Exotic Paths To The Stars JOHN CRAMER

Published by Gregory Benford on December 1st, 2015

Everyone knows from pop science fiction such as Star Wars and Star Trek that ideas of how to cross immense distances in a twinkling of time do emerge from the odd and sometimes extravagant realms of theoretical physics. How plausible are such notions?

The truthful answer is that no one knows. Progress in the furthest realms of General Relativity and quantum mechanics must proceed from experiment, and there are few lab experiments that can touch on such issues. To survey the current landscape of such thinking, the 100 Year Starship Symposium held an Exotic Technologies Session chaired by John Cramer. Here he reports on the major ideas treated there, with some insightful criticisms of his own, and much background material useful to the interested but non-specialist observer. One recalls the Mark Twain observation, “There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”

Exotic Paths To The Stars

John Cramer

I.  Introduction

 

When I first came to Seattle in the mid-1960s to assume my new faculty position at the University of Washington, I remarked to one of my new Physics Department colleagues that the magnificent views of Mt. Rainier, available from many parts of the city, gave Seattle a special and unique flavor and ambiance.

“You, know,” he said, “Rainier is dormant at the moment, but it’s still an active volcano.  It erupts every five thousand years.  The geological record shows regular thick ash falls from Rainier and giant mud flows down the glacier-fed river valleys, where a lot of people live now.”

“Really,” I said.  “When was the last eruption?”

“Five thousand years ago,” he said with a quirky smile.

That anecdote provides a good analogy to our present situation, as residents of this planet.  All of our “eggs”, our cities, our people, our art and culture, our accumulated knowledge and understanding, are presently contained in one pretty blue “basket” called Planet Earth, which orbits in a Solar System that is configured to hurl very large rocks in our direction at random intervals.

It is estimated that a total of about 14 million tons of meteoritic material falls upon Planet Earth each year, much of it from the debris of asteroids and comets.  Meteors come in all sizes, and approximately 60 giant meteorites five or more kilometers in diameter have impacted Planet Earth in the past 600 million years. Even the smallest of these would have carved a crater some 95 kilometers across and produced an extinction event.

The geological fossil records shows evidence of “punctuated equilibrium”, extended periods in which life forms expand and fit themselves into the available ecological niches, punctuated by extinction events in which many species become extinct and the survivors scramble to adapt to the new conditions1.  Life on Planet Earth may have been “pumped” on a fast track to its present state of evolution by this cycle of extinction and regeneration.  We may owe our very existence to this pump of evolution2, but we do not want to get caught in the next pump cycle.  We, as a species, need to diversify, to place our eggs in many baskets instead of just one, before the forces of nature conspire to produce another extinction event that could include us.

The basic problem with such a “basket diversification” project is that we reside at the bottom of a very deep gravity well, from which the laws of physics make it very difficult for us to escape.  The only escape method presently in use involves giant chemical rockets that burn and eject vast volumes of expensive and toxic fuel in order to lift tiny payloads part-way out of the gravity well of the Earth.

And even if we can escape most of Earth’s gravity well, things are not much better in near-Earth orbit.  The Solar System, outside Earth’s protective atmosphere and shielding magnetic field, is a fairly hostile place, a hard vacuum environment in which the Sun’s flares and storms send out wave after wave of sterilizing radiation.

Further, the human biology seems to require the pull of gravity for a healthy existence.  Extended periods in low gravity lead to calcium loss and muscular and skeletal degeneration.  Our micro-gee International Space Station is an unhealthy place for long-term habitation, and astronauts return from extended stays there as near-invalids.

The other planets and moons of the Solar System, potential sources of the needed pull of gravity, are not promising sites for human habitation.  Mars is too cold, too remote from the Sun, and has a thin atmosphere, mostly carbon dioxide with a pressure of 1/100 of an Earth atmosphere.  Venus is much too hot, with a surface temperature around 870 °F and an atmospheric pressure, mostly carbon dioxide, about 90 times that of Earth.  Moons, asteroids, and artificial space habitats with centrifugal pseudo-gravity3 may be better sites for human colonies, but they all would have problems with low gravity, radiation shielding, and resource transport.  To find a true Earth-like habitat, we need to leave the Solar System for the earth-like planets orbiting other stars.

But if escaping Earth’s gravity well is difficult, travel to the stars is many orders of magnitude more difficult.  Fairly optimistic studies of interstellar travel, presented at the 100YSS Symposium in 2011, show very convincingly that there is little hope of reaching the nearby stars in a human lifetime using any conventional propulsion techniques, even with propulsion systems involving nuclear energy.   The universe is simply too big, and the stars are too far away.

 

Hieronymus Bosch  (c.1450-1516)
Ascent of the Blessed
The Doge’s Palace, Venice, Italy

To reach the stars, we need propulsion techniques that somehow circumvent Newton’s 3rd law and do not require the storage, transport, and expulsion of large volumes of reaction mass.  Or even better, we need trans-spatial shortcuts like wormholes that avoid the need to traverse the enormous distances between stars.  In short, because conventional technologies are inadequate, the human-lifetime-scale pathways to the stars require over-the-horizon “exotic” technologies, perhaps like the one illustrated here by Hieronymus Bosch.

 

I was Chairman of the Exotic Technologies Session held on October 1, 2011, at the 100 year Starship Symposium in Orlando Florida.  This chapter draws on the talks given in that session, but it does not represent a summary of the presentations.  Rather, I want focus on three lines of development in the area of exotic technologies that were featured at the Symposium, developments that might allow us to reach the stars on a time scale of a human lifetime: (1) propellantless space drives4, (2) warp drives5,6, and (3) wormholes7,8.  With reference to the latter two topics, I will also discuss some cautions from the theoretical physics community about the application of general relativity to “metric engineered” devices like wormholes and warp drives that require exotic matter.

 

 

II. Space Drives

 

The term “space drive” refers to an exotic technology that does not presently exist and that would allow the propulsion of a space vehicle without the need for rocket-style expulsion (or reflection) of reaction mass-energy.  In the leadoff talk of the Exotic Technologies track of the 100YSS Symposium, Marc G. Millis summarized the current prospects for space drives9.  He concluded that “although no propulsion breakthroughs appear imminent, the subject has matured to (the stage) where the relevant questions have been broached and are beginning to be answered.”  In this section, I want to consider the topic further and to discuss one of the most promising space drive developments, one involving Mach’s principle and inertia variation.

