Stephen P. King (email@example.com)
Thu, 30 Sep 1999 22:31:30 -0400
Hitoshi Kitada wrote:
> Dear Stephen,
> Stephen P. King <firstname.lastname@example.org> wrote:
> Subject: [time 838] Re: [Time 837]
> > Dear Friends,
> > Here is am example of that I was talking about in my last post!
> > Subject:Re: Does a fundamental time exist in GR and QM?
> > Date: 1999/09/23
> > Author: Toby Bartels <email@example.com>
> > > Vesselin G Gueorguiev <firstname.lastname@example.org>
> > > wrote:
> > > I could be wrong, but I tend to think of any chart as a physical observer
> > > who is siting at the origin and does measurements.
> > A physical observer provides only an *infinitesimal* chart.
> > As an observer, I define x,y,z,t axes going out from me (the origin),
> > but I can't describe how the axes will curve as they leave me.
> This is exactly what I assume about local systems. The observer (each of us)
> does not know beforehand how the space is curved. We have to assume our system
> is the standard, thus it does not have any curvature. Viz. our local system
> must be Euclidean for each of us.
Yes, but is it Euclidean as given by some external absolute standard?
No! We have to look carefully at this. Each LS has its own measure of
"Euclidean". Since there is no common space or connection to parallel
transport some hypothetical absolute rigid ruler, it is impossible to
discover a contradiction between the measures of each LS. This would
appear to violate my falsifiability notion, but it does not. ;-)
The difficulty that this line of thinking has for many is that it
denies the possibility of an absolute standard for finite entities. I
personally do not see a problem with this as it eliminates the last
vestiges of preferred frames.
I can see that when we introduce the notion that the LS is subjective,
it implies a solipsism of sorts! But this is a bonus, not a failure. The
key point is that there is not just one observer/LS that has its world
of experience as "virtual images" or "figments of their mind", all LSs
do! Just like Leibnitzian monads, we do not need windows only
constructable "harmony", e.g. not "pre-ordained"!
> > So, I can't define a chart large enough to contain two distinct points
> > and any geodesic linking them -- which is what you wanted here.
> In this point I differ from his. We each cannot know the curvature if it
> existed, even if we could reach to the inifinite point in our local system as
> far as we remain inside it. Only when we open our eyes and see the outside,
> the outside tells us it might be different from our own world (LS). Thus
> observation gives us GR.
I think that it is what we refer to as "communicating about our
observations" that gives us GR. An observation, in the passive sense,
can not reveal curvature, as you point out. When we "communicate", we
are simulating what other LSs would perceive, and since their identity
(Matti's SELF) is different, a difference, or better put, distortion
appears in our perceptions.
The subtle nature of bisimulation is the key to understanding this
notion. We can never escape from Platonic Cave's chains and bindings -
the "inside", but we can simulate "what it might be like" outside! Note
that when we say "it might be like X", we are talking about
probabilities! ;-) What we need to discuss is how LSs can "simulate"
each others behavior! Bisimulation is a pair of systems simulating each
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