The
young Scottish engineer John Scott Russell (1808-1882) was conducting
experiments on the most efficient hull design for canal boats when he made a
remarkable scientific discovery.As
he wrote at the time:

"I was
observing the motion of a boat which was rapidly drawn along a narrow channel by
a pair of horses, when the boat suddenly stopped - not so the mass of water in
the channel which it had put in motion; it accumulated round the prow of the
vessel in a state of violent agitation, then suddenly leaving it behind, rolled
forward with great velocity, assuming the form of a large solitary elevation, a
rounded, smooth and well-defined heap of water, which continued its course along
the channel apparently without change of form or diminution of speed. I
followed it on horseback, and overtook it still rolling on at a rate of some
eight or nine miles an hour, preserving its original figure some thirty feet
long and a foot to a foot and a half in height. Its height gradually diminished,
and after a chase of one or two miles I lost it in the windings of the
channel."

Russell
was later able to reproduce the phenomenon he had observed in a
water-filled wave tank.What he discovered was
the soliton, a self-reinforcing wave
packet that maintains its shape while it propagates forward at a constant
velocity.Solitons were originally a
phenomenon peculiar to hydrodynamics, but, as it turns out, they also appear in
many other areas of physics.

In
particular, the Alcubierre Warp Drive, first published in 1994 and described two years later in this column in the November-1996
issue of Analog,
is an example of a soliton moving through space-time itself.The Alcubierre soliton moves forward at a pre-determined (possibly
superluminal) speed by collapsing the space in the front of the propagating
space warp and compensating by expanding the space in the rear.The mechanism is the same one that expands space itself in the general
relativity of an expanding universe.

Unfortunately
for those of us who are would-be users, the
Alcubierre Warp Drive
has a few "minor" engineering problems.While the drive is in operation, it is not possible to communicate
between the interior passenger-plus-crew area and the exterior of the "warp
bubble".This makes is
impossible for the crew to exercise speed control and steering or even for the
passengers to see what's passing by outside or is looming straight ahead. There
are also problems with Hawking radiation bombardment and with stress-energy
buildup that we will not discuss here.But
perhaps the most serious problem is that the construction of an Alcubierre Warp
soliton would require a truly enormous quantity of negative
mass-energy.

With
our present technology, we can perhaps create a thin spatial region containing a
small amount of negative energy by using the Casimir effect.According to quantum field theory, in the gap between two grounded
conducting (preferably superconducting) plates the energy becomes negative due
to the suppression of long-wavelength vacuum modes, i.e., waves too long to fit
in the plate gap.Thus, we can
create a thin region containing a small bit of negative energy.However, the magnitude of the negative mass-energy needed by the original
Alcubierre Warp Drive
travelling at lightspeed greatly exceeds what we might ever hope to produce,In particular, it is about -6×10^{62} kg!

In
magnitude, that value exceeds the amount of positive mass-energy present in the
entire visible universe.There
has been theoretical work aimed at bringing that negative-mass requirement of
the
Alcubierre Drive
down to a more reasonable value. In
fact, some particular work by the founder of NASA's Eagle Lab in
Houston
found that, with somewhat speculative assumptions, the required mass might be
reduced to about a ton of negative mass-energy.That's much better, but the problem remains that we do not have the
technology to produce even that relatively modest amount of negative
mass-energy.Experimental physicists
and astronomers have conducted searches for negative- (and even imaginary-) mass
particles in our universe, but they have never observed any at all.

In
a recent paper, Dr. Erik W. Lentz, presently a postdoc at
Germany
's Göttingen University Institute for Astrophysics (and who received his PhD in
astrophysics at my own
University
of
Washington
) has demonstrated that there is a positive-energy
space-time soliton solution of Einstein's equations of general relativity.Using the Arnowitt, Deser, and Misner (ADM) formulation of general
relativity and a hyperbolic rather than linear or elliptic relation for the ADM
"shift vector", Lentz has been able to construct a moving, possibly
superluminal, soliton that involves only positive mass-energy.His soliton is constructed to contain a relatively flat-space central
region with minimal tidal forces, in which internal proper time corresponds to
outside time (i.e., no relativistic time dilation), and internal observers move
with the speed of the soliton itself without feeling inertial forces.The transport logistics of the
Lentz Drive
are similar to those of the
Alcubierre Drive
.

The
Lentz soliton has a "delta" shape formed from about seven
diamond-shaped blocks of specially-configured ADM shift vectors "flying in
formation" to surround the flat interior region and to move it forward.The volume of local space that is expanded or contracted by the Lentz
soliton is rather complex, containing multiple regions corresponding to negative
and positive hyperbolic space expansions.In
contrast, the Alcubierre soliton contains only one negative and one positive
expansion region.The weak energy
condition of general relativity, which is strongly violated by the
Alcubierre Warp Drive
, is satisfied by the Lentz soliton, and it also satisfies the momentum
condition of general relativity.

