has extended and added to the knowledge base
of this research. The essential features of these solutions are that wormholes
possess a traversable throat in which there is no horizon or singularity. For
the purpose of this study, we also impose the additional constraint that
travel through the wormhole is causal, although, this is not a necessary
constraint in general. When these properties are employed together with the
GTR field equations, it becomes necessary to introduce an exotic material in
the wormhole’s throat which generates its spacetime curvature.
Maccone (1995) extended and matched LeviCivita’s solution
to the Morris and Thorne solution and claimed that the earlier describes a
wormhole in spacetime. More specifically, Maccone claims that static
homogeneous magnetic/electric fields with cylindrical symmetry can create
spacetime curvature which manifests itself as a traversable wormhole. Although
the claim of inducing spacetime curvature is correct, LeviCivita’s metric
solution is not a wormhole. A nearterm lab experiment based on Maccone’s
analysis will be discussed. It is my intent to introduce a new space
propulsion concept which employs the creation of traversable wormholes by
virtue of ultrahigh magnetic fields in conjunction with exotic matterenergy
fields. I call this propulsion concept "Wormhole Induction Propulsion" or WHIP.
It is speculated that future WHIP spacecraft could deploy ultrahigh magnetic
fields along with exotic matter energy fields (e.g. radial electric or
magnetic fields, Casimir energy field, etc.) in space to create a wormhole and
then apply conventional space propulsion to move through the throat to reach
the other side in a matter of minutes or days, whence the spacecraft emerges
several AU’s or lightyears away from its starting point. The requirement for
conventional propulsion in WHIP spacecraft would be strictly limited by the
need for short travel through the wormhole throat as well as for orbital
maneuvering near distant worlds. The integrated system comprising the magnetic
induction/exotic field wormhole and conventional propulsion units could be
called WHIPIT or "Wormhole Induction Propulsion Integrated Technology."
THEORETICAL BRIEF
LeviCivita’s spacetime metric for a static uniform
magnetic field was originally conceived by Pauli (1981):
(1),
where
and
are integration
constants which are determined by appropriate boundary conditions and
…
are Cartesian
coordinates (…
= space,
= time) with
orthographic projection. The important parameter in (1) is:
(2)
which measures the radius of spacetime curvature induced by a homogeneous
magnetic field with cylindrical symmetry (axis,
) about the
direction of the field (G = universal gravitation constant, c =
speed of light, B = magnetic field intensity in Tesla,
m _{0} = vacuum permeability  all
in mks units). From the coefficient of
in (1), Maccone
derived the "speed of light function" which gives the gravitationally induced
variation of light speed within the curvature region:
(3).
At the center of this region (),
this becomes:
(4),
for where
.
Equation (4) is based on the assumption that the magnetic field is created by
a solenoid of length L oriented along the zaxis, and that c
= 3x10^{8} m/sec at the solenoid’s ends (z =
± L/2), while at
z = 0, c slows down according to (4) because of the presence of the
artificially induced spacetime curvature. Further, Maccone inverted equation
(4) and solved for B to get:
(5).
Equations (2), (4) and (5) are formulae to use for creating and detecting
spacetime curvature in the lab.
TECHNICAL ISSUES
Traversable wormholes are creatures of classical GTR and
represent nontrivial topology change in the spacetime manifold. This makes
mathematicians cringe because it raises the question of whether topology can
change or fluctuate to accommodate wormhole creation. Black holes and naked
singularities are also creatures of GTR representing nontrivial topology
change in spacetime, yet they are accepted by the astrophysics and
mathematical communities — the former by Hubble Space Telescope discoveries
and the latter by theoretical arguments due to Kip Thorne, Stephen Hawking,
Roger Penrose and others. The BohmAharonov effect is another example which
owes its existence to nontrivial topology change in the manifold. The
topology change (censorship) theorems discussed in Visser (1995) make precise
mathematical statements about the "mathematician’s topology" (topology of
spacetime is fixed!), however, Visser correctly points out that this is a
mathematical abstraction. In fact, Visser (1990) proved that the existence of
an everywhere Lorentzian metric in spacetime is not a sufficient condition to
prevent topology change. Furthermore, Visser (1990, 1995) elaborates that
physical probes are not sensitive to this mathematical abstraction, but
instead they typically couple to the geometrical features of space. Visser
(1990) also showed that it is possible for geometrical effects to mimic the
effects of topology change. Topology is too limited a tool to accurately
characterize a generic traversable wormhole; in general one needs geometric
information to detect the presence of a wormhole, or more precisely to locate
the wormhole throat (Visser, private communication, 1997).
