I wished it wouldn't come to this.
Let us explore a hypothetical type of force field, a spacetime distortion of a different kind, that could possibly enable time travel, teleportation, practical space travel, and even relative immortality. By a "different" type of spacetime distortion, we mean different from those typically encountered in general relativity discussions. Of course, we can only speculate how such a field might be produced. At the least, we would have to be able to reconfigure matter at the quark level in such a way as to bring the nuclear strong force into play on a macro scale. That is not likely to happen anytime soon, but if it ever should, we show that a list of startling consequences would directly follow.
The goals - Our present generation's most futuristic wishes, fantasies, dreams, and objectives are breathtaking in scope. One might try to dismiss them as frivolous and unimportant, saying "They're just wishful fantasies." Wrong. They are our collective imagination at work, irresistibly pulling us in a certain direction. We are forming and shaping them as we speak, through the medium of futuristic and sci-fi books, magazines, movies, and television. The most universal are that we want to travel safely throughout the universe at near instantaneous speeds; we want a shield around our vessel that prevents impacts by foreign objects and protects us from harmful space radiation; we want to totally escape the grip of gravity and inertia; we want to be able to transport ourselves or other objects by dematerializing at one spot and reappearing at another; we want to be able to completely conceal and cloak our vehicle; we want to be able to travel in time, so as to see the full sweep of the past and the future; we want control over everything that we see; we want to become immortal, omnipotent, and omniscient, insofar as possible; we want to be in the presence of and commune with God; and we want a full escape from the vagaries of sickness, accident, and war. We truly want to live a Star Trek existence.
Clearly, our goals dictate that we will need to distort space and time in ways that have yet to be observed, or at least identified as such, anywhere in the universe. We will have to construct some sort of magical machine that will make physical matter behave in ways that have certainly never been observed in nature. Here, we shall simply postulate a type of force field that, if our machine could produce it, would instantly make possible all of our goals. The rest of the paper will expand upon the idea, its consequences, and how it might be achieved.
The Postulate - In the far future, we will be able to create some magical, exotic material that, together with a field generator that activates and controls it, can create a bipolar surface discontinuity in spacetime, as follows: Consider a thin plate made of this material. On one side of the plate, let it create an outward compression of spacetime away from the plate, opposite the effects of a black hole. Let there be a discontinuity across the thickness of the plate. On the other side, let the effects be reversed to an inward stretching of spacetime toward the plate, as in a black hole. Let the intensity of the effects drop off strongly with distance from the plate. A plot of the intensity of the effects versus perpendicular distance from the plate would have the appearance of a tangent function, with the discontinuity at the plate, representing an infinite-amplitude planar shock to the fabric of spacetime. Let there be controls on the field generator that can adjust the amplitude of the compression/stretching discontinuity, from infinity smoothly down to zero.
The way that we would use this material is to wrap a thin layer of it around a spherical vessel that is large enough to contain the field generator and controls and carry passengers. Outside, let it strongly compress space itself and all of its contents radially outward from the surface of the vessel. Across the thickness of the skin, let the compression drop discontinuously and reverse to an infinite stretching of space at the inner surface, dropping back to normal as the polarity-reversed mirror image of the outward compression. Of course, the enclosed spherical shape of the inner surface will cause the inside spacetime distortion to be intensified and the steepest gradients forced closer to the wall, because now the stretching force is coming from all directions at once. However, we are talking about a "micro black hole" produced by a relatively minuscule and gravitationally insignificant quantity of structured exotic matter.
That's it. Simple to say, unknown how to do. Some will say, "But you have essentially proposed dipolar gravity, somewhat like magnetism. We know of no type of matter in nature that is like that." Of course not. None exists, that we know of. We will have to create/configure it from the most fundamental building blocks of matter. Not today, not tomorrow, but eventually, when we know much more about fundamental physics. The real message of this paper is not in any exotic matter, but is in the shape of the spacetime distortion that we have postulated. Note to mathematicians and first-principle purists: We are not going to attempt to prove the postulate. We merely state it as a "what-if," then examine its many interesting consequences.
I am strongly confident that the statements that are about to be made are compatible with general relativity in the same way that the Schwarzschild spherically-symmetric solution describes the effects around a non-rotating black hole. The situations are qualitatively similar. The real message of this paper is in the shape of the spacetime distortion that we have postulated and in the list of startling consequences that follow, should it ever become possible.
As our postulate states, we want our magical machine to distort space in its vicinity, but in a special way. We did not specify an inward gravitational distortion, as in typical general relativity discussions, because we cannot be irresistibly attracting everything in the vicinity to our machine, nor can we tolerate it being heavily attracted to the Earth. If there is to be a distortion external to the machine, then it must be a compression of space and its contents near the machine, that would not only not attract anything, but would deflect contact, neutralize gravity, and shield from normal physical effects. For reasons that will become clear, we have proposed not a single surface singularity at the hull, but a double-layered singularity of opposite polarities, like an isolated, standing shock impulse in spacetime.
We can qualitatively illustrate the compression field with a simple formula (purely an ad hoc, illustrative device):
r = ( r - r ) + ( r ) ^3 / ( r - r ) ^2
app 0 0 / 0
where r is the radial distance from our spherical vessel, r0 is the radius of our vessel, and rapp is the apparent distance from the vessel from a physics standpoint. There is a far field, where distance goes normally:
r = ( r - r )
app 0
and a near field, where a (1/distance)-squared effect takes over:
r = ( r ) ^3 / ( r - r ) ^2
app 0 / 0
The cubed term in the numerator is just a convenient scaling factor that also maintains consistency in the dimensional units. The important thing to notice is that the apparent distance increases, not decreases, with approach, until the apparent distance at the hull of the machine (r-r0=0) is infinity! The contribution of the near field term drops off sharply with distance away from the hull. For example, if the radius of the machine is sixteen feet, then the near field contribution changes the apparent distance by only about 0.1 foot at a distance of about 200 feet from the hull. Near-field formulas with even steeper dropoffs can be envisioned. 
