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           Wormholes, Loopholes in General Relativity


             Concepts in Advanced Field Propulsion

There are two general schemes in general relativity which allow for travel which exceeds the speed of light for a local observer. The first of these was discovered by Gödel as a possible solution to Einstein's equations on gravitation. The solution by Gödel is that if space and time were bent into a loop then backward travel through time would become possible. The Gödel solution is often referred to a Closed Time like Curvature (CTC), which is essentially a time machine in the frame work of general relativity. Perhaps the easiest way to construct these sort of time machines is to gather up some cosmic string fragments, transforming a locally flat space into a conic region. This would alter the speed of light as seen by outside observer depending on their radial distance, thus in theory it would become possible to shake your own hand.

However in modern times the "wormhole" has become very popular for the allowance of Faster Than Light (FTL) travel. There are perhaps two reasons for this, wormholes could allow for interstellar distances to be traveled in very short times, and as a CTC can allow for time travel. In short a wormhole is what it sounds like, a loophole in the theory of spacetime which allows for apparent FTL travel. Its origins were discovered by Einstein and Rosen and is sometimes called the Einstein-Rosen bridge (more often than not it is referred as the throat of the wormhole), as general relativity is a symmetric theory when a black hole forms so is a mirror copy. If the singularities of these two spacetimes were to meet they would form a bridge between the two universes, however the intense gravitational forces at the bridge quickly act collapse it. This interesting effect would have remained nothing more than a mathematical curiosity until Morris and Thorne revisited the Einstein-Rosen bridge.

Morris and Thorne discovered that a wormhole could be held open to allow for travel between the two universes if they obeyed a set of predetermined parameters. For a transverseable wormhole something known as a flare out condition was needed, the flare out condition is something that violates the conservation laws in general relativity. This bizarre form of energy has been coined exotic energy because it behaves in an usual manner as it acts to resist gravitational collapse. If such a bizarre sort of energy existed and in large enough numbers it could resist the gravitational pressures associated with the Einstein-Rosen bridge. If exotic energy exist in nature then one can play around with wormholes, at least mathematically to study their behavior to see if such things can exist in the universe.

First form a geometrical point of view attaching our universe to a mirror universe is not much different than a wormhole connecting to another wormhole somewhere else in our universe. This would make interstellar distance transverseable, at least in theory and it is this reason that famous astronomer Carl Sagan used these objects in his novel Contact. Although the properties of wormholes in the same universe are much more difficult to treat, but in this context wormholes can also act as time machines. In special relativity there is something known as the twin's paradox in which one twin ages more slowly by traveling at great speeds in comparison to the twin at rest. You can apply this to wormhole one tunnel can spin slowly and the other very fast creating a time difference between the throats, and then you are left with a time machine.

In short CTCs and wormholes allow for shortcuts in space just as following a curved path on world map is a shorter distance than a straight line as seen by projection maps. They are clever tricks to go around the light barrier but their paths are much more complicated and require exotic things to do so. Cosmic string fragments for example are energy masses allowed to exist through string theory and not necessarily general relativity. Exotic energy however can exist in spacetime as it is known to exist at least in small form through the complex interactions found in quantum mechanics. But for exotic energy to be of use it must be found in a scale which is currently unknown to science, wormholes no matter how beautiful have serious problems. It is also clear to see why these fascinating geometries are considered loopholes in the theory and not facts of the theory, however in physics it has been shown that it only takes one author to change this.

                Concepts in Advanced Field Propulsion

                                                                                                 R K Obousy

                                                                    Department of Physics

                                                                    University of Leicester

                                                                               Jan 1999


This project explores recent theories that suggest the possibility of creating propellentless field propulsion through the modification of spacetime. Topics of interest include the coupling of gravity and electromagnetism, vacuum fluctuation energy, warp drives, wormholes and quantum mechanical tunneling.


1 Introduction

2 Zero Point Vacuum Physics

2.1 Introduction to the Vacuum

2.2 Wheelers Interpretation of the Vacuum

2.3 Observable Effects of the Vacuum - The Casimir Effect

2.4 Experimental Verification of the Casimir Effect

2.5 Vacuum Zero-Point Field and the Large-scale Structure of the Universe

2.6 Extracting Energy from the Vacuum

2.7 Thermodynamic Considerations

The Concept of Inertia

Machs Principle

A New Model of Inertia

Background Physics

Results and Interpretation

Application to Propulsion

The Relativistic Approach

4.1 The Alcubierre Warp Drive  

4.2 Warp Drive Causality Considerations

4.3 Einstein-Rosen Bridges or 'Wormholes'

4.4 Introduction to Wormhole Concepts

4.5 Wormhole Causality Considerations

4.6 Vacuum Squeezing

4.7 Looking for Evidence of Natural Wormholes

Quantum Mechanic and Photon Barrier Tünneling Time

5.1 History

5.2 Present Experimental Evidence

Concluding Remarks


Appendix a - Material Gathering

Appendix b - Hypothetical Lecture Course

Appendix g - Questions and Exercises

Appendix d - Correspondance

7 Bibliography

1 Introduction

Since the special theory of relativity entered mainstream scientific thinking, the idea that any object could travel faster than electromagnetic radiation in a vacuum lay as taboo. In 1996 the eminent space agency NASA broke this taboo with the creation of the Breakthrough Propulsion Physics program (BPP) with the aim of achieving the ultimate breakthroughs in transportation. The breakthroughs required to revolutionise space travel and to make superluminal (faster than light) travel a reality, according to the BPP, can be broken down into the following three categories:

MASS – Discover new propulsion methods that eliminate or drastically reduce the need for propellant. This implies discovering new ways to create motion, presumably by manipulating inertia, gravity, or by any other interactions between matter, fields and spacetime.

SPEED – Discover how to attain the ultimate achievable transit speeds to dramatically reduce travel times. This implies discovering a means to move a vehicle at or near the actual maximum speed limit for motion through space or through the motion of spacetime itself.

ENERGY – Discover fundamentally new modes of onboard energy generation to power these propulsion devices.

There have been several recent advances in science that have reawakened consideration that new propulsion mechanisms may lie in wait of discovery. Recent experiments and Quantum theory have revealed that space may contain enormous levels of vacuum electromagnetic energy. This has led to questioning if this vacuum energy can be used as an energy source or a propulsive reaction mass for space travel. Next, new theories suggest that gravity and inertia are electromagnetic effects related to this vacuum energy. It is known from observed phenomena and from the established physics of General Relativity that gravity, electromagnetism, and spacetime are inter-related phenomena. These ideas have led to questioning if gravitational or inertial forces can be created or modified using electromagnetism. Also, theories have emerged from General Relativity about the nature of spacetime that suggest that the light-speed barrier, described by Special Relativity, might be circumvented by altering spacetime itself. These ‘wormhole’ and ‘warp drive’ theories have reawakened consideration that the light-speed limit of space travel may be circumvented. Today, it is still unknown whether these emerging theories are correct and, even if they are correct, if they can become viable candidates for creating propulsion breakthroughs. This portfolio aims to review the current popular ideas from a non-mathematical angle.

I was able to gain access to the NASA BPP limited access Online Project Management System after explaining my project to the powers that be. The OPMS is a serious of Internet sites dedicated to specific projects, containing documents and email addresses of researchers involved in the projects. The advanced interstellar propulsion wing is one of several wings, each focusing on specific technologies or concepts. I also created a web site to supplement this project. BPP links and interesting sites aswell as the complete portfolio are included:

2 The Zero-Point Vacuum Energy

A common theme throughout this paper is the ethereal Zero-Point Vacuum Energy. The term ‘zero-point’ refers to zero degrees Kelvin, which means this energy exists even in the absence of all heat. This energy is interpreted as being inherent to the fabric of space itself. In this section the vacuum paradigm will be explained as well as evidence for its existence offered, and its relevance to this paper discussed.