Despite
the virtue of its positive energy, the amount of mass-energy needed to form a
Lentz soliton is a major problem,Lentz
estimates that a soliton moving at the speed of light with a diameter of 200
meters and a shell thickness of 1 meter would require a mass-energy of around
1/10 of a solar mass, not a universe-worth but still a dismayingly large value.He points out, however, that techniques already in the literature have
shown that it is possible to greatly reduce the mass-magnitude required by the
Alcuiberre drive.These techniques
could probably be similarly applied to the Lentz soliton drive, reducing the
required mass-energy to a more obtainable value.

Perhaps
the most intriguing aspect of the
Lentz Soliton Drive
is its connection to a conducting electromagnetic plasma.The stress-energy of a plasma and classical electromagnetic fields can
provide the source for producing Lentz's space-time soliton.Lentz indicates in his paper that much theoretical work remains to be
done to take advantage of this.Physics
at the interface between plasma physics and the AMD version of general
relativity needs to be explored much more thoroughly, both analytically and
numerically.Lentz says: "... it is an appealing proposition to incorporate the degrees and
dynamics of the plasma into the geometric computation.One could self-consistently simulate the creation, propagation and
dismantlement phases of the solition at both sub- and superluminal speeds."He observes that in this era of gravitational-wave astronomy there
are a growing number of accurate numerical codes capable of describing fields
and fluids in relativistic space-time, and these could be applied to soliton
issues.

On
the experimental and observational fronts, unfortunately, the plasmas that we
are able to produce in the laboratory, even at ITER and the Princeton and
Livermore
fusion experiments, contain many orders of magnitude too little energy to
produce any solitons like the ones Lentz describes.Fortunately, there may be an astrophysical alternative.When an aging star with a mass between about ten and twenty-five times
that of our sun uses up its fusion fuel, it collapses and produces a supernova
that culminates in the creation of a rapidly spinning neutron star with a radius
of about 10 kilometers and a mass of about 1.4 times that of our Sun. All
stars are believed to have sizable magnetic fields.During the collapse their magnetic field lines are trapped in the
collapsing medium and compressed to remarkably high field strengths that range
in their neutron star remnants from 10^{4} and 10^{11} tesla.Neutron stars at the high end of this magnetic field range are
called magnetars.They are the astronomical sources of regular bursts of gamma rays,
and they have fields ranging from 10^{8} to 10^{11} tesla. (For
scale, here on the ground the state-of-the-art niobium-titanium superconducting
magnets used in the CERN LHC facility produce magnetic fields of about 8.6
tesla, and their designers hope to move up to about 10 tesla.)

At
the huge magnetic field of 10^{11} tesla (which corresponds to a
magnetic field mass-energy density of about 4.4×10^{10}^{ }kilograms
per cubic meter), there is the possibility that a magnetar
"star-quake" acting on the ultra-magnetized plasma surrounding a
magnetar might spontaneously produce a Lentz soliton, moving away from the
source magnetar at a large, possibly even superluminal, speed.Such an event might be observable using radio or optical interferometry
or gravitational wave detection.This
raises the exciting possibility that Lentz solitons might already exist in our
universe, and they might be detectable if we turn the right observational tools
in their direction.

This
column appears in a science fiction magazine, where speculation and
extrapolation are appropriate.Therefore,
indulge me a bit.The vision of
magnetars spawning solitons that might be "tamed" and used for
superluminal travel suggests many SF plot-line scenarios.Consider perhaps space-cowboys attaching themselves to the exterior of a
bucking newly spawned soliton, gradually bringing it under control, creating an
aperture to admit interior infrastructure, passengers, and crew, and sending it
on its way to the stars at superluminal speeds, to be wrangled to a stop by
other space cowboys at the destination end of the journey.Or perhaps Analog's authors have better ideas ...

The bottom line is that we now have the prospect
of an FTL space drive that is embedded in general relativity and that can be
made without the need for negative mass-energy.Watch this column for future progress in the theory and observation of
Lentz solitons.

John
G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of
quantum mechanics, The
Quantum Handshake - Entanglement, Nonlocality, and Transactions,
(Springer, January-2016) is available online as a hardcover or eBook at:http://www.springer.com/gp/book/9783319246406
or https://www.amazon.com/dp/3319246402.

Alternate
View Columns Online: Electronic reprints of 212 or more "The Alternate
View" columns by John G. Cramer published in Analog
between 1984 and the present are currently available online at: http://www.npl.washington.edu/av
.

References:

The
Alcuiberre Warp Drive
: Miguel Alcubierre, " The warp drive: hyper-fast travel within
general relativity", Classical and
Quantum Gravity11 L73-L77
(1994): arXiv: gr-qc/0009013.

Lentz
Positive-Mass Solitons: "Breaking the Warp Barrier:Hyper-Fast
Solitons in Einstein-Maxwell Plasma Theory", Erik W. Lentz, June 15, 2020; arXiv:1910.03887
[hep-ex].

The
ADM Version of General Relativity: R. Arnowitt, S. Deser, and C. Misner, "Dynamical Structure and
Definition of Energy in General Relativity", Physical
Review116 1322–1330 (1959).