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

        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.