2.1 Introduction to the Vacuum

The classical notion of a vacuum is that of a region of space devoid of all matter and energy. To all intents and purposes a void of nothingness. Today there is no doubt that a region of space can, in principle be emptied of all matter, however, a region of vacuum is neither empty nor featureless. It has a complex structure, which cannot be eliminated by any conceivable means.

The first step to creating an experimental vacuum is to remove all matter –solids, liquids and gases. When all matter has been removed, space is still not empty. It remains filled with electromagnetic radiation. Part of this radiation is thermal and can be removed via cooling, but the another component is far subtler. Even if the temperature could be cooled to absolute zero, a pattern of fluctuating electromagnetic waves would remain. It is this residual radiation which has been analysed only in recent years. It is an intrinsic property of space and time, of the vacuum and cannot be suppressed.9

To understand the origin of the residual radiation we must picture the universe as being a cobweb of quantum fields24 and matter as being specific distortions of this field. According to Feynman, "Because of Heisenberg’s uncertainty principle, the field oscillators can never be strictly at rest. As a consequence, even in the ground state with the lowest possible energy, there still exists the so called zero-point oscillations of frequency w , having energy hbar w /2. Hence the oscillatory nature of the EM field of radiation leads to the zero-point oscillations of this field in the vacuum state which has the lowest possible energy. The physical vacuum is not an empty space but is ‘populated’ with zero point oscillations, which are the cause of the spontaneous emission of radiation from atoms." One ‘everyday’ example is the presence of a certain amount of ‘noise’ in a microwave receiver that can never be eradicated, no matter how perfect the technology.

Can a space filled with fluctuations of electric flux be consistent with special relativity? Boyer21 showed that, by invoking 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.

This cubic frequency relation implies the absurd result that the energy density of the ZPE at each point in space is infinite. A similar problem plagues quantum electrodynamics where infinities are renormalized away. Some type of frequency cut-off is required to create a finite, quantitative theory.

2.2 Wheelers Interpretation of the Vacuum

Wheeler applied the theory of general relativity to the ZPE to create a natural cutoff in his theory of geometrodynamics30. 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’ (See Section 4.3)

His calculation yielded microscopic channels on the order of 10-33 cm having a energy density of 1094 grams/cm3 (10107 J/cm3). 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 modelled 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.

2.3 Observable Effects of the Vacuum – The Casimir Effect

Of the known experiments that support the case for the vacuum energy, the most cited is the ‘Casimir Effect’, named after the discoverer Hendrik Casimir of the Philips Research laboratories in 1948. Two parallel, closely spaced, conducting plates will mutually attract15. This attractive force is due to the exclusion of electromagnetic modes between the plates and has magnitude per unit area

F/A = p 2 hbar c / 240 a4 (2)

Where a is the plate separation.

This is most easily understood by considering fig.1


Fig 1.The conductive plates reflect electromagnetic waves. For a wave to be reflected there must be a node of the electric field. This implies only specific modes can exist between the interior surfaces of the plates. On the exterior of the plates, all waves are reflected. This sets up a difference in pressure, which leads the two plates to attract each other.

The conclusion of a report by Milonni13 is that the Casimir force is a consequence of the radiation pressure associated with the QED vacuum field with zero-point energy hbarw /2 per mode of the field. It is thus not surprising that the Casimir force is attractive, since the modes in the space outside the plates form a continuum, whereas those inside are restricted to discrete wave vectors. There are ‘more’ modes outside to push the plates together by radiation pressure than there are modes to push them apart. This argument is superficial in that both the inward and outward radiation pressures are infinite. The fact that the net radiation pressure is repulsive emerges after taking into account certain properties of the zeros of spherical Bessel functions, based on the work of Boyer20.

2.4 Experimental Verification of the Caimir Effect

Despite intensive theoretical attention the Casimir Effect has received, there ha in fact only been one attempt at its measurement. The measurement, a reported by Sparnaay in 1958, showed an attractive force ‘not inconsistent with’ the prediction of equation 2, but with effectively 100% error18.

A recent (1997) paper by Lamoreaux of the University of Washington12, measures the force with an agreement with the theory of 5%. The conclusion of the paper is of an ‘unambiguous demonstration of the Casimir force’.

2.5 Vacuum Zero–Point Field and the Large Scale Structure of the Universe

There exists an as-of-yet-unanswered question in modern cosmology regarding the inhomogeneous distribution of matter in the universe. A recent (1995) paper by Cole, Haisch and Rueda (CHR) apply a subtle finding of Einstein22, regarding the dynamics of charged particles in random radiations, to model the formation of cosmic voids and further cosmic structures14.

Einstein and Hopf realised that an electromagnetically interacting particle immersed in random radiation is subject to two counteracting effects: an inducing excitation that tends, on average, to increase the particles kinetic energy, and a counteracting dissipation due to a drag force originating in the Doppler shift of the radiation as seen by the particle in motion. However, if the radiation is the Lorentz invariant vacuum electromagnetic ZPF, the second effect is necessarily absent. A consequence of that is that at ultra low densities in an electron-proton plasma, a pressure instability appears that induces the expansion of regions of lower density at the expense of regions of higher density. The expansion-compression continues until critical values of the parameters are reached at which the pressure instability is counteracted by ordinary gas pressures and any trapped magnetic field lines. The CHR paper shows that charged particles, once the ZPF is taken into account, appear to have the correct properties in an astrophysical environment that could account for the inhomogenity of the universe.

The paper concludes, "We are encouraged that a cosmic mechanism appears to exist that is consistent with both the CMB and the growing evidence for structures on the large scale…an interesting paradigm shift is suggested with possibly profound implications for our understanding of cosmology."

2.6 Extracting Energy from the Vacuum

With such large values, it might seem that the effects of electromagnetic zero-point energy should be obvious, but this is not the case because of its extremely uniform density. Just as a vase standing in a room is not likely to fall over spontaneously, so a vase bombarded uniformly on all sides by millions of Ping-Pong balls would not do likewise because of the balanced conditions of the uniform bombardment. The only evidence of such a barrage might be a minute ‘jiggling’ of the vase, and similar mechanisms are believed to be involved in the quantum ‘jiggle’ of zero-point motion.

As to where the ubiquitous electromagnetic zero-point energy comes from, historically there have been two schools of thought: existence as part of the boundary conditions of the universe, or generation by the (quantum-fluctuation) motion of charged particles that constitute matter. A straightforward calculation of the latter possibility has recently been carried out by Puthoff23.

Whatever school of thought one follows, it is difficult to deny the existence of the ZPF. As to whether the energy of this field can be utilised is another matter. Forward10 cites a positive argument for the case. "Though there is no rigorous proof that the vacuum field is a conservative field, such as gravity, it is highly likely otherwise it would be possible to design machines using the Casimir force to extract an infinite amount of energy from the vacuum".

Even if the vacuum-fluctuation field is a conservative field, that does not mean that it would be impossible to extract energy from the field. The gravity field of Earth is a conservative field, and yet hydroelectric dams extract energy from this field by using water coming from a region of higher gravitational potential. Fundamentally, the extracted energy came from the sun, which evaporated the water from the oceans and placed it in lakes at a higher potential. The dam is then a mechanism that uses the gravitational force as a ‘catalyst’. It would not be unreasonable to assume an analogous mechanism in extraction of Zero-Point energy.