The basic problem with the space drive concept is Newton’s 3rd law of motion, one form of the law of conservation of momentum.  In conventional rocket propulsion, a space vehicle can be propelled forward and increase its forward momentum only if propellant with an equal and opposite incremental momentum is expelled as exhaust.  No internal motion, no shaking, spinning, or orbiting of masses, no tilting of eccentric flywheels, can produce any net momentum change in the overall object.  Something must go backwards if something else goes forward.

As a work-around to avoid carrying onboard reaction mass, emission, reflection, or absorption of light from a beam of light (laser or incoherent) or radio waves  could, in principle, produce significant propulsion and momentum change in a space vehicle that does not carry and expel reaction mass (solar sails or beam riders).  The problem with such schemes is that the momentum content of light is very small, only its energy divided by the speed of light, and therefore the thrust (in newtons) is the power (in watts) divided by the speed of light.  The speed of light is a large number, making the energy cost is very high for a small change in momentum.

Nevertheless, light sailing and light beam propulsion are possibilities.  They are tricky because the resulting momentum increment must always have a momentum component away from the light source (e.g., the sun or drive laser).  They are  expensive because many square kilometers of light sail and/or multi-megawatt lasers are required to achieve thrust comparable to rocket propulsion.  They are inefficient because large quantities of light energy are required for small quantities of momentum change, with most of the light beam energy reflected away and wasted, in the sense that it does not end up as kinetic energy.

Millis’ overview of possible space-drive technologies briefly mentioned the work of Prof. James Woodward of Cal. State Fullerton on Mach’s principle and inertia variation.  However, there have been some new results since the Symposium that I would like to discuss further.

First, what is Mach’s principle?  The physical property of mass has two distinct aspects, gravitational mass and inertial mass.   Gravitational mass produces and responds to gravitational fields.  It is represented by the two mass factors in Newton’s inverse-square law of gravity (F12 = G m1m2/r122).  Inertial mass is the tendency of matter to resists acceleration.  It is represented by the mass factor in Newton’s 2nd law of motion (F=ma).  These two aspects of mass always track one another.   There are no known objects with a large inertial mass and a small gravitational mass, or vice versa.  One of the deep mysteries of physics is the connection between inertial and gravitational mass.

Ernst Mach (1838–1916) was an Austrian physicist whose unpublished ideas about the origin of inertia influenced Einstein10.  Mach’s principle, as elucidated by Einstein, attempts to connect inertia with gravitation by suggesting that the resistance of inertial mass to acceleration arises from the long-range gravitational forces from all the other masses in the universe acting on a massive object (so that, in an universe empty of other masses, there would be no inertia).  In essence, Mach’ principle asserts that inertial and gravitational mass must be the same because inertia is, at its roots, a gravitational effect.

Albert Einstein liked Mach’s principle and used its implications to formulate his famous equivalence principle, a cornerstone of general relativity, which asserts that gravitational and inertial mass are indistinguishable in all situations.  In a small isolated room, according to the equivalence principle, it would be impossible to determine from local measurements whether the room was on the surface of the Earth in a 1 g gravitational field or was in a rocket ship accelerating at 1 g through gravity-free space.  The equivalence principle is now generally accepted in physics, and general relativity (GR) has become our standard model of gravity, but its underlying basis in Mach’s principle has never been properly derived, understood, or tested until now.

Dennis Sciama11 used a simplified low-field reduction of Einstein’s general relativity equations to show that in a uniform flat universe, long range gravitational interactions produce a force that resists acceleration, producing inertia.  James Woodward12, 4 extended the work of Sciama by considering the time dependent inertial effects that occur when mass-energy is in flow, i.e., when mass-energy is moved from one part of the system to another while the system is being accelerated.

The Woodward/Sciama result is surprising.  It predicts fairly large time-dependent variations in inertia, the tendency of matter to resist acceleration.  Most gravitational effects predicted in general relativity, e.g., the gravitational deflection of light, frame dragging, gravitational time dilation, etc., are exceedingly small and difficult to observe, because the algebraic expressions describing them always have a numerator that includes Newton’s gravitational constant G, a physical constant that has a very small value due to the weakness of gravity as a force.  The inertial transient effects predicted by the Woodward/Sciama calculations are unusual and different, in that they have G in the denominator, with the result that dividing by a small number (G) produces a sizable effect.

Can varying the inertial mass of an object produce thrust, for example by pushing it forward when the inertial mass is low and pulling it backward when the inertial mass is high, thereby “rowing” through space?  Woodward has tested for a net thrust from this effect using piezoelectric devices that combine stored energy with accelerated motion.  His results are unpublished and have not been confirmed by others who have attempted to reproduce them13.  However, the recent work, showing thrust of a few tens of micronewtons, has been posted on the internet and widely discussed14.  It has the possibility of being a real effect.

However, I would like to introduce a cautionary note here about thrust from inertial mass variation and momentum conservation.  The relativistically invariant form of Newton’s 2nd Law, as applied to Woodward-type thrusters, should be F = dp/dt, where F is the thrust produced and p = m v is the momentum of the system producing the thrust, with inertial mass m and velocity v.  When the mass is constant with time, this equation becomes F = m a, the classical form of Newton’s 2nd Law that Woodward uses in predicting the thrust derived from his calculations and that is the basis for the “rowing” space-drive effect described above.

However, when the inertial mass is varying with time, as it should be in the system of interest, the appropriate form of Newton’s 2nd Law is F = m a + v dm/dt, i.e., one must time-differentiate both the varying velocity and the varying mass factors that form the momentum.  It turns out that in any mass-varying space drive, the 2nd term produces a force that exactly cancels the force derived from the first term, so that, if both force terms are generated within the system, no net thrust is produced, even in a system where the inertial mass can be caused to vary with time.  Woodward claims that the 2nd term is not an internal force, but is a distant and external one because of the way that inertial mass and momentum couple to distant objects, so that it represents the reaction force that the rest of the universe receives from the action-at-a-distance of the drive.  This is an interesting argument that may or may not be correct.  In his talk in the Exotic Technologies track of the 100YSS Symposium, Eric Davis15 perhaps provided some support for this view by presenting arguments, in the context of FTL space warps, that conservation laws, and in particular momentum conservation, are local flat-space rules based on symmetries and may not directly apply to large-scale situations in which curved space and general relativity are important.  If Woodward’s reported observations of thrust can be verified, that should perhaps settle this issue.

