SpaceTime Hypersurfing

by Michael Szpir

from Volume 82 of American Scientist

In some future history, 1994 may be remembered as the year that the warp drive was first conceived to be a physical possibility. Long a cliche' of science- fiction writing, the warp drive has transported countless fictional characters through light-years of interstellar space in the time it takes for you or me to travel to the market. Unfortunately for real-world travelers, the warp drive has always been thought to be inconsistent with the laws of physics.

But all this has changed. In the May issue of Classical and Quantum Gravity, Miguel Alcubierre, a physicist at the University of Wales describes a space-travel scenario that bears an uncanny resemblance to the warp drive of science fiction. With Alcubierre's warp drive, we could reach any place in the universe in as short a time as we please!

The warp drive envisioned by Alcubierre is made possible by the subleties of Einstein's general theory of relativity. According to Einstein, spacetime (the union of the three dimensions of space with the dimension of time) is not an inert substrate, but rather a dynamical entity that twists and distorts under the influence of concentrations of energy. Alcubierre suggests that it might be possible to exploit this phenomenon to travel from one star to another faster than the speed of light. This could be done by creating a disturbance in spacetime such that the region directly in front of a spaceship is contracted while the region directly behind the spaceship is expanded. This distortion of spacetime would, in effect, propel the spaceship forward like a surfer riding the crest of a breaking wave. At first glance this mechanism would appear to violate Einstein's special theory of relativity, which holds that no object can travel faster than light. Violations of this law lead to causal paradoxes, in which actors in the present can alter their own past. Yet Alcubierre shows that his warp drive does not, in fact, lead to such violations. The reason is that light also travels in spacetime, and is carried along just as the spaceship is. The light beam is still traveling at the speed of light, relative to the spaceship, which itself is not accelerating relative to the spacetime in its immediate vicinity. Although Alcubierre's warp drive does not engender any causal paradoxes, one might still be concerned for a space traveler's welfare. To get to a distant star and back in only moments, the traveler would have to be accelerated at a very large rate, effectively turning him into soup. Or at least this would be true, if not for the fact that accelerations are relative in general relativity.

Although the acceleration of the spaceship as seen by someone on Earth would be enormous, the acceleration experienced by the space traveler would be zero! The space traveler would be weightless, just as astronauts are in orbit around the Earth. Finally, Alcubierre also shows that a traveler using his warp drive would experience no time dilation. One of the predictions of Einstein's special theory of relativity is that time flows at different rates (Keely said that 'Time is Gravity') for observers moving relative to one another. Consider two space travelers, John W. and Campbell Jr., who decide to visit the great galaxy of Andromeda, which is about 2 million light-years away. John travels in a spaceship that advertises "one Earth gravity all the way." Campbell spends most of the trip traveling near the speed of light. Because of time dilation, Campbell is able to survive the trip, aging only 60 years in the process. However, because the galaxy is 2 million light years away, about 4 million years pass on Earth before Campbell gets home. In contrast, John is able to make the journey to the galaxy and be back in time for supper on Earth!

Of course, there is no such thing as a free lunch (or supper). The key to Alcubierre's warp drive is something called exotic matter. Exotic matter has the curious property of having a negative energy density, unlike normal matter (the stuff that makes up people, planets and stars), which has a positive energy density. Two bits of matter that have the same energy density are attracted to each other by gravity. In contrast, bits of positive and negative energy matter would be repelled by gravity. It is the negative energy density of exotic matter that powers the warp drive. A negative energy density is not the nonsensical thing it appears to be. Indeed, in 1948 the Dutch physicist Hendrik Casimir first predicted that one could observe the effects of negative energy densities. He reasoned that if negative energy densities existed, two closely spaced parallel conducting plates in a vacuum would be attracted to one another. This phenomenon, now called the Casimir effect, was measured in 1958 by M. Sparnaay, and is usually taken to be a confirmation that negative energy densities are possible. Exotic matter of a slightly different type is also invoked in the modern theory of cosmology known as inflation. According to the theory of inflation, exotic matter in the early universe (moments after the big bang) had a positive energy density, but a very large negative pressure. The negative pressure was so large that it counteracted the effects of the positive energy density. The result was an expansion of spacetime so rapid that two observers originally very close to each other would be carried apart faster than the speed of light.

This paradigm of spacetime expansion provided the motivation for Alcubierre's warp drive. There are, of course, 'technical details' to be worked out before the aerospace firms can start building starships. Foremost among these is the production of exotic matter. Alcubierre has not given that aspect of the problem much thought. Although he is an avid reader of science fiction, he does not intend to pursue the subject much further. Currently, he spends most of his time working on other problems with general relativity. The warp-drive scenario, he says, is a very simple thing that he came up with in his spare time. Perhaps the problem will be taken up by some future physicists in their 'spare time'. The rewards could be astronomical.

Faster than Light Experiments

 
QUANTUM MECHANICS has been with us for over sixty years and has been thoroughly put through its paces both experimentally and theoretically. Yet physicists continue to be haunted by its strange implications - virtual particles, antimatter, negative energy, energy, dinger's cat. Now it appears there is something else to add to the list: light that travels faster than light. Recent and past experiments that show that C can not only be slowed, but also speeded up have been in the science news forefront for the past two years. Einstein's special theory of relativity says that anything that travelled faster than light would also have to travel backwards in time. So if light can travel faster than light, shouldn't it be possible to send signals backwards in time, causing all sorts of mayhem, with effects taking place before anything ought to have caused them? Well, not exactly. It turns out that the quantum world is so strange that it is, after all, possible to break Einstein's speed limit. Until very recently the consensus was that this would not violate Einstein's theories.

But some tantalising new results reported at a meeting last month are not so easy to explain away. If they prove true, relativity theory could be in trouble. The heart of all such experiments actually goes back to something that has been around for generations. One is the concept of tunnel effects. The other has to do with the structure of the medium photons(the carrier of light) is traveling in. Ever since white light was split apart into its seperate components or frequencies we have been changing the speed of light just slightly. But that effect is due to a slowing of C in a diffraction medium. Now along comes experiments that show the group velocity of a propogated wave of light in a wave guide can be made to far exceed C. Notice, I mentioned group velocity here. This concept of a group velocity traveling greater than C has been around in the electronics communication field as long as we have had microwaves and wave guides. Several decades back it was noticed that a magnetic image of a signal traveling in a wave guide moves ahead of the actual signal. That image actually does travel faster than C and experiments have proved this many times over as does the wave guide math.

The problem has always been that it is an image that cannot be used to transmit data of any type, except perhaps if a proper detector could be fashioned so that an on/off data stream was used. To date, I know of no one who has directly tried this. Now we have something new on the horizon. In particular, there is the work of Raymond Chiao and colleagues at the University of California at Berkeley. Chiao has been pioneering a range of experiments that probe the twilight zone of quantum mechanics - an alien world where ghostly particles can spontaneously appear and disappear, where objects can pass through solid walls and where everything seems to dance to a different tune depending on whether or not you happen to be watching. Quantum tunnelling is, in itself, a remarkable phenomenon because it involves particles travelling through barriers that ought to be impenetrable. If you throw a ball at a wall you expect the ball to bounce back, not to pass straight through it. Yet subatomic particles pull off the quantum equivalent of this feat with consummate ease. According to quantum theory there is a distinct, albeit small, probability that a particle can tunnel its way through a barrier even if it does not have enough energy to jump over.

The probability declines exponentially with barrier thickness so for all practical purposes quantum tunnelling is usually observed only when barriers are no thicker than a few atomic layers. Nevertheless, quantum tunnelling has many practical applications - playing a major role in nuclear fusion, in electronic devices such as the tunnel diode, and in tunnelling electron microscopes, the highest resolution microscopes in existence. What Chiao and others have done is measure how long it takes particles of light - photons - to tunnel through a barrier. Their rationale was a pile of theoretical calculations, some per formed as long ago as the 1930s, which suggested a strange idea. In 1932, L. MacColl of Bell Labs wrote: "When a particle tunnels through a barrier, it does so without any appreciable delay." The implications of this, though, did not become apparent until 1955 when Eugene Wigner and his student L. Eisenbud at Princeton analysed the problem and concluded that under some circumstances tunnelling particles could actually travel faster than light. This bizarre conclusion has been re-examined and argued about by theoreticians over the decades.

