Wormholes

Wormholes, Loopholes in General Relativity

And

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

Abstract

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.

Contents

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

Appendices

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