We note here that the Mach/Schiama/Woodward approach may also have possible implications for starship travel in another way.  There is second negative-definite term in the Woodward/Sciama inertia variation calculation that could have important general relativity implications for wormholes and warp drives.  This will be discussed in Section V below.  However, we note that at least one physicist has questioned16 the whether Woodward’s second term is implicit in the derivation of the first term.

 

 

III.  Cautionary Note:  Limits to Exotic Applications of General Relativity

 

When I was in studying physics in graduate school, the calculations of general relativity were done exclusively by hypothesizing a configuration of mass-energy and then calculating the “metric” or distortion of space time that it produced.  This conventional approach has lead to many interesting results, but none that could be considered “exotic” or “unphysical”.

But there is another way to do such calculations in general relativity, an approach that has been labeled “metric engineering”.  One specifies a space-time metric that will produce some desired result, for example a wormhole or a warp drive, and then calculates the distribution of masses and forces that would be required to produce such a metric, with all its consequences.  General relativity, used in this way, becomes “exotic”, suggesting the possibility of transversable wormholes, faster-than-light warp drives, and even time machines.

Dr. Keith Olum, in the final Exotic Technologies paper of the 100YSS Symposium of 2011, presented a cautionary note that emphasized that the exotic solutions to Einstein’s equations of general relativity, which appear to provide a pathway to the stars, may not be realizable17.

Many of the theoretical physicists who work with general relativity have had fundamental objections to the very idea of wormholes and warp drives, which they consider to be unphysical.  Some of them have decided that one should erect a “picket fence” around those solutions of Einstein’s equations that are considered to be physically reasonable, and to place exotica like stable transversable wormholes, faster-than-light warp drives, and time machines in the forbidden area outside the fence, excluded because it is presumed that Nature does not allow such disreputable objects to exist. They are, in effect, attempting to discover new laws of physics that would place restrictions forbidding certain GR solutions.

In discussing the behavior of collapsed-matter singularities in general relativity, Hawking and Ellis18 introduced a number of “energy conditions” that, in their view, had to be observed by acceptable solutions of general relativity and might represent the picket fence mentioned above.  The first of these is called the Weak Energy Condition (WEC).  In essence, the WEC assumes that negative energy is the source of “problems” with GR and requires that for all observers, the local energy in all space-time locations must be greater than or equal to zero.  In other words, if any possible observer would see a negative energy, then that solution of Einstein’s equations is excluded by the WEC. A less restrictive variant of the WEC is the Average Weak Energy Condition (AWEC), which requires that when time-averaged along some arbitrary world-line through all time, the net energy must be greater than or equal to zero, so that any time period when the energy is negative must be compensated by a period of positive energy.  In his talk in the Exotic Technologies track of the 100YSS Symposium, Eric Davis15 provided a detailed description and analysis of these energy  conditions.

The WEC, AWEC, and the other similar energy rules are “made-up” laws of Nature and are not derivable from general relativity itself. They appear to be obeyed for observations of all known forms of matter and energy that do not fall within the domain of quantum mechanics.  However, even for simple situations involving quantum phenomena (examples: the Casimir effect, squeezed vacuum, and the Hawking evaporation of black holes), the WEC and AWEC are both violated.

More recently Ford and Roman19,20 have derived from quantum field theory certain quantum inequalities (QI) that must be observed by solutions of the equations of general relativity.  Basically, one chooses a “sampling function”, some bell-shaped curve having unit area and a width that specifies a particular restricted region of time.  This function is then used with quantum field theory methods to average the energy per unit volume of a field within the time-sampling envelope and to place limits on how much negative energy is allowed to exist for how long.

These quantum inequalities are bad news for would-be practitioners of metric engineering.  Taken at face value, the QI say that stable wormholes may be impossible and that a warp drive might, at best, exist for too short a time to go anywhere.  While a wormhole might wink into existence during the short time that the negative energy is present, it would wink out of existence again before any matter could pass through it.  It appears that within the QI conditions, when negative energy is created, it is either too small in magnitude or too brief in duration to do anything interesting.

However, it is not clear whether Woodward’s proposed techniques employing inertia transients (see Section V below) are subject to the QI limitations.  Further, there are reasons to doubt that quantum field theory can be trusted in its application to the field-energy situations envisioned by the QI calculations.

We know that quantum field theory must be wrong, in some fundamental way. It attributes far too much positive energy to space-time itself. The density of “dark energy”, the irreducible intrinsic energy in a given volume of space, as deduced from the observations of astrophysicists investigating Type Ia supernovas and the space-frequency structure of the cosmic microwave background is about 6.7 x 10-10 joules per cubic meter.  The same quantity, as calculated by quantum field theory, is about 1040 joules per cubic meter. Thus, quantum field theory has missed the mark in this very fundamental calculation involving energy density by about 50 orders of magnitude!

Therefore, until quantum field theory (or its quantum gravity successor) can accurately predict the energy content of the vacuum, I feel that the restrictions that it places on metric engineering cannot be taken completely seriously.  Woodward21 has also argued that the derivation of the QI involves use of the 2nd law of thermodynamics in a way that may be inappropriate for artificially produced wormholes.  These arguments perhaps leave the pathway to the stars, as represented by the doorway presented by metric engineering solutions of general relativity, open just a crack.

 

 

IV.  Warp Drives and General Relativity

 

General relativity treats special relativity as a restricted sub-theory that applies locally to any region of space sufficiently small and flat that its gravity-induced curvature can be neglected.  General relativity does not forbid faster-than-light (FTL) travel or communication, but it does require that the local restrictions of special relativity must be observed. In other words, light speed is the local speed limit, but the broader considerations of general relativity may provide an end-run way of circumventing this local statute.

One example of FTL motion allowed by general relativity is the expansion of the universe itself.  As the universe expands, new space is being created between any two separated objects. The objects themselves may be at rest with respect to their local environment and with respect to the cosmic microwave background, but the distance between the objects may grow at a rate greater than the speed of light. According to the standard model of cosmology, remote parts of our universe are receding from us at FTL speeds, and therefore are completely unreachable and isolated from us.  As the rate of expansion of the universe increases due to the action of dark energy, a growing volume of the universe is disappearing over this redshift horizon and becoming inaccessible to us.

Another example of effective FTL motion is a wormhole connecting two widely separated locations in space, say five light-years apart. An object might take a few minutes to move with at low speed through the neck of a wormhole, observing the local speed-limit laws all the way.  However, by transiting the wormhole the object has traveled five light years in a few minutes, producing an effective speed of a million times the velocity of light.