The problem is that many ways of looking at it seem to leave common sense behind. What actually happens in the tunnel effect is that the wave nature of a particle comes into play. As that particle hits that barrier its wave function starts to collapse. From the perspective of one who works with String Theory the outer membrane extension collapses. If the barrier is small enough, that waveform will not totally collapse before the opposite side of the barrier is reached. In that case, the wave re-expands again on the other side and the particle pops back into its existance as a particle-wave again. To an outside observer the particle vanishes at one point and reappears again at another point. This barrier jumping goes on all the time in semi-conductors in equiptment like this computer. But there is an aspect that even Dirac noticed to this function that does seem to exceed C. Certain aspects of a particle’s state can be communicated across distances faster than Light is able to travel. Dirac choice to ignore these aspects even though he once worked the math out and showed it followed a modified Lorentz formula. I mentioned that aspect on my own site in the proof from other theories section. To date, I believe M-Theory has been the only field of study that has confronted these controdictions and found an answer that obeys relativity to the letter. What most have always ignored is that just like Dirac’s formulas for the electron predicted an oppsite counterpart, so does Relativity. Einstein, himself, noted the possible existance of what is now called Tacyions. Particles that travel faster than light. But, like so many after him, he choice to ignore those states. What M-Theory does is find an answer to why we cannot observe those states.

They exist in a higher dimensional framework that is compacted smaller than the Plank scale. As I mentioned to Geometrodynamics in an email and to others my own modified M-Theory is the same as regular M-Theory in that it is actually an 11D framework. I just choice to ignore time in my discussion of 6D space-time because it simplifies things. Time and velocity there do exist. But at a higher rate from ours. What we experience as time passage in relation to motion is actually a combination of two time frame’s that add to make a different value. Just as the energies in both sub-spaces add together or blend together to make the values we can measure in particles and fields. Does this imply time runs backwards in 6D space? No, not within its own time frame. Only in relation to our perspective. Cause and effect within each time frame still follow a set path. But each of those paths is opposite in the other frame. Its like a mirror image. Left and right are reversed in a mirror. But the image is still the same image. Only the symmetry is changed by reversal.

On Kant and Einstein's First Principles
One of the major problems, as good as relativity is that the philosophical implications of the likelihood that observation will continue to reveal an infinite universe have never been actually decently considered. It is very true that Einstein well answered Kant's Antinomy of Space, but his method does so without answering the Antinomy of Time. Part of this is the finite and unbounded principle that almost all of us in physics use. Indeed, it is almost counter-logic to state such. A finite universe by its very nature has to have a boundary or event horizon. Otherwise, the universe one is describing would be infinite. That boundary is formed by the most extreme point in all directions, given uniform expansion which evidence points to, of both matter and energy. Consider such a uniform expanding sphere of photons and thus, discount any non-uniform changes in expansion rate. Such a system must by nature have a boundary. Else, what it is expanding into would have to be considered part of the system in question. Since that which it is expanding into cannot be considered the same vacuum state as our present universe. One cannot consider it to be part of our universe, except as possible another sub-space. Secondly, since nothing can be determined by experiment or observation about this unique sub-space owing to the fact it would be an absolute zero. I do not feel a zero can be considered a true sub-space.

I have made reference to Kant, herein. Some have tried to claim that Kant implied in his ideas, though he predates such, that, non-Euclidean geometry is logically impossible. I personally do not believe that is a correct interpretation of Kant. I personally follow some like Leonard Nelson, "Philosophy and Axiomatic," Socratic Method and Critical Philosophy, Dover, 1965; p.164. Kant to us simply though the axioms of geometry are synthetic. Thus it is not truly analytic. We base our geometry on observation and to a certain extent on visualization. This applies to both normal Euclidean geometry and non-Euclidean geometry. Non-Euclidean geometry did not change our spatial imagination, it only proved what Kant had already implicitly claimed: the synthetic and axiomatically independent character of the first principles of geometry.

If Kant is right then we will never be able to imagine the appearance of Lobachevskian or multi-dimensional non-Euclidean spaces, or to model them without extrinsic curvature, however well we understand the analytic equations. But I do not feel this prevents us from coming to grips with a real answer to Kant on both space and time. This has been the crux of our problem not only here in our discussions. But it is a fundamental problem across the board in both Physics and Cosmology. We all tend to use different terms when it comes to time. Most of our definitions of space all remain the same. Weither one choices to follow the Newtonian approach, that of Einstein, that of M-Theory, or any other approach. It’s when we start describing our fundamentals of time that we all diverge. Put this on the record. I am not saying my own definition of time is any better than anyone else’s. But I do feel it goes a long way to defining time and removing the original problem of the Boundary problem. As such, it does attempt to at least go a bit beyond Einstein and give an answer to Kant on both space and time.
The Special Theory of relativity is nothing less than an adaption of physical principles to Maxwell-Lorentz Electrodynamics. It takes the assumption of Euclidean Geometry that is valid for ridged bodies, the inertial frame, and inertia. It combines them with the invariance of the velocity of light from electrodynamics. To get these two to agree it had to abandon the concept of absolute time. That much is shown in Einstein’s own lecture to the Nordic Assembly of Naturalist on July 11, 1923. However, what most forget is that GR does not follow Euclidean Geometry. As such, GR itself modifies SR. GR is built upon a higher dimensional form of geometry. It is non-Euclidean and as such it abandons those original asumptions and takes them as strickly a seperate case. The biggest thing that GR does do is it keeps those assumptions from Electrodynamics. As such, it agrees with the invariance of the speed of light in the vacuum. But, it even more stipulates that the geometry of that vacuum controls that invariance.

Since early times we have known that if you change that vacuum state you alter the speed of light. Light in water, for instance travels at 75% of its velocity in a vacuum. In fact, in water certain things can and do travel faster than light. So thus, we do have proof that the invariance of C only pertains to the normal vacuum state. It also only would pertain to the present state of that vacuum. When one tries to abstract backwards in time towards T=0 one incounters a state where the vacuum density overall changes. One cannot by principle then assume that invariance as seen in our present state holds true then. Nor can we by principle hold that it would hold true under all changed states of that vacuum. Thus, relativity does have its limits. Like it or not. Those limits are defined by the terms that C remains constant in the vacuum as we now observe it and know it to be. Beyond that one simply cannot state otherwise unless one desires to go against the very fundamental underpinnings of relativity itself and against the one who wrote that theory.

Natural FTL States Explained.Consider the interval given by ds^2 = A(z,r)dct^2 - A-1(z,r)dz^2 - dr^2 - r^2dq^2. A will go to 1 as r goes to ¥ . A will be -1 at r = 0 for a finite length along z of (a,b) and again A will go to 1 as z goes to ± ¥ . A coordinate transformation that reduces this interval to the form of special relativity at the location of an observer between (a,b) at r = 0 is given by ct = z', z = ct'. Time ct and space z are folded over in this region. This results in a velocity transformation u = c^2/u'.

Thus an object still with respect to this local frame moves from point a to point b instantaneously. Now a boost can be done from the local inertial S' frame to another local inertial frame S" and the transformation will be Lorentz. This leads to the general transformation from a local frame to the remote frame given by ct = gz' + gbetact' and x = gct' + gbetax'. But this are inverted compared to the Lorentz transformation equations. b is the velocity of S" with respect to S'. This leads to the velocity transformation u =c^2(1 + vu'/c^2)/(u' + v). Now the fastest S" can move with respect to S' is v = c and this results in u = c. Thus we see that for this case of space-time folding c is the speed minimum instead of the speed maximum. This same effect happens in matter cross the event horizon of a Blackhole. Thus under the event horizon, the coordinate speed of light falling radialy into a Schwartzschild hole is a speed minimum for in falling objects rather than a speed maximum. It is also the same effect arrived at in crossing the membrane into 6D space-time.

In it has been referenced that in two-dimensional space-time modeling of the effects of Alcubierre’s Warp Drive Theory there has been discovered that the vacuum stress energy of a quantified massless field would diverge on the Horizon as it formed. This extended to a 4D model shows that an infinite amount of energy would be formed from the divergence, and by semi-classical back reaction such would prevent a ship from achieving any usable warp field beyond that of C. However, this does not rule out attaining C itself or any fraction of C via a similar method. Even the attainment of C by any space ship would be a fundamental increase in our ability to travel in space. So the field of both negative energy and warp field generation does deserve further research. It certainly hints that there exists at least on mathematically and modeling grounds ability to extend our current velocities of space travel to that horizon boarder. There has also been research done by those originally involved in this and other Institutions that have shown those divergences can be at least at the model level worked around into something that allows carrying the field on up in velocity gain. Some of those have even shown far less energy requirements of negative energy to achieve that effect.

It is the effect that interests me the most in their model. The Alcubeirre solution allows a craft or any object to have an apparent speed relative to an observer elsewhere, which is greater than the speed of light. This is achieved by an effect caused by space-time expanding behind the craft and being compressed in front of the craft. There does remain a possible means of achieving the same effect without the usage of negative energy. The structure of 6D space-time with the effects of 4D space-time canceled out would be one of rapid expansion back towards its normal state of a perfect vacuum state. If the 4D portion could be canceled out behind a ship this same effect could be generated. This could be possibly done by using an effective opposite going phase wave type field in that area that cancels the normal positive going phase wave within a given region of space. The biggest problems concern creation of that transtating wave, as I have chosen to call it. And focusing such a field projection so a craft or object can remain in its own bubble of normal space-time within. Such a field generation, while by no means impossible in the future, is beyond our present capability of generating at this time. But it does open an interesting field of research that should be pursued.

