Talking to Future and Past Selves (was No Planck limit for time!???)

From: Lee Corbin (lcorbin@tsoft.com)
Date: Sun Feb 23 2003 - 18:07:38 MST

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    Damien writes

    > My suggestion had been that by using this fact (if it is one!) you could
    > establish a code with your future self (or descendents/later collaborators)
    > permitting a message to be sent back to the present, depending on the
    > absence or presence of absorbers at various locations.

    Okay, so here's a scenario that illustrates the difficulty
    I see. The year is 2010 and one DB is anxious to establish
    communication with a future self. Since going faster than
    light is not possible, he's concluded that he must contact
    himself after a Tipler Omega point has begun to form.

    So with the suitable kind of radio telescope, he aims at
    a very specific place in the sky known to as many decimal
    places as possible. Sure enough, the transmitter has
    trouble now and then, and in such a way as to reveal the
    desired message. A future person, who could only be DB
    himself (because of the nature of the personal information
    communicated) speaks to him!

    Then DB is hit by a bus, or fails to get frozen, or some
    other horrible thing happens to him. Then, 97 billion
    years later, during the big crunch, quite a number of
    versions of DB are run by the Omega Point. Some want
    to talk to the original DB. One in particular "remembers"
    the right coordinates, and starts picking up photons there
    (with the permission of the Omega Point, of course.)

    Now then. This becomes overly complicated in terms of
    MWI, because in MWI, it *definitely* will happen that
    on October 9, 2010, a DB will do just as indicated.
    And furthermore, on October 9, 97,003,192,226 A.D.
    the "receiving" DB will establish contact. But we
    would have to ask the probability of this, and thus
    enquire into the density or measure of this slice.
    So we avoid this for now.

    The remote DB tries hard to remember exactly how his
    end of the conversation went back in 2010. Fortunately,
    he's been equipped with some notes provided by the
    Omega point, who collected photons at other places
    which depict the notes nicely.

    However, any finite set of notes will be subject to
    random perturbations as the remote DB reads them and
    recalls how the conversation went. This will affect
    the local DB, and the possibility of "noise" and
    feedback will either halt communications or push them
    onto a fixed point. Or---more likely---a periodic
    solution will obtain, with a cycle of points in the
    space being reached. To illustrate, remote guy recalls
    A being said, but says A in such a way that B is heard,
    which causes B to be said later, but C is heard, and
    eventually we are back to A. In non-linear dynamics,
    this is call a periodic solution. A fixed point is
    a periodic solution with period 1.

    This is similar to a known method of dealing with
    time travel in SF. In one of my favorite stories,
    "Other Tracks", the protagonist opportunistically
    changes the past, and, after he's got what he wants,
    changes it back again. We can interpret this as an
    ensemble of universes (similar to the ergodic
    hypothesis in physics), where the point in the state
    space eventually returns arbitrarily close to where
    it began. In other words, a periodic solution, or
    an "asymptotically periodic" orbit is obtained.
    (See the best book on non-linear dynamics, namely
    "Chaos: An Introduction to Dynamical Systems", by
    Kathleen T. Alligood, Time D. Sauer, and James A.
    Yorke(!), which is at the same time very accessible
    and yet technically rather thorough.)

    > I still think it's a rather nifty idea. But I wonder
    > if I might have lifted it from a Greg Egan determinism
    > short story. (I don't have his collections handy, alas.)

    I haven't seen it before, and I read Axiomatic pretty
    carefully. (Of course, he's written quite a few more
    short stories than that.)

    Lee



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