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Does Born rigidity describe particle creation?

  1. Mar 31, 2012 #1
    I'd appreciate some help understanding Rindler coordinates better: I found a visual that seems to illustrate particle pair production with a Rindler horizon while describing Born rigidity. [Sounds like the Unruh effect to me.]

    [As background, recent discussions on particle pair production associated with horizons of various sorts include these:


    [Hubble sphere horizon] and


    [Unruh Effect]

    This discussion will relate.]


    Wikipedia says, in part:

    and I thought 'this sounds a lot like the 'particle pair' discussions in Physicsforums....

    This Wikipedia 'half picture' [diagram] of Rindler coordinates is not so insightful as THIS source and description:


    regarding Born rigidity...... and check out this description:

    There is a lot of language in the overall mathpages description which I don't understand but the above description stood out to me. It seems just like the beginning of a description and visual representation of particle pair production!!

    What do you think???? and why??

    [a] old hat,
    [c] pathetically lame

    Anybody know of other coordinate diagrams that address similar perspectives on Schwarzschild and FLRW descriptions for back holes, cosmology, respectively?? Hubble

    [Isn't there something very similar inside a black hole horizon with Schwarschild coordinates to this:..."accelerating in the opposite direction in both space and in time.... ??" where signs change and 'x takes on the values of time'...moving towards the black hole singularity???]

    thank you
    Last edited: Mar 31, 2012
  2. jcsd
  3. Apr 5, 2012 #2
    I can offer some insights to my own question, if not a complete answer yet, from comments beginning with post #36 here:


    A few key insights:


    But whether or just how the Hubble sphere eventually meets criteria is not yet clear from the discussion.
  4. Apr 6, 2012 #3
    Seems I left out the conclusion part of post #2:

    Coordinates, frames, type of acceleration, and type of horizon all affect apparent/ observed particle creation....
  5. Apr 6, 2012 #4


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    When I read your first post I was puzzled by the connection you made between Born rigidity and the existence of horizons. They seem to be independent concepts, each of a different kind. Born rigidity relates the worldlines of a bunch of accelerating partcles and looks at the case when they are part of a pice of matter, whereas Rindler horizons appear for any accelerating frame. The appearance of horizons lead to apparent particle creation for the accelerating observer, but I can't see how this relates to Born rigidity.
  6. Apr 10, 2012 #5
    They used to seem different to me, too, but see how the last link in the original post above, mathpages, begins the description of Born rigidity:

    In the diagram there, Born rigidity focuses on the rigid rod, in red, on the right while I am focusing on the particles 'disappearing/hidden' in the left hand side of the Rindler chart....beyond the 'horizon'....particles to the left 'disappear' from the accelerating observer ...

    And the Wikipedia comment from above on rigidity:

    seems to confirm such a horizon. This is the same thing going on with the Rindler horizon in the Unruh affect!!!
  7. Apr 10, 2012 #6
    I am puzzled by this Mathpages quote mentioned in the OP:
    As I understand it, Born rigid motion ensures that the proper distance between any two points on the rod remains constant from the point of view of observers accelerating with the rod. To be "part of the Born acceleration" surely this condition has to met and if the rod extends beyond the pivot point then the condition is not met. No physical rod can extend across the pivot point under these acceleration conditions without being torn apart. Even if we consider individual disconnected particles undergoing this acceleration pattern, it is not possible for observers co-accelerating with the particles on the right to communicate or compare measurements with observers co-accelerating with the particles on the left.

    The two sides of the pivot point are separated by an effective event horizon but the analogy to a black hole is limited. Free falling observers inside a black hole can see events outside the black hole so neither side of the pivot point is equivalent to the inside of a black hole. The top region is the region most like the inside of a black hole because objects and information can enter that region but cannot leave. The equivalence between Rindler acceleration and a black hole also breaks down when we note that there is no equivalent of an absolute singularity that is at the centre of a black hole. This means we have to be careful about drawing conclusions about black holes from studying Rindler charts as there are obvious differences.

    For an extended rod with points accelerating proportional to 1/x there can be no physical part of the rod at x=0 because that would require infinite acceleration. This is where the apparent Rindler horizon is located for the accelerating observers. While Unrah particle production is generally recognised as being a real effect, the Born rigid acceleration graph does not demonstrate in any tangible way how particle production occurs under these conditions. Reference to the "particle horizon" only mean the region from which particles could not have travelled in the lifetime of the universe and does not imply the region where particle pairs are produced. It is just saying "IF particles are emitted from behind this line then it is not possible for the accelerating observers to see them", which is different from saying "particles are produced here".
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