Landis (1997) has made technical criticisms of Maccone’s
(1995) work suggesting that the LeviCivita metric in the presence of a
uniform magnetic field does not form a wormhole within the Morris and Thorne
(1988) framework. While the latter view is correct, the technical arguments
are not accurate or complete. Changing the coordinate system from Cartesian to
cylindrical (x^{1} = rcosj
, x^{2} = rsinj
, x^{3} = z, let x^{4}
= t) puts equation (1) into the form (Maccone, 1995):
(6).
This is a cleaner form, but what is the LeviCivita metric
really? We can find out from making a change of (radial) variable by letting
r = asinq
, dr = acosq
dq
and substituting these into equation (6):
(7),
where a is the constant radius defined by equation
(2). The spatial part of (7),
, is recognized as
the threemetric of a hypercylinder S^{2 }x
Â . So
equation (7) shows that LeviCivita’s spacetime metric is simply a
hypercylinder with a position dependent gravitational potential: no
asymptotically flat region, no flaredout wormhole mouth and no wormhole
throat. Maccone’s equations for the radial (hyperbolic) pressure, stress and
energy density of the "magnetic wormhole" configuration are thus incorrect.
In addition, directing attention on the behavior of
wormhole geometry at asymptotic infinity is not too profitable. Visser (private
communication, 1997; Hochberg and Visser, 1997) demonstrates that it is only
the behavior near the wormhole throat that is critical to understanding what
is going on, and that a generic throat can be defined without having to make
all the symmetry assumptions and without assuming the existence of an
asymptotically flat spacetime to embed the wormhole in. One only needs to know
the generic features of the geometry near the throat in order to guarantee
violations of the null energy condition (NEC; see Hawking and Ellis, 1973) for
certain open regions near the throat (Visser, private communication, 1997).
There are general theorems of differential geometry that guarantee that there
must be NEC violations (meaning exotic matterenergy is present) at a wormhole
throat. In view of this, however, it is known that static radial electric or
magnetic fields are borderline exotic when threading a wormhole if their
tension were infinitesimally larger, for a given energy density (Herrmann,
1989; Hawking and Ellis, 1973). Other exotic (energy condition violating)
matterenergy fields are known to be squeezed states of the electromagnetic
field, Casimir (electromagnetic zeropoint) energy and other quantum fields/states/effects.
With respect to creating wormholes, these have the unfortunate reputation of
alarming physicists. This is unfounded since all the energy condition
hypotheses have been experimentally tested in the laboratory and
experimentally shown to be false — 25 years before their formulation (Visser,
1990 and references cited therein). Violating the energy conditions commits no
offense against nature.
EXPERIMENTAL APPROACH
Table I below shows the radius of curvature generated by a
range of magnetic field strengths via equation (2). Equations (2), (4) and (5)
suggest a way to perform a laboratory experiment whereby one could apply a
powerful static homogeneous (cylindrically symmetric) magnetic field in a
vacuum, thereby creating spacetime curvature in principle, and measure the
speed of a light beam through it. A measurable slowing of c in this
arrangement would demonstrate that a curvature effect has been created in the
experiment. The achievable precision in measuring this
Table I. Radius of Spacetime Curvature Induced by BField
B ( x 3.484 Tesla) 
a (meters) 
1 
10^{18} (105.7
ly) 
10^{2} 
10^{16} (1.06
ly) 
10^{3} 
10^{15} (0.11
ly) 
10^{5} 
10^{13} (66.7
AU) 
10^{7} 
10^{11} (0.67
AU) 
10^{9} 
10^{9} (1.44
Solar Radii) 
10^{12} 
10^{6} (0.16
Earth Radii) 
10^{15} 
10^{3} 
10^{18} 
1 
ly = lightyear, AU = Astronomical Unit
would be c  v(0) or c^{2}
 v^{2}(0) as seen from equation (5). Electric
fields could also be used to create the same effect, however, the field
strengths required to accomplish the same radius of curvature or slowing of
c is seventeen times larger than magnetic field strengths (Maccone, 1995).
From Table I, it is apparent that laboratory magnetic field
strengths would need to be > 10^{9}  10^{10} Tesla so
that a significant radius of curvature and slowing of c can be measured.