In his 1984 paper for the Hughes Research Laboratories, Forward10 describes how one could, in principle build what he calls a ‘vacuum fluctuation battery’ by using the Casimir force to do work on a stack of charged conducting plates. On reading the paper I was confused as to whether Forward was actually implying that endless energy could, in principle be extracted from the background. Dr Forward is a member of the OPMS described in the introduction and I was able to find his email and question his paper. The full correspondence can be found in Appendix d . The crux was that before his paper everyone believed that it was impossible to extract energy from the vacuum, after the paper was written it was acknowledged that you could, but ‘quibbled about the details’. His advice to me was to accept that the vacuum field is probably conservative and focus on the vacuum equivalent of the hydroturbine generator in a dam.

2.7 Thermodynamic Considerations

A full treatment of the thermodynamics regarding the extraction of energy/heat from the vacuum can be found in the 1993 paper Extracting Energy and Heat from the Vacuum by Cole and Puthoff11. No comment was made in the paper as to how energy would be extracted and indeed the comment is made that "considerable technological effort might need to be expended to adequately harness such energy". The authors however, merely concentrate on determining whether any of the laws of thermodynamics are contradicted in the conception of ‘harnessing vacuum energy’. In a serious of insightful thought experiments, combined with standard thermodynamic theory, the paper concludes that in principle devices such as those conceptualised in Forwards paper are possible.

3 The Concept of Inertia

An understanding of inertia would play a key role in the development of any new propulsion system as it is this property of matter that provides the very resistance to motion that we seek to create.

3.1 Machs Principle

To some scientists the concept of inertia does not need explaining, it simply ‘is’. But since the concept was first coined by Galileo in the 17th century, some scientists have wondered if perhaps inertia is not intrinsic to matter at all, but is somehow acquired. Eminent thinkers who have tackled the problem include Feynman and Einstein, who tried-and failed-to show that inertia was related to the arrangement of matter in the universe. This line of thinking was largely inspired by the German philosopher Ernst Mach, who argued (ca 1883) that since motion would appear to be devoid of meaning in the absence of surrounding matter, the local property of inertia must somehow be a function of the cosmic distribution of all other matter. Mach’s principle8 has remained more a philosophical statement rather than a testable scientific proposition. The fact that matter has inertia is a postulate of physic, and while special and general relativity both involve the inertial properties of matter, they provide no deeper insight into the origin of inertia.

3.2 A New Model of Inertia

Recently Haisch7 analysed a hypothesis of Sakharov27 that Newtonian gravity could be interpreted as a van der Waals type force induced by the electromagnetic fluctuations of the vacuum, the so called Zero Point Field or ZPF. Sakharov, originally searching to derive Einstein's phenomenological equations for general relativity from a more fundamental set of assumptions came to the conclusion that the entire panoply of general relativistic phenomena could be seen as induced effects brought about by changes in the quantum-fluctuation energy of the vacuum due to the presence of matter.

In Haisch’s analysis, ordinary neutral matter is treated as a collection of electromagnetically interacting polarizable particles made of charged point-mass subparticles (partons). It is a simple model in which at ultra-high Planckian energies, matter appears as if formed of small elementary constituents that respond like oscillators, characterised by a radiation damping constant G and a characteristic frequency w 0. The effect of the ZPF is to induce a Zitterbewegung motion (literal translation – jiggling) in the parton (fig.2) in a manner entirely analogous to that of the bound oscillators used to represent the interface of matter with EM radiation by Planck and others.

The consequence of this Zitterbewegung is an averaged energy imparted to the parton, which has an associated long-range, van der Waals, radiation field which can be identified with Newtonian gravity.

Haisch, in a recent collaboration with Rueda and Puthoff in a 1994 paper entitled ‘Inertia as a Zero-Point–field Lorentz Force7’ furthered the concept and showed that there is an uninvestigated Lorentz force that arises in any accelerated reference frame from the interaction of partons with the vacuum ZPF. The Lorentz force produces an opposition to the acceleration of material objects at a macroscopic level and has the correct characteristics to account for inertia. Thus stated: inertia is an electromagnetic resistance arising from the known spectral distortion of the ZPF in accelerated frames.


Fig 2. Harmonic Oscillator treatment reveals the effect of zero-point radiation on matter. The oscillator consists of a parton attached to an ideal, frictionless spring. When the parton is in motion, it oscillates about it’s point of equilibrium, emmiting radiation at the frequency of oscillations. The radiation dissipates energy and so in the absence of zero-point radiation and at a temperature of absolute zero the parton eventually comes to rest. In actuality zero-point radiation continually imparts random impulses to the parton so that it never comes to rest. This is Zitterbewegung motion

3.3 Background Physics

The spectral distortion spoken of is a quantum vacuum phenomenon first described by the British Physicist, Paul Davies and William Unruh19 in 1974 as part of an analysis connected with black-holes and relativistic astrophysics. In the so-called Davies-Unruh effect a physical system undergoing a uniform acceleration a, relative to an inertial frame behaves as though it is immersed in a thermal bath at temperature:

T= ha/4p ck

Where the symbols take their usual values.

Although this effect is too small to measure Haisch, a high-energy astrophysicst, and Puthoff, a quantum theorist began independently contemplating a connection with inertia. On meeting with Rueda, an electrodynamics theorist with the necessary experience required to tackle such a problem the three decided to collaborate.

In there analysis conventional quantum field theory was replaced by an approach known as stochastic electrodynamics (SED), which accepts a priori the existence of vacuum fluctuations, and then applies a classical approach to particles and electromagnetism.

SED has been applied to the very real effects attributable to ZPF-matter interactions such as the Casimir Effect16, the Lamb shift, the van der Waals forces, diamagnetism, spontaneous emission (radioactivity) and quantum noise. That these effects are due to the ZPF is well known from QED and also SED analyses.

3.4 Results and Interpretations

The SED technique used for calculating the effects of the electric and magnetic components of the ZPF on a parton is similar to a method introduced by Einstein and Hopf22. The particle (parton) acts as a harmonic oscillator with a characteristic frequency w 0, free to vibrate in a plane perpendicular to the plane of acceleration.

The acceleration process meets with a resistance from the ZPF, which is a function of a radiation reaction-damping constant G defining the interaction of the parton with the radiation field. This is interpreted as inertia associated with the parton, i.e. the inertial mass of the Planck oscillator and can be expressed as

Mi = (hw p/2p c2)G w p (1)

w p = (2p c5/hG)1/2

Mi is the inertial mass,w p is the Planck frequency and the other symbols take their usual values.

The situation is most easily visualised by referring back to the lower diagram of fig1. In an accelerated frame the magnitude of the Zitterbewegung induced oscillations are on average higher than in the stationary or uniformly moving frame as predicted by the Davies-Unruh effect. The consequence of this is to increase the magnitude of the Lorentz interaction on the parton, which manifests itself as inertia. The higher the acceleration, the higher the resisting force.

It is important to note that the Zero-Point spectrum is defined by a cubic solution, which maintains Lorentz invariance. A spectrum defined by such a cubic is the same for all unaccelerated observers, independent of velocity.

3.5 Applications to Propulsion

A complete description of inertia and it’s properties would prove invaluable in any attempt to build inertia-free starships – though it is obviously too early to consider any applications from this somewhat radical new theory. However, the researchers maintain that there may soon be hard evidence supporting there claim from experiments that will search for changes in mass of electrons when they are exposed to powerful laser beams.

In the Rueda-Puthoff-Haisch paper (RPH) the parton is described as a sub elementary electro-magnetically interacting polarizable particle and is considered to be a ‘Planckian-oscillator’ – the most elementary oscillator conceivable. The Lorentz resistance is said to act perpendicular to the oscillator. My interpretation of the applications of this theory lies in the subtlety of the Lorentz force acting perpendicularly to the oscillation of the parton, or more precisely, has a maximum effect when perpendicular and a minimum effect when parallel to the acceleration vector (fig.3).