One method that is also disserving of mention is that uncontrolled energy violations are an intrinsic part of any brane based low energy approximation to String Theory. They also occur in M-Theory. The possible results of these energy violations are transverable wormholes, ability to avoid a singularity condition, and production of negative energy. Some of this has been referenced before in ...  by Carlos Barcelo & Mat Visser with the Physics Department at Washington University. In fact, his own work has shown others have noted the time reversed mirror universe effect in other String Theories. Just usually most have considered it a nulled out condition with our universe being a sort of baby universe attached to it via the membrane as a horizon point. One thing I have noted in his work is that the only known stable conditions for such do invoke a negative cosmological constant. This in light of the discovered speeded up expansion and my own modeling, which includes such shows, that at least we may be on the right track. It is also interesting that some models do allow a dual membrane or boundary condition to exist. This would make in our discussion C states a similar condition. But they do not forbid a slip over effect by any means. The real problem would be control of such which I still believe is beyond our knowledge at this time. But the door does remain open to such. I find it remarkable considering the categorical acceptance of relativity as an absolute condition that the scientific community has gotten this far in an open discussion of at least the possibility that relativity may be only a portion of a larger picture. It seems Science is poised to literally take such a step to go beyond the classical in its understanding. We live in unique times, which may allow a lot of the dreams and desires of man to be fulfilled. Only time and research and new definitions stand in our way at present.

STABLE CTC SOLUTION FROM A MODIFIED M-THEORY

To remove those condition from a static formulated transversible wormhole solution, that generate violation to classical energy conditions, to Einstein’s equations one must do the following: using generalization from a Misner space which has been modified if one analytically continues the maximal extended Misner Metric so that ds^2= -du^2+dw^2+(dx^2)^2+(dx^3)^2 to the Euclidean section so that u=iota zeta we obtain a Misner instanton on the section where w and zeta are both real. The Euclidean time, t, and the closed spacelike coordinate are both periodic, the later having a period of 2PiT^2. Going back to the Lorentzian sector we find that the period of the closed coordinate becomes lineraly dependent on the physical time.

Using automorphic fields in the Hadamard function one can obtain a quantized condition for time. This gives us a figure on the order of the Plank time. This confines such a stable wormhole condition to the general area of the Plank scale. Which my own theory has stipulated in its modified form is that area defined by the Membrane itself. Thus, for the mention in my work of the tube within a tube structure. These Plank scale wormholes are the true source of the true virtual aspects of the vacuum. Its an overlap zone of two distinct space-times which has boundary conditions on both sides. As an object accelerates towards C it is this same boundary or horizon that object encounters when the Time defined horizon solution for the universe is imposed in our modeling. The question becomes since energy itself intermixes in this region. How can one jump or slip across that barrier.

Some Proposed Material on FTL Warp Theory

Special relativity is only a special case of physics within a more general theory known as general relativity. In general relativity the vacuum speed of light is locally invariant, but not globally invariant. The vacuum speed of light remote from a given observer need not be c. It can be greater than c and can vary with direction depending on the gravitational field involved. Because this is allowed starships that travel between the stars faster than c are not ruled out a-priori within the physics of general relativity.

In 1994 physicist Miguel Alcubierre of the University of Wales published how to use general relativity to consider a space-time geometry, actual warp drives, that would undo the special relativistic time dilation effects and allow for faster than c travel in the May issue of Classical and Quantum Gravity. His space-time geometry would also allow for acceleration of the ship without any internal forces crushing the crew. They would feel weightless as the ship accelerated. Unfortunately in the arbitrary manner that the metric was developed it was shown by Pfenning & Ford to require a lot of negative energy that would violate a few quantum mechanics energy conditions and a greater magnitude of it than all the mass of the known universe.

A case of the space-time geometry that he had derived can be represented in the following equation
ds^2 = dct^2 - (dx - betafdct)^2 - dy^2 - dz^2f can be any function of the coordinates that is one at the location of the starship and zero far from it. Transforming coordinates to a particular choice of the starship coordinate frame and allowing it to travel faster than c (b > 1), coordinate singularities crop up in the equation corresponding to event horizons in front of and behind the ship enclosing it in a mathematical bubble. This is called the warp bubble. Even though the event horizons remain for any choice of ship frame, there is a choice for star ship coordinates for which the singular nature is transformed away.

Chris Van Den Broeck of the Institute for Theoretical Physics at the Catholic University of Leuven, Belgium, came up with an alteration for this space-time geometry that would retain all of the desired warp drive qualities but reduced the negative energy requirements down to the order of a transversable wormhole.

The space-time geometry can be represented by this equation ds^2 = dct^2 - B^2[(dx - beta fdct)^2 + dy^2 + dz^2 B can be any function that is large near the starship and one far from it though he used a specific top hat function for his example calculations. That not only brought the negative energy requirements down to a hopefully one day reachable goal but it also solved one of the quantum mechanics energy condition violations.

To consider these transformation as extended to four dimensional space-time with arbitrarily time dependent acceleration. We also present the ship frame energy density T00 from a four dimensional calculation and note that the 4d classical calculation is everywhere finite.

Consider an Alcubierre interval given according to a remote frame's cylindrical coordinates by
ds^2 = (1 - beta^2f^2)dct^2 + 2bfdctdz - dz^2 - dr^2 - r^2df^2
Where f is a function that is 1 at the location of the ship and zero far from it.
We start out with the first transformation
z' = z - òctbetadct
Where b is first expressed here as a function of time ct.
With some algebra for simplification this results in
ds^2 = [1 - beta^2(1 - f)^2]dct^2 - 2b(1 - f)dctdz' - dz^2 - dr^2 - r^2df^2
Let g = 1 - f and this becomes
ds^2 = (1 - beta2g^2)dct^2 - 2bgdctdz' - dz'^2 - dr^2 - r^2df^2

Notice that this returned the original intervals form with a reversal on the sign of b and a reversal of the boundary conditions for g. Now we notice that at r = 0, this interval becomes the interval for special relativity transformed to cylindrical coordinates. Thus, we have found a transformation to a frame based local to the ship. One can also verify that in these coordinates the relevant affine connections vanish at r = 0. Basically, there are several models to work with when it comes to the subject of warp drives. The problem in all cases is generating the negative energy.

First Principles of FTL Travel

The first principle of warp technology will be that the main reason we will ever exceed the light speed limit is inertia. As a body approaches the light speed limit, C, it's mass due to kinetic energy gain will increase exponentially up to infinity at C. Our second problem is Time which means that time must stand still to a body moving at C or the principle of relativity will be violated. I'll get to the second problem later.

Field acceleration refers to the acceleration of the body by applying the momentum to the components, which make up the body rather than to the body itself. The difference may seem small, however, it is profound. In older forms of propulsion, force is applied from the power plants and is subject to inertia as it propagates through the body to change its inertial state. With a field accelerator, the body is immersed in the field and biased to a certain inertial state. There is no inertial effect since the force does not have to propagate across the body.

Any quantum force of sufficient capacity can produce a warp field. Gravitation is the most often expressed force, however, electromagnetism is the most used force since it is the most controllable and understood. It is also important to note that electro weak force, of which electromagnetic force is a subset, is kinetic whereas the strong force is static. Static forces are difficult to bias and often require an actual imbalance in the field to achieve the warp effect. Kinetic forces have a polarity and can easily be biased in their natural flows without applying undue stress to the structure of the body involved. This was why I have referenced a group of frequencies EM field in my own work with the phase shifted ahead of individual phase waves of the particles that make up the craft. Match the Phase wave frequency and even though a phase wave differs from an EM wave the two will interact with each other.

Field acceleration handles the time question as well. The body within the field experiences no inertia and is therefore in a state of stable inertia all the time. Such bodies are moving at sub light velocities sufficiently small as not to experience major time dilation. It is the surrounding space, which is warped by the allererator field. Quantum acceleration of the entire field frame compresses space in an isolinear fashion. I mentioned a few times in my own proposal .5C. Besides the lessening of dilation effects. It is also a velocity that we could achieve in the future.

Other proposed methods of FTL travel work along simular lines to achieve the same effect.

There are 5 basic proposed methods of achieving Faster than Light motion as far as solid matter states. They are: 1. Alcunierre’s method and those based upon his original idea. 2. The Phase Shift Method. 3. The Phase Canceling Method. 4. The Jump Gate Approach. 5. QESAT or Quantum Entangled Spin Altered Transport, as I have chosen to call it.

All of these methods work by either altering the vacuum structure of space-time or by utilizing the odd behaviour shown in Quantum Mechanics. None of these methods in any fashion violate anything generally established under Relativity. They simply alter the conditions and thus change the perimeters. While the last method is interesting in some forms I have heard proposed. It does have the problem of establishing a near rest carbon copy of the original craft or object one wishes to accelerate. The Jump Gate proposal while possible is way beyond our capability at this time and most likely any time in the near future. I believe only the first three methods are a worthy area of focus at this time. They are more related than unrelated and cross research benefit exists. They all could benefit from research in the Quantum Entanglement field.