Experiments employing chemical explosive/implosive magnetic technologies would
be an ideal arrangement for this. The limit of magnetic field generation for
chemical explosives/implosives is ~
several x 10^{3} Tesla and the quantum limit for
ordinary metals is ~
50,000 Tesla. Explosion/implosion work done by Russian (MC1 generator,
ISTC grant), Los Alamos National Lab (ATLAS), National High Magnetic Field Lab
and Sandia National Lab (SATURN) investigators have employed magnetic
solenoids of good homogeneity with lengths of
~ 10 cm, having peak rateofrise
of field of ~ 10^{9}
Tesla/sec where a few nanoseconds is spent at 1000 Tesla, and
which is long enough for a good measurement of c (J. Solem, private
communication, 1997). Further, with picosecond pulses, c could be
measured to a part in 10^{2} or 10^{3}. At 1000 Tesla,
c^{2}  v^{2}(0)
» 0 m^{2}/sec^{2
}and the radius of curvature is 0.368 lightyears. If the peak
rateofrise of field (~ 10^{9} Tesla/sec) can be used, then a
radius of curvature £
several x 10^{6} km can be generated along with c^{2}
 v^{2}(0)
³ several x 10^{4} m^{2}/sec^{2}.
It will be necessary to consider advancing the stateofart
of magnetic induction technologies in order to reach static field strengths
that are > 10^{9}  10^{10} Tesla. Extremely sensitive
measurements of c at the one part in 10^{6} or 10^{7}
level may be necessary for laboratory experiments involving field strengths of
~ 10^{9} Tesla.
Magnetic induction technologies based on nuclear explosives/implosives may
need to be seriously considered in order to achieve large magnitude results.
An order of magnitude calculation indicates that magnetic fields generated by
nuclear pulsed energy methods could be magnified to (brief) static values of
³ 10^{9}
Tesla by factors of the nucleartochemical binding energy ratio (³
10^{6}). Other experimental methods employing CW lasers,
repetitivepulse free electron lasers, neutron beampumped UO_{2}
lasers, pulsed laserplasma interactions or pulsed hot (theta pinch) plasmas
either generate insufficient magnetic field strengths for our purposes or
cannot generate them at all within their operating modes (see also Table II).
Table II. Current High and Ultrahigh Magnetic Field Generation
Technologies
Magnetic Field Strength (Tesla) 
Field Generation Technology 
10  300 
Superconductivity, Hybrid Magnets,
Pulsed Magnets^{a} 
360 
Magnetic flux compression by
electromagnetic force^{a} 
400 
Oneturn coil connected to strong
laser produced plasma^{a} 
~
10^{3} 
High powered pulsed lasers^{a} 
1000  3000 
Magnetic flux compression by
chemical explosion^{b} 
10^{2}  10^{5} 
White Dwarf stars^{c} 
10^{7}  10^{9} 
Neutron stars^{c} 
³
10^{9} 
Magnetic flux compression by nuclear
explosion^{a} 
^{a} D. Judd, private
communication, 1997
^{b} J. Solem, private
communication, 1997
^{c} S. Stephens, private
communication, 1995
WHIP SPACECRAFT CONCEPT
WHIP spacecraft will have multifunction integrated
technology for propulsion. The Wormhole Induction Propulsion Integrated
Technology (WHIPIT) would entail two modes. The first mode is an advanced
conventional system (chemical, nuclear fission/fusion, ion/plasma, antimatter,
etc.) which would provide propulsion through the wormhole throat, orbital
maneuvering capability near stellar or planetary bodies, and spacecraft
attitude control and orbit corrections. An important system driver affecting
mission performance and cost is the overall propellant massfraction required
for this mode. A desirable constraint limiting this to acceptable (low) levels
should be that an advanced conventional system would regenerate its onboard
fuel supply internally or that it obtain and process its fuel supply from the
situ space environment. Other important constraints and/or performance
requirements to consider for this propulsion mode would include specific
impulse, thrust, energy conversion schemes, etc. Further discussion of these
is beyond the scope of this paper and is left for the reader to explore on
their own.
The second WHIPIT mode is the stardrive component. This
would provide the necessary propulsion to rapidly move the spacecraft over
interplanetary or interstellar distances through a traversable wormhole. The
system would generate a static, cylindrically symmetric ultrahigh magnetic
field to create a hypercylinder curvature envelope (gravity well) near the
spacecraft to prestress space into a pseudowormhole configuration. The
radius of the hypercylinder envelope should be no smaller than the largest
linear dimension of the spacecraft. As the spacecraft is gravitated into the
envelope, the fieldgenerator system then changes the cylindrical magnetic
field into a radial configuration while giving it a tension that is greater
than its energy density. A traversable wormhole throat is then induced near
the spacecraft where the hypercylinder and throat geometries are patched
together (see figure 3). The conventional propulsion mode then kicks on to
nudge the spacecraft through the throat and send its occupants on their way to
adventure. This scenario would apply if ultrahigh electric fields were
employed instead. If optimization of wormhole throat (geometry) creation and
hyperspace tunneling distance requires a fully exotic energy field to thread
the throat, then the propulsion system would need to be capable of generating
and deploying a Casimir (or other exotic) energy field. Although ultrahigh
magnetic/electric and exotic field generation schemes are speculative, further
discussion is beyond the scope of this paper and will be left for future work.