Fig3. Illustrating the Lorentz force acting highest with the oscillator perpendicular to the acceleration vector and lowest for the parallel vector

In actuality the paper suggests a statistical nature behind inertia. Consider a ‘lump’ of ordinary matter (macroscopic). To all intents and purposes the sub-elementary partons (assuming they exist) orient themselves randomly(below), and thus oscillate through a number of planes.

However, equation 1 suggests a parton mass on the order of 10-137 Kg implying an incredibly high number of partons in any ‘lump’, and a virtual statistical certainty therefore that one lump of matter will behave like another of equal size.

The partons are describes as having a charge (be it fractional). If the work of RPH proves valid then it may be possible to ‘plane-polarise’ the parton oscillations (below) parallel to the acceleration vector. This would result in minimal or even zero resistance to motion.

As this is purely conjecture on my behalf, I decided to contact Dr Puthoff and pose this hypothesis to him. The full correspondance can be found in Appendix d . Dr Puthoff admitted the idea was interesting and explained how indeed the equations would break down for partons oscillating parallel to the acceleration vector. He suggested thinking more about how one might shield the partons from specific ZPF modes that induce the random oscillations.

It may even be possible that this very effect has been observed today in the experimental Fusion reactors which have reported anomalous reductions in mass for brief periods while high magnetic fields and temperatures are observed. This is pure conjecture but remains an interesting excursion into the possibilities of this new concept of inertia.

4 The Relativistic Approach

The idea that one can somehow circumvent the speed of light barrier within the framework of General Relativity has been particularly popular within the last two decades. Exotic phenomena such as wormholes and specific spacetime metrics have been described. This section aims to review these ideas within the framework of orthodox relativity.

4.1 The Alcubierre ‘Warp Drive’

The theoretical physicist...

Miguel Alcubierre was born in Mexico City, where he lived until 1990 when he travelled to Cardiff in the UK to enter graduate school at the University of Wales. He received his PhD from that institution in 1993 for research in numerical general relativity, solving Einstein's gravitational equations with fast computers. In 1994 Alcubierre produced an idea which grew from his work in general relativity. His paper describes an unusual solution to Einstein's equations of general relativity, described in the title as a ‘warp drive’, and in the abstract as ‘a modification of space time in a way that allows a space ship to travel at an arbitrarily large speed’. 25

In the context of special relativity, the speed of light is the absolute speed limit of the universe for any object having a real mass, for two reasons. First, giving a fast object even more kinetic energy has the main effect of causing an increase in mass-energy rather than speed, with mass-energy approaching infinite as speed tends to the velocity of light. By this mechanism, relativistic mass increase limits massive objects to sub-light velocities.

There is also a second faster than light (FTL) prohibition. Special relativity is based on the treatment of all reference frames (i.e., co-ordinate system moving at some constant velocity) with perfect even-handedness and ‘democracy’. Therefore, FTL communication is implicitly ruled out by special relativity because it could be used to perform ‘simultaneity tests’ of the readings of separated clocks which would reveal the preferred or ‘true’ reference frame of the universe. The existence of such a preferred frame is in conflict with special relativity.

General relativity treats special relativity as a restricted sub-theory that applies locally to any region of space sufficiently small that its curvature can be neglected. General relativity does not forbid faster-than-light travel or communication, but it does require that the local restrictions of special relativity must apply. In other words, light speed is the local speed limit, but the broader considerations of general relativity may provide a way of circumventing this local statute. One example of this is a wormhole26 connecting two widely separated locations in space.

Another example of FTL in general relativity is the expansion of the universe itself. As the universe expands, new space is being created between any two separated objects. The objects may be at rest with respect to their local environment and with respect to the cosmic microwave background, but the distance between them may grow at a rate greater than the velocity of light. According to the standard model of cosmology, parts of the universe are receding from us at FTL speeds, and therefore are completely isolated from us. As the rate of expansion of the universe diminishes due to the pull of gravity, remote parts of the universe that have been out of light-speed contact with us since the Big Bang are coming over the lightspeed horizon and becoming newly visible to our region of the universe.

Alcubierre has proposed a way of overcoming the FTL speed limit that is analogous to the expansion of the universe, but on a more local scale. He has developed a metric that describes a region of flat space surrounded by a ‘warp’ that propels it forward at any arbitrary velocity, including FTL speeds. Alcubierre's warp (fig.4) is constructed of hyperbolic tangent functions which create a very specific distortion of space at the edges of the flat-space volume. In effect, new space is rapidly being created (like an expanding universe) at the back side of the moving volume, and existing space is being annihilated (like a universe collapsing to a Big Crunch) at the front side of the moving volume. Thus, a space ship within the volume of the Alcubierre warp (and the volume itself) would be pushed forward by the expansion of space at its rear and the contraction of space in front.

Fig 4. Figure from Alcubierre's paper showing the curvature of space in the region of the travelling warp

The Alcubierre warp metric has some unusual aspects. Since a ship at the centre of the moving volume of the metric is at rest with respect to locally flat space, there are no relativistic mass increase or time dilation effects. The on-board spaceship clock runs at the same speed as the clock of an external observer, and that observer will detect no increase in the mass of the moving ship, even when it travels at FTL speeds. Moreover, Alcubierre has shown that even when the ship is accelerating, it travels on a free-fall geodesic. In other words, a ship using the warp to accelerate and decelerate is always in free fall, and the crew would experience no accelerational gee-forces. Enormous tidal forces would be present near the edges of the flat-space volume because of the large space curvature there, but by suitable specification of the metric, these would be made very small within the volume occupied by the ship.

There are two ‘catches’ in the Alcubierre warp drive scheme. The first is that, while his warp metric is a valid solution of Einstein's equations of general relativity, we have no idea how to produce such a distortion of space-time. Its implementation would require the imposition of radical curvature on extended regions of space. Within our present state of knowledge, the only way of producing curved space is by using mass, and the masses we have available for works of engineering lead to negligible space curvature. Moreover, even if we could do engineering with mini black it is not clear how an Alcubierre warp could be produced.

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

4.2 Warp Drive Causality Considerations

The possibilities for FTL travel or communication implicit in the Alcubierre drive raise the possibility of causality violations and ‘timelike loops’, i.e., back-in-time communication and time travel. Alcubierre points out that his metric contains no such closed causal loops, and so is free of their paradoxes. However, he speculates that it would probably be possible to construct a metric similar to the one he presented which would contain such loops.

4.3 Einstein-Rosen Bridges or 'Wormholes'

The idea of a wormhole comes from Einstein's theory of general relativity using ‘Schwartzschild geometry’, a way of inscribing a space-time co-ordinate system on the highly curved space in the vicinity of a black hole. There are in fact two wormhole definitions, the Lorentzian as described by Kip Thorne and his colleagues, formulated through the formalisms of General Relativity. The second is the Euclidean wormhole, formulated in Hawkings adventures in quantum gravity. The two are not related and it is the latter that is discussed in this section.

4.4 Introduction to Wormhole Concepts

A wormhole is a funnel-shaped tunnel that can connect one complete universe with another or can connect two separated regions of the same universe. In the latter case it is a short path connecting two distant locations in space. However, there is a basic problem with wormholes as a transport system. Wormholes, as described by the equations of general relativity, are dismayingly unstable. In fact, any wormhole connection that happens to form between two points in space should pinch closed again so rapidly that neither material objects nor light-beam messages can pass across the wormhole ‘bridge’ during its brief existence. Thus a wormhole, at least in its pristine form, is unsuitable for instantaneous space transport Most physicists will find this result very satisfying, for it avoids a simultaneity paradox.