NEGATIVE ENERGY FIELD GENERATION FROM THE ZPF AND AMPLIFICATION METHODS

Scientists through the 19th century believed in the existence of an ether, which was modeled as a material substance that could support the wave propagation of light.

The famous Michelson-Morley experiment failed to detect the expected ether wind produced by the earth's motion through it. At the turn of the century Einstein used this result to support the theory of special relativity. When this became accepted, the scientific community rejected the existence of the ether. Thus classical physicists came to consider the vacuum of space to be truly empty. The classical model was only to last until the 1930's when quantum mechanics became accepted. From quantum mechanics arose a mathematical term in the description of the ground state of any oscillating system called the zero-point energy.

The term "zero-point" refers to zero degrees Kelvin, which means this energy, exists even in the absence of all heat. The energy was interpreted as being INHERENT TO THE FABRIC OF SPACE ITSELF.

Dirac showed how electron-positron pair production could arise from the vacuum fluctuations and quantum electrodynamics was born.

The Heisenberg uncertainty principle allowed quantum mechanical systems to "borrow" this energy for short periods of time. The Vacuum, filled up with something new came back into science not modeled as a material substance but rather as a randomly fluctuating energy field. In Some recent versions of M-Theory, mine included this Field is itself a combination of two separate space-time fields itself. More on this later, however.

The question has been raised. Does this fit with Relativity? If, so, does it modify Relativity to any extent?

Now, before I continue to answer this question I first want to state what relativity actually states. Simply put, the speed of light remains constant at 186300 miles per second in the vacuum. But relativity also says more. It says that for a stationary observer (Stationary here meaning relatively so, as compared to an object being observed) an object moving or accelerating will not only appear to shrink in length, any clock reference from the stationary point to that of the moving object will show a time shrinking effect the faster that object moves. This is all according to Lorentz formula that predates Relativity from the time Newton’s Aether or ether was still believed in. This effect has been tested to the limits of our capability of velocity at present and found to match the experiments exactly within error range.

Boyer showed that, by invoking the postulate of  Lorentz invariance, the spectral energy density p of the zero-point fluctuations must have the particular form as a function of frequency w : p(w) = kw3 where the constant k is related to Planck's constant as commonly called Plank’s Constant Crossed. This result gives a quantitative basis to the theory of random electrodynamics, which strives to show that quantum mechanical effects arise FROM MATTER'S INTERACTION WITH THE ZERO-POINT ENERGY. However, when you work out the math the ZPF should generate an infinite amount of energy. Yet, in relativity it doesn’t. Something is modifying the vacuum. A similar problem plagues quantum electrodynamics where infinities are renormalized away. Some type of frequency cutoff is required to create a finite, quantitative theory.

Wheeler applied the theory of general relativity to the ZPE to create a natural cutoff in his theory of geometrodynamics. In general relativity the fabric of space curves as a function of energy density.
When the density becomes sufficiently great, space pinches like it's forming a black hole. This gives rise to the formation of hyperspace structures that Wheeler called "wormholes." These Wormholes those of us who work with String Theory are familiar with. To us they are the event horizon, so to speak between 6D Higg’s space-time and our 4D graviton space-time. We call them the Membrane or String depending upon which version you happen to follow. Wheeler’s calculation yielded microscopic channels on the order of 10-33 (to the -33rd) cm having a (mass equivalent) energy density of 10+94 (to the 94th) grams/cm3 (cubed). Notice how these correspond to the String scale? The resulting view is that the fabric of space consists of constantly forming and annihilating pairs of microscopic "mini" blackholes and whiteholes which channel electric flux into and out of our three dimensional space.

These mini holes manifest dynamics, which could be modeled as a turbulent, virtual plasma that Wheeler calls the "quantum foam." In this view the elementary particles are like bubbles or vortices arising from the dynamics of the vacuum energy. In my own Modification to M-Theory I showed they can actually be pictured as shell like extensions of the membrane itself which does restore the particle concept to the theory and maintains aspects of older models like the dual standing wave model, the Waveicle from ether theory, the wave-particle model from Einstein’s time, and the Compton Vortex model derived from QM. But like regular M-Theory I do so without the need of unnatural renormalization.

Recent experiments that utilize the Casmir effect have shown this zero point field not only does exist. They have shown that at least on small scales we can modify that energy level. We can actually remove energy from it and produce an area of negative energy density within a localized region. But, there does remain possible ways to increase this negative energy field. Many have been proposed. One basic method is to use a factor about the field that is already known to our advantage. That being that if you add energy into it like via heat from a local plasma field. You get a resulting larger negative energy field. The question isn’t a matter of can it be done. Its been experimented with and shown to work. The question is how to amplify such an effect.

In 1977 the Nobel Prize in chemistry was given for defining the conditions under which a system could evolve from randomness toward coherence. The conditions are that the system must be
1. far from equilibrium,
2. nonlinear in its dynamics and
3. have an energy flux through it.
These conditions are expressed in general system theory terms, and it turns out that the already published theories of the ZPE can, under certain circumstances, fulfill these conditions. Adding energy into the ZPF via heat is one tested method to force the system or field towards coherence. What hasn’t been tested is how much energy is needed to reach coherence and how this modification to the vacuum effects the speed of light as a constant. In theory, based upon sound math, but untested currently by experiments since we’ve never achieved a true coherent state yet, the velocity of light in such a region should be vastly higher than in our current vacuum state. Indeed, in theory it could be raised many orders higher.

The odd thing is even any negative energy in a given region should alter C. Why no one to date as tested this with a Casmir plate setup is beyond me. An actual test could be setup and performed in even a home situation. Create as semi circular wave-guide just large enough to allow a laser beam to travel down its lengths. Have the open end of the waveguide open to 2 mm-separated plates of a length of choice. Have a second laser diode set to fire across through this gap just matching ½ wavelength of the main lasers pulse. Have a detector for the diode laser beam at the other side of the plates utilized with timing measurement for the passage of the beam across the gap. Have this inside of a vacuum chamber.

Then run your experiment. The amount of negative energy present can be calculated by force= (Pi^2*h-cross*C/240*a^4)A with a = distance of gap and A = area of plates. This was why I said size of plates is your choice. The more area covered the larger the effect you generate. The separation I choice was connected with ½ wavelength of hydrogen to remove any natural effects from space around you.

Now the field setup under regular proposed warp programs utilizes a sweeping effect where in front of the ship a region of compression is formed while behind the ship a region of expanding space is created. This, by what ever field proposal one choices to follow produces a moving frame situation for the ship whereby it actually moves forward at any given velocity because space itself is moving. Similar to how our universe itself expands moving the galaxies along with it. I have already gone into some of the math behind this. But, what I am proposing is a modification to this approach. That modification is based upon finding an exact field coil configuration that produces a linear amplification of each coils effect so that the craft while existing in its own space-normal ZPF condition exists in a sort of cone shaped external field of negative energy region that expands space behind the craft. That expansion behind the craft would produce a similar effect to a surfboard riding upon a wave and take advantage of the craft being surrounded by a region where C no longer equals its current value.

The trick then becomes alignment of the twin field generators so that a narrow point is formed in front of the ship since any blunt region would produce a shear effect and tend of build up an energy shock wave that would slow the ship down. One may have to literally bring the space normal horizon of the inward field up right next to the back of the craft by pointing the field coils front ward in towards the craft with their aft section pointed out. Unless some means of projecting the whole field can be found; Shape of the craft will determine how much this must be done. For right now I will ignore the issue of producing a linear chain amplification effect. I will instead go back to one normal proposed field generation method and see how this looks modified into a single aligned field situation and then combine the results as if we had two field generators then work on shaping it to the desired outcome. For sake of not backtracking in my work I will utilize one that allows for the generation of such a field without an undue huge amount of negative energy. Exact energy will have to await experiments to not only determine each coherence zone. But also the possible range of C within such zones. Then we can better figure out the range of the field across space from each field coil setup.

So this method will not be exact. It will simply give us a basic geometric model to work from.
In Hiscock's 2d calculation a scalar field could easily be found because of the form the metric took. ds^2 = (1 +2phi/c^2)dct^2 - dz^2/(1 + 2phi/c^2). However, I do agree that more than one scalar field configuration can be derived.

For one, it has already been mentioned in arXiv.org@gr-qc/0009013 5 Sep 2000 "The Warp Drive : Hyper-Fast Travel within General Relativity" Miguel Alcubierre University of Wales in Cardiff UK that metrics can be generated under which less negative energy is required to achieve the proposed Top Hat field shape. For two, these metrics have not been shifted in shape to generate the type of field we are seeking here. For three, I agree with ZcPhysics in his online comment that we should be able to globally transform the space-time to that form in 4 dimension which can't be done. The scalar field is a "linearized" and weak field approximation for this particular form of a space-time metric. The energy density can classically by arrived at by t^00 = -(7c^2/8piG)(phi,j*phi,j) using Einstein summation.

