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The Lentz Soliton FTL Drive

by John G. Cramer

Alternate View Column AV-209
Keywords: soliton, space drive, warp drive, general relativity, ADM formulation, Alcuiberre drive, Lentz drive
Published in the November-December-2020 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 07/19/2020 and is copyrighted ©2020 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

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 -6×1062 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 104 and 1011 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 108 to 1011 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 1011 tesla (which corresponds to a magnetic field mass-energy density of about 4.4×1010 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: or

SF Novels by John Cramer:  Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and .  His new novel, Fermi's Question may be coming soon.

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: .


The Alcuiberre Warp Drive :
Miguel Alcubierre, " The warp drive: hyper-fast travel within general relativity", Classical and Quantum Gravity 11 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:2006.07125 [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 Review 116 1322-1330 (1959).

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