The satisfying instability of wormholes was originally called into question over a decade ago in a paper by Michael Morris, Kip Thorne, and Ulvi Yurtsever published26 in the conservative and prestigious journal Physical Review Letters. The authors describe how an ‘advanced civilisation’ might: (a) create a large wormhole; (b) stabilise it to prevent its re-collapse; and (c) convert it to a time machine, a device for travelling or at least communicating back and forth in time. This remarkable paper, which borders on science fiction in its approach, has a very serious purpose. There is presently no well-established theory that can accommodate both quantum mechanics and the physics of strong gravitational fields within the same mathematical framework. The paper of Morris, Thorne, and Yurtsever is a vehicle for guessing, in a rather unorthodox way, what restrictions a proper theory of quantum gravity might place on the physics of wormholes. The authors demonstrate that general relativity contains within its framework mechanisms that appear to permit both faster-than-light travel and time travel. If these physical calamities are to be averted, the authors argue, it can only be done through a proper theory of quantum gravity.

Empty space, when examined with quantum theory on a sufficiently small distance scale, is not empty at all. Even at nuclear dimensions (10-15 m) empty space is filled with particle-antiparticle pairs that are continually flashing into a brief existence, ‘borrowing’ energy from the universe according to the Heisenberg Uncertainty Principle. If the length-scale is contracted to a size appropriate to quantum gravity (10-35 m) this quantum fireworks intensifies to a "quantum foam" of violent fluctuations in the topology and geometry of space itself (See section 2.2). Quantum black holes form and vanish in a span of time of 10-23 seconds. In this environment Morris, Thorne, and Yurtsever speculate, it may be possible for a civilisation considerably more advanced than ours, to ‘pull a wormhole out of the quantum foam and enlarging it to classical size’ to create a connection between two nearby points in space.

To stabilise the wormhole pulled from the quantum foam, preventing its immediate re-collapse, Morris, Thorne, and Yurtsever propose to use an electric field of such enormous strength that it creates enough energy in the mouth of the wormhole to force it to remain open. They suggest that this might be accomplished by placing a pair of spheres with equal electric charges at the two spatial entrances of the wormhole. The spheres would be held in place by a delicate balance, the force of their gravitational attraction just offsetting the force of their electrical repulsion. Such a system might be very small, an atom-scale opening permitting the passage of only a few photons at a time, or it might be large enough to pass a large vehicle. Having produced this stabilised wormhole the engineering can begin. The size of the connection can be enlarged or contracted depending on energy considerations. The two portal ends of the wormhole connection can be separated from each other. For example, a portal placed aboard a space ship might be carried to some location many light years away. Such a trip might require a long time, but during the trip and afterwards instantaneous communication and transport through the wormhole would be available.

4.5 Wormhole Causality Considerations

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

Now suppose, in the spirit of the Twin Paradox of special relativity, that portal B is placed aboard a space ship while portal A remains on Earth. The ship carrying B, say, accelerates rapidly to 86.6% of light speed and travels a distance of one light-year, then reverses its course and returns to Earth at the same speed. On its arrival portals A and B are placed near one another. At 86.6% of the velocity of light any clock aboard the ship will run at just half the speed of a similar clock on Earth due to relativistic time dilation. Therefore at the end of the trip the ship's clock will be one year slow, as compared to an identical clock that remained on Earth. And, as Morris, Thorne, and Yurtsever point out, portal B will also be one year slow as compared with portal A. Now a message sent through B to A will emerge one year in the future of B, and a message sent through A to B will emerge one year in the past of A! Similarly a traveler making the same trips through the wormhole will travel one year into the future or the past. The wormhole connection through space has been transformed to a connection through time, a wormhole time machine.

This somewhat heretical prediction still, in fact, preserves relativity. The restrictions usually associated with special relativity implicitly assume that no time travel is possible. Clearly one could travel, in effect, at an infinite velocity by travelling from one place to another at some sub-light velocity and then on arrival travel backwards in time to the instant of departure. To put it another way, the simultaneity measurements prohibited by special relativity must lead to a definite and unambiguous determination of the simultaneous readings of two clocks separated in space. The clock-comparisons made possible by wormholes are not definite, because one clock could be in the future of the other, displaced by any time interval produced by the travel histories of the portals. Special relativity, which after all is embedded in the theory of general relativity that produced these revelations about wormhole physics, is preserved.

The law of physics that would be destroyed by the construction of a wormhole space-time connection is causality, the principle that prohibits communication backwards in time, that requires a cause to precede its effects in time sequence in all space-time reference frames. Causality as a law of the universe would not survive even a two-way communications link across time, let alone a portal permitting ‘trans-temporal’ matter transmission.

The principal purpose of Morris, Thorne, and Yurtsever in discussing what an advanced civilisation might do with wormholes is to demonstrate in effect that if causality is to be preserved as a law of physics, it must be saved at the quantum level. Quantum gravity, a theory-to-be, which has not yet been developed, must impose some new physical limitations that make impossible the production of stable wormholes by the Morris-Thorne-Yurtsever scenario. General relativity, our present theory of gravity, prohibits neither faster-than-light space travel nor time travel with wormholes, but it does require that the two go together.

4.6 Vacuum Squeezing

At Vanderbilt University, David Hochberg and Thomas W. Kephart have discovered that gravity itself can produce regions of negative energy. Within these regions, we may conjecture, stable wormholes may form naturally, particularly during the early Big Bang28.

Discoveries by Morris-Thorne-Yurtsever (MTY) suggest that a Lorentzian wormhole can be stabilised by creating a zone of negative energy in the wormhole throat, the place where it has maximum space-time curvature. They suggested creating the needed negative energy region by using a ‘parallel plate capacitor’ made with a pair of superconducting spheres carrying huge electrical charges and separated by a very small gap, employing the Casimir to make the zone of negative energy by suppressing electromagnetic fluctuations of the vacuum and reducing the vacuum energy to a value less than zero. In the MTY scenario, the hypothetical advanced civilisation (one that could convert whole suns to mass-energy for civil engineering projects) would extract from the "quantum foam" one of the many wormholes that wink into and out of existence at ultra-small distance scales, expand the selected wormhole to macroscopic dimensions by adding energy, and stabilise it by placing the two charged superconducting spheres in the wormhole mouths (or portals). The portals could then be transported to widely separated regions of space to provide FTL communication and travel.

However, Lorentzian wormholes have their problems. The MTY scheme, while valuable as establishing an in-principle method of stabilising wormholes, would be very difficult to implement in practice, even by the hypothetical advanced civilization. The two superconducting spheres must be suspended with a very narrow separation, without external supports to hold them up or precisely position them, in a delicate balance between gravitational and Casimir forces pulling them together and electrical repulsion of their charges pushing them apart. The electrical charges needed for the two spheres are so large that there would probably be violent electrical discharges to the surroundings or the FTL traveller.

As it turns out, wormholes may come prefabricated by nature. Hochberg and Kephart have discovered that gravity itself can produce regions of ‘squeezed vacuum’ characterised by negative energy within which natural wormholes might form. To understand this the ‘squeezing’ of quantum mechanical states must be considered. In quantum mechanics, Heisenberg's uncertainty principle, for certain "conjugate" pairs of measurable quantities (examples are position and momentum or energy and time), requires that the product of the uncertainties of the two quantities can never be less than an irreducible minimum value given by Planck's constant divided by 2p . If we try to measure the position of an electron with extreme precision, for example, we find that this can only be done at the expense of the measured momentum of the same electron, which becomes very uncertain as a result of the position measurement.