Fourthly, I also agree that the 16 other tensor components have never been properly treated from GR over to this field approach. Nor has this field been honestly looked at from an 11D perspective available under M-Theory or my own dual time modification to it. Agreeing that those tensors from GR define the normal composite geometry of space-time that results from the admixture of 6D Higg’s space-time into 4D Graviton space-time. Lets for sake of argument here only concentrate upon the 4D solution then.

In doing a linearized weak field approximation four more restrictions can be placed on the potentials in linearizing the result that reduces the number of independent potentials to 6. The restriction that has to be done to linearize the result allows for 4 more restrictions because there remains some choices of frame. In the end this still leaves 2 independent scalar potentials. Fortunately the classical result as calculated by the ship frame is that the energy density is given only by one element of the contravariant Einstein tensor G^00. We know what that is and so we know what GR says the energy density is. Coordinate frame energy density = T^00 = (c^4/8piG)G^00. Thus, we can actually ignore the Scalar component if we so choice because we can already obtain it from that which we already have.

Now in following a further proposed modification to this field we will reintroduce a time dilation term into the ship frame's interval. Only we will use different boundary conditions for it. We will keep A = 1 both at the location of the ship, and far from it, but allow it to become large in the warped region. This is achieved by the simplest means possible in my proposed field generation method. Since each warp field generator would produce an equal negative energy region. With the effect focused outward away from the ship slightly by the field coil setup the actual inward going portion of such fields would overlap and cancel their effect out in the region of the ship. This yields a space normal time region , which is again restored at the fringes of the outward going field. From the standpoint of a geometric picture of space-time around the ship and extending outwards one has actually created a dual event horizon situation as far as time goes. The inner one is the shell of the canceled out field inside of which normal time flow is restored.

The outer one is formed at the boundary where normal time resumes and within which we have a negative energy field that allows motion faster than C to exist.

Now, if these field generators are placed alongside of the ship in extended position in parallel to the ship they would form two main elongated spheres of negative energy region with a heart shaped blunted front end and a spanning out rear field effect. That blunt front region would create a disturbance wake in its path through space-time that would literally pile up particles in the ship’s path. That would defeat our purpose and create undue stress on our ship. But if we place them at a proper angle to the ship we can narrow that blunt end effect to a finer point region similar how the hulls of supersonic aircraft were narrowed to reduce the shockwave effect of supersonic flight through the atmosphere. Internal wise this would produce a wider zone of space normal time flow in front of the ship than behind. I also believe that elevating them slight above the plane of the ship would also nearly eliminate any shock front transfer against the craft’s direct line of motion. Sort of like cocking that shock motion up and away from the craft. This would, however, generate a shock wake behind the craft that spreads out and disperses as the field reduces in strength towards the outer event horizon. Its effects on the stability of the coherent modified ZPF would have to be studied further to discover any ill effects it might produce. My hunch without any actual figures is that quantum effects would cancel such out or dissipate it through the medium itself by further heating the ZPF through particle pair production. The position of the craft in relation to its cone shaped field would best be chosen to approximate a craft riding on the leading edge of a wave crest so as to harness the most forward motion from the field’s effects. At this point we reduce our discussion to those of main drive system and how to achieve that linear amplification effect with our field coils.

One thing that must be counted into overall discussion of velocity here is that unlike the original proposed warp fields ours would utilize expanding space behind the ship to propel our craft forward instead of a combination like the Top Hat version does. Thus, velocity would depend upon the thrust output of the main drive combined with how fast space behind the craft is spreading out. The moving frames concept is here unified with its own speed component and that of the initial drive system. So the faster the main drive can propel our ship the higher velocity one can gain within each stable domain. Also, the faster one can have the space behind the craft expand the higher a velocity one can achieve. So now we have two design perimeters to figure into our craft design. That and the crafts shape.

Theoretical physics depends on the idea of symmetry. Symmetry means certain things do not change when other things do change. The changes can be passive, i.e. changes in a frame of reference or point of view POV, or perspective. The changes can also be active as in the displacement or rotation of an object in space. Symmetries and conservation laws are two sides of the same coin.

Translate an object along the straightest path possible in space. If there is a symmetry there, the linear momentum of the object is conserved. This is force free motion. Therefore, Newton's idea of "force" really arises as a broken transitional symmetry. Symmetry under displacement in time conserves the total energy of the displaced object. Symmetry of rotation of an object about an axis in space conserves the component of total angular momentum along that axis. Torque is a property of a broken rotational symmetry. In addition to these external symmetries associated with movement in space and time there are the "internal" or "gauge" symmetries that cause the electromagnetic force field, the weak force field of beta radioactive decay of nuclei, and the strong force field that binds quarks into nucleons and mesons. The residue of the strong force is the nuclear force that binds nucleons (protons and neutrons) into the nuclei of atoms. The binding of atoms into molecules, liquids, neutral plasmas of ionized gases and solid state crystals is purely from the electromagnetic force field together with the Bohm quantum bit pilot waves of "active information" and a new kind of nonclassical symmetry called permutation symmetry among identical quantum objects. Note, under conditions of Dicke "super-radiance" with a lot of fermion photon emitters concentrated within a single wavelength of the real photon radiation, the fermions "cooperate", analogous to the Mossbauer effect used in the 1960 Pound-Rebka experiment showing the gravity redshift, to mimic a Bose-Einstein "condensate" (Nature, August 16, 2001, p.689, J. Javanainen).

Now when we refer to the idea of coherent states to the ZPF we are actually speaking of points were that ZPF as it undergoes a phase transition reaches a symmetry conservation point. Simple Casmir Plate experiments force the vacuum to reach a lower energy state by the fact that the placement of those plates prevents some of the normal virtual particles from forming. The idea of heating that vacuum point is simply a means to increase the excitation of the vacuum itself and thus to produce a stronger energy negative state within that region. As the negative energy rises the field strength of this negative energy increases and thus its reach across space-time increases. But, the fact remains there should be naturally occuring coherent regions forming stair steps or domains on the way down towards a literal zero field. I take this from the Quantum nature of the vacuum as we presently observe it.

Part of the answer to why we have matter in the first place is stability under conditions of spontaneous broken continuous symmetry whereby those particles reach a coherent state with the ZPF locally. But that only gives us the baseline for the vacuum in its assumed lowest energy state. Its assumed to be lowest because it is stable. However, picturing a deep shelf with a ball sitting on it could be considered stable. Yet, with the right push that ball could drop off towards an even more stable coherent condition. When we set up an experiment with those plates we are actually taking a small portion of the ZPF field lower. Doing the same and heating the local vacuum region is taking it lower still. Our question is where is the next coherent range between our present state and the bottom. Normally this would be a function of temperature too. Our present vacuum is sometimes called a frozen vacuum. The closest to the bottom we can reach would then be absolute zero.

For example, the locally ordered, or nonrandom, field of a laser or a superfluid or a superconductor has long range phase coherence forming an "interferogram" in space-time that can be roughly thought of as implicit or "implicate" (Bohm) holographic information storage. This kind of coherent signal is in stark opposition the random zero point quantum noise fluctuations of the vacuum, and also classical noise. Such a coherent long-range phased state is a superposition of different numbers of bosons, either real or virtual. If virtual it can be a "superfluid" coherent derandomizing of the zero point fluctuations of the "normal" component of the quantum vacuum. Indeed, the Higgs mechanism in which lepto-quarks get their inertial rest mass in the standard model is a good example. Though in my own Modification to M-Theory this is replaced with a field hidden in 6D space-time, instead of a regular particle as the standard model would propose. But the example shows directly what we are after here. Finding those states in which the random fluctuations of the ZPF become derandomized into a set coherent state.

There is a reason I seek this out. Those Coherent regions should have a definite set velocity range within each of them. While I could generate a field of a set given strength to achieve my derived effect. Velocity then would simply be dependent upon its negative energy addition to that of our craft’s primary thrust system and the expansion rate of the energy field behind the ship. The other would literally multiply these by a certain given internal factor. To give an example, for argument sake lets say in the first case our craft could achieve .5C. Lets say that with the field on our craft could achieve 1C. In this lower Coherent range it might achieve 2C because that region actually multiples or doubles any given velocity to maintain its coherent condition. Step down to the next Coherent zone and we get 4C or 6C depending upon how it multiples velocity. Now you begin to see what I am after. Letting nature do some of the extra work for us.

To locate one such possible point I need to backtrack into a separate but related field of work. Newton recognized that the fall of an apple, the tides and the orbits of the planets as aspects of a single phenomenon, gravity. Maxwell unified electricity, magnetism and light. Each synthesis extends our understanding and leads eventually to new applications. Einstein unified space and time into one format of space-time. Then he spent the last years of his life seeking to Unify Gravity and the EM field to no major avail.

