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Monsieur Van Den Broeck

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  • cyrano@aqua.ocn.ne.jp
    has moved the concept of a warp drive another step along its path from a fictional SF prop-idea to a well founded physics concept that might one day be
    Message 1 of 1 , Mar 21, 2001
      has moved the concept of a "warp drive" another step
      along its path from a fictional SF prop-idea to a well
      founded physics concept that might one day be
      realized. This improvement on the Alcubierre warp
      drive was devised by general relativity theorist Chris
      Van Den Broeck of the Catholic University of Leuven in
      Belgium. He has eliminated seemingly insurmountable
      problems with the Alcubierre warp-drive scheme. His
      improvement employs topological gymnastics to keep the
      interior of the warp bubble large while making its
      external surface very small. But before describing Van
      Den Broeck’s work, I’ll summarize the Alcubierre warp
      drive concept itself, first featured in my column
      (#81) in the November-‘96 Analog.

      Until 1994 a "warp drive" was one of the myths of
      science fiction, a rubber-science concept used
      principally to permit space-opera heroes to flit from
      one star system to another at faster-than-light
      speeds, moving the plot forward in the process. Those
      familiar with the laws of physics saw the warp drive
      as a flagrant violation of the principles of special
      relativity, conservation of energy, and
      physics-as-we-know-it. It was tolerated as an
      excessive but perhaps necessary use of literary
      license by SF authors.

      The status of the warp drive changed dramatically in
      1994, when Dr. Miguel Alcubierre published a paper
      entitled "The Warp Drive: hyper-fast travel within
      general relativity" in the journal Classical and
      Quantum Gravity. Alcubierre is a theoretical physicist
      from Mexico who in 1994 was working at the University
      of Wales and is now at the Albert Einstein Institute
      in Potsdam, Germany. Also a fan of SF, he was steeped
      in the SF tradition and turned his physics expertise
      to the task of considering how a warp drive might be
      constructed within the restrictions of general
      relativity, our present "standard model" of gravity.
      Alcubierre constructed a "metric", a mathematical
      specification of the curvature of space-time that had
      all the characteristics of a SF warp-drive including
      the capability for faster-than-light travel.
      Surprisingly, Alcubierre’s warp-drive metric is a
      solution of Einstein’s equations of general relativity
      and is completely consistent with them. Science
      fiction’s warp drive had been given a consistent
      theoretical and mathematical basis.

      When theoretical physicist use general relativity,
      their normal procedure is to start with some
      distribution of massive objects and to calculate the
      metric describing space-time curvature that such a
      distribution would produce. Alcubierre reversed this
      procedure. Without worrying about how it might be
      formed, he constructed a metric that could transport
      volume of flat space, perhaps containing a spaceship,
      at superluminal speed. This was accomplished by
      placing the volume of flat space inside a "bubble’ of
      highly curved space, then destroying space in front of
      the bubble while creating new space behind it.
      Effectively, the warp bubble is driven forward by
      creating and annihilating space as if a local Big Bang
      were occurring at the rear of the space ship while a
      local Big Crunch was occurring in front of it.

      How does Alcubierre’s metric manage to move an object
      faster than the speed of light? Isn’t that in direct
      contradiction to Einstein’s special theory of
      relativity? Actually, no. General relativity treats
      special relativity as a restricted sub-theory that
      applies locally to any region of space that is
      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 context of
      general relativity may provide ways of circumventing
      this local statute. One example of this is a wormhole
      (see my AV columns, Analog 6/89 and 5/90) connecting
      two widely separated locations in space, say five
      light-years apart. An object might take a few minutes
      to move with at low speed through the neck of a
      wormhole, observing the local speed-limit laws all the
      way. However, by transiting the wormhole the object
      has traveled five light years in a few minutes,
      producing an effective speed of a million times the
      velocity of light.

      Another example of a faster than light phenomenon is
      the expansion of the universe itself. As the universe
      expands, new space is created between any two
      separated objects. The objects may each be at rest in
      their local space-time, but nevertheless the distance
      between them may grow at a rate that is much greater
      than the speed of light. According to the current
      standard model of cosmology, most of the universe is
      receding from us at FTL speeds and therefore is
      completely isolated from us.

      Alcubierre’s metric uses an analogous expansion of
      space to drive the warp bubble forward. However, since
      the ship within the bubble is at rest in its local
      space, the occupants will feel no acceleration forces
      when the forward speed of the bubble changes, nor will
      they experience the "usual" relativistic effects of
      mass increase and time dilation. If an Alcubierre
      warp-drive ship travels 100 light years at 100 times
      the velocity of light, to both the occupants and
      outside observers the trip takes one year, no more and
      no less.


      --------------------------------------------------------------------------------

      Alcubierre’s publication stimulated a flurry of
      activity among general relativity theorists, who
      investigated the implications of the new idea, It was
      found, by himself and others, that Alcubierre’s
      original warp-drive idea had a number of serious
      problems. It violated the strong, dominant, and weak
      energy conditions of general relativity. The net
      energy of the warp bubble, as it turned out, was
      extremely large and negative. For example, a warp
      bubble 100 meters in radius that might contain a space
      ship of reasonable size would have a net negative
      energy that was roughly ten times larger in magnitude
      than the entire (positive) energy of the visible
      universe. Another problem was that the walls of the
      bubble would have to be so thin that they could not be
      constructed with matter, even "collapsed matter" of
      nuclear density. It was also found that most of the
      warp bubble is disconnected from a sizable part of the
      external negative energy region. Therefore, the
      surface part of the bubble could not be carried along
      and would have to be continuously generated
      externally. The drive could not be self-contained or
      self-operated. These problems have seemed so
      overwhelming that recent attention has been focused on
      alternatives like the Krasnikov Tube (see my column
      #86 in the September-’97 Analog) that might present
      fewer problems of implementation and control.