There is also another way in which measurements are limited by quantum mechanics. It is the zitterbewegung or zero-point motion. In complex quantum systems containing many semi-independent quantum oscillators, the zero-point motion represents a quantum noise that is superimposed on any measurement of the system. If an attempt is made to cool the system by removing the heat energy, the zero-point motion represents a rock bottom, a limit below which straightforward cooling cannot go.

There is a technique, however, for making the system colder. In quantum mechanics the energy and the frequency of a quantum oscillator system are interchangeable, differing only by a constant multiplier. Further, in the context of Heisenberg's uncertainty principle, the conjugate variable to the frequency is the phase, in other words, the starting angle for an individual quantum oscillation. Phase is difficult to measure and is usually ignored in characterising complex quantum systems. However, it has its uses. Recently it has been realised that in many quantum systems the limits to measurement precision imposed by zero-point motion can be breached by converting frequency noise into phase noise, keeping the product within the limits dictated by the uncertainty principle while reducing the variations in frequency (and therefore energy). If this technique is applied to a light beam, the result is called ‘squeezed light’. Recent work in quantum optics using squeezed light has demonstrated that old measurement noise limits considered unbreachable can now be surpassed with ease.

The squeezing effect investigated by Hochberg and Kephart, however, was not for light but for the vacuum itself. The theory of quantum electrodynamics tells us that the vacuum, when examined on very small distance scales is not empty at all; it seethes with a kind of fireworks called vacuum fluctuations. Pairs of ‘virtual’ (energy non-conserving) particles of many kinds continually wink into existence, live briefly on the energy credit extended by Heisenberg's uncertainty principle, and then annihilate and vanish when the bill for their energy debts falls due a few picoseconds or femtoseconds later. These vacuum fluctuations can be squeezed in the same way that light beams or systems of atoms can be squeezed, and the result is a vacuum that has an energy less than zero, in other words, a region of negative energy of just the kind needed for wormhole stabilisation.

Hochberg and Kephart used a technique of general relativity called a Rindler transformation to show that over a period of time the vacuum in the presence of a gravitational field is squeezed. They found that near compact gravitational objects like black holes, substantial squeezing of vacuum fluctuations occurs at all wavelengths greater than about the Schwarzschild radius of the object.

There are two important consequences of the results of Hochberg and Kephart . First, in the MTY work on Lorentzian wormholes it was found necessary to violate the weak energy condition. The weak energy condition does not have the status of a physical law, but it is a condition that holds in normal situations. There were speculations that its violation might be in conflict with quantum gravity, making stable Lorentzian wormholes impossible. This is apparently incorrect. Hochberg and Kephart have now demonstrated that the natural and inevitable squeezing of the vacuum as it evolves in a strong gravitational field is in violation of the weak energy condition. This places the TMY work on a more secure foundation.

There is another consequence of squeezed vacuum that is more important. It appears that in the early universe and perhaps in other energy-rich environments the conditions are right for producing natural self-stabilising wormholes (without the need to invoke MTY's advanced civilisation to create them). Such wormholes, created in the Big Bang during the inflationary phase and afterwards, might be around today, spanning small or vast distances in space and waiting only to be found and expanded to a usable size. They might even connect one bubble-universe with another from which it is otherwise completely isolated.

Further, if such wormhole remnants of the Big Bang do exist, it is unlikely that the two separated ends of the wormhole could have had exactly the same history of velocity, acceleration, and relativistic time dilation, and so there will almost inevitably be a difference in the positions in time as well as in space for the two wormhole portals. Therefore, if such natural wormholes with their portal ends not too far apart could be found and expanded one could that a natural time machine exists.

4.7 Looking For Evidence of Natural Wormholes

In a 1995 paper titled ‘Natural Wormholes as Gravitational Lenses’29 by Cramer and others, it is suggested that the early universe may have laid suitable conditions for the formation of natural wormholes. Visser31 has suggested a particular configuration in which a wormhole is held open by exotic material similar to the cosmic string solutions to the Einstein Field Equations. To satisfy the field equations the string framing these ‘Visser’ wormholes must have a negative tension and therefore a negative mass density(this violates the null energy condition – though it is possible to prove that in a generic curved space the principle fails). The total mass of the wormhole is calculated by adding the negative mass of these ‘struts’ to the effective positive mass density of the wormhole’s gravitational field. Depending on the details of the model, the overall mass of the wormhole could be positive, zero or negative.

If a particle with a positive electric charge passes through such a wormhole, it’s lines of force give the wormhole entrance mouth a net +ve charge, and the exit a net negative charge (Fig 5). Similarly, when a massive object passes through the wormhole, the same back reaction mechanism might cause the entrance mouth to gain mass and the exit mouth to lose mass. In the 1995 Cramer et al paper, a situation is described in which the exit wormhole mouth acquires a net negative mass. This leads to what is described as a ‘positive-negative imbalance’ in which stellar scale negative mass structures form.

One might argue that if a gravitationally attractive positive mass acts as a convergent lens, then one might expect a gravitationally repulsive negative mass object to act as a divergent lens causing background stars to briefly dim. This argument would prove to be incorrect according to the Cramer et al paper and a scheme is described whereby one could look for the specific light curves of what are referred to as ‘GNACHO’s’-a Gravitationally Negative Anomalous Compact Halo Object’. The lensing effects are of the same magnitude as the recently discovered Massive Compact Halo Objects-MACHO’s.

Fig 5. Left shows the lines of charge emanating from a particle. Right shows the effect of passing a charge through the wormhole. The mouth acquires a net positive charge and the exit a net negative charge. An analogy can be made when passing mass through the wormhole.

Since three groups are currently conducting searches for gravitational lensing the Cramer et al paper concludes that the searches be slightly broadened so that the signatures of the GNACHO’s are not overlooked by overspecific data selection criterion and software cuts. Any result may answer the question of whether quantum field theory is consistent with negative mass that is flat and semi-clasical.

5 Quantum Mechanics and Photon Barrier Tunnelling Time

A controversy is presently raging in certain physics journals and conferences over whether Einstein's speed of light barrier has been breached by light itself. In particular, Prof. Günther Nimtz and his group at the University of Cologne, Germany have published results showing that they used microwaves to transmit what might be interpreted as a signal, Mozart's 40th Symphony, over a path length of 11.4 centimeters at 4.7 times the speed of light

The purpose of this section is to show that even today the universal ‘speed limit’ Einstein imposed on us ninety-four years ago may be being broken.

5.1 History

One of the most remarkable consequences of quantum mechanics is the ability of particles to reach energy states classically forbidden to them in the process known as ‘tunnelling’.

One interesting question never addressed by the early pioneers of this theory is how long a particle spends in leaking through a barrier. This question was finally addressed in 1955 by Eugene Wigner and his student Leonard Eisenbud, who calculated the time required for the peak of the wave packet to pass trough the barrier. Their conclusion was very strange. They found that under certain circumstances, this transit time reaches a constant value that is independent of the width of the barrier. For a wide barrier and a constant time the corresponding transit velocity, i.e., distance divided by time, can easily become faster than the velocity of light. At the time of publication the apparent violation of Einsteinian causality implicit in the Eisenbud-Wigner calculation was ignored because it used the non-relativistic Schrödinger formalism. Later Hartman derived the same result from a more rigorous formalism.

5.2 Present Experimental Evidence

The paradox of FTL barrier transit velocity has not received much interest until recently, when it has been confronted by new experimental work from two independent directions. Work in experimental laser optics performed at the University of California at Berkeley by Raymond Chiao34 and his group has used interferometry and ‘down-converting’ crystals to perform photon-pair timing measurements at the level of about a femtosecond (10-15 sec). They have been able to clock the passage of single photons of visible light through an optical barrier made of multiply reflecting layers of transparent material acting as a destructive interference filter that selectively absorbs the photons of interest. Most of the photons striking the barrier are absorbed inside and do not emerge, but the few surviving photons traverse the barrier in a time of about 1.5 femtoseconds. The velocity derived from this measurement by dividing barrier thickness by transit time is 1.7 times the velocity of light.