Now, consider how this works, from a physics standpoint. Suppose that we have a fully-energized machine centered on the origin of coordinates, and an observer out in the far field. Assume, for the moment, that the observer can actually see the machine, contrary to what we will postulate, later. Let the observer approach the machine with a uniform motion. As long as he is in the far field, the machine will loom larger as the observer approaches, just as in our everyday experience. However, as he enters the near field, the nearer he actually approaches, the farther away that it will seem that the machine is located. It will seem to our visual observer that either (a) the machine is running away from him, or (b) the observer has inexplicably reversed direction!
Although we have specified dual compression/black-hole-like surface singularities, both are based on a relatively minuscule and gravitationally insignificant amount of exotic matter, hence the effects will drop off quickly away from the hull, in, say, tens of feet. We want a controllable, spherically configured micro black hole (in relative terms) inside the vessel and its compression opposite on the outside.
The postulated spacetime discontinuity would completely isolate our vessel. That includes an isolation in time, as follows. At the outer surface, space is infinitely compressed. However, as general relativity already tells us, we cannot do this without also distorting the local time scale. Exactly how, we have a clue from black hole theory. Around a nonrotating black hole, space is stretched inward toward the center, and time is slowed by increasing amounts as the stretching intensifies and the event horizon is approached. At the event horizon, time s s entirely, as viewed from outside. Similarly but oppositely, our machine compresses space external to itself, reaching a singularity at the hull. Therefore, we may reasonably speculate that the flow of time will increase for any object approaching our machine, and will approach infinity at the hull. Consequently, we have postulated a spherical singularity in space and time. The interior of our machine is separated by the enclosing spacetime discontinuity from the rest of the universe. Specifically, it is isolated from the local time frame. It becomes its own miniature universe.
The alert reader by now may have suspected that a spherical shell of our activated, exotic material, by itself, might be highly unstable. Possibly not. Go back to the postulate for a moment. A flat sheet of the activated material, upon first look, would appear to have a tendency fire off toward the "stretch" side at an unrestrained speed because the "compress" side is pushing and the "stretch" side is pulling, both in the same direction. Similarly, if we formed it into an unsupported spherical shape, it appears that it would Bam! tend to collapse to a point at the center. However, a closer look reveals that this might not be the case. The "compress" side is the key. Think of what would be required to establish the compression gradient. The vessel cannot be creating the gradient with the outer hull as the origination point. That would imply that it was somehow, in effect, creating new spacetime which could then be compressed and pushed away. More plausible is that the exotic material creates a sort of reverse-gradient gravity (inverted gravity?) that increases in intensity with distance. Then, the greater gravitational pull at greater distance would supply the necessary compressive action between itself and the hull. It is still a gravitational force, just of a different character in its field of influence. If the foregoing is so, then the "compress" side does not push, it pulls. Not only that, the antisymmetry of the proposed spacetime discontinuity suggests that the opposing "compress" and "stretch" pulls exactly balance out.
Another way to illustrate the external compression gradient is as follows: For a moment, think of empty space as an isotropic, transparent, compressible, elastic material that is under static pressure. It has a uniform compressibility and is uniformly compressed to a fixed degree, so there is no gradient in empty spaces away from massive objects. Now, think of the external effects of our machine as some kind of force field that locally increases the compressibility of this "space material" [alternatively: locally decreases the gravitational constant G] with the near-hull gradient that we have proposed, in effect locally reducing the pressure. The rest of our hypothetical space medium, with its higher pressure, would uniformly and conformally squeeze more of itself in around our vessel until, at all points, the near-hull space is further compressed until its pressure is uniformly brought back up to that of space at large. Under this view, our external force field is short-ranged, but of unknown type. Clearly, if it can be created, then it will be constituted out of presently-unknown nuclear or sub-nuclear forces arrayed in completely unnatural configuration.
Our machine, when fully energized, would neither gravitationally attract nor repel any other ordinary material object. The reason is simple. The infinitely-compressed space near the hull acts as an apparently infinite-distance separation between the machine and the rest of the universe. This would certainly occur if the gravitational constant G goes to zero at the outer surface of our machine. Check off the goal "escapes the grip of gravity."
So now we come to a most profound realization: An infinite spacetime compression as described would literally push the real universe away in all directions. The local geodesic lines near the position of the machine would be forced to detour around it. The machine, especially from its own viewpoint, effectively retreats to infinity and becomes isolated from the entire universe. We can illustrate the shape of geodesic lines by use of our qualitative formula from above:
r = ( r - r ) + ( r ) ^3 / ( r - r ) ^2
app 0 0 / 0
Again, let our spherical vessel be centered on the origin of coordinates, and let a small test object approach with a uniform motion on a non-impacting line. First, consider the case wherein the two objects have no dynamical interaction (roughly as it would be with the machine deenergized); the test object would pass by on a straight line geodesic with closest approach, R. This closest approach is "real," in the sense of our everyday experience. Now, let the field be energized, and let the line of motion of the test object pass through the edge of the near field. Consider what happens if we require the (apparent) conservation of angular momentum. At what would have been the point of closest approach with the machine off, now the apparent point of closest approach is displaced to:
R = ( R - r ) + ( r ) ^3 / ( R - r ) ^2
app 0 0 / 0
which is outside of the unaffected line of motion. The compression field locally deflects a geodesic line outward and around our machine, in such a way as to maintain the original angular momentum. Notice that, once past closest approach, the geodesic line curves back to the original, unaffected line upon exit from the near field. All of this is just a simple, qualitative illustration. The precise behavior could be determined by a rigorous, general-relativistic calculation.
By now, some readers are thinking to themselves, "This is just an antigravity device," and are losing interest. However, it does not gravitationally repel anything. Rather, it neutralizes the pull of gravity from all directions. It would be more proper to call its effects "gravity shielding." It is definitely not a white hole, because it does not spew out matter.
