Stephen P. King (stephenk1@home.com)
Thu, 02 Sep 1999 18:09:54 -0400

Dear Bill,

WDEshleman@aol.com wrote:
[WDE]
> > > Here are some of my thoughts about change pulled from my abstract.
> > >
> > > This proposal begins with the argument that the linear operators (x), that
> > > dictate the evolution of the state of an object, are themselves measured in
> > > present states (NOW), not past states (PAST). That is, if NOW = PAST + x *
> > > PAST, then NOW/PAST = 1 + x, a trivial result allowing all values of x.
> > > On the other hand, if it realized that it is more logical and consistent
> > > that, NOW = PAST + x * NOW, then NOW/PAST = 1/(1 - x), a most interesting
> > > result that prevents x from achieving unity.
> [SPK]
> > Very neat! So is unity achieved asymptotically in the infinite limit,
> > Lim i -> \inf. : x = 0 ? I am having a hard time with the math. :-(
> > (dyslexia sucks!)
>
> [WDE]
> Associating x with PAST states,
> if NOW = PAST + x * PAST => NOW = PAST * (1 + x)
> => NOW/PAST = (1 + x), this is classical (common sense) change.
>
> Or associating x with NOW states,
> if NOW = PAST + x * NOW => NOW - x * NOW = PAST
> => NOW * (1 - x) = PAST => NOW/PAST = 1/(1 - x),
> this is relativistic (singularity) change. That is,
> NOW = PAST/(1 - x). Not, NOW = PAST * (1 + x)
>
> [SPK]
>
> > Can we think of worlds in terms of different NOW/PAST pairs?
>
> [WDE]
> I don't think of worlds as NOW/PAST pairs, but you may have
> something there. I see the PAST as always gone and that
> associating a "change operator" with the PAST is relativistically
> wrong (or relativity suggests that it's wrong). Matti, if you are
> misguided, but I look at this as a relativistic first principle,
> independent of geometry.

(information states encoded in physical events, which are in NOW). While
the PAST (events) is indeed gone, never to return, we project or infer a
FUTURE state/event from a comparison of PAST and NOW. Can we define this
"chance operator" such that we do not need to consider a single operator
for *all* observers, but one that is indentifiable with each observer.
The idea is that each observer was its own time, its own clocking of
the change it can observe, so the notion of NOW/PAST pairs as worlds
would identify the unique history of each observer. This is a radical
shift from thinking of observers as being embedded in a single
space-time to the notion of associating with each observer a space-time
of its own that can "overlap" with that of others.
This is different from the usual MWI, in that the worlds are not all
strictly orthogonal to each other, they can "cast shadows" on each
other! I think that there might be a correlation between the way these
"shadows" move as the angle varies and relativistic effects! I have no
idea how to phrase this mathematically! :-( BTW, that is the
dimensionality of the shadow of a 4-dimensional object?

Onward,

Stephen

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