I think one of the essential difference between Jacques' point of view and
some of the rest of us (James?, Bruno?, Russell?, Gilles? and myself) is that
Jacques does not accept the principle of identity of indistinguishable and we
do. This principle, I think, was first enounciated by Leibniz. Depending if
it is accepted or not, it leads to very different conclusions regarding how
consciousness is affected by the branching of the wave function. Other issues
involve absolutism or relativism of measure and the linkage between worlds
and consciousness. I will explore this issues in the following questions
which may be the basis for further discussion.
First Question. The principle of identity of indistinguishable applied to the
wave function.
Is it possible for two (local) portions of the universal wave function
originating from different (local) pasts, to "merge" that is to become
identical. The output merged "measure" of this process would then be the sum
of the two input "measures."
So if the first input portion is X and the second input portion is Y then the
resulting wave would be X+Y. (This question ignores the Self Sampling issues)
I assume that "measure" is in some way related (or identical) to the
probability = Square(|X +Y|) of the wave function.
Second Question. Is there really branching?
I am not sure if the branching and merging processes are at all possible in
the first place or just an artifact of the way we look at the wave function.
If the wave function is mapped in Wheeler's phase space, then, assuming
purely deterministic laws, is it true to say that two trajectories in this
space could never cross (or merge except in the limit)? and for the same
reasons, could never branch? (I think this question is related to the
Lyapunov stability theorem) How is this absence of branching and merging
reconciled with the branching (and merging) that we take for granted in the
MWI?
Third Question. The principle of identity of indistinguishable applied to
consciousness.
Assuming that it is possible for two (local) portions of the wave function to
"merge," then, is it true to say that two different consciousness
independently expressed by these two portions, become one and same at the
merging point?
Fourth Question. Absolutism vs Relativity of measure.
Is "measure" an absolute quantity, invariant with the observer, such as the
distance between two points along a geodesic in space-time? Or is measure a
relative quantity that depends on the observer, such as length, time, or
velocity?
I think that Jacques believes in the absolute version of measure and some of
the rest of us, in the relative version. This question raises a hornet's nest
because, and depending on the answer, it leads to different conclusions
regarding Quantum Suicide (QS).
Fifth Question. Measuring Your Own Measure.
Can an observer observe or measure his own "measure?" How could one set up an
experiment to make such a measurement? Would that experiment involve
estimating how unlikely our world is? In other words if our world is found to
be very improbable then our measure would be low, otherwise our measure would
be high. The problem here is that if we assume the Plenitude to be an
infinite set of possibilities, then any world would have a probability of
zero. Absolutists would be satisfied with playing around with infinitesimal
probabilities and would fight tooth and nail for maximizing those
infinitesimals at all cost thus shunning QS as a "crackpot idea". Relativists
would in a sense "RENORMALIZE" their own probability of existence by using
the conditional probability GIVEN the existence of the self. Thus, accoding
to them, the probability that they exist given that they exist is one. The
Relative Self Sampling Assumption (RSSA) is the conditional probability given
the self, and the Absolute Self Sampling Assumption (ASSA) is the plain
probability.
Sixth Question. Linkage between worlds and consciousness.
I am here venturing in an area in which I know very little. However, I think
it relates to the controversy betweenby David Lewis,"On the Plurality of
Worlds," and Saul Kripke, a colleague of Lewis at Princeton University, who
is the champion of ersatz modal realism. Is a particular consciousness linked
to a single world, or is it kind of "spread out" like a quantum cloud over
a multiplicity of worlds, for example like an electron is spread out in a
probabilistic wave? (In fact maybe the quantum wave IS THE CONSCIOUSNESS
WAVE). In other words, does consciousness have extension across worlds?
Related to this question is the issue of how much difference is required
between two consciousness for them to cease to be identical. In other words
what is the TOLERANCE required by Leibniz principle of identity of
indistinguishable. How can we define this tolerance? Is this difference
physical or psychological? Is this tolerance defined by Planck's constant? Or
is it defined by a "Turing type" test in which the difference is significant
to an individual ONLY IF HE PERCEIVES IT TO BE SIGNIFICANT? Who is the
observer for the "Turing type" test? The Self? Others?
Again, as in previous issues, I think that some of us have championed the one
consciousness - one world system and others have supported the one
consciousness - multi-world system. And each point of view leads to radically
different conclusions regarding QS.
I have raised many questions, I think enough work to keep busy far into the
next millenium. Forgive me if I attributed to you beliefs that you do not
have. In the absence of a firm index of ideas with champions and challengers
I find it difficult to know exactly what you are thinking.
George Levy
Received on Sat Sep 25 1999 - 23:14:20 PDT
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:06 PST