In 1979 Weinberg, Salam and Glashow were awarded the Nobel Prize for their unification of the EM force with the Weak Force responsible for atomic decay based upon an adaptation of ‘t Hooft’s renormalization from an earlier developed theory for the Strong Force called Quantum Chromodynamics or QCD for short.
In modern times we now have String Theory and M-Theory as the primary avenue towards unifying the last hold out force Gravity with all the rest. This is based upon supersymmetry, which arose after the success of the other two commonly referenced as the Standard Model.

My focal point for this discussion will be the predicted Quark/Hadron transition range. Lets for sake of argument here assume its range projected below the normal ZPF field range would equal such a Coherence zone. Now both energy and temperature can and are expressed using the same basic unit. The common measure of energy is the electron volt. 1 eV equals 1.6 * 10^-5 joules, which we find, used in physics to describe temperature. This transition range lies at 2 to 3 GeV according to the standard model. So lets say the coherence band in the ZPF we are after lies 2 to 3 GeV less than our current Normal ZPF state. To reach such a state we need to induce 150 to 200 MeV temperature differences into the local ZPF. Very reachable by even being heated via a high power laser.

Now, lets perform a renormalization method and say that the normal ZPF state equals a state where current velocity ranges extend from zero to C. Take the M from MeV and exchange it for 1 million. Now plug in our current range and shift it 150 to 200 million. Let’s say we choice the low side and put it at 150 million. This gives a velocity increase of 1.5 million times whatever value we plug in from a space normal condition. This example is not a real one. But it does show how one could find the increase factor. Now, lets try and find a more usable one.

Let’s use the same one. But focus on a stable state. For the normal, non-transitionaing state of the Proton the density is 1 GeV per fm^3. We know in the normal vacuum this is a stable state. Lets then see what we find for the electron. We have 500 KeV per fm^3. Let’s say that at 500 KeV down the scale from our current ZPF we have a stable range. If we follow the other example we’d have an increase of say C to a velocity of 9.315^10 miles per second with a minimum velocity of 500,000 miles per second. That base then sets slightly higher than 2.683 times our current Max for the ZPF.

Now back to my original example for our proposed ship. If its space normal velocity is .5C. Then its new velocity in this higher domain would be 4.6575^10 miles per second. Here again you have to remember no one has found or tested even one of these coherent zones. So none of these figures are actual. But they do provide a good exercise by which you can get a picture of how velocity/ energy density/temperature could be related.
Basically my own assumption is that if you half the energy density of our current vacuum state you double the effective velocity. Under that assumption those before mentioned ranges would be many powers of domains lower than even that. But following the assumption that ½ ZPF would equal a velocity range from .5C to 2C for an equal space normal range of 0 to C. What then remains to determine is simply how fast the energy density decreases for a given temperature input.

Now in engineering terms the velocity of light in free space c is given by the expression of the relationship between the magnetic permeability and dielectric permittivity of the vacuum. However, both of these are controled by the energy density of the ZPF. Thus, altering the ZPF does alter those two factor. Now since, the dilectric permittivity = 8.854 x 10-12 F/m and the magnetic permeability = 4 x 10-7 H/m , with C= 1/(µ00)1/2 in the normal ZPF. We do know that the dilectric permittivity changes under a localized area with the Casmir Effect. In short, as emphasized by Wesson, the speed of light c is context-dependent and not as fundamental as widely believed.

This is the area of most needed research. What we need is a system to generate the Casmir Effect into a wider localized area of space-time. Usuable velocity increases could be achieved for any Coherent state where the dilectric permittivity is cut by ½ of greater. But, given our present slow velocity of reaction rocketry. What we need is actually a cut of many magnitudes with the whole potential velocity scale shifted from its present 0 to C range to one of C to C^2. This then would open up space travel to wider scale potential and allow us to utilize our present drive systems and still get out of our local neighborhood. At say such a shifted scale we could achieve .1C. Our upper velocity range would then become 3470769000 MPS or 18630 times C. This puts everything under 20,000 LY from earth with a two year or less round trip mission. Well within the time scale of some long range planned future missions within our local system.

Remember this is all simply brain storming. The only thing we do know to date is that if you alter ZPF like in Casmir Experiments you alter the velocity of light. We do not know if we can increase such a field to cover a wide area. Nor weither we can mold such a field into a usable shape either along my projected lines of those mentioned in conventional warp theory models that resemble a Top Hat type field. We do know by the math one can be made to be stable. But no one to date has made one of those stable field solutions, nor have they tried considering we haven’t developed the means to amplify such a field yet. This remains then one huge wide open field of research for those future scientists. But the fundamental ground work is being laid by current scientists through their work being published on the Los Alamos Archives System.

ZPF History
The ZPF was first introduced by Max Plank in 1911 as a renewed investigation of the relationship between matter and radiation or energy as related to a blackbody. The formula is well known that 1/2hv +B(v,t). From this a quantum oscilator should have a finite ZPF energy even at absolute zero. Einstein-Hopf required a ZPF function in their work only with hv instead of Planks version. Nerst in 1916 first proposed a universal ZPF. However, it was Mulliken in 1925 that first conducted and experimentally proved not only the existance of the ZPF, but also provided the first experimental proof of Heisenburg-Schrodinger Quantum Mechanics. To date the most dramatic example of the ZPF being used is its role in maintaining helium in a liquid under its own vapor pressure at near absolute zero. The first person to demonstrate by math that C varies under different boundary conditions was Scharnhorst in 1998 with his work that shows a Casimir effect altered ZPF works as an accelerating medium. Its this kind of medium that in the last year or so was in the news showing light speeded up and slowed down under certain conditions. Hawking had some on this with his modification added to Galphabeta so that it equals 8PiTalphabeta+U where U is a small term that perturbs the system from its classical solution. But it remains Scharnhorst's work that has given us the best indication that C can be varied.

1.) The metric g is a sole dynamic field, and the theory contains no arbitrary functions or parameters, apart from the value of the Newtonian coupling constant G, which is measurable in laboratory experiments. Throughout this, I will ignore the cosmological constant . Although it has significance for quantum field theory, quantum gravity, and cosmology, on the scale of the solar-system or of stellar systems its effects are negligible, for values ofcorresponding to a cosmological closure density.

The field equations of GR are derivable from an invariant action principle. Generally it takes the form Guv=Ruv1/2guvR=8PiGTuv. Now, some propose Guv(x)+Delta(x)guv(x) = -(8PiC^4)Tuv(x). But the normal would actually be for a negative region such that Guv=-(8PiGTuv) which yields a result the same as a normal 4D model of GR only a reversed region or manifold in which gravity here has been reversed. My reason for this is that the variance of G with the introduction of U, simular to Hawking's method is actually a product of the cosmological factor which for finite local areas is for all intense zero. To accomplish this most introduce exotic matter. However, the same general effect arise within a lowered ZPF condition such that the negative then is accomplished via a subtraction of normal energy within a given localized region.

The negative then becomes simply a matter of difference. An example of such a region is that produced by the Casimir Effect. Since this doesn’t create any major violation of CWC. I believe we can ignore such. I base this upon the fact that even this negative field, though displaying a fall off effect of 1/r^7, does extend beyond the small local region. Since, according to Scharnhorst, and latter verified by other accelerating medium experiments this does yield a velocity increase to C without a violation of SR because one is dealing with a special frame of reference I see no major reason to modify GR to achieve a FTL condition when the normal method will achieve the same. All one needs is to treat the reference frame of the ship as a Nulled Region in which the normal ZPF condition is restored due to two Negative ZPF zones overlapping.(ie –1*-1=1), then have the external field non-stationary with respect to the craft and non-symmetriic. If the effect sweeps backwards in concentric larger areas the net effect is the same as Alcubierre’s method and those based upon it without the requirement of huge energy factors, nor a violation of any WEC effects. Basically you achieve this by changing the space locally into an accelerating medium and have the ship exist within a region where the reference frames are moving outside of it. Far simplier effect and requiring far less energy to produce especially if a method of enhancing the Casimir effect can be found.

Gravity vs Anti-Gravity

The speed of gravitational radiation (Cgw) depends upon the specific model of Gravitation that you use. There are quite a few competing models (all consistent with all experiments to date) including of course Einstein's but also Brans-Dicke and several families of others. All metric models can support gravity waves. But not all predict radiation propogation at Cgw = Cem.

There is a class of theories with "prior geometry", in which, there is an additional metric which does not depend only on the local matter density. In such theories, Cgw != Cem in general.

However, there is good evidence that Cgw is in fact at least almost Cem. We observe high energy cosmic rays in the 1020 to 1021 eV region. Such particles are travelling at up to (1-10-18)*Cem. If Cgw < Cem, then particles with Cgw < v < Cem will radiate Cherenkov gravitational radiation into the vacuum, and decelerate from the back reaction. So evidence of these very fast cosmic rays is good evidence that Cgw >= (1-10-18)*Cem, very close indeed to Cem. Bottom line: in a purely Einsteinian universe, Cgw = Cem.