The most visually-apparent effect that we would notice about the machine is a relativistic shift in the wavelength of emitted light that is opposite the gravitational redshift; that is, a blue shift. We know that high electromagnetic intensities can ionize air and cause a visible glow. Our machine will likely generate near-field electromagnetic or other effects that ionize air. Because of the local compression of space, any photon emitted in the vicinity of our machine's surface will have its wavelength shortened. There will be high ultraviolet and X-ray effects around our machine when it is less than fully energized (some ordinary light will be shifted through the ultraviolet into the X-ray range). However, the amount of blue shift will not be a constant quantity. We will have to asymmetrically distort our local field in order to move from place to place. We will be continually varying the intensity and shape of our field, much as an automobile driver is continually adjusting the gas pedal, so that any light emitted from our machine will be blue-shifted to varying degrees, such that at any given instant all or parts of the machine might appear red, green, yellow, blue, brilliant ultraviolet, and so on.
The outward compression distortion of space is compatible with the notion of a warp drive. If the compression is not precisely symmetrical, then the inverted-gravity pull on one side will not be balanced by the opposing pull from the other side, and the machine will shoot away toward the strong side. In order to move in this way, the compression singularity will always have to be reduced below absolute on some portion of the vessel, hence a moving vessel will always give off light or other energy in the local reality. As we explain below, the moving machine literally "parts space" and its contents, hence moves without resistance. The fully-energized machine fades from view, travels "outside of reality" to another position, then reappears when deenergized. There is no apparent obstacle to traveling up to and including the speed of light, and possibly more. Check off the goal "travels around the universe essentially instantaneously." More on this, below.
As a warp drive, this proposed field configuration and hypothetical means of operation are different from those of the Alcubierre drive [M. Alcubierre, "The Warp Drive: Hyper-Fast Travel Within General Relativity," Classical and Quantum Gravity, 11(L73-L77), 1994]. Alcubierre's drive maintains a local space and time frame of reference for the moving object itself, while warping space only behind and in front of the object. Although based upon general relativity calculations, Alcubierre's drive has as many unanswered questions as the present postulate, including how to achieve it. We are equally entitled go ahead and speculate freely, here.
The compression discontinuity across the outer skin of the hull provides access to a key parameter for control purposes. From the inside of the vessel, we have access to the narrow, black-hole-like gradient near the hull. Perhaps a shaped plate of some exotic or even ordinary material, when inserted into the space of the wall gradient, could reduce it in that spot. Or, perhaps some energy beam of some sort, when directed onto a spot on the inside of the active hull, could cause the exotic matter in that spot to slightly change its state or internal organization, with the same result as before. In either case, that spot will have a net reduction in the intensity of its spacetime discontinuity.
For a large object, it might be difficult to achieve field symmetry precise enough to allow standing still while energized. We might need to spin the field generator or perhaps the hull of our machine to nullify that last thousandth of a percent of asymmetry. It could also be done by short control bursts from the field generator to localized spots on the hull, similar in effect to the stabilizer jets on our current space probes that are operated with short, impulse bursts. An external observer might see these as flashing and/or rotating lights of various colors, depending upon the degree of the spot impulse bursts to the field, consequently the compressional blueshift at those spots. We assume that we can adequately control the overall field intensity and gross symmetry and asymmetry. For example, we could produce a skipping motion with our machine by applying the basic asymmetry for forward motion, then superimposing a lesser component of asymmetry that is slowly rotated.
The compression singularity prevents other objects from approaching our vessel. That is because its effect is opposite to that around a black hole. The inward-stretched distortion of spacetime around a black hole fatally pulls everything in. Around an "inverted black hole" of the type that we propose for our magical machine, the postulated outward compression of spacetime will push not only spacetime itself away, but also all of its contents. Our machine will hold everything at arm's length - nothing can get in! Any material object or photon that might otherwise hit it is simply deflected and detoured around, along the geodesic lines of the spacetime in which it is embedded. In some sense, it would be like trying to hit something that is positioned an infinite distance away.
If we stood back and looked at a stationary, fully-energized machine minus its halo (if any), we would see nothing! When the machine is energized, it fades from view. One might ask, "Where does it go?" The answer is, "Nowhere." It is still in the same place. The geodesic lines of the real universe are deflected and flow around it similar to a laminar flow in water. We would be able to see an object directly behind the machine as if nothing were blocking the view. Check off the goal "conceals and cloaks." Even if we got close enough that we were in the steep field gradient near the machine and the geodesic lines of space were diverging sharply in order to flow around the machine, we could still look straight ahead and see an object directly behind the machine. We wouldn't have to look left or right in the direction of the diverging lines because our head and eyes are distorted along with the space, in such a way that we see no net effects! Remember that the physical dimensions and shapes of material objects are distorted right along with the spacetime in which they are embedded.
There is a well-known mathematical description of such a laminar flow. In two dimensions, classical complex variable theory can be used to calculate an analytic expression (function) giving the conformal mapping of rectilinear coordinate lines flowing past a circular object. This pattern would be further distorted by the near-field compression gradient. The author has developed a 4-D extension of the 2-D classical complex variables. It can be used to generate a corresponding analytical expression for a 4-D hypersphere, which may or may not appear as a sphere when viewed in three dimensions. For the mathematical system, see [C. M. Davenport, "A Commutative Hypercomplex Algebra With Associated Function Theory," in R. Ablamowicz, P. Lounesto, J. M. Parra, Eds., Clifford Algebras With Numeric And Symbolic Computations, Birkhauser Boston, 1996].
A way to illustrate the inability of an observer to see the energized vessel is as follows: Consider a four-inch-diameter fiberoptic cable made up of millions of hair-thin, individual optical fibers bound up tightly together, with both ends carefully ground off flat and smooth. Let the cable be fixed in a straight path, representing a normal line of sight. An observer can look through the cable and have a view of what is outside the far end. Think of the individual fibers as the world lines of photons in spacetime. Now, go to the middle of the cable and unbind a section and pull the fibers apart into two bundles. The observer cannot tell by just looking through the cable (along her normal sight line) that you have done this; she has the same view out the far end as before. Next, insert some solid object into the space that you created by pulling the cable apart. Again, the observer cannot tell that the solid object is there just by looking down the cable, the normal sight line, though she is technically "looking straight at it." She continues to see the same view as before, which is now directly behind the object. Of course, the solid object represents our machine.