Miguel Alcubierre, using the technique of metric engineering described above, proposed a way of beating the FTL speed limit that is somewhat like the expansion of the universe, but on a more local scale5.  He developed a “metric” for general relativity, a mathematical representation of the curvature of space, that is completely consistent with Einstein’s equations.  It describes a region of flat space surrounded by a spatial “warp bubble” that propels the flat region forward at any arbitrary velocity, including FTL speeds.

Alcubierre’s warp is constructed from mathematical hyperbolic tangent functions that create a very peculiar distortion of space at the edges of the flat-space volume.  In effect, new space is rapidly being created (like an expanding universe) at the back side of the moving flat-space volume, and pre-existing space is being annihilated (like a universe collapsing to a Big Crunch) at the front side of the moving flat-space volume.  Thus, a space ship within the volume of the Alcubierre warp bubble (and the flat-space volume itself) would be pushed forward by the expansion of space at its rear and the contraction of space in front.

 

Expansion (red) and contraction (blue) of space
in the Alcubierre warp drive metric

 

For those familiar with usual rules of special relativity, with its Lorentz contraction, mass increase, and time dilation, the Alcubierre warp metric has some rather peculiar aspects.  Since a ship at the center of the moving volume of the metric is at rest with respect to locally flat space, there are no relativistic mass increase or time dilation effects.  The on-board spaceship clock runs at the same speed as the clock of an external observer, and that observer will detect no increase in the mass of the moving ship, even when it travels at FTL speeds.  Moreover, Alcubierre has shown that even when the ship is accelerating, it is always in free fall, and the crew would experience no accelerational gee-forces when it starts and stops.  Enormous tidal forces would be present near the edges of the flat-space volume because of the very large space curvature there, but by suitable specification of the metric, these could be made negligible within the volume occupied by the ship.  Talks in the Exotic Technologies track of the 100YSS Symposium by Eric Davis15 and Harold White22 contain additional discussions of the Alcubierre warp metric, possible extensions and improvements, and its control.

All of this, for those of us who would like to go to the stars without the annoying limitations imposed by special relativity, appears to be too good to be true. “What’s the catch?” we ask. As it turns out, there are several “catches” in the Alcubierre warp drive scheme.  The first is that, while his warp metric is a valid solution of Einstein’s equations of general relativity, we have no idea how to produce such a distortion of space-time.  Its implementation would require the imposition of radical curvature on extended regions of space.  Within our present state of knowledge, the only way of producing curved space is by using mass, and the masses we have available for works of engineering lead to negligible space curvature.  Moreover, even if we could do engineering with mini black holes (which have lots of curved space near their surfaces) it is not clear how an Alcubierre warp could be produced.  Further, it is not clear how the warp bubble could be steered or controlled, since the interior volume of the warp bubble is completely isolated from the outside, so that steering commands, control information, and views of the outside would be completely blocked.  We note, however, that if quantum nonlocality could be used for signaling, an issue that is currently being investigated by the author23, that development would solve the problem of warp-bubble control.

Alcubierre has also pointed out a more fundamental problem with his warp drive. General relativity provides a procedure for determining how much energy density (energy per unit volume) is implicit in a given metric (or curvature of space-time).  He shows that the energy density is negative, rather large, and proportional to the square of the velocity with which the warp moves forward.  This means that all of the proposed energy conditions (see Section IV) of general relativity are violated, which can be taken as arguments against the possibility of creating a working Alcubierre drive. Alcubierre, following the lead of wormhole theorists, argues that quantum field theory permits the existence of regions of negative energy density under special circumstances, and cites the Casimir effect as an example. Thus, the situation for the Alcubierre drive is similar to that of stable wormholes: they are solutions to the equations of general relativity, but one would need “exotic matter” with large quantities of  negative mass-energy to actually produce them, and we have none at the moment.

At the 2011 100 Year Starship Symposium, NASA’s Harold “Sonny” White reviewed the Alcubierre scheme. He discussed techniques for minimizing the amount of exotic matter required, and showed his plans for an optical interferometer that could be used to attempt observation of the small distortions in space-time that might be induced in the vicinity of a high-voltage toroidal capacitor device22.  This he characterized as an initial step in the direction of producing the space-time distortions of a magnitude that would be needed for a true warp-drive of the type described by Alcubierre.  A recent check with Dr. White indicated that the interferometer has now been constructed and tested, and a novel interference-pattern filtering technique has been devised for improving its sensitivity, but the space-distortion tests themselves have not yet been performed24.

In his talk at the 2011 100 Year Starship Symposium, Eric Davis also reported that a combined effort of EarthTech International, Inc. and Lockheed-Martin is using  meta-materials to create optical analogues that simulate the behavior of wormholes and warp drives in the laboratory15.  We await the results of these interesting efforts.

 

 

 

 

 

V.  Worm Holes and General Relativity

 

In 1916, Albert Einstein first introduced his general theory of relativity, the theory that to this day remains our standard model for gravitation25. Twenty years later, he and his long-time collaborator Nathan Rosen published a paper showing that implicit in the general relativity formalism is a curved-space structure that can join two distant regions of space-time through a tunnel-like curved-space shortcut26.  Their purpose was not to promote travel to the stars, but to explain the existence of fundamental particles like electrons and positrons by describing them as the ends of space-tunnels threaded by electric lines of force. The lines of electric flux would go in at the electron end of the tunnel and emerge at the positron end.  This Einstein-Rosen electron model was subsequently shown to have a serious problem when it was demonstrated that the smallest possible mass-energy of such a curved-space topology is larger than that of a Planck mass, a few micrograms, and far larger than the 511 keV mass-energy of an electron.

The Einstein-Rosen work was disturbing to many physicists of the time because such a “tunnel” through space-time, which came to be known in the late 1930s and 40s as an Einstein-Rosen Bridge, could in principle allow the transmission of information and matter faster than the speed of light.  In 1962 John A. Wheeler and Robert W. Fuller discovered that the Einstein-Rosen bridge space-time structure, which Wheeler re-christened as a “wormhole,” was dynamically unstable in field-free space27.  They showed that if such a wormhole somehow opened, it would close up again before even a single photon could be transmitted through it, thereby preventing superluminal transmission of information.