In my own model, based upon a dual time M-Theory of 11D format our 4D manifold is a product of the overlap of two sub-space-time manifolds. In it, Cgw is a product of two components. One componet is negative and the other is positive. In one, the propogation velocity is slightly less than C. In the other it is faster than C. Now, in the absence of the first component Space-time would expand at a 7D level. This is exactly opposite of the effect gravity has upon space-time. But it is a condition that only happens naturally in a mechanism tied to the cosmological constant and dependent upon local matter density. This, does not preclude the usage of artificial means to achieve a simular local effect. One possible area is altering the local density by altering the ZPF. Another would be canceling the local effect of the less than C component. This could be done possible through a transtation method. However, in either case this isn’t anti-gravity in its strict sence. True anti-gravity would require negative mass.

Now when it concerns EM and GR the stress-energy tensor is a generalization of the three dimensional stress tensor developed late in the last century and used by all materials science engineers to compute stresses in solid materials. It turns out that the force per unit area in the direction v across a plane with normal n depends linearly on both n and v, i.e. it is measured by a tensor. Let V be an n-dimensional real vector space with basis {e_1, ... e_n}. A tensor is just a multilinear map such as T: V x V x V* -- R This particular tensor takes arguments u,v, xi, where u,v are vectors and xi is a covector on V. Covectors are linear mappings xi: V -- R. You can think of u,v as column vectors and xi as a row vector, where xi(v) is [ v^(1) ] [ v^(2) ] xi(v) = [x1_(1), xi_(2), ... xi_(n)] [ ... ] [ v^(n) ] (In this context, subscripts in parentheses are often used for the components of row vectors, and superscripts in parentheses for the components of column vectors. Thus, v_1 is a column vector and v_1^(2) is the second component of that vector; xi^2 is a row vector and xi^2_(1) is the first component of that row vector.) V* is the space of covectors on V and it too has a basis, the dual basis o^j defined by { 1 if k=j o^j(e_k) = { 0 else There are n such basis vectors, so V* is n dimensional just like V. Saying that T is "multilinear" means that T( a_1 u_1 + a_2 u_2, v, xi) = a_1 T(u_1,v,xi) + a_2 T(u_2,v,xi) and similarly for the other two arguments. This means that we can completely define the values of T on any triple u,v,xi by defining its values on triples of basis vectors T^{(i)(j)}_(k) = T(e_i, e_j, o^k) For, given u,v,xi we can write them as linear combinations of the basis vectors {e_j}: u = u^(i) e_i = u^(1) e_1 + u^(2) e_2 + ... u^(n) e_n v = v^(j) e_j xi = xi_(k) o^k (where we sum over repeated indices one up, one down, as suggested in the first line above) and then by the multilinearity T(u,v,xi) = T(u^(i) e_i, v,xi) = u^(i) T(e_i,v,xi) = u^(i) T(e_i, v^(j) e_j, xi) = u^(i) v^(j) T(e_i, e_j, xi) = u^(i) v^(j) T(e_i, e_j, xi_(k) o^k) = u^(i) v^(j) xi_(k) T(e_i, e_j, o^k) = T^{(i)(j)}_(k) u^(i) v^(j) xi_(k) Notice this is a triple sum over the n^3 numbers T^{(i)(j)}_(k). These numbers are the components of the tensor and they are analogous to the n components of a vector or covector. But, just as with vectors, representations of tensors with respect to the basis {e_i & e_j & o^k} of V & V & V* comes with a price; the components change if we change to a new basis, in a manner completely analogous to the way the components of a vector change if we adopt a new basis for V.

Suffice it to say that (o^j & o^k)(u,v) = o^j(u) o^k(v) where we have multiplication of real numbers on the right. The point of introducing tensor products is that it is often convenient to think about a tensor as a linear map on a new vector space V & V & V* rather than a multilinear map on V x V x V*.) If A is an invertible matrix, it provides a coordinate change to a new basis of the vector space V given by e'_j = A e_j = a_(j)^(k) e_k where a_(j)^(k) are the components of the matrix A. If u = u^(j) e_j then the new components are given by u = u^(j) A^(-1) e'_j = u^(j) B e'_j = u^(j) b^(k)_(j) e'_k or (replacing the dummy index k by j') u^(j') = u^(j) b^(j')_(j) Here, B is just A^(-1) and b^(j')_(j) are the n^2 components of B. This induces a corresponding change of dual basis o'^j = o^j A^{-1} Note that this gives { 1 k=j o'^j (e'_k) = o^j A^(-1) A e_k = o^j e_k = { 0 else as required for {o'^j} to give the dual basis to {e'_k}. We must transform the components T^{(i)(j)}_(k) in order to compute values of T as triple sums over components expressed in the new basis and its dual. In analogy with the expression u^(j') = u^(j) b^(j')_(j) for vectors we have the change of basis expression xi_(j') = xi_(j) a^(j')_(j) For tensors this law looks like T^{(i')(j')}_(k') = T^{(i)(j)}_(k) b^(i')_(i) b^(j')_(j) a^(k')_(k) I stress once more that, for -each- of the n^3 components of T, this is a triple sum over n^3 terms. To make sense of it, get a large sheet of paper and write out all the sums for say the case n=2. The stress tensor S: V x V -- R thus is associated with n^2 components in a particular basis, which we can write as a matrix [ s^{(1)(1)} s^{(1)(2)} s^{(1)(3)} ] [ s^{(2)(1)} s^{(2)(2)} s^{(2)(3)} ] [ s^{(3)(1)} s^{(3)(2)} s^{(3)(3)} ] Here, s^{(1)(3)} (for example) measures the stress across the plane orthogonal to e_1 in the direction e_3. These numbers represent all the pressures and stresses in some material at a single point in space. It is very important that S is a -symmetric- matrix: the force per unit area across the plane normal to e_j in the direction e_k equals the force per unit area across the plane normal to e_k in the direction e_j. This means we can always diagonalize the matrix by a proper choice of basis. The eigenvalues are called pressures and the eigenvectors are the "principal directions" of S. The stress-energy tensor or matter tensor of GR incorporates this stress tensor, fluxes, and energy density, at a single event in space-time, into a single multilinear object, which is also a tensor T: V x V -- R, except that now V is E^(1,3). Once again we can write it as a matrix:

Density | three flux components

-----------|--------------------------- flux | stress tensor.

A vector -field- is a smooth map assigning a vector to each point in space (or space-time) and similarly for tensor fields. Thus, the matter tensor -field- assigns a tensor (a multilinear map) to each point in space-time. A change of coordinates on spacetime induces a change in basis in the tangent space at each point in space-time, and thus induces changes in the components of the multilinear map at each event.

If the density also vanishes the result is considered a vacuum. To the extent that it vanishes dictates the bottom line for that vacuum state. It also determines the propagation velocity of C. For each particle there is a local coherent solution to that vacuum. Indead, our 4D manifold contains multiple solutions locally. Some add to that state and others subtract from the ground state. Globally, these add to a ZPF condition that is at least 120 places smaller than what classical theory would predict. That canceling mechanism I have already discussed in my own model and theory.

Now, in QM, vacuum fluctuations give rise to a matter tensor of the form [ rho 0 0 0 ] [ 0 -rho 0 0 ] [ 0 0 -rho 0 ] [ 0 0 0 -rho ] I have been at pains to emphasize that strictly speaking, a solution in gtr must not only satisfy Einstein's field equation G^{(a)(b)} = 8 pi T^{(a)(b)} but also the dominant energy condition, which says that when we have chosen coordinates diagonalizing the matter tensor, the density of mass-energy T^{(0)(0)} must be positive and moreover must be strictly larger than the absolute value of the other three eigenvalues (the principal pressures). In the field equation, note that the Einstein tensor G is computed entirely in terms of the geometry (by taking a sort of "trace" of the Riemann curvature tensor to get the Ricci tensor R, and then subtracting off a term rather like writing A - t I when defining the characteristic polynomial of A as det(A - tI). But lowering the local ZPF does not violate this premise. In all cases the density issue remains positive and larger than the principle pressure. So this doesn’t call into effect any violation of WEC. Nor does it require negative mass or anti-gravity. So the solution to Alcubierre’s warp formula that utilize an altered ZPF condition have no reason to actually have to satisfy any problems raised on the WEC violation. This, is also the reason that the Casimir effect and other accelerating medium effects can exist in the first place without major structure problems in space-time. They simply do not generate such.