From inside, we would have no way of looking out of a fully-energized machine, because photons from the outside are deflected around the compression singularity at the hull. However, even if light could cross the singularity, its intensity would be reduced to zero, because in effect our compression field has caused us to retreat to infinity from the rest of the universe. Our cross section for impingement of light has been effectively reduced to zero. Moreover, the black-hole event horizon on the inside would not let photons pass. However, if we lowered the intensity of the spacetime discontinuity to some large but finite value, then a few photons would begin to get in and we would begin to see the brighter objects in the sky. Check off the goal "protects from harmful space radiation."
From outside, if we directed light photons toward an energized machine's known position, we would not see any reflection because the photons would simply follow the deflected geodesic lines around it. In effect, the machine would create an isolated pocket, a kernel, in the otherwise smooth fabric of spacetime. For yet another illustration, think of 3-D space as a large stack of silk sheets. They form a smooth continuum. We could devise a set of Cartesian 3-D coordinates that lie along the "fabric" lines of space. Now, insert a marble somewhere between the sheets in the stack. All of the "fabric" of space is still there, but now it curves around and encloses this foreign object. The coordinate lines curve with it. The marble, of course, is our magical machine. It is there, but outside of the local spacetime. Photons would move in the now-distorted laminar layers of spacetime that are deflected around the object.
The laminar flow of world lines around the machine would produce some startling capabilities. Consider a machine that, unactivated, is 32 feet in diameter in local space. Let it be completely enclosed in a hangar with only one opening to the outside, a door only three feet wide. Now energize the machine and have it move toward the door. From the machine's perspective, external objects seem to flow outward, out of the way, and around the side, untouched. As the machine approaches the narrow doorway, the door frame seems to bulge outward and pass smoothly around the sides. Our large machine has just slipped through a small opening! We take this example to the limit and let the "doorway" be the spaces between atoms in a real substance. Our machine can pass through walls! This is shape-shifting carried to the extreme.
Outside observers would not see a large machine deforming and squeezing through a small opening. Instead, they would see the fully-energized machine fade from view and then reappear outside the hangar when deenergized. For all practical purposes, the compression field causes the machine to effectively shrink to a point, when viewed in the local reality and when it escapes interaction with the local reality. Done rapidly, the machine would appear to "wink out." Inside the machine, it may be that no noticeable effects will occur, because passengers, machinery, internal framework, and all are distorted along with the internal spacetime in such a way as to maintain all spatial relationships.
In case the reader missed it, we just gave the basis for teleportation. Unlike in Star Trek, it is not just people that are teleported, but whole transporting vessels. We didn't disassemble the teleported object atom by atom and then reassemble it at the destination; we took it whole "outside of reality," transported it, then brought it back. Check off the goal "teleportation."
For another example, consider a bullet fired radially toward the center point of our spherical vessel. As the bullet approaches from outside the field, at first it experiences the normal uniform decrease with time of the distance between itself and the surface of the vessel. As it begins to encounter the compression field, that effect reverses and it begins to experience an apparently increasing distance opening up between itself and the vessel. It is as if our vessel is retreating from it. However, as the bullet enters the field, its rate of time passage speeds up by an exactly compensating amount. The distance is apparently increasing because of the compression, but the bullet is speeding up by the exact same degree. The net effect: Nothing! The bullet continues to progress at the exact same rate, as seen by the outside observer. As it gets to the vessel's surface, a tiny opening develops in the nose of the bullet, then it flattens and flares outward, follows the deflected geodesic lines, and flows thinly and smoothly around the whole vessel like a greased balloon being pulled over a bowling ball. The outside observer sees none of this. Of course, as this is happening, the bullet cannot be aware of it, either, because to be so would imply either that part of the bullet is penetrating the infinite compression barrier, or something from inside is doing so. Each particle of the bullet is riding its own, distinct, deflected geodesic line, not at an atomic level, but at the most fundamental particle level. This would be a quantum interaction between, for example, individual quarks in the bullet and the structured "quark sheet" on the hull of our vessel. On the other side of the vessel, the geodesic lines come back together and the bullet smoothly re-forms and continues on the exact same line as before. As far as the outside observer can tell, the bullet has made a perfectly normal, straight-line motion, and nothing was there for it to hit. Check off the goal "shields against impact by foreign objects."
Two fully-energized machines of this type could never collide. If they approached on a slightly off-center collision path, then each would deform the others' near field, but they would deflect, deform, and smoothly slide around each other. If on a direct, head-on path through the geometric centers of the activated hulls and if both machines were identical and perfectly symmetrical, right down to the quark level, which they could never be, then both would come to a s and flatten into a plane perpendicular to the line of motion. Such an event would be astronomically improbable. If two partially-energized machines approached closely enough, then the compression fields directly between them could add up to greater amplitude than that at either hull. That would reverse the gradient, thereby reversing the effect to one of gravitational attraction. The machines could collide. However, unlike for the fully-energized case, they could detect each others' proximity and take evasive action. Consequently, our machine would have to be equipped with automatic controls and considerable intelligence and behaviors of its own, to the extent that it might actually seem alive while in operation.
With its space compression field fully up, infinite in amplitude, our machine is invisible and protected from external effects as described above. We are fully cloaked. Our defensive shields are up. No one can even determine our position. Spock would be proud. However, unlike in Star Trek, we can't even "open channel" and view anything external to the machine. We have exited the real universe. But, if we lower the compression amplitude slightly, then our protection is no longer perfect. We begin to come back. Our machine might become faintly visible, mostly transparent, and only partially materialized. Parts of the translucent machine might glow in the local reality. We may receive signals from the outside. We can now "on-screen" that pesky Klingon vessel. If we continue to lower the amplitude, then a local observer will see our machine simply fade into view. At cutoff of the warp drive, we are fully back into the local reality.
