Stephen P. King (stephenk1@home.com)
Thu, 15 Apr 1999 12:19:22 -0400
Dear Hitoshi and Friends,
Thank you for possessing this problem. :) It is one that I have been
thinking about for a long time. First I have some clarification
questions...
Hitoshi Kitada wrote:
>
> Dear Time Folks,
>
> Let me propose a problem about the direction of time, which, at least
> seemingly, has a form that has not been considered before. That is partly a
> reminiscence of [time 199] and hinted by Ben's remark [time 198].
>
> Direction of time or Does the free will exist?
>
> Let us consider the following observation:
>
> Let an observer O observe a local system L'=(L1,L2,X) or L=(L1,L2). Here L1
> and L2 is the direct objects of observation of O and X is some automatic
> apparatus that observes the system L=(L1,L2).
Here we have a choice of observables, L or L'; I am assuming that they
are observationally mutually exclusive, e.g. O observers L xor L'.
How are O and X defined in terms of local systems? They seem to be
classical and, upon thinking further, X looks to be another observer
itself. Perhaps we can think of it as one of Peter's "secondary
observers"... ( cf. [time 191])
> In this situation, Wheeler's quantum eraser illustrated in Ben Goertzel's
> GOERTZEL.html (http://goertzel.org/dynapsyc/1995/GOERTZEL.html):
>
> > In fact, according to (Wheeler, 1980), this even works
> > if the choice is <b>delayed</b> -- then one has the phenomenon
> > of the "quantum eraser." In other words, suppose one has a
> > <b>machine</b> record which slit each particle passed through.
> > If after a few hours one destroys the machine's records
> > without having looked at them, and only <b>afterwards</b>
> > looks at the plate, then result is the same as if the
> > information had never existed; the plate shows that the
> > particles behaved like waves. But in the same scenario, if
> > one looks at the machine's information before one erases it,
> > the picture on the plate is quite different: it is consistent
> > with whatever the machine said.
>
> may be restated as follows:
>
> If O looks at L', then what O sees in the future about L
> is different from what O sees when O looks only at L. (1)
Here it seems that the meaning of "past" and "future" needs to be
carefully examined. Can we understand this terms "sees" as meaning
logically inference? I am trying to think of this in terms of Peter's
Interactive Machine paradigm. If we could show that a LS is equivalent
to a finite IM, we could easily bring in the power of Peter's analysis
in to play. :) http://www.cs.brown.edu/~pw/papers/bcj1.pdf
> We may regard this as an experimental fact (provided that the situation
> describes exactly Wheeler's quantum eraser).
>
> Wheeler's case may be rephrased:
>
> The present affects the future. (1')
Is this meaning strict material causation, in the sense that a
primitive lightcone structure could be constructed using an array of
Observers O_i exchanging signals. It is the "thermodynamic arrow" that,
I believe, holds the key to thinking of an asymmetry between evolutions
toward the past or future. But on a side note, independent of any
observation, an LS's time arrow can only be considered as having a
superposition of directions. This relates to my earlier questions about
time vectors. :)
> Let us consider the observation with time order reversed. The question in this
> case is if the following is correct or not:
>
> If O looks at L', then what O sees in the past about L
> is different from what O sees when O looks only at L. (2)
>
> This would be paraphrased:
>
> The future affects the present. (2')
We are starting to think seriously about the ontological question of
causation and temporal transitivity! :) It is well known, that systems
described by invertible dynamics do not have an "arrow of time" (cf. M.
C. Mackey "Time's Arrow: The Origins of Thermodynamic Behavior".
Springer-Verlag, 1992 http://www.cnd.mcgill.ca/bios/mackey/mackey.html);
we need to look at the scattering state dynamics of LSs to see if they
satisfy "f* exactness" or some equivalent.
I believe that there is there is an analogy between the difference
between "bound and scattering states" and Mackey's "dynamical systems
and traces" (pg. 111 ibid.) and thus there is a way of defining LSs as
having a define time arrow.
> Turning to the direction of time, I think it may be understood as the
> direction of one's own time when he sees the outside. If we understand the
> direction of time in this way, we have two alternatives with (2):
>
> If (2) is true, then the observer's time is reversible,
>
> while
>
> if (2) is false, then the observer's time is irreversible.
>
> (2) may be tested by experiments, similarly to Wheeler's.
>
> If the direction of time is that of the observer's subjective time as I
> proposed, my claim is thus that we can find by experiments if time has the
> direction or not.
Of course, it is the act of observation that implies that a fixing of
frame has occurred and that such fixes a chronological ordering. But, we
can *not* assume such distributive orderings exist *ab initio*, since
the computation of such is an NP-Complete problem and thus is
irreducible to mere postulations of "microcausality".
http://www.uncg.edu/mat/avg/avgnp/node9.html
> This might sound a silly assertion, as we feel we experience the direction of
> time in daily life. But the statement (2) could be a direct test of asymmetry
> of subjective time, and I think the direction of time has not been examined in
> this way.
>
> Another point about (2) is that, if (2) is true, we have to think it asserting
> that all is inevitable fate, or all is determined but we cannot know which
> result actually occurs. This point would be illustrated by the following
> passage adapted from [time 199]:
>
> We assume (2) is true.
>
> An observer O is informed that an apparatus X records some data about his
> objects L1 and L2, but does not see the data on X. He makes observation
> of L=(L1,L2). Then he is planned to walk a corridor to the point where the
> corridor forks into two directions. Beforehand another person brought the
> apparatus X at the end of one of the two corridors. Whether or not
> he (observer O) sees X at the end of the corridor depends on his
> choice which corridor he takes. If he knows that his observation of L is
> the same as the data that he will see the apparatus X, then he knows
> that he will choose the correct corridor where the apparatus X is at
> the end, whichever way he takes. Or if he knows his observation does
> not match those data, he knows in advance he will choose the wrong way.
>
> In short, _if (2) is true_, O must choose one right way always, whichever
> direction he takes at the branch, if the data coincide with those that he will
> see the apparatus X. He _can_ choose one of the two at his will, but his
> choice has been determined in the sense that he has _no ability_ to change his
> fate to see the apparatus X.
>
> So if (2) is true, no free will exists,
>
> or
>
> if (2) is false, the free will may exist.
Are we defining free will as strictly contradicting determinism at all
levels, could we have free choise externally and determinism interiorly
to LSs?
In Computer science we distinguish between "linear time" and "branching
time" computations. The former assume complete initiality ab initio
("all choices made at the outset") and the latter eliminates initiality
requirements ("choices made on-the fly to take into account the latest
information")
http://boole.stanford.edu/chuguide.html#P3
http://boole.stanford.edu/chuguide.html#gupthes
It seems that if we consider that LSs "evolve", then it is not trivial
to consider that we could think of them as "adaptive" systems, and such
adaptations can well represent branching time types of computations.
> I.e.
>
> if the direction of time does not exist, the free will does not exist,
>
> or
>
> if the direction of time exists, the free will may exist.
>
> This problem may relate with the Classical/QM features of our world: Even if
> (2) is true, we have our free will at each stage (QM aspect), but the fate as
> a whole is determined (Classical aspect). If (2) is not true, then such
> restrictions do not exist and we might have true free will.
We are faced here with the ontological question of the "reality" of an
it-itself unknowable quantum mechanical Universe and whether its finite
subsets can be known. The method of how knowledge evolves is itself
exposed to analysis.
> Hitoshi
Onward to the Unknown,
Stephen
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