A hypothetical WHIP spacecraft concept is depicted in Figure 4.
CONCLUSIONS
A candidate for breakthrough propulsion physics has been
identified in the form of a traversable wormhole created by virtue of
ultrahigh magnetic or electric fields with an additional exotic energy
component. Maccone (1995) claimed that cylindrically symmetric ultrahigh
magnetic (electric) fields can create a traversable wormhole in the Morris and
Thorne (1988) framework. It has been shown that this is incorrect. Instead, a
hypercylinder curvature effect having a position dependent gravitational
potential is induced. This effect can be used to create a wormhole by patching
the hypercylinder envelope to a throat that is induced by either radially
stressing the ultrahigh field or employing additional exotic energy. Maccone
correctly showed that the speed of light through the hypercylinder region is
slowed by the magnetic induced gravitational field there. This suggests a way
to perform laboratory experiments whereby one could apply an ultrahigh
magnetic field in a vacuum, thereby creating a hypercylinder curvature effect,
and measure the speed of a light beam through it. While chemical explosive/implosive
magnetic induction technology has achieved static field strengths of
~ several x 10^{3}
Tesla, the peak rateofrise of field is
~ 10^{9} Tesla/sec.
Field strengths > 10^{9}  10^{10} Tesla would need to
be generated to impart a measurable slowing of light speed in this scenario.
It is proposed that the peak rateofrise of field be exploited as a means to
achieve this goal in the nearterm. Magnetic induction technologies based on
nuclear explosives/implosives may need to be considered in order to achieve
results of larger magnitude. A Wormhole Induction Propulsion system has been
introduced to exploit the possibilities of traversable wormholes.
ACKNOWLEDGEMENTS
I wish to thank Marc Millis for allowing me to use WHIP and
WHIPIT which he coined at the February, 1997 NASA Breakthrough Propulsion
Physics Regional Brainstorming Workshop at Austin, TX. My gratitude to Matt
Visser for his many valuable suggestions and comments on this work. I also
thank Dean Judd, Johndale Solem, George Hathaway and John Alexander for their
technical contributions and remarks. This research is partially supported by
the National Institute for Discovery Science. ( Figure 4:
Hypothetical WHIP spacecraft concept. / Figure 1: Embedded space
representation of a Morris and Thorne (1988) traversable wormhole.
Figure 3: Hypothetical view of
two wormhole
mouths patched to a hypercylinder curvature
envelope. The small (large) configuration
results from the radius of curvature induced
by a larger (smaller) ultrahigh magnetic field.

Figure 2: What a wormhole mouth might look
like to space travelers.

REFERENCES
Maccone, C. (1995) "Interstellar Travel Through Magnetic Wormholes",
JBIS, Vol. 48, No. 11, pp. 453458.
LeviCivita, T. (1917) "Realtà fisica di alcuni spazi normali del Bianchi",
Rendiconti della Reale Accademia dei Lincei, Series 5, Vol. 26, pp.
519533.
Morris, M. and Thorne, K. (1988) "Wormholes in spacetime and their use for
interstellar travel: A tool for teaching general relativity", Am. J. Phys.,
Vol. 56, No. 5, pp. 395412.
Visser, M. (1995) Lorentzian Wormholes  From Einstein to Hawking,
AIP Press, Woodbury, NY.
Pauli, W. (1981) Theory of Relativity, Dover reprint, New York, pp.
171172.
Visser, M. (1990) "Wormholes, baby universes, and causality", Phys. Rev.
D, Vol. 41, No. 4, pp. 11161124.
Landis, G. (1997) "Magnetic Wormholes And The LeviCivita Solution To The
Einstein Equation", JBIS, Vol. 50, No. 4, pp. 155157.
Hochberg, D. and Visser, M. (1997) "Geometric structure of the generic
static traversable wormhole throat", LANL Abstract grqc/9704082, to
appear in Phys. Rev. D.
Hawking, S. W. and Ellis, G. F. R. (1973) The LargeScale Structure of
SpaceTime, Cambridge Univ. Press, Cambridge, pp. 8891 and pp. 9596.
Herrmann, F. (1989) "Energy density and stress: A new approach to teaching
electromagnetism", Am. J. Phys., Vol. 57, No. 8, pp. 707714.
Prepared for the Proceedings of the NASA Breakthrough Propulsion Physics
Workshop, NASA Lewis Research Center, Cleveland, Ohio (Aug. 1214, 1997). To
appear in the NASA Proceedings, 1998.
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