      Now, however, Dr. Van Den Broeck has proposed an
      improvement on Alcubierre’s scheme that appears to
      solve many of its problems. Van Den Broeck observed
      that most of the undesirable effects of Alcubierre’s
      drive scale with the volume or surface area of the
      warp bubble. Therefore, his simple solution is to make
      the radius of the warp bubble so small that the
      problems go away. In doing this, he makes use of
      another trick from general relativity. The interior
      volume of a region of space bounded by a closed
      surface, because of space curvature, can be made much
      larger than the flat-space volume bounded by its
      surface. In curved space the inside volume of a sphere
      of radius R can be much greater than 4/3pR3.

      The new metric of the Van Den Broeck/Alcubierre warp
      bubble is like a bulls-eye target with a center
      (Region 1) surrounded by three concentric rings
      (Regions 2-4). The central sphere in Region 1 is flat
      space large enough to hold a spaceship. Region 2 is a
      spherical shell containing distorted space that
      connects the large interior volume of Region 1 to an
      exterior region that is smaller in radius by a factor
      of 1/a. Region 3 is a transition region of flat space,
      a spherical shell with a volume much less than that of
      Region 1. Region 4 is a spherical shell that is
      Alcubierre’s warp bubble, but now with a very small
      radius. Van Den Broeck makes the radius of Region 1
      about 100 meters, and sets a to 1034, so that Region 4
      is only about 3 ´ 10-32 meters in radius. With such a
      small radius, if the warp bubble travels at 10 times
      the velocity of light the amount of negative
      mass-energy it would require is only about –0.06
      grams. Even if it travels at 100 times the velocity of
      light, it would require is only about –56 kilograms of
      negative mass-energy. Region 2, where the volume of
      space is compressed from inside to outside also
      requires a quantity of negative mass-energy, but Van
      Den Broeck calculates that it is only about –4 grams.
      These small quantities of negative energy eliminate
      many of the problems of Alcubierre’s original concept.

      However, even with these improvements, there would
      still be very severe "engineering problems" with any
      implementation of the scheme. First, although the
      interior of the warp bubble may be quite spacious, its
      exterior is only 3 ´ 10-32 meters in radius, mush
      smaller than a proton and approaching the Planck
      length (1.62 ´ 10-35 meters) in size. This is close
      enough to the minimum length-scale of the universe
      that such a size reduction is doubtful due to quantum
      effects. Moreover, since the diameter of the warp
      bubble is many orders of magnitude smaller than a
      wavelength of visible light (about 4 ´ 10-7 meters)
      there would be no possibility of seeing out from
      inside the bubble. Any trip would be a blind one, with
      no possibility of seeing or steering. Moreover, while
      the magnitude of energy required to form a warp bubble
      becomes more reasonable in Van Den Broeck’s warp
      drive, the energy density requirement remains
      unphysically large.

      And how could our space travelers enter the bubble or
      exit again at the end of their trip? Van Den Broeck’s
      calculations indicate that slowing the bubble to a
      near stop might permit it to be expanded to any
      desired size. However, such an expansion would
      decrease the wall thickness, and it is not clear what
      would happen if the wall thickness became smaller than
      the Planck length. Van Den Broeck ends his paper by
      commenting that while the first warp-drive space
      flight remains a long way off, perhaps it has become
      slightly less improbable with the new scenario for a
      warp bubble.


      --------------------------------------------------------------------------------

      >From the point of view of science fiction, even the
      application of general relativity to create a volume
      of space that is larger on the inside than on the
      outside is very appealing. It would, for example,
      solve the book storage space problem for may of us.
      Further, I cannot wait until this principle is applied
      to airplane seats!

      Van Den Broeck’s warp drive is a large volume of flat
      space that is connected to normal space by a tiny
      "neck". It therefore resembles the more familiar
      general relativity topologies of wormholes or "baby
      universes" and perhaps has a similar behavior. This
      raises the issue of how the neck is prevented from
      pinching off altogether, isolating our space travelers
      in a new universe of their own rather than
      transporting them to a new part of the old one.

      I should also comment that these calculations were
      performed without a proper understanding of the
      unknown theory-to-be that we call "quantum gravity". A
      warp bubble with a diameter near the Planck scale will
      be affected by quantum gravity effects and
      corrections. In particular, my previous column (12/99
      Analog) described the possibility that extra space
      dimensions affecting gravity may be rolled up into
      loops about a millimeter in diameter. If this were the
      case, it would modify general relativity at the
      millimeter scale and would almost certainly render Van
      Den Broeck’s metric unachievable.

      Thus extra space dimensions might block the path to
      faster-than-light travel. Ours is certainly an
      interesting universe, and it grows more interesting as
      we understand it more fully.


      --------------------------------------------------------------------------------

      AV Columns On-Line: Electronic reprints of over 100
      "The Alternate View" columns by John G. Cramer, all
      previously published in Analog, are available on-line
      at the URL: http://www.npl.washington.edu/av. The
      preprint referenced below can be obtained at:
      http://xxx.lanl.gov



      References:

      General Relativity: C.W. Misner, K.S. Thorne, and J.A.
      Wheeler, Gravitation, W.H. Freeman (1973).

      The Alcubierre Warp Drive: Miguel Alcubierre,
      Classical and Quantum Gravity, v. 11, L73-L77, (1994).


      The Micro-Warp Drive: C. Van Den Broeck, preprint
      hep-ph/9805217 , LANL Archive, (April 2, 1999).



      Une injustice faite à un seul est une menace faite à tous

      Montesquieu (1689-1755)
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