In 1989 the instability of wormholes was called into question when Michael Morris, Kip Thorne, and Ulvi Yurtsever described how an “advanced civilization” might: (a) create a large wormhole; (b) stabilize it to prevent its re-collapse; and (c) convert it to a time machine, a device for traveling (or at least communicating) back and forth in time7. This remarkable paper, which borders on science fiction in its approach, has a very serious purpose. There is presently no well-established theory (quantum gravity) that can accommodate both quantum mechanics and the physics of strong gravitational fields within the same mathematical framework.  The paper of Morris, Thorne, and Yurtsever is a vehicle for guessing, in a rather unorthodox way, what restrictions a proper theory of quantum gravity might place on the physics of wormholes. The authors demonstrate that general relativity contains within its framework mechanisms that appear to permit both faster-than-light travel and time travel.  If these physical “calamities” (as viewed by some physicists) are to be averted, the authors argue, it can only be done through a proper theory of quantum gravity.

How could a wormhole be created?  Empty space, when examined with quantum field theory on a sufficiently small distance scale, is not empty at all.  Even at nuclear dimensions (10-13 cm) empty space is filled with particle-antiparticle pairs that are continually flashing into a brief existence, bankrolled on the credit of borrowed mass-energy, only to wink out of existence again as the law of conservation of energy reasserts itself.  Heisenberg’s uncertainty principle provides the “cover” that makes such energy juggling possible.  If the length-scale is contracted to a size appropriate to quantum gravity (10-33 cm) this quantum fireworks should intensify to become a “quantum foam” of violent fluctuations in the topology and geometry of space itself.  Quantum black holes should form and vanish in a span of time of 10-23 seconds; highly curved and convoluted regions of space-time in any physically allowed configuration should have a similarly brief existence.  In this environment, Morris, Thorne, and Yurtsever speculated, it may be possible for a civilization, one considerably more advanced than ours, to pull a wormhole out of the quantum foam, stabilize it, and enlarge it enormously to create a connection between two nearby points in space.  This would exploit the well-known quantum mechanical process called “tunneling”, a jump from one allowed energy state to another across a barrier of intermediate states that are forbidden by energy conservation.

To stabilize a wormhole pulled from the quantum foam, preventing its immediate re-collapse, Morris, Thorne, and Yurtsever proposed to use the Casimir effect in the mouth of the wormhole, creating a region of negative mass-energy that would force it to remain open.  They suggest that this might be accomplished by placing a pair of spheres with equal electric charges at the two spatial entrances of the wormhole. The spheres would be held in place by a delicate balance, the attractive Casimir force between them just offsetting the force of their electrical repulsion.  Such a system might be very small, an atom-scale opening permitting the passage of only a few photons at a time, or it might be large enough to pass a large space vehicle.

Having produced this stabilized wormhole, the engineering can begin.  The size of the connection can be enlarged or contracted depending on energy considerations.  The two portal ends of the wormhole connection can be separated from each other.  For example, a portal placed aboard a space ship might be carried to some location many light years away.  Such a trip might require a long time, but during the trip and afterwards instantaneous two-way communication and even transport through the wormhole might be available.

This brings us to the last point of the Morris, Thorne, and Yurtsever paper, the construction of a time machine. Suppose that initially a wormhole establishes a connection between two spatial points A and B that have no motion with respect to each other and are simultaneous in time.  By “simultaneous”, a slippery concept in relativity, we mean that an observer at A who determines a clock reading at B would get the same reading via normal space (by light beam signals corrected for transit time, for example) as he would through the wormhole.

Now suppose, in the spirit of the Twin Paradox of special relativity, that portal B is placed aboard a space ship while portal A remains on Earth. The ship carrying B, say, accelerates rapidly to 86.6% of light speed and travels a distance of 0.866 light-years, then reverses its course and returns to Earth at the same speed. On its arrival, portals A and B are placed near one another.  At 86.6% of the velocity of light, due to relativistic time dilation, from the point of view of an Earth observer any clock aboard the ship will run at just half the speed of a similar clock on Earth.  From the point of view of an observer on Earth, the round trip has taken two years, but from the point of view of an observer on the ship, the round trip has taken one year.  Therefore at the end of the trip the ship’s clock will be one year slow, as compared to an identical clock that had remained on Earth.

And, as Morris, Thorne, and Yurtsever point out, portal B will also be one year slow as compared with portal A.  Now a message that is sent through B to A will emerge one year in the future of B, and a message sent through A to B will emerge one year in the past of A!  We can send messages back and forward in time.  Similarly, a traveler making the same trips through the wormhole would travel one year into the future or the past.  The wormhole connection through space has been transformed to a connection through time, a wormhole time machine.

Do wormholes, embodying faster-than-light space travel (even with space-separated simultaneous wormholes) as well as time travel (from time-separated wormholes), demonstrate that special relativity is wrong?  Do wormholes indicate that Einstein’s special relativity speed limit is wrong?  Not at all.  The restrictions usually associated with special relativity implicitly assume that no time travel is possible.  Clearly one could travel, in effect, at an infinite velocity by traveling from one place to another at some sub-light velocity and then on arrival traveling backwards in time to the instant of departure.  To put it another way, the simultaneity measurements prohibited by special relativity must lead to a definite and unambiguous determination of the simultaneous readings of two clocks separated in space.  The clock-comparisons made possible by wormholes are not definite, because one clock could be in the future of the other, displaced by any time interval produced by the travel histories of the portals.  Special relativity, which after all is embedded in the theory of general relativity that produced these revelations about wormhole physics, must be preserved.

What law of physics gets destroyed by the construction of a wormhole space-time connection? Causality, the mysterious principle that prohibits communication backwards in time, that requires a cause to precede its effects in time sequence in all space-time reference frames.  Causality as a law of the universe would not survive even a two-way communications link across time, let alone a portal permitting trans-time matter transmission. This bothers a lot of physicists.

Eric Davis15 argues that causality is routinely violated in many situations in general relativity and is perhaps only a local flat-space constraint, like Lorentz invariance.

The problem with all of this, of course, is that we have neither relativistic starships nor any technology for capturing and stabilizing wormholes.  At present, we are able to produce only small regions containing negative mass-energy in magnitudes that are tiny compared to what would be needed to stabilize a wormhole, even if one were available to stabilize.  Is there any hope of addressing this problem?

