Chapter 15: Faster-than-Light Approaches in General Relativity

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                               Notes by David A Roffman on Chapter 15 of

                                FRONTIERS IN PROPULSION SCIENCE

    Chapter by Eric W. Davis, Institute for Advanced Studies at Austin, Austin Texas


        This chapter considers some common space travel options in science fiction, such as warp drives, wormholes, and faster than light travel (FTL).  While all of these options may be possible, some are more viable than others.  To achieve any of the previous options, it is necessary to create very specialized local geometries, and to obtain negative energy.  Negative energy has a negative energy density, and is negative because of its special ability to create wormholes.  Despite being created in the lab, physicists fear using its name because of the sensationalist aspects.

       To utilize any of the advanced technology in the last paragraph, violations of energy conditions amongst other things must occur.  A way to obtain negative energy is to squeeze quantum vacuum states.  A few more methods are the Casimir effect, static radial electric (and magnetic) fields (by high intensity tabletop lasers), and gravitationally squeezed electromagnetic zero-point-fluctuations (ZPF).  The static fields are static while at peak intensity. 

    By reducing the energy below the ZPF, the vacuum becomes squeezed, resulting in negative energy.  This is because the definition of the vacuum is a state having vanishing energy.  By having less energy than this, it has a renormalized (negative) expectation value of energy density.  So, the vacuum oscillates between a negative and positive energy density, with it being on average more positive.  As a side note, zero-point-energy is the lowest energy  an object can have as given by the Uncertainty Principle.

    Energy could come from this squeezed vacuum by use of an ultrahigh intensity laser coupled with fast moving mirrors.  For the book’s example, both pulses (positive and negative) are equal in time interval release.  Rapidly rotating mirrors in this setup would serve the purpose of separating the positive and negative energy, if the beams hit the mirror at a very shallow angle.  Another method would be to superimpose photons upon each other in order to create a beam of negative energy.  The tools for understanding negative energy have just become available.

   Negative energy is produced naturally by gravity, which drags ZPF downward.  There is supposedly a halo of some negative energy around the Earth and other astronomical bodies.  So, gravity naturally creates squeezed vacuum states needed to create wormholes.  We have no way to gravitationally squeeze fields in the lab.

    The most renowned way to produce negative energy is to use the Casimir effect.  This effect can be extended via a moving mirror (electrically conducting).  Accelerating such a mirror creates a negative energy flux.  Frequency distribution changes with acceleration.  However, the mirror effect is not very significant in terms of producing an operational system, as there are better ways to produce negative energy than this.  Side note:  Accelerating charges creates radiation (photons).

    The electromagnetic Casimir effect can be used to generate a wormhole, but there is a catch.  Very small cavity separations are needed to create a decent sized wormhole.  But such small plate separations destroy the Casimir effect, as Van der Waals forces take over at these distances.

    So far transversable wormholes and warp drives have been discussed.  All credible theories in this area are full of wormholes, time machines, and a warp drive of sorts.  Most situations involving faster than light travel involve the general theory of relativity, and some alterations and mass. 

   Transversable wormholes must use exact metric solutions.  The following are some desired requirements: travel through a wormhole must be less than one year as seen by travelers and outside observers, no time dilation for travelers via relativistic effect, no more than 1g for travelers, travel though the wormhole must not exceed the speed of light, travelers must not be torn to shreds by the wormhole walls, no event horizon, and no singularity (ex. black hole).  With a wormhole, only the wormhole mouth is of importance (as far as physics is concerned).

    Alcubierre derived a four dimensional warp drive setup.  A space craft within such a warp bubble never exceeds the speed of light, although it may look that way on the outside.  Others have devised warp tube concepts.  However, any warp drive would actually be quite slow, and would require immense amounts of negative energy to achieve even that.

   Wormholes, while possible, still require quite a bit of negative energy.  The amount rapidly increases as the wormhole widens in size.  But the warp drive requires even more energy than the wormhole.  As such, warp drives will never be technologically feasible, unless new geometries and ways to generate massive amounts of negative energy are found.

   Quantum inequalities (QI) are conjecture extending from the Heisenberg uncertainty principle.  Some of postulates are (1) a longer negative energy pulse results in a weaker negative one, (2) the positive pulse to follow must exceed the strength of the negative pulse, and (3) longer time interval between the two pulses results in a larger positive pulse. These conditions are all violated by the Casimir effect (and other effects).  This has not been verified by lab experimentation. 

    The net energy stored in a warp bubble should be not as much as the total rest energy of the space craft (this imposes a speed limit).  Warp bubbles would be slow; in fact, some may be at a snail’s pace (literally).  Side note: If the energy of an object is much less than its rest energy, then it is non-relativistic. Some equations yield results to show that a wormhole requires little negative energy.  While wormholes are the most possible route to interstellar space (and a recipe is provided by general relativity for geometric and material components), no one knows how to build one.  It is of great curiosity whether a wormhole can be found and enlarged, or one must be built from scratch.

     Negative energy is responsible (predicted) in nature for lensing, chromaticity, and micro and macro lensing events.  Spectral analysis can distinguish between these negative energy effects, and that of positive energy.  Gamma ray bursts have been shown to contain negative energy.  It is suggested that negative energy may have existed in comparative amounts to regular energy in the moments after the big bang. 

     Whenever light strikes a negative energy region, the light rays fly outward, leaving a zero umbra region.  This doesn’t compare to divergence, as light enhancement can be far greater.  We have the technology today to detect any abnormalities produced in a lab by negative energy.  The results of Davies and Ottewill show that temperature (kinetic energy of particles, if things with rest mass are being discussed) drops result from negative energy.  Wormholes directly imply time machines that can be easily built, but would require much effort.  There are opportunities to break causality in general relativity.  Some have put forth that there is no predestined time line (includes general relativity).  Time machines are also known as closed timelike curves.  They could exist at least at the semi-classical quantum gravity theory level.  Local chronology doesn’t imply a global one.  Some say that temporal paradoxes are nonexistent. Causality may be maintained in relativistic field theories, even if there is faster than light travel. 

      In terms of conservation of momentum, a warp drive may emit radiation.  However, much more research is needed.  Conservation of momentum for faster-than-light travel has yet to be published in literature.  I do not believe that FTL is possible, as anything that has mass cannot exceed or even reach the speed of light due to the relativistic factor.  This blows up to infinity (and hence so does the energy, which is not allowed) as the speed reaches the speed of light.  Only massless particles (such as photons and gravitons) may travel at the speed of light in a vacuum.  The only way to have FTL is to use negative mass squared, which mean the mass is imaginary.  This is nonsense.  If the mass were negative it would correspond to mass having a sort of "charge" like the columb force or the strong force (a minus sign is not a complex number), and I could understand it.  However I do believe wormholes are possible as negative mass is involved and not imaginary mass.