Our vessel will have no inertia while fully energized. According to Mach's Principle, the fact that mass exhibits inertia (resistance to acceleration or deceleration) is due to the combined effects of the gravitational pulls of the rest of the distant masses in the universe. Note that the inverted gravity that compresses spacetime around our machine is, in effect, far-field gravity due to far-away masses, that which is postulated by Mach's principle to be the basis of inertia. Its pull is balanced and neutralized by the intervening compressed spacetime, and with it the property of inertia for our vessel. We can make sharp, acute-angle turns at high speed. Our magical machine must contravene inertia for itself and its contents; otherwise, if we are zipping along at 0.9c and make a sudden turn, our machine will be ripped apart, and us with it. As we have already argued, our machine literally exits the universe and escapes all its obstacles and restrictions, gravity and gravity-based inertia included. Check off the goal "escapes effects of inertia."
From our perspective inside the machine, we move along without resistance and inertia because space itself, and everything that it contains, parts and flows around our machine, then comes back together smoothly, without turbulence, after we have passed. We can exceed the speed of sound in air without producing a sonic boom. From the perspective of an external observer, our machine effectively shrinks to a point when fully energized, hence never disturbs anything in passing. 
Our vessel has properties like those of a photon. It can start as a material object, apparently dematerialize, travel without disturbance to another location unseen and apparently without mass and inertia, then reappear. Similarly, a photon is generated from certain interactions involving real matter, travels invisibly and without mass to another location, then reappears in an interaction with another material object, as if it has mass. It does, in fact, have equivalence to mass, per Einstein's famous equation.
No doubt, if we can design a machine such as we have described, it will be capable of gradual transitions from one four-space position or condition to another. As mentioned earlier, we can have it to partially materialize into the local world space. We might want to do so in order to observe or manipulate something in the local area without being seen. A large machine might partially come into local space in such a way as to be transparent and not palpable, but might have to expose visual effects around certain of its internal operating systems, such as a glow around the core of its warp drive. An observer on the ground might see just a glowing blob in the sky, yet might be within the transparent boundaries of the machine. Being partially shielded from the natural surroundings, the internal space would probably exhibit noticeable and unnatural effects because of the modified time scale. For example, the slowed time would interfere with the normal processes of electricity. Lights would go off and automobile ignition systems would go dead. The normal, ambient sounds might cease. An enclosed observer might be expected to describe the atmosphere as "eerie" or "weird." He/she might get a stifling sense that everything is happening in slow motion. We could even tune the field closely enough that the hull is still invisible, yet an observer could bump against it.
Even if it is only partially materialized, we might still be able to suspend normal physical effects and limitations within the invisible boundaries of our machine. For example, with our mechanical material-handling devices, which under these conditions are transparent to the ground observer, we might be able to move local objects, such as a car, around. To the observer, the car would appear to levitate from one point to another. If the aforementioned effects are achievable, then we should also be able to make just a small part of our machine, such as an entryway, fully materialize into local reality. The rest of the machine would remain invisible. A local inhabitant taken aboard the craft would be amazed to find that it is a far larger machine inside than it appeared externally.
It is reasonable to assume that our machine can, in one of its modes of operation, absorb rather than emit light, radiant heat, and other electromagnetic radiation. It would have to be while the machine is standing still, because as we argued above, a moving machine will emit light and other radiation; also, the amplitude of the compression discontinuity would have to be lowered in order for photons to get through and be absorbed. If the machine is in absorb mode, then the ambient temperature would be lowered in the external field gradient around our machine. Taken low enough, the temperature would produce conditions that cause the condensation of atmospheric water vapor. An external observer might see an unusually-shaped cloud that holds its shape and position against a prevailing breeze. Certain lenticular-shaped clouds, that are seen all over the world, fit the bill. If someone got into a helicopter and went up and flew through the cloud, it would be found to have no more substance than any other cloud, because our machine would be in its own little universe that is only partially and impalpably impinged upon the observer's world. Even the prevailing breeze might not be deflected, but might flow through the volume occupied by the cloud. A careful experiment could be performed that would measure the temperature and degree of condensation as a probe is traversed across the widest diameter of the cloud. It would be expected to show unusual gradient shapes.
Thus far, we have delayed examination of the possible conditions inside the proposed machine. As we said, the internal spacetime would be stretched radially outward toward a black-hole-like singularity at the hull, but the steepest gradient would be confined to very close to the hull. What about the rest of the internal space?
Now, hold your breath, suspend incredulity, and consider this: The field gradient could be configured such that the black-hole event horizon covers not just a concentric shell, but near-uniformly some concentric portion of the internal volume. This would be due to the fact that, in effect, we have a black hole pulling not just from one point singularity, but from all directions, simultaneously. Inside this central volume, the passage of time would be s ped, entirely, as far as the external world is concerned. Assuming that the human organism could survive and function in such an alien environment and the machine could be kept fully energized indefinitely, the passengers would be immortal. They would not age on a long trip into deep space. Check off the goal "to become immortal."
We have presumed control over the field intensity, consequently we could also set it such that time would be only dramatically slowed. Anyone inside would experience what might appear to them as a normal rate of time, but which would be much slower than that outside. If a local inhabitant is taken aboard an operating machine, then her rate of time passage will be dramatically slowed while she is inside. When she is returned outside, she will find that the local time has advanced beyond that shown on her watch. For example, if the passage of time on the inside is one-tenth of that outside, and the local person spends one minute inside (as measured by a watch that she carries), then when she returns, ten minutes of local time have elapsed. By just comparing her watch with the local clocks, she will declare that she has nine minutes of "missing time." But not really. She has had a continuous timeline of existence, but just at varying rates of time passage.