SIDE NOTE

I do not know how many here know the formula for Capacity. But I have noticed an odd relationship between this and a Casimir effected ZPF. Basically, if you treat those seperated plates as plates of a capacitor as the distance of seperation decrease the force due to the Casimir Effect increases while the capacitance decreases. Thus, capacitance follows the energy range of the ZPF and inversely follows the External force being generated. All of these are variables controled by the area of the plates and the seperation of the plates. For a vacuum K in the capacatance formula effectivly equals 1 with the formula being C=2.25^-7(KA/S) with A being area and S being seperation distance when using inches as our scale. As an example, with A=.5 sq. inches and S=.01 inches the capacitance =11.3 mf Plugging those values into the formula for the force externally generated in a Casimir setup we get 2.535639415^-25 gram per inches squared. I haven't yet tried this with a charge present across the gap. But I suspect there is a relationship between modifying the ZPF(As such local intertia) and an EM field. This might tie in with some who have proposed theories that strong EM Fields counter gravity. This would be because while gravity curves space-time the EM field would tend to straighten or stiffen space-time in a local region thus, working against gravity. However, my guess is they are incorrect and the EM field actually helps curve space-time. An externally applied EM field present between those plates would at first glance raise the ZPF, not lower it. So, perhaps we have here proof that Gravity and EM perform a simular task when it comes to curving space-time. Which makes sence when one considers that a given amount energy confined within an area is equal to a given amount of mass in an area.

When the poles of a freely suspended charged capacitor (even in vacuum) were placed on a horizontal axis, a forward thrust would be produced which would move the capacitor in the direction of the positive pole. The direction of thrust would reverse in conjunction with a polarity change. This is the phenomenon known as the Biefield-Brown Effect.

Now when you examine this effect it is actually proof of what I was trying to show and not anti-gravity at all. Those who call it anti-gravity neglect the fact that EM forces far outpower gravity. Secondly, while a strong charge causes local curvature, the direction of force to that charge will produce motion on freely seperated plates. If you look at the setup of the Biefield-Brown Effect and a Casimir Effect and that I mentioned before they are simply copies of each other. Now when a charge is induced across those plates by direct current that charge will seek to move from its negative plate to the positive and even though it can't move, unless that charge is greater than the local dielectric breakdown voltage, it still produces a force in the direction of that positive plate. This accounts for that so called anti-gravity result. Another words, its not anti-gravity at all. Its simply a matter of force being applied in a certain direction producing thrust. That thrust ballances at a certain point when its force equals gravities force in that local region. Put in the simplest terms when the electron force towards the positive plate equals gravities force downward in the other direction the two ballance out and you have levitation, yes, anti-gravity no. Basically, I could perform the same task with a small fan thruster who's output exactly matched gravity's push downward at a given altitude.

Thus, I would tend to discount EM fields being able to create anti-gravity effects.

THE CAUCY PROBLEM & DR NATARIO

A Cauchy surface is an equal-time surface. As a result there is a confusion between the concept of "Cauchy surface" and "time". In solving the Cauchy problem, what you're actually doing is providing a relation between the data {q(S)} which resides on one Cauchy surface S to the data {q(T)} which resides on another T. So, when one talks about evolution, one is talking about "evolving" quantities which are actually functionals q(S) of Cauchy surfaces S, not functions q(t) of time t. But in Newtonian Physics, you can get away with this confusion because the two concepts coincide. Basically, you have the equivalence:

Historical Time = Coordinate Time

where
"Historical Time" = the arena in which evolution takes place = S "Coordinate Time" = t>br> In Relativity this is not the case. So the issue invariably arises that when one generalizes a theory from its Newtonian form to its Relativistic form: which concept of time applies, "coordinate" or "historical"? Here, with the Warp Metric we actually have a static inner region around the craft that is Newtonian, and an outer Bi-polar region that is relativistic; it has an expanded Lorentz Invarient Frame. So, the concept of a shielded area is pre-built into Warp Mechanics in the first place. However, this complicates the inherient Cauchy Problem.

Natario’s basic mistake was he didn’t take into account the effects the expanded Lorentz Invarient frame have upon the incoming photon’s blue shift. Yes, they are Blue shifted. But, they are not as hot as he portrayed them in his article. Secondly, he didn’t apply a proper Cauchy Evolution to the issue. He failed to consider even the simply shielding that Newtonian frame provides around the craft. Coming from a region experiencing blue shifting and crossing into a freefall region marks the crossing of a boundary. The evolution of those particles has now been changed. Going from a hyper accelerated region into a region in total freefall is close to having a speeding car slam into a brick wall. The photons are bound to bleed off energy fast.

In Relativity, the state W(S) (classical or quantum) is actually a functional of S. The state W(S) is really nothing more than a summary of the Cauchy data for S. When solving the evolution problem, all you're doing is providing a map:
E(T, S): W(S) |-> W(T)
that relates the state on T to the state on S. In Quantum Theory, for instance, this map would be the (generalized) evolution operator U(T, S). Though it's not widely recognized, this operator is well-defined even where S and T are overlapping or intersecting Cauchy surfaces.
Now when making the transition from the Lagrangian formulation to the Hamiltonian formulation in Newtonian space, one takes a space-time region V whose boundary dV has the shape:
dV = VF - VI + V0
VI = Initial hypersurface
VF = Final hypersurface = the "same" 3-volume at a later time
V0 = The 2+1 dimensional "side" boundary
and the only way to get rid of the "boundary" terms is to push the side boundary V0 off to spatial infinity.
In a Relativistic space, one has the rather unusual phenomenon whereby finite (compact) space-time regions V exist which are bounded SOLELY by spacelike surfaces:
dV = VF - VI
V = compact N-region
VI = "initial" N-1 spacelike boundary
VF = "final" N-1 spacelike boundary
The space-like hypersurfaces intersect on a common N-2 boundary:
d(VI) = d(VF) = VA = N-2 Anchor
Here again a point Natario seems to have neglected.
Consider the case where you have a Minkowski space and you have two Cauchy surfaces S, T which coincide up to the Anchor; but with surface S following VI, and surface T following VF:
S = C + VI; T = C + VF
dC = VA = d(VI) = d(VF)
C goes out to spatial infinity
The basic principles underlying a purely local formulation of the Cauchy problem are:
(A) The evolution E(T, S): W(S) |-> W(T) is a function only of the physics within region V.
(B) The state W factors such that
W(S) = W1(VI) x W2(C)
W(T) = W1(VF) x W2(C)
with E(VF, VI): W1(VI) |-> W1(VF)
(C) The transition E(VF, VI) is independent of the Lagrangian outside the region V
and most importantly:
(D) The transition E(VF, VI) is independent of the global structure of spacetime outside of V.
When one formulates the Lagrangian principle of least action over the region V, the result is a local generalization of the Hamiltonian formulation which applies soley to the region V.

It does not apply once the Boundary is crossed. And yet, Natario in his work assumes it does. He never once treats the Warp region in its basic parts formed by the changes in the Lorentz frame. Nor, does he properly treat the crossing of the internal shield boundary around the ship itself.

Continuing on, we find:
The surfaces VI and VF are connected by a homotopy of surfaces all sharing the common anchor VA
VI = V(0); VF = V(1)
d(V(t)) = VA, for t between 0 and 1
V = union of the V(t) as t ranges from 0 to 1

The homotopy parameter t is what plays the role of "historical" time and is the evolution parameter in the generalized Hamiltonian formulation. Here again, the common anchor issue was ignored in Natario’s work.
Science needs critics. They keep us straight. But, we need critics who utilize proper science and proper treatment of the subjects. I have to side with Dr.Pfenning on this one that Dr. Natario has not ruled out Warp Drive.

Below is a list of some recognized research links in the first.

http://www.geocities.com/alcwarp - The Alcubierre Warp http://www.geocities.com/einswarp
- Alcubierre Warp http://members.tripod.com/da_theoretical1
- Page of Edward Halerewicz http://force-of-nature.iwarp.com/warpshel.htm
- Page of WarpDriveGuy(Simon Jenks) http://www.aei-potsdam.mpg.de/office/alcubierre.ht...
- Miguel Alcubierre's Bio http://force-of-nature.iwarp.com/warpzero.htm
- Pfenning and Ford's ideas http://force-of-nature.iwarp.com/warpone.htm - Chris Van Den Broeck's Warp-Bubble http://popularmechanics.com/popmech/sci/9712STSPM....
- NASA's Anti-Gravity Machine http://popularmechanics.com/popmech/sci/0010STRSCM...
- Ning Li Electro-Gravity Research article http://www.warp-drive.org
http://arXiv.org - arXiv.org - Scientific Research
http://force-of-nature.iwarp.com/links.htm - Warp-Drive.org - Useful Links Page
http://force-of-nature.iwarp.com/gravitypaper.html - A Mechanism for Quantum Gravity
http://arXiv.org/find/gr-qc/1/abs:+AND+warp+drive/... - Warp Drive Query at arXiv.org
http://www.physics.wustl.edu/~visser - Matt Visser Homepage
http://pancake.uchicago.edu/~carroll - Sean M Carroll Homepage
http://www.imo.physik.uni-muenchen.de/~mbaum/poste... - German Explanation for Warp Bubbles
http://www.cogs.susx.ac.uk/lab/nlp/gazdar/teach/at... - British (Sussex University) explanation
http://www.physics.uoguelph.ca/poisson/mitch/ - Michael John Pfenning Home Page
http://web.ukonline.co.uk/Members/ad.johnson/astrn...
 

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