I wrote that it was
> not possible in my version of the many-minds interpretation
to
> define ``birth rank as [ ] position in the class of all [ ]
> observer-branch-moments''. The best we can do is to look at an
> observer's own personal current evidence as to his birth rank.
> This can be quite ambiguous and, in general, will be a matter for
> interpretation rather than mathematical definition.
Nick Bostrom <nick.domain.name.hidden> replied
> Are you saying that it is not possible in your model to define the
> class of all points in time on all branches of the universal wave
> function which are at a temporal distance of, say, 10 years from
> the start of the world (assuming there was a point when the
> world (i.e. the whole tree of branching possibilities) started?
> (This is not a rhetorical question but a clarificationary one. And
> I'm not asking whether we could identify those points, but
> whether the class of such points is defined.)
Yes, I am saying that.
First of all, I would be unhappy with the requirement to specify a
unique hyperplane of simultaneity.
More generally, many problems arise when we try to understand the
nature of time in modern physical theories. Prior to relativity
theory, it seemed that there was a natual succession of
universally-valid ``nows'' apparent simultaneously to everyone alive
at the time. Times other than the present now had happened or
would happen but were not currently in existence. Special
relativity, however, taught us that simultaneity is
frame-dependent and introduced the idea of reality as a
four-dimensional spacetime. According to general relativity, time
is path-dependent. In the quasi-classical cosmology of the world
we seem to live in, time appears on all inextendible paths to have
begun with a big bang, but on some of those paths it may come to an
end in a black hole, while on others it may continue for ever.
What will the right picture be if we ever manage to quantize
general relativity? I suspect that we should allow for the
possibility of black holes being formed as a result of uncertain
``quantum events'' -- it may be harder to choose to construct a black
hole than to kill a cat but it is not unimaginable. This suggests that
time is not just frame dependent and path dependent, but even
observer dependent.
Now, partly in order to deal with the problem of time in special
relativity, I have developed a many-minds interpretation of
quantum theory which involves information being definite only
separately for each individual observer. The information observed
by an observer is specified by sequences of local quantum
states associated with the life history of that observer.
Applied to the EPR-Bell situation, for example, this means that
when Alice measures a spin, her current state expresses
a possible observed spin direction. (This is a local process.)
When Bob measures a spin, his current state expresses a possible
observed spin direction. (And this too is a local process.) Finally,
another local process occurs when Alice and Bob compare their
observations (or rather, when each separately observes the
appearance of the other). The observed correlations which
result are determined by the initial singlet state which was
effectively previously observed separately by both.
I believe that, in many ways, this provides a very satisfactory and
explicit solution to the problem of what it might mean for time to
be observer-dependent.
But if time is observer-dependent, then it is hard in general to
compare times between different observers.
This means that I do not view the ``birth rank'' problem as being
well-posed for my theory. Nevertheless, the broader problem of the
extent to which we should expect to see ourselves as being
``typical'' observers is one which I think is both absolutely crucial
and very hard to deal with. I appreciate Bostrom's work because I
think that he is helping to clarify some of the issues involved in
that problem.
I also think that whether we are typical observers and whether
time is observer-dependent are questions which are relevant for
any ``theory of everything''.
I wrote saying that
> I believe that there is no conceivable algorithm which could take
> elements of the set of observers as I define it (well-defined and
> countable although that is) and attach unambiguous birth ranks to
> each one of them.
Bostrom replied
> Do you mean effectively computable algorithm?
> I don't see why it would make a difference if the reference could
> not be exactly computed in a finite time.
No. I just referred to an algorithm to stress that I really am
serious when I use words like ``unambiguous'' and ``well-defined''.
I wrote
> As I see it, *the question* is ``Given what I have learned
> from my life up to now, how should I predict my future?''
Bostrom replied
> I'm not sure whether we are really disagreeing on this point,
> although I would insist that one sort of question we may
> meaningfully ask is not just what my own future will be but also
> what the world is like (and was like in the past) in general.
I am afraid that we are disagreeing here, because I do not agree that
``the world'' exists in anything like the way that Bostrom implies.
Matthew Donald (matthew.donald.domain.name.hidden)
web site:
http://www.poco.phy.cam.ac.uk/~mjd1014
``a many-minds interpretation of quantum theory''
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Received on Thu Oct 19 2000 - 06:33:18 PDT