Note carefully that the spacetime distortion internal to the machine, with time s ped, is declared to be so only when compared with external conditions away from the field. In other words, it is what an external observer would measure, but not necessarily what a passenger inside the machine would experience. The passengers' physical dimensions and shapes and all of their surroundings (their frame of reference, including time) would be distorted right along with the internal spacetime, with the result that they might not perceive any effect, other than odd shifts in the wavelengths of the ambient light.
This "frozen time," along with essentially massless, inertia-free, resistance-free motion at high speed, the ability to avoid collisions with material objects, and the shielding from space radiation would make cosmic travel practical, though unlike anything that has gone before. Check off the goal "travel safely at high speeds around the universe." 
Hypothesizing about time travel into the past or future presents a much thornier problem. We first have to plausibly hypothesize "if" and "where" the universe of the past exists, for example, and the form in which it exists, before we can rationally talk about traveling "to" it. This is a subject that has been thrashed to death in the sci-fi literature, with as many competing theories as there are authors and commentators. Here, we shall simply present one of our own, and see where it may lead.
We start by asking, "What aspect of reality reliably continues into the future?" because in the future, the said aspect will have become an important part of the past at that time, wherever and however it might exist. The first thing that springs to mind is material objects with mass. For example, a high-purity gold block kept in a favorable and protected environment will continue essentially unchanged over long time periods. Material mass and its configuration in and around us provides our framework for "reality," i.e., the earth, sky, rivers, oceans, roads, cities, people, our physical bodies, etc. We can go further and assert that it is really the primary components of atoms, i.e., the electrons, protons, and neutrons, that we are talking about, because atoms are relatively easily torn apart, but their primary components as named are all much longer-lived under hostile conditions. It doesn't seem promising to go down to the next more fundamental level because quarks, which make up protons and neutrons, by themselves in isolation are extremely short-lived. It is the primary particles that last long enough to provide our continuing framework for reality.
There is at least one other element that must be included: the photons, of all wavelengths. They carry energy about from place to place. Some of them have existed literally from the beginning of time, over ten billion years, freely flying across the universe. Moreover, they are involved in almost all interactions among the atoms of real matter and among the fundamental particles that make up matter. We might also need other fundamental particles in the mix, such as neutrinos, but that would be just an elaboration upon the same principles that we are about to discuss. 
Our hypothetical model of the universe and its "past" at a minimum must somehow keep track of all individual photons, electrons, protons, and neutrons in the universe since the beginning of time. It must continuously record their positions, directions of motion, masses, energies, speeds of motion, and other physics parameters, such that all of their actions could in theory be reconstructed.
To this end, we propose a 4-D block universe with three space dimensions and one of time. We are not suggesting predestination, as will be explained below. A way to globally visualize it is as follows: Suppose, for a moment, that the spatial, 3-D universe is only the size of a basketball; its 4-D block representation including time would then elongate it in the time direction as time elapses, giving it the appearance of a cylinder continually growing along the time direction. Any point on the time axis would then index a complete, 3-D copy of the universe with its evolutionary state as of that instant. From instant to instant, the copies flow smoothly into each other. Of course, the real universe apparently fills all of space, so its movement in the time direction would be a lateral "time" shift of every particle in the universe, in unison. In this block universe, the entire existence of any one of our fundamental particles is represented by a long, twisting, darting, filamentary world line that trends in the general direction of the time axis and that shows the particle's position and path of motion at any given time. The filaments have fuzzy cross-sectional boundaries based on the quantum-mechanical wave-packet description. The filaments (particles) interact among themselves according to the rules given by the Feynman diagrams. In all their twists, turns, and wandering, these world-line filaments must obey certain rules of engagement, the laws of physics, in all their contacts and interactions. We allow that world lines can abruptly appear, run for some time, then disappear. For example, a photon can be created out of the interaction of two material particles, travel some distance, then disappear in another interaction with a material object.
We want our 4-D block universe to have four coordinate axes (dimensions) that are qualitatively the same. That is, if time t is to be a factor in the fourth coordinate, then it will need an accompanying coefficient that has units of distance divided by time (i.e., speed). We propose that the fourth coordinate be ct, where c is the speed of light in a vacuum, for reasons that will become clear, later. In other words, we postulate that the entire 3-D universe is moving laterally to itself in the direction of the time axis with a speed c. We don't sense this in any spatial way because we and all of our surroundings are moving right along with it, just as we cannot independently sense that we are rifling along at 67,000 miles per hour with the Earth in its orbit around the Sun. The entire 3-D universe is uniformly in the same frame of reference as far as this motion is concerned. We sense it merely as a passage of time.
We will use the following terminology. Consider a universe that starts out with a fixed (but unimaginably large!) set of particles with given physics characteristics and with a set of physics laws that govern their interactions, including creation and destruction of particles. Now, set this universe into motion and let it play out its existence along the time axis, like clockwork, with only the physics laws and quantum statistics to guide its evolution. At the leading edge in time, the latest snapshot is the universal Present, so many aeons after the beginning. It is where all action takes place. Before that, every previous, completed action anywhere in the universe is preserved in the world lines of a 4-D block Past, frozen in time. Every particle is accounted for and every interaction is recorded in the world lines. Where is this putative block Past, you may ask? It is all around us, coexisting and recorded in the same 3-D space, but just in earlier times, each instant of which indexes a snapshot of the whole universe and its state of evolution at that time. The Past is not some remote, mysterious place; rather, it is an extremely large collection of world lines in four dimensions and their varying arrangements at different points along the time axis. We further hypothesize a 4-D block Future, into which continues all the world lines of the Present. As we shall explain, free will actions and quantum statistics in the Present can modify any fixed or predetermined aspects of the Future.
In the foregoing, we have hypothesized a (literal) universal Past, Present, and Future, existing simultaneously in different partitions of 4-D space. However, because of special relativity, every observer in the universe will have a different perception of these three. We will use "local Past," "local Present," and "local Future" to account for the observer's bias due to relativity. Because of special relativity, when any observer looks out into the universe, she is looking into the universal Past, her special view of it being denoted here as part of the local Past. 
