WDEshleman@aol.com
Tue, 7 Sep 1999 09:24:37 EDT
response is at the end
[WDE]
> > I've now read your paper on local times. Usually when I read
> > I find my intuitions evaporate and my notions crushed, but
> > when I read your work I find that you agree that relativity alters
> > the subjective experience of the observer, but to say that the
> > Schrodinger perspective is the objective perspective for local
> > systems? I will accept that. It is interesting to note that a
> > "factorial operator" will transform
> >
> > 1/(1-x) = (1+x+x^2+x^3+ ...) to
> > exp(x) = (1+x+x^2/2!+x^3/3!+...).
> >
> > As you say in your paper, "The quantum phenomena occurring in a local
> > system follow non-relativistic quantum mechanics, but the observed
> > values of quantum mechanical quantities should be corrected according
> > to the classical relativity so that the corrected values equal the values
> > predicted by the (non-relativistic) quantum mechanics."
> >
> > Would not the "factorial operator" qualify as a corrector?
>
[HK]
> Yes, if you mean by the factorial operator the one that transforms n to n!,
> your statement is right and justifies the transformation from QM to
> Relativity
> and vice versa, on the level of calculus/mathematical rules. I postulated
> this
> relation between QM and relativity as a mathematical framework and proved
> its
> consistency as a mathematical theorem. We have justifications on the same
> level: I think you can assure the consistency of the two views related by
> the
> transformation by the factorial operator with some additional words.
>
> As a corrector, the factorial operator transformation might be useful in
> applications and would make the understanding of the consistent
unification
> of
> the two seemingly contradictory views easier.
>
> >
> > Sincerely,
> >
> > Bill
> >
>
> Best wishes,
> Hitoshi
Hitoshi,
You say in your paper that "The quantum mechanical
phenomena between two local systems appear only
when they are combined as a single local system. In
the local system the interaction and forces propagate
with infinite velocity or in other words, they are
unobservable."
In my analysis of infinite products equal to 1/(1-x) there
is a reason to infer that black holes, atoms, and the
universe as a whole all have event horizons inside of
which we cannot observe. That is, black holes and atoms
have event horizons at 1/0.7035 * GM/c^2 = 1.4 * GM/c^2
and the universe has an event horizon at,
0.7035 * c/2 * sqrt(3/pi/G/rho), where rho is the density
of the universe. Interactions inside or beyond the
event horizons are unobservable, but I have reservations
as to whether Faster Than Light propagations occur in
these regions, or whether they are necessary at all.
Here is my reasoning:
1/(1-x) = prod{ [1+x^(2^n)]^(1/2^n) : n=0,infinity }
* prod{ 1/[1-x^(2^n)]^(1/2^n) : n=1,infinity }
or,
1/(1-x) = A * B
I am almost forced to admit that A is the objective part
and B is the subjective part. Therefore to correct the
observation we must simply remove the relativistic part
to reveal what really happened. Now we have another
candidate for the QM principle of objective change.
Here are the candidates:
1) Psi(t+dt) = (1+x) * Psi(t)
2) Psi(t+dt) = exp(x) * Psi(t)
3) Psi(t+dt) = prod{ [1+x^(2^n)]^(1/2^n) : n=0,infinity } * Psi(t),
and the mixture of objective and subjective change,
4) Psi(t+dt) = Psi(t) / (1-x)
If we accept eq. 3 as a candidate for objective change,
we notice first that it is the closest yet to eq. 2. Second,
eq. 3 does not go to infinity when x = 1; eq. 3 evaluates
to the value of 4 (not eq. 4) at x=1. That is,
4 = 2 * 2^(1/2) * 2^(1/4) * 2^(1/8) * 2^(1/16) * * *. While
eq. 2 is 2.718... at x=1. Now, and here is the problem,
eq. 3 does not converge for x > 1. I must conclude that
a) either the propagation inside the event horizon is at the
speed of light or b) that the speed of light inside the event
horizon is actually zero and that communication between
points is FTL due to the direct contact between
incompressible matter points. I prefer b), but cannot
exclude a). This may seem so academic and so
hypothetical as to be ignored, but at this time my main
effort is for consistency not believability. The properties
of my infinite products are so beautiful that I can't put them
aside because of the concern that I may be correct. :-(
Your positive feedback so far is greately appreciated,
but this is where I tend to loose people, because, if I am
wrong, there no reason to keep "kicking a dead horse."
So, be critical, you may save me 20 years of work, after
which I would only be in possession of a pure mathematical
object having nothing to do with reality. Come to think of
it, that might not be so bad after all...
Sincerely,
Bill
http://members.tripod.com/~EshlemanW/
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