However, Chiao and his group do not characterise their result as an FTL violation of Einsteinian causality. They point out that the operation of their interference filter requires multiple reflections at the many layer interfaces of their device, and a certain time is required for the destructive interference effect to build up. Thus, their barrier has a higher transmission for the part of the photon wave packet that arrives first, and much stronger suppression of the part of the wave packet that arrives later. This will cause the wave envelope to "advance", with the early part of the wave envelope dominating the transmission process. The photon thus appears to emerge earlier because of the time-variable transmission of the filter.

The experimental measurements of Nimtz35 and his co-workers at the University of Cologne operate in a very different domain. They use 8.7 GHz microwaves (free space wavelength 3.4 cm) traveling in a rectangular wave-guide that contains a ‘barrier’ section of reduced dimensions, in which the incoming microwaves are strongly attenuated. Nimtz and his group have performed both time-domain and frequency-domain measurements demonstrating that their experimental configuration extends well into the region predicted by Eisenbud and Wigner and by Hartman where the barrier transit time becomes constant. In particular, Aichmann and Nimtz have recently transmitted Mozart's 40th Symphony as frequency modulated microwaves through an 11.4 cm length of barrier wave guide at an FTL group velocity of 4.7c, receiving audibly recognisable music from the microwave photons that survived their barrier passage. The transit time through the barrier was about 81 picoseconds and was observed to be constant for barriers with widths varying from 4.0 cm to 11.4 cm.

The work of the Nimtz group raises the question of whether Einsteinian causality has in fact been violated and has spawned a controversy. The players in it, as is characteristic of careful scientists, have engaged in a careful tableau of discussion of various definitions of "velocity" and "causality" that skirt any claim of the fall of Einsteinian causality. One contingent has suggested that the FTL speed in the Nimtz experiment, like that of the Chiao group, might result from time-varying transmission probability in the barrier waveguide. The other argues that the filter advance of the Chiao group is peculiar to their filter type and does not apply to the Nimtz results.

What is meant by a signal has also been a matter of debate. For example, Mozart's 40th Symphony, while it is certainly a signal in some sense, does not contain modulation envelopes or switching edges that rise in 80 picoseconds and could thus place Einsteinian causality under stress by conspicuously arriving too early. Further, since any increase in barrier thickness brings with it a corresponding and exponentially increasing attenuation of any signal, it is not feasible to increase the barrier thickness to distances large enough that the causal implications of a constant barrier transit time become more apparent.

Perhaps this is no longer a matter of theories or definitions, but an experimental question that should be treated as such. The Nimtz apparatus can be viewed as one element of a longer multi-stage device that could reach the goal of directly testing Einsteinian causality. Such a device would be constructed of many stages providing long Nimtz barrier transmission elements alternating with short fast amplification and pulse restoration elements for transmitting frequency-modulated digital signals of the high bandwidth. A digital signal would be sent through a barrier element, received and cleaned up to restore its digital pulse structure and remove the effects of attenuation and noise, then amplified and transmitted through the next barrier element. This should be possible with no loss of information from stage to stage.

Provided each such element-pair provided a net FTL group velocity, such pairs could be iterated to obtain very long transmission path lengths. It should thus be possible, given sufficient funds, to construct a device even kilometres long to provide a definitive test of Einsteinian causality and perhaps an unambiguous demonstration of FTL signal transmission. Or perhaps there are underlying problems that make this goal impossible. If so the author doesn’t see them

6 Concluding Remarks

The author was pleasantly surprised by the growing community of physicists that remain optimistic to the idea that Einstein’s ‘universal speed-limit’ is more a statement of the limits of our technology and present understanding rather than an intrinsic property of the universe that all intelligent beings must and will ultimately adhere to.

From the papers studied the author has grown increasingly convinced as to the relevance of the ZPF in modern physics. The subject is presently being tackled with appreciable enthusiasm and it appears that there is little disagreement that the vacuum could ultimately be harnessed as an energy source. Indeed, the ability of science to provide ever more complex and subtle methods of harnessing unseen energies has a formidable reputation. Few would have ever predicted atomic energy a century ago.

The question as to whether the vacuum could provide the understanding behind the property of matter known is inertia is another intriguing possibility. The model helps to explain fundamental questions such as why gravity is only attractive, cannot be shielded and also why it is so much smaller in comparison to the other known forces of nature. It is also an elegant and aesthetically pleasing paradigm that dispels the conceptual absurdities of quantum theory that plague the more philosophical scientists.


Appendix a -Material Gathering

The initial urge to conduct this project was a result of the author being made aware of the NASA Breakthrough Physics Propulsion Program (BPP), which is described in some detail in 1.1. The program has a dedicated web-site, which is divided into a public and a limited access. Before the author gained access to the latter site, the former was explored thoroughly and provided the initial references that lay the foundations to pursue the various branches of the research tree.

The Internet proved invaluable as a research tool, with a plethora of discussions and commentaries on various aspects of current FTL theories. Leicester University Library and the BIDS service served as the backbone of the project providing hard copies of all research papers reviewed.

The author originally believed that the project would revolve around the new concepts in General Relativity that permit entities such as wormholes and ‘warp-drives’. Although this was covered in some detail I believe the crux of this portfolio to be the new concepts in Zero-Point Physics and their applications to space-time and mass.

This section summarises the works studied and suggests follow-up material. The section is subdivided into the following sections; BPP Concepts, Zero-Point Physics, Relativistic Physics, Quantum-Physics. All the papers studied can be found in section 2.

Appendix b - Hypothetical Lecture Course

This section outlines notes for a short course of lectures on the topic of this portfolio.

Lecture 1 and 2 – Introduction to Breakthrough Propulsion Physics

Designed to introduce students to the concepts of spacetime and the failure of modern theories in explaining the origin of inertia. Machs principle will be introduced. The concept of the Zero-Point Field will be introduced and the history of it’s emergence into modern physics. Quantum Chromodynamics will be briefly mentioned aswell as the ideas of Stochastic Electrodynamics.

The early scientist’s belief in the ether and its subsequent lack of experimental evidence will be covered. The fundamental ideas of Special relativity will be reviewed, such as the equivalence of all frames of reference. Then the ideas of General relativity will also be reviewed and the emphasis on Einsteins re-introduction of the ether concept under the new label of the ‘space-time metric’.

Lecture 3, 4 and 5 – The Zero-Point Field

The physical evidence behind the ZPF i.e. the Casimir effect, the Lamb-shift, Van-der Walls forces, diamagnetism, spontaneous emission and quantum noise will be discussed, aswell as their governing equations.

The spectrum of the ZPF will be discussed aswell as the relevance of the cubic solution to maintain Lorentz invariance. The Davies-Unruh prediction will be introduced and its relation to the predictions of Rueda, Puthoff and Haisch in their interpretation of inertia as a consequence of the ZPF interacting with hypothetical partons via a Lorentz coupling.

The findings of Einstein and Hopf on random radiation interacting with a charged particle will be covered, leading on to the ZPF interpretation of the large scale structure of the universe.

Lecture 6 and 7 – Stochastic Electrodynamics

The SED approach will be covered, introducing the idea of a ZPF introduced a-priori, without invoking QED. The elementary equations will also be introduced and applied to cases usually left to the domain of quantum theory.