The Past as described is fixed, frozen in time, but it is not dead. If something should cause a disturbance in the block Past, which normally does not ever occur, then some interesting things would happen. Take the case, for example, wherein we reach back and somehow destroy/remove a single photon at some specific instant in the foregone Past. Its world line from that point forward in time does not instantaneously snuff out. That would imply faster than light communication, in conflict with special relativity. Instead, it begins to dissolve away, beginning at the point of disturbance and moving forward, like an explosives fuse. The point of dissolution moves forward with a speed c, keeping agreement with relativity. Strangely, though we destroyed the photon at some point in time, and it is missing in some subsequent time interval, it continues to exist at later times until the disturbance, which is moving at speed c, reaches those later times and locations. Moreover, if we reach in and pluck a photon world line like a guitar string, in effect turning it in another direction in space, then the disturbance moves forward along the world line exactly as given above, with a speed c. We reach a remarkable insight: we recognize that disturbances in the world lines of any and all particles in the Past, material or virtual, must move forward in time like a new "local Present," because it is necessary for keeping proper relationships, physics interactions, and coordination among them. However, any such disturbances in the Past never catch up to the universal Present because it is also moving forward in time with the same speed.
The Present is continually growing out of, building upon, expanding upon, evolving out of, this fixed Past. Once an action is completed in the Present, it then is added to the fixed Past. The "moving front" of the Present has the same speed as the lateral movement of the universe along the time axis, c. It is like a quantum-mechanically thin cross section in time of the 4-D block universe, moving with speed c along the time axis. Of course, the "cross section" is a full 3-D view of the entire universe.
As physicist Richard Feynman has explained, all of the elementary particle interactions work as well with time reversed. Indeed, our model, which tracks elementary particles, works as well if we could somehow move along the time axis in the negative direction. There would be no qualitative difference in its operation, but normal observers would be startled to see everything start to replay in reverse order.
Let us try to globally illustrate this model. We have to make some outlandish assumptions in order to do so. First, assume that we, the observers of the illustration, are higher-dimensional beings who can somehow exit and step back from the 3-D universe and see it in its entirety. Further, suppose we can view it by some means other than photons, so that we can actually see the world line structure that we have outlined above. Let us step away far enough that we see the 3-D spatial universe as a ball-like object with the apparent size of a basketball, and orient our viewing position such that we can actually "see" in the time dimension (i.e., at a right angle to the time axis). Now let the universe grow or run its existence by some short interval of time t in the fashion that we have described above. The basketball-like object will move laterally a distance ct along the time axis. World lines of proper quantum-mechanical thickness will run smoothly and continuously from the old to the new positions of each and every particle in the universe. As time continues, these world lines continue to grow and extend, and from our supernatural viewpoint the ball of the universe grows into a cylinder along the time axis. The diameter of the cylinder at different points on the time axis might stay constant (static universe), grow over time (expanding universe), shrink (contracting universe), or periodically cycle (recurring Big Bang), depending upon the overall gravitational attraction among the mass-bearing particles. If we zoom in close enough on the cylinder, then we can see the fine, world-line structure of the universe, looking like a tangled bundle of spaghetti.
Continuing our same supernatural viewpoint, we examine how a material object would appear. Of course, we would be looking at the organized, coherent bundle of its constituent world lines, which grows along the time axis. Let us make one small change and view snapshots as time progresses so that we can see 3-D objects. Consider our spherical vessel of diameter D. If we are moving with it at speed c along the time axis, then it will appear normal, with diameter D. If we are stationary and it zooms by at speed c, it will appear as an ellipsoid strongly flattened almost into a plane perpendicular to the time axis. Its apparent thickness in time is derived from the simple relation cdt=D, or dt=D/c. Remember, we are not viewing with photons and do not have a typical special relativity scenario.
This model of the universe has a Past, which is everything from its beginning up to its current state of evolution. It has a universal Present, which is a moving snapshot that is so many aeons beyond the beginning, in the same sense that the universe is said to be some 13 billion years old. Its Past is continually being grown and extended by the Present behaviors of its constituent particles. Moreover, there is a way for we supernatural observers to get back inside this Past construct and replay/review the action from some point in time, forward. We simply get back in as an infinitesimal point observer, so as not to disturb anything, and view in normal 3-D with photons, then move in the time direction with speed c (easier said than done). As we move through the fixed, 4-D, frozen block universe of the Past, we perceive a quantum-mechanically thin 3-D cross section in time of the world-line cylinder, which looks to us like the normal 3-D universe, and solely our movement in the time direction brings to life and perfectly replays all of the bygone actions. There is one difference, however, between this and normal reality: while we are moving through this fixed block of the Past without interaction, our "local future" is fixed, and we merely replay it out.
In this model, as we replay the Past as described, and if we could zoom in close enough, we would see individual particles flying about in all directions as they normally do, as if they have complete freedom of motion. However, this is an illusion. The particle world lines are fixed in 4-D spacetime. There is only one motion, which is the observer's 3-D, thin-slice view that is moving along the time axis. What we see are the cross sections of the long, fixed, but wandering particle world lines with our moving, thin-slice view in time. A cross section of a particle world line with a quantum-mechanically small time extent appears to us as an isolated particle. The particles appear fuzzy and indefinite because their world line cross sections and even our thin-slice viewing window each have an associated quantum probability function.
What of the Future? All is strictly speculative, but it is logical to consider an extension of the same constructs as used in the Past and Present. Therefore, we hypothesize a fixed, default, 4-D block Future, which is continually being eaten away, modified, and reconstructed into the Past by the moving Present. It extends to infinity along the time axis. The Present and the already-there Future are joined, world line to world line, particle to particle, just like for any section of the Past. No actions occur anywhere outside of the Present, excluding time-travel disturbances. If no new disturbances are introduced in the moving Present, then the default Future would unfold logically out of the current state of the Present, and an infinitesimal, 3-D point viewer using photons would see a completely predestined Future, regardless of how random it might look. 
