>
> 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.
Yes this is quite possible, and corresponds to histories being
forgotten. For example, there are many details about the world of the
dinosaurs that will never be known, so many quantum histories in the
past have merged to form our present. Another point of view is that
the past trajectories are merged until such time as one performs an
observation (eg discovers a fossil, or whatever) that separates
them. At which point, we have a separation of the trajectories, each
with a different augmented history.
>
> 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.
Yes it is an artifact of the way we perceive 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?
Trajectories only exist in the classical projections made by concious
observers, the concept is meaningless (as far as I can tell) for the
universal wavefunction (which instead has a single (deterministic)
evolution). As such, the observer's trajectories do indeed branch and
merge, as discussed above.
(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?
By merging trajectories, the histories of the conciousnesses are shared, and
mutually consistent. What does it mean to merge two conciousnesses?
>
> 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).
I believe measure is an absolute quantity, as defined by
Jacques. However, it has little bearing on QTI, an opinion for which I
reamin in a state of disagreement with Jacques.
>
> 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.
This idea has been explored in some sci fi books, but I'm not sure it
can be consistently done.
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.
Again, I don't believe measure (at least the absolute measure as
defined by Jacques, and which is the only consistent definition IMHO)
has any bearing on decision theory. You see the measure is absolute -
it is unchanged by any decisions we may (perhaps only preceive to) make.
In decision theory, we should just ask ourselves what history do we
want to follow, and bugger the other "yous" that have different ideas.
>
> 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?
>
Since each world is very much in the eye of the observer, the latter
type statement is perhaps the closest to the mark. However, one may
ask the question, how does an observer observe different worlds in
order to make a comparison, when by definition, the world is defined
by what the observer sees. It could be you're asking a meaningless question.
> 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
>
>
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Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Wed Oct 06 1999 - 23:03:28 PDT