As mentioned above, an “end run” idea comes from the work of James Woodward, as discussed in section II above.  Woodward’s derivation of the inertial transient effects of Mach’s principle in the presence of energy flow includes two terms, the larger one proportional to the second derivative of the fluctuating energy flow and the smaller one proportional to the square of its first derivative21.  The second inertia term is always negative, oscillating at twice the drive frequency between zero change in inertial mass and a reduced inertial mass.  In the tests that Woodward has performed so far, the second term has always been negligible and undetectable.

However, as described in Section II above, the Mach effects depend strongly on the driving frequency, and at sufficiently high frequencies and energy flows, the second term offers the possibility of driving the inertial mass of the system to zero, or even to negative values.  Woodward also offers arguments, based on the Arnowitt, Deser, and Misner theory of the electron28, 29, that interesting non-linear dynamic effects should occur when the mass of a system approaches zero.  Woodward argues that these dynamic effects may conspire to reveal the intrinsic “bare” mass of electrons, which is large and negative21.  We note that the existence of the 2nd mass-fluctuation term has never been tested experimentally, even in the work of Woodward.

Davis15 has pointed out another possible approach to the generation of negative energy for metric engineering purposes.  Ford and Svatier30,31 have published two papers describing action of parabolic-cylinder mirror reflectors that create a line focus, along which the quantum fluctuations of the vacuum are greatly magnified.  With a behavior similar to the gap in a the two-plate Casimir-effect configuration, this mirror configuration creates a region of negative energy density, such that a net electromagnetic force on atoms near the line focus would be in the direction that would draw them into the focus region.  In naive calculations with ideal situations, the fluctuation magnitudes and negative energy density at the line focus go singular as the focus is approached, suggesting that very large magnitudes of negative energy might be achieved at the line focus.  However, the authors argue that this extreme behavior will be limited by wavelength limits when the reflection of quantum modes ceases at the plasma frequency of the mirror.  They suggest an experimental test of the effect similar to that already performed for the Casimir effect, in which an atomic beam is deflected by the forces near the focus line.  The implication of their experimental predictions of the expected deflections is that the effect is comparable in magnitude to the Casimir effect, i.e., not very large.  Nevertheless, this development appears to offer the possibility of developing large negative energy densities in a limited region that might match the requirements of the “thin-shell” wormhole and warp drive configurations that have been proposed.

Thus, in principle we have two nascent technologies that might satisfy the requirements for exotic matter and negative mass-energy that would be needed for metric engineering.  It is clear that further investigation and testing in these areas should be encouraged and funded.

 

 

VI.   Wormholes and Back-Reaction

 

Many scenarios that have been proposed for the use of wormholes in space travel situations turn out to be impossible.  For example, refueling and providing reaction mass to a starship through an on-board wormhole portal would not work.  This is because there are rules derived from general relativity about wormhole care and feeding that come under the general heading of “back reaction”32.  Wormhole back reaction is in essence the changes required in wormhole-portal characteristics (mass-energy, momentum, charge, angular momentum) so as to preserve all of the local conservation laws.

Because of wormhole back reaction, it is not possible to change the amount of conserved quantities in the local space region in the vicinity of either of the two wormhole mouths.  If an electric charge disappears into a wormhole mouth, the entry mouth becomes electrically charged with the just quantity of electric charge that passed through it.  The charge has disappeared through the wormhole portal, but has been replaced by a charge on the wormhole portal itself (think of the lines of electric flux threading the wormhole and stuck there by topology).  Similarly, if a mass goes through, the entry mouth becomes more massive.  If a high momentum particle goes through, the entry mouth acquires that momentum and is pushed forward.  And if a spinning flywheel goes through, the entrance mouth will acquire an angular momentum in the direction of the flywheel spin.  In this way, the local mass-energy, charge, momentum, and angular momentum in the vicinity of the wormhole entry mouth do not change.  No mass-energy, charge, momentum, or angular momentum can magically appear or disappear.  The wormhole entrance mouth itself takes up the slack.

 

Similarly, if a positive electric charge emerges from the wormhole’s exit mouth, the mouth acquires an equal and opposite charge, so that the net charge in the region does not change.  The charges cancel to zero because there was no charge in the region before the appearance of the emerging charge.  An emerging massive particle similarly causes the exit mouth to lose mass-energy, and an emerging high momentum particle gives the exit mouth a recoil momentum in the opposite direction.  This is how back reaction works.  The local situation with conserved quantities before wormhole transits must be the same as the local situation after wormhole transits.

The effect of back-reaction in changing the mass of a wormhole mouth raises a flag of caution.  The wormhole of interest is presumed to be stabilized against its intrinsic tendency to collapse and close off.  This stabilization may be affected or even destroyed  by back reaction effects.  How massive can the mass-gaining wormhole mouth become, and how small the can mass-losing wormhole mouth be allowed to become before stability is lost.  Can the exit mouth’s mass go to zero?  Can it go negative?  Managing the masses (and other conserved quantities) could set important limits on the use of wormholes, even if we could find a way to produce and stabilize them.

 

 

VII.  Sending Wormholes to the Stars

 

Now I want to turn to a scheme for reaching the stars well within human lifetimes, using accelerated wormhole portals.  I discussed this scheme briefly during the panel discussion that ended the Exotic Technologies section of the 2011 100 Year Starship Symposium33.  It is, as far as I know, a new and unprecedented scheme for “ship-less” space travel that I invented and first published in one of my Analog columns in May-199034 and followed up in a May-2012 column35.

Even if we assume that we have been able to produce a wormhole that was stabilized by one of the schemes discussed above, each wormhole portal or mouth would presumably be surrounded by massive machinery, cryostats, power cables, etc., and the curvature of space in the vicinity of the aperture might create tidal forces that make it impossible for a space traveler to survive wormhole passage.  However, Matt Visser has metric-engineered a different solution to Einstein’s equations of general relativity from that to Morris, Thorne, and Yurtsever, in which the wormhole is stabilized by another artifact of general relativity, a negative-tension cosmic string36.  Such an object would be self contained, have no dangerous space curvature except near the cosmic string surfaces, and could, in principle, be very large or very small, even down to the Planck-length scale.  A Visser wormhole might also occur naturally in the aftermath of the Big Bang, since both of its components are GR solutions.  We can also hypothesize that if there were passive stability problems with a Visser wormhole, it might be dynamically stabilized externally by an active negative feedback system acting directly on and through one of the wormhole mouths.