Lecture 8 to 11 – General Relativity, Wormholes and Warp Drives

Einstein’s field equations will be introduced after tensor manipulation is covered. The course will not concentrate on convincing the student of the validity of GR, but will focus on the applications of his field equations. The Alcubierre warp drive will be used as an example of metrics that violate the weak energy principle, but which can in principle be used as a device to accelerate space-vehicles to an arbitrarily large speed. Causality will be strictly adhered to, as is the case in the Alcubierre warp drive. An example of similar metrics which violate causality will also be contemplated such as the Krasnikov tube.

The work of Morris, Thorne and Yurtsever will be introduced and the implications of there work in predicting the form of a quantum theory of gravity.

Lecture 12 – The Breakthrough Physics Propulsion Program

The NASA run BPP will be discussed. It’s recent developments and strategies will be introduced. The course will end on an interactive student-lecturer discussion on how the topics developed in the course could be applied. The purpose of this is to encourage intelligent, visionary thinking in the mostly young minds of the students.

Appendix g - Questions and Exercises

The following questions aim to test the students’ ability on the various disciplines contained within this portfolio.

On the Casimir Force

The Casimir Interaction Energy per unit area u between two conducting plates separated by a distance a can be given by

u = U/A = -p hc/1440a3

Where U is the interaction energy, A is the plate area and the other symbols take their usual values

i) Calculate the Resulting force between two plates given a total plate area of 1m2 and a plate separation of 6m m.

ii) Suggest why the 1/a4 dependence might break down when the plate separation is very small, say 100nm.

On the Zero-Point Field

Outline the fundamental differences between gravity and the other known forces and explain these differences assuming a ubiquitous ZPF interpretation of gravity.


1 i)The force per unit area, P is acquired by differentiating the interaction energy w.r.t the plate separation.

P = F/A = -du/da = p hc/480a4

Inserting values gives

P = 3.142 x 6.63x10-34 x 3x108/ 480 x (6x10-6)4

P = 1 m N

ii) Good experiments on conducting plates have proved to be extremely difficult. Recent experiments have used conducting surfaces made of flat silicon-crystal plates and amorphous silicon deposited on a glass lens. The forces showed a 1/a4 dependance down to about 300nm. The data then deviated strongly, indicating a lack of surface smoothness.

The answer to be looked for would be lack of surface smoothness.

The properties of gravity that are in conflict with the other known forces are:

It’s relative weakness – Gravity is on the order of 10-37 times weaker that electromagnetism when considering the forces between two charged particles.

Gravity is known to be an attractive only force, conflicting with the other three forces, which can be both attractive and repulsive.

Gravity cannot be shielded, there are various known methods to shield the other known forces.

In relation to the ZPF paradigm, the relative weakness of the gravitational force under ordinary circumstances can be shown to be due to the fact that the coupling constant G depends inversely on the large value of the high-frequency cut-off of the zero-point-fluctuation spectrum. The existence of positive but not negative mass is traceable to a positive-only kinetic-energy basis for the mass parameter. The fact that gravity cannot be shielded is a consequence of the fact that quantum zero-point-fluctuation ‘noise’ in general cannot be shielded, a factor which in other contexts sets a lower limit on the detectability of electromagnetic signals.

Appendix d - Correspondance

Correspondence with Dr Hal Puthoff


Dear Dr Puthoff,

My name is Richard and I am a 4th year Masters student from the UK writing my final year thesis on concepts of advanced propulsion and preparing a lecture to give to my peers on the subject. I am also a member of the BPP which is how I found your email. I hope you do not mind me writing to you but I wanted you to verify a queery of mine with regard to your co-written 1994 paper 'Inertia as a Zero-Point Lorentz Force'.

In the paper the parton is described as a 'harmonic oscillator...free to vibrate in a plane perpendicular to the direction of acceleration'. My interpretation of the applications of this theory lies in the subtlety of the Lorentz force acting perpendicularly to the oscillation of the parton, or more precisely, has a maximum effect when perpendicular and a minimum effect when parallel to the acceleration vector.

My question is this:

Am I correct in assuming that a parton oscillating parallel to the acceleration vector experiences no or little resistance to motion?

If so, do you believe it would be possible to 'polarise' the parton oscillations in matter?

I hope you find the time to reply to my question.

Yours sincerely,

Richard K Obousy


A very interesting question! Of course, we assume that the parton motion is the zitterbewegung motion driven by the ZPF, so that it always has components in all directions, and random at that. Therefore, there is always such motion perpendicular to the direction of acceleration and therefore an inertial force response generated.

To be honest, I don't know the answer to your question. If the parton motion were constrained to be in the direction of acceleration, certainly our calculation would break down and it would seem that perhaps this would reduce the scattering cross section, thereby reducing inertia. If you have an idea of how one might do this, it would certainly be worth investigating the consequences!

Best regards,

Hal Puthoff

Correspondence with Dr R Forward


Dear Dr Forward,

Thank-you for the reference to your paper, I have secured a request from my library.

I would like to take the opportunity to ask you a brief question regarding a 1984 paper of yours titled 'extracting electrical energy from the vacuum by cohesion of charged foliated conductors', where you describe how one could in principle construct a 'vacuum fluctuation battery'. I am a little confused as to the crux of the paper. Is it that 1) More energy can be extracted from the vacuum than is required to charge the battery or rather, 2) similar to your analogy with a hydroelectric damn that pumps water back up to a higher potential during low demand (with an overall energy loss obviously) can store energy but with an overall loss.

If it is 2 then do you know if it is more efficient than conventional energy cells, or is the point simply that it is possible to store energy via vacuum interactions.

I hope you can find the time to provide me with the answer. It is a fascinating concept and I remain optimistic to the future of vacuum energy extraction.

Yours Sincerely,

Richard Obousy

4th Yr MPhys

email: rko1@le.ac.uk

tel: 0116 2471904 (UK)



BEFORE I wrote the paper, everyone said that it was -impossible- to extract energy from the vacuum. AFTER I wrote the paper, everyone had to acknowledge that you -could- extract energy from the vacuum, but began to quibble about the details. The spiral design won't work very efficiently... The amount of energy extracted is extremely small... You are really getting the energy from the surface energy of the aluminum, not the vacuum... Even if it worked perfectly it would be no better per pound than a regular battery... Energy extraction from the vacuum is a conservative process, you have to put as much energy into making the leaves of aluminum as you will ever get out of the battery... etc... etc...Yes, it is very likely that the vacuum field is a conservative one, like gravity. BUT, no one has proved it yet. In fact, there is an experiment mentioned in my Mass Modification paper (an antiproton in a vacuum chamber) which can check on that. The amount of energy you can get out of my aluminum foil battery is limited to the total surface energy of all the foils. For foils that one can think of making that are thick enough to reflect ultraviolet light, so the Casimir attraction effect works, say 20 nm (70 atoms) thick, then the maximum amount of energy you get out per pound of aluminum is considerably less than that of a battery. To get -up- to chemical energies, you will have to accrete individual atoms using the van der Walls force, which is the Casimir force for single atoms instead of conducting plates.My advice is to accept the fact that the vacuum field is probably conservative, and invent the vacuum equivalent of the hydroturbine generator in a dam. I am sending you a lead to the NASA Breakthrough Propulsion Physics program, in case you are not aware of it.

Best of luck in your future studies,


7 Bibliography

1. NASA Breakthrough Physics Propulsion Program - Marc G.Mills


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34. Measurement of Single-Photon Barrier Tunnelling Time – A Steinberg, P Kwiat, Y Chiao

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36. L MacColl, Phys. Rev. Vol. 40, pp621, 1932.

37. R Chiao, Physica (Amsterdam) Vol. 175B, pp257, 1991.AlcubierreWarpDrive · Alcubierre Warp Drive


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