In order to avoid a completely predestined future, we must allow for the free will of animate organisms in the Present and the disturbances that they would propagate into the Future. The disturbances would not be racing ahead into the Future, but would be merely modifying the otherwise fixed Future in the Present, as the latter advances. That is, true free will would erase and reconstruct parts of the preexisting Future as they are encountered. For example, if we consider a remote, uninhabited area of Antarctica, we see that if it is left alone, it has a preordained future. But, we can by free will go into the area and build a small city, thereby altering its future. However, this is not so completely simple as it seems. Free will is based in the brain, which is a material object made up of electrons, protons, and neutrons, all of which have world lines indistinguishable from those of all other objects with mass. Making a free will choice involves merely rearranging the relationships of some of the world lines of the brain, and we could equally well argue that those changes were "already there" in our world lines in a fixed, frozen Future, and we merely encounter them in passing in the Present. In the latter view, free will is an illusion, even though we may "get the notion" before the putative free-will action, thereby causing us to think that we are the independent originator and cause of the action. But even "getting the notion," itself, is just another rearrangement of some of the world lines of the particles that make up the brain, qualitatively indistinguishable from those for any other action, predestined or not.
Similarly, we include statistics, particularly quantum statistics, in this model, for the same reason. However, the fact that statistics apparently cause all actions to be uncertain until they actually occur, and the future likewise, might also be an illusion. The simple fact that we cannot predict for any specific particle exactly when there will be an abrupt change, gives us no help in deciding between predestined or not. In this model, once an action and the concomitant world line modifications have occurred and are in the fixed Past, they have no qualitative differences from any others.
So, to summarize: We hypothesize a 4-D block universe with a Past, Present, and Future existing simultaneously in the same 3-D space, but strung out along the time axis. We experience it as a thin cross section in time of the 4-D block universe, which appears to us as the full 3-D universe. The time cross sections of the strung-out world lines appear to us as point particles that make up all matter. They appear to move about freely because their world lines intersect the 3-D, thin-slice universe of the Present at different spots as time progresses. The Past is right here, all around us. The model works equally well with only inanimate material objects or with animate objects with free will added to the mix, and with or without random statistics. We can actually see into the Past because photons from there can reach us, as witness our radio astronomy views of the earliest galaxies. If no new, non-predestined actions are executed in the Present, then we play out a fixed, predestined Future. However, we allow for human free will and quantum statistics in the Present that can cause a modification of any predestined Future. If we somehow insert ourselves as material bodies at some time point in the Past and at some 3-D different location, then we become a new part of that local reality and create a disturbance in the world lines which then propagates forward in time, and us with it, causing us to automatically start re-living a now-modified Past. In this view, a human body is just a group of coordinated, localized disturbances in a coherent bundle of world lines of primary particles, propagating forward together in time.
Having a hypothetical model of the universe, we may now plausibly speculate about time travel. Clearly, in order to achieve it in the most general sense, our vessel has to escape the normal movement of the real universe along the time axis. We have already discussed how our machine can exit the real universe and s time in its interior. From that, we deduced that it could jump forward to a "then present" simply by staying energized for the desired time interval, then deenergizing, and we as operators would not have aged. Therefore, we have a form of time travel to the future. However, there is a subtle twist. By this type of action, we are not simply cruising ahead freely in time and viewing what will happen at that later time. Instead, we are stepping aside and letting the universe continue to evolve without us, letting everything happen that will in the interval, and then later stepping back into reality, unaged. We then become a part of that future state of the universe. We are missing from the universe in the interval, and we forfeit our normal existence in the interval because we have stayed in our vessel. The twist is, it is a subtly different future because it does not account for our own lives and any potential actions that we might have taken after the departure time, had we stayed there. We aren't in it because our world lines were terminated by the absolute spacetime discontinuity around our energized machine as we departed. As a result, we can't time-lapse forward and see snapshots of our own lives as they play out. If we so travel forward far enough, then we forfeit the rest of what would have been our natural lives from the departure time forward. Instead, we spend that time in our vessel.
How to go back in time, whatever may be there or not, is less clear. We can't simply do the reverse of the above and "undo creation" or run it in reverse. This time, we have to sail against the winds of time, so to speak. We will have to purposefully and proactively travel and navigate into the fixed, 4-D block Past, not simply by stepping aside and letting something happen. This presents a problem, because when we energize our machine we are automatically stepping aside. 
There is a clue in the structure of our model of time. It evokes a "time as a river" metaphor. Consider a set of axes with distance along the +x-axis and time along the +y-axis. World lines of the elementary particles grow and trend upward in the +y-direction. For purposes of this illustration, let the world lines be parallel. They represent the "current of time," because in our model any disturbance in them is swept upward as if being carried by a current. The universal Present, with its time cross section containing that which we perceive as material objects, including ourselves, is also swept along as if in a current. The metaphor really comes into play when we consider what happens when we try to navigate across this stream (travel some distance). Suppose that we want to travel a distance S=vT, where v is our speed and T is the elapsed time of travel. As we try to navigate across, our vessel is swept downstream like a boat in a current in the time direction. In time T, our vessel drifts downstream by a "time distance" of cT, precisely the distance advanced by the universal Present. We always end up in the universal Present because we are always keeping pace with it. An observer at our point of departure will see us go straight to our destination, because the observer is drifting in the current with us. We can use any speed up to and including c, and these statements continue to hold.
In this "time as a river" metaphor, we and our unenergized machine would be rushing "downriver" with the "current," along with everything else. However, if we get into the machine and energize it in place, then we suddenly s our "downriver" motion, and the "current" flows smoothly and conformally around our machine. If we then move rapidly across the "river" (i.e., move spatially in any direction), we tend to drift "upriver" against the "current," into our local past, as follows:
When we include special relativity in the context of this "river" metaphor, we come to a crucial insight. As we know from established relativity physics, inexplicable and counterintuitive as it is, that spatial movement slows the passage of time for the moving object, as compared to that for a stationary observer. The slowing strongly increases as the speed approaches c. At the speed of light, it appear