Let us assume that we have the capability of producing such Visser wormholes and controlling their size.  If we keep a wormhole mouth microscopic in mass and size, it behaves much like a fundamental particle with a very large mass, perhaps somewhat in excess of the Planck mass of  21.8 micrograms.  For the purposes of calculation, let us assume that we can produce a stabilized microscopic wormhole with a mass of, say, ten Planck masses or 218 micrograms.

Now, we take the two wormhole mouths of this object and thread lines of electrical force through them, until we have passed about 20 coulombs of charge through the  wormhole.  This can be done, in principle, with a 20 microampere electron beam passing through the wormhole for about 12 days.  The result is that the wormhole mouth will now have the same charge-to-mass ratio as a proton and will behave like a proton in the electric and magnetic fields of a particle accelerator.  (We note that such an object would have to have some minimum radius, because if the electric field at the throat was too strong, it would pull positrons out of the vacuum and reduce the charge by field emission.)

Now we transport what we will henceforth call the “traveling wormhole mouth” to Meyrin, Switzerland near Geneva and put it into CERN’s new Large Hadronic Collider (LHC) there.  The other wormhole mouth remains in our laboratory, along with various stabilizing and steering equipment (described later).  We assume that by the time that we are able to do this, the LHC will have achieved its full design capacity and will be able to accelerate each of its colliding proton beams to 7 TeV (7 x 1012 electron volts).  We use the LHC to accelerate the wormhole mouth to the same energy per unit rest mass as a 7 TeV proton, extract the beam that contains it, point it at a star of interest, and send it on its way.  (Presumably, we would do this in an operation with a number of wormhole-mouths pointed at a selection of candidate stars that might have earth-like planets in orbit around them.)

A proton with a total energy of 7.0 TeV will have a Lorentz gamma factor (g = [1-(v/c)2]  = E/M) of 7,455.  The accelerated wormhole mouth will have the same Lorentz factor.  This is the factor by which the total mass-energy E of the proton moving at this high velocity v exceeds its rest mass M.  It is also the factor by which time dilates, i.e., by which the clock of a hypothetical observer riding on the proton would slow down.  The wormhole is traveling at a velocity that is only a tiny fraction less than the speed of light, so it travels a distance of one light-year in one year.  However, to an observer riding on the wormhole mouth, because of relativistic time dilation the distance of one light year is covered in only 1/7,455 of a year or 70.5 minutes.

Moreover, back on Earth if we peek through the wormhole mouth at rest in our laboratory, we see the universe from the perspective of an observer riding on the traveling wormhole mouth.  In other words, in 70.5 minutes after its launch from CERN, through the wormhole we will view the universe one light year away.  Later, in 11.7 hours we will view the surroundings 10 light-years away.  In 4.9 days, we will view the surroundings 100 light years away.  And so on.

This is a remarkable result.  How is it possible that, if the traveling wormhole mouth requires 100 years, as viewed from Earth, to travel 100 light years, we can view its destination as observers looking through the wormhole in a bit less than 5 days?  It is because, as pointed out by Morris, Thorne and Yurtserver7, the special relativity of time dilation makes a wormhole with one high-velocity mouth into a time machine.  The wormhole mouth, which from our perspective has taken 100 years to reach a point 100 light years away, connects back in time to its departure point only 5 days after it left.  In effect, it has moved 100 light years at a speed of 7,455 c.

But could the traveling wormhole mouth be aimed so accurately from its start at CERN that it might it actually pass through another star system many light years away, to survey its planets, etc.?  And could it stop when it got there?   The fortunate answer is yes.

Momentum back reaction can be used to steer the traveling wormhole mouth.   The direction of travel, as viewed through the wormhole, can be monitored.  Course corrections can be made by directing a high-intensity light beam through the laboratory based wormhole mouth at right angles to the direction of travel.  The beam will emerge from the traveling wormhole mouth “sideways” giving it momentum sideways momentum in the other direction.  The exit mouth will lose a bit of mass-energy in this process, but it will also be gaining some mass energy as interstellar gas passes through it and emerges from the laboratory wormhole mouth.  We note that, in terms of momentum change vs. mass gain of the wormhole mouth, the use of light is preferable to high energy particles, even though the momentum carried by light is only its energy divided by the speed of light, because it keeps the wormhole mass gain/loss small per unit momentum change.

Assuming precision steering can be accomplished by applying such momentum changes, stopping is not too difficult.  The exit mouth will still have the large electric charge used for acceleration in the LHC and consequently will lose energy rapidly by ionizing interactions as it passes through any gas.  It can be steered to make passes through the upper atmospheres of planets or to have grazing collisions with atmosphere of the star itself, until its great initial velocity has been dissipated.  In this process, considerable mass will pass through the traveling mouth, and it will gain this mass-energy by back reaction.  This can be compensated by sending low-velocity mass through in the other direction.  The large charge can be reduced at the same time by sending charged particles through.

The decelerated wormhole mouth can tour the star system, propelled by high momentum beams sent through the stay-at-home mouth in the laboratory.  Such steering will tend to reduce the wormhole mass, partially compensating for the mass-gain it received in decelerating and perhaps in sampling planetary atmospheres.

Now that the wormhole mouth has arrived at the star system of interest, a survey of the planets can begin.  We assume that we have laboratory control of the diameter of the wormhole mouth, and that it can be enlarged to a diameter that is convenient for sampling.  If a habitable planet is found, the wormhole mouth can be brought to its surface, and samples can be extracted through the wormhole and analyzed, (perhaps sending compensating mass back in the other direction to keep the wormhole mouth masses in balance).

Ultimately, when the survey is complete, the wormhole can be expanded, permitting robot precursors, planetary explorers, colonists, and freight to move through.  Again, the mass of the wormhole mouths would have to be managed, moving equal masses in the two directions during wormhole transits, perhaps by sending compensating masses of water through pipes.  This scheme could allow very rapid travel to and colonization of various star systems containing earth-like planets.  Thus, if stable wormholes are possible at all, they may represent a path to the stars that would sweep away many of our previous concepts and prejudices about how the stars can and should be reached.

 

Is there any problem with causality created by using what is in essence a time machine to reach the stars?  Perhaps.  The issue is whether a timelike loop can be established.  Although the space-time interval from some event at the distant star to the observation of that event on Earth, as viewed through the wormhole, represents two-way communication across a space-like separation, there is no causality problem because there is no loop.

