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