However, a causality problem could arise if similar but independent wormhole connections were established with accelerated wormhole mouths sent from the distant star system back to Earth, or even to another star system that had been similarly contacted by the Earth.  In that case, transit through one wormhole followed by the other would constitute a timelike loop.  Stephen Hawking has suggested that Nature will prevent the establishment of any timelike loop through an exponential rise in vacuum fluctuations that would destroy some elements of the incipient loop37.  Thus, an attempt to set up the second link might result in an explosion.  The moral is that such wormhole connections must originate from only one central cite.  Any attempt at replication from another site might lead to disaster.

The scheme described above focuses on reaching “local” stars, i.e., those in our galaxy and does not take into account the intrinsic accelerating expansion of the universe.  One of my Analog readers, Tom Mazanec, argued that by the time we are actually able to manipulate micro-wormholes as if they were fundamental particles, we might have already built particle accelerators that could accelerate protons to far higher energies the 7 TeV available from the LHC.  We might contemplate reaching huge Lorentz factors that could allow us to probe very remote parts of the universe where the recession velocity from cosmological expansion becomes important.  We might even contemplate approaching the redshift horizon, beyond which a part of the universe is supposed to be unreachable.  In that region of near-light-speed recession, the wormhole would eventually match velocities with the receding region until it was at rest with respect to the average matter resident there.  It could never actually reach the redshift horizon from here.  However, we might contemplate setting up operations at this edge of the redshift horizon and building a new particle accelerator to shoot wormholes out to the new redshift horizon appropriate to that region of the universe.  In that way, we might step our way to otherwise unreachable parts of the universe.

This brings us to a variation of the famous Fermi Paradox: if interstellar wormhole transport is possible, shouldn’t the technologically advanced civilizations of our galaxy already be sending tiny accelerated wormhole portals in our direction? Then, where are they?

Perhaps they are already here. Cosmic ray physicists have occasionally observed strange super-energetic cosmic ray detection events, the so-called “Centauro Events”38.  These are cosmic ray particles with incredibly high energies that, when striking Earth’s upper atmosphere, produce a large shower of particles that contains too many gamma rays and too few muons, as compared to more normal cosmic ray shower events. Despite many attempts, the Centauro Events presently lack any explanation based on any known physics.  However, an accelerated wormhole mouth with a large electric charge should have a large gamma-ray to muon production ratio in such collisions, since it would have large electromagnetic interactions but should have no strong or weak interactions with the matter with which it collided.

Cosmic ray experts conventionally assume that whatever else they are, Centauro Events must be a natural phenomenon, not an artifact of some advanced civilization. But that assumption could be wrong.  It is interesting to contemplate the possibility that some advanced civilization may be mapping the galaxy with accelerated wormhole portals, sending little time-dilated observation points out into the cosmos as peep-holes for viewing the wonders of the universe.  And perhaps, when a particularly promising or interesting scene comes into view, the peep hole is halted and expanded into a portal through which a Visitor can pass.

 

 

VII.  Conclusion

 

The Exotic Technologies track of the 100 Year Starship Symposium, held on Saturday, October 1, 2011, explored some of the aspects of exotic technology that might be used to reach the stars.  Presentations by Millis9, White22, Davis15, Maclay, McCulloch, Christea, Sarfatti, and Olum17, and the panel discussion that followed33, gave a variety of perspectives on the possible use of unconventional technologies to reach the stars, and included some interesting ideas.

In this chapter, I have discussed some of them, and I have extended the discussion in directions that I consider to be the most promising for the application of exotic technologies to the 100 Year Starship Project.  There is much work to be done, but the stars are out there, and we urgently need to find a way to reach them.  Otherwise, all of our eggs remain in a pretty blue basket that has so far undergone at least 60 extinction catastrophes, with more to come.

 

 

 

VIII.  References

 

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  16. Davis, Eric (private communication, 2012).
  17. Olum, Keith, “Does General Relativity Permit Superluminal Travel?”, paper given at the DARPA/NASA 100 Year Starship Symposium, October 1, 2011.
  18. Hawking, S. W. and G. F. R. Ellis, The Large-Scale Structure of Space-Time, Cambridge Univ. Press, Cambridge, pp. 88-91, 95-96, (1973).
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  20. Roman, Thomas A.,”Some Thoughts on Energy Conditions and Wormholes”, Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity and Gravitation, September 23, 2004; gr-qc/0409090.
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  22. White, Harold, “Warp Field Mechanics 101”, paper given at the DARPA/NASA 100 Year Starship Symposium, October 1, 2011.
  23. Cramer, J. G., see reports from CENPA Annual Reports on “Testing Nonlocal Communication”, http://faculty.washington.edu/jcramer/NLS/NL_signal.htm .
  24. White, Harold, private communication (2012).
  25. Einstein, Albert, “Die Grundlage der Allgemeinen Relativitätstheorie”, Annalen der Physik 49, (1916).
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  28. Arnowitt, R., Deser, S. and Misner, C.W., “Gravitational-Electromagnetic Coupling and the Classical Self-Energy Problem”, Physical Review 120, 313 – 320 (1960)
  29. Arnowitt, R., Deser, S. and Misner, C.W., “Interior Schwarschild Solutions and Interpretation of Source Terms”, Physical Review 120, 321 – 324 (1960).
  30. Ford , L. H. and N. F. Svaiter, “Focusing vacuum fluctuations,” Phys. Rev. A 62, 062105 (2000).
  31. Ford, L. H. and N. F. Svaiter, “Focusing vacuum fluctuations. II,” Phys. Rev. A 66, 062106 (2002).
  32. Visser, Matt, Lorentzian Wormholes: From Einstein To Hawking, AIP Series in Computational and Applied Mathematical Physics (1995); ISBN 978-1-56396-394-0.
  33. “Panel  Discussion: Can Exotic Science Lead to Starship Propulsion?”, Participants: J. G. Cramer (moderator), M. G. Millis, H. White, E. Davis, and G. Nordley at the DARPA/NASA 100 Year Starship Symposium, October 1, 2011.
  34. Cramer, John G., ” Wormholes II: Getting There in No Time”, Analog Science Fiction & Fact Magazine, (May-1990); http://www.npl.washington.edu/AV/altvw33.html.
  35. Cramer, John G., “Shooting Wormholes to the Stars”, Analog Science Fiction & Fact Magazine, (May-2012); http://www.npl.washington.edu/AV/altvw162.html .
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  38. Angelis, Aris, “The mysteries of cosmic rays”, CERN Courier, January 29, 1999, http://cerncourier.com/cws/